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Microscopic (Dis)order and Dynamics of Cations in Mixed FA/MA Lead Halide Perovskites

  • Helen Grüninger*
    Helen Grüninger
    Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
    *H.G.: email, [email protected]
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    Orcidhttp://orcid.org/0000-0002-5422-7003
  • , 
  • Menno Bokdam*
    Menno Bokdam
    Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria
    Faculty of Science and Technology and MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
    *M.G.: email, [email protected]
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  • , 
  • Nico Leupold
    Nico Leupold
    Department of Functional Materials, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
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  • , 
  • Paul Tinnemans
    Paul Tinnemans
    Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
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  • , 
  • Ralf Moos
    Ralf Moos
    Department of Functional Materials, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
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  • , 
  • Gilles A. De Wijs
    Gilles A. De Wijs
    Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
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    Orcidhttp://orcid.org/0000-0002-1818-0738
  • , 
  • Fabian Panzer
    Fabian Panzer
    Department of Functional Materials, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
    Soft Matter Optoelectronics, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
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    Orcidhttp://orcid.org/0000-0002-2191-9011
  • , and 
  • Arno P. M. Kentgens*
    Arno P. M. Kentgens
    Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
    *A.P.M.K.: email, [email protected]
    More by Arno P. M. Kentgens
    Orcidhttp://orcid.org/0000-0001-5893-4488
Cite this: J. Phys. Chem. C 2021, 125, 3, 1742–1753
Publication Date (Web):January 15, 2021
https://doi.org/10.1021/acs.jpcc.0c10042

Copyright © 2021 The Authors. Published by American Chemical Society. This publication is licensed under CC-BY.

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Abstract

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Recent developments in the field of high efficiency perovskite solar cells are based on stabilization of the perovskite crystal structure of FAPbI3 while preserving its excellent optoelectronic properties. Compositional engineering of, for example, MA or Br mixed into FAPbI3 results in the desired effects, but detailed knowledge of local structural features, such as local (dis)order or cation interactions of formamidinium (FA) and methylammonium (MA), is still limited. This knowledge is, however, crucial for their further development. Here, we shed light on the microscopic distribution of MA and FA in mixed perovskites MA1–xFAxPbI3 and MA0.15FA0.85PbI2.55Br0.45 by combining high-resolution double-quantum 1H solid-state nuclear magnetic resonance (NMR) spectroscopy with state-of-the-art near-first-principles accuracy molecular dynamics (MD) simulations using machine-learning force-fields (MLFFs). We show that on a small local scale, partial MA and FA clustering takes place over the whole MA/FA compositional range. A reasonable driving force for the clustering might be an increase of the dynamical freedom of FA cations in FA-rich regions. While MA0.15FA0.85PbI2.55Br0.45 displays similar MA and FA ordering as the MA1–xFAxPbI3 systems, the average cation–cation interaction strength increased significantly in this double mixed material, indicating a restriction of the space accessible to the cations or their partial immobilization upon Br– incorporation. Our results shed light on the heterogeneities in cation composition of mixed halide perovskites, helping to exploit their full optoelectronic potential.

 Special Issue

Published as part of The Journal of Physical Chemistry virtual special issue “Hellmut Eckert Festschrift”.

Introduction

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Over the past decade, lead halide perovskites have attracted great interest due to their potential application in solar cells, with excellent power conversion efficiencies of currently up to 25.5%. (1) Other efficient perovskite-based optoelectronic devices, such as light-emitting diodes and X-ray detectors, were demonstrated as well. (2−6) A key aspect is the simplicity of tuning the composition of halide perovskites, which makes it possible to adapt their structural and optoelectronic properties, such as phase transitions, band gap energy, as well as charge-carrier lifetimes and mobilities, (7−11) to achieve desired properties for the different applications. Halide perovskites typically have an APbX3 composition, in which Pb2+ forms corner-sharing PbX6 octahedra with X being a halide (X = Cl–, Br–, or I–). (8,12,13) The dodecahedral A site is occupied by a monovalent cation, typically methylammonium (CH3NH3+, MA), formamidinium (CH3(NH2)2+, FA), or Cs+. (12,14) The first efficient perovskite solar cells were realized using ternary halide perovskites, especially MAPbI3, before a further increase in efficiencies above 20% was achieved on the basis of mixed multinary halide perovskites, (15,16) such as a “triple cation” perovskite of the form MAxFA0.95–xCs0.05Pb(I1–yBry)3. (17) However, these highly alloyed perovskites show phase segregation especially under illumination, (18,19) limiting their optoelectronic performance and long-term stability. (20,21) In recent years, the highest perovskite solar cell efficiencies of >23% were achieved with perovskites that again have a less complex stoichiometry, e.g., double cation perovskites (17) or even simple FAPbI3. (22,23) The latter requires stabilization into its optoelectronically desired α-phase, (24−26) which can be achieved by adding a second cation, e.g., MA. (26−28) Upon incorporation of MA in FA-based perovskites, the Goldschmidt tolerance factor is better fulfilled, (29) decreasing strain within the structure and thus improving charge transport properties. (30,31)
This recent progress has made it very clear how extremely sensitive the optoelectronic performance and stability of halide perovskites are with respect to their stoichiometry and compositional microstructure. (9,32−37) Developing a fundamental understanding of structure–property relations is crucial to further advance perovskite-based optoelectronic devices. Even though the mixing behavior of A cations in the perovskite structure was the focus of various works in the past, (26,38−43) a complete understanding of the microstructure of A cation mixtures is not yet established.
Nuclear magnetic resonance (NMR) spectroscopy provides an accurate probe of the local environment of different functional groups embedded in the crystal structure. NMR spectroscopy of perovskites has proven valuable to accurately probe the cation ratios of mixed compositions, halide order and disorder, halide or cation phase segregation, and cation dynamics. (25,26,42,44) Organic A cation mixtures can be analyzed in terms of types, ratios, and dynamics by high-resolution 1H, 13C, and 14N NMR spectroscopy. (26,42,45−49) Furthermore, 13C magic angle spinning (MAS) NMR offers a sensitive probe for the phase purity of single and mixed cation perovskites. (48)2H and 14N NMR experiments are especially useful to study cation dynamics, which have been evaluated for the parent MA lead halide perovskite compounds (45−47,49,50) and MA/FA and MA/guanidinum mixed systems. (26,39) Often NMR spectroscopic studies are complemented with first-principles simulations to obtain even more detailed information about the investigated material structure. (51−53) However, the description of disordered systems requires a large set of models and large supercells rendering it computationally expensive, (54−56) which is aggravated if dynamics play an important role and need to be modeled in addition, such as in halide perovskites. Recent developments in machine-learning force-fields (MLFFs) opened up the possibility of achieving near first-principles accuracy molecular dynamics (MD) trajectories of thousands of atoms on a nanosecond time scale. (57) This allows for capturing cation dynamics and gaining detailed information about the microstructure in perovskites by MD simulation approaches. These MLFF MDs are able to resolve the entropy-driven phase transitions in MAPbI3 and other related (inorganic) perovskites with great accuracy. (57,58)
In this work, we investigate the perovskite microstructure in detail, i.e., distribution and order/disorder of FA and MA in mixed halide perovskites of the form of MA1–xFAxPbI3 and MA0.15FA0.85PbI2.55Br0.45. High-resolution 1H MAS NMR spectroscopy based on double-quantum (DQ) coherences allows us to identify individual 1H–1H correlations (55,59−61) of MA and FA cations in close proximity and to quantify the 1H dipolar interactions. Through a combination of the DQ NMR data with MLFF MD simulations of the disordered and highly dynamic MA1–xFAxPbI3 systems, we are able to identify and quantify the effects that influence the experimentally determined 1H–1H dipolar couplings. Here, we also find that the latter significantly increases upon Br– incorporation in the perovskite structure. The knowledge about the nature of the dipolar couplings enables us to quantitatively analyze the relative occurrence of contacts between different cations in the 2D 1H–1H DQSQ MAS NMR spectra. This analysis indicates the presence of local compositional fluctuations due to a partial clustering of MA and FA cations over the entire investigated compositional range.

Experimental and Computational Methods

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Synthesis

We synthesized the powders employing a mechanochemical approach (62) by ball-milling in a Fritsch “Pulverisette 5/4” planetary ball mill. The reactants (FAI, MAI, MABr, PbI2, and PbBr2 or already completely synthesized hybrid perovskites) were weighed to the desired stoichiometry (see Supporting Information for exact amounts) and transferred into an 80 mL stabilized ZrO2 milling jar, containing stabilized ZrO2 milling balls with 10 mm diameter. Then, 7–11 ml of cyclohexane was added as a milling agent. The powders were milled at 400 rpm for 5 min. Then milling was paused for 20 min to allow cooling of the jar. The procedure was repeated until the desired milling time was reached. The cyclohexane was evaporated by opening the finished milling jar and leaving it at room temperature in air for 15 min. Finally, we sieved the powder with a 90 μm sieve. The resulting powders were transferred into an inert atmosphere for storage. FAI, MAI, and MABr were synthesized as described in ref (62), while PbI2 (purity >99.8%) and PbBr2 (purity >98%) were purchased from Sigma-Aldrich.

X-ray Diffraction

For powder diffraction analysis, samples were prepared inside a glovebox by hermetically sealing the powder in a 0.5 mm soda lime glass capillary. The X-ray diffractograms were recorded in capillary mode on a Panalytical Empyrean diffractometer using Cu Kα radiation and a PIXcel3D 1 × 1 detector.

Solid-State NMR Spectroscopy

NMR spectra were recorded on Varian VNMRS systems operating at a magnetic field strength of 9.4 T (400 MHz) and 20.0 T (850 MHz). Probe heads used were a Varian 3.2 mm T3 HXY (400 MHz) and a Varian 1.6 mm T3 HXY (850 MHz) probe. The chemical shift was referenced using lead nitrate for 207Pb (−3494 ppm) and using adamantane for 1H (1.85 ppm) and 13C (38.5 ppm) as secondary references. All experiments were performed at room temperature and using boil-off nitrogen for performing MAS.
207Pb MAS NMR spectra were recorded at 5 kHz spinning speed with a recycle delay of 0.5 s.
Single-pulse excitation (SPE) 13C MAS NMR spectra were recorded at 12.5 kHz MAS rate, with a recycle delay of 75–90 s to ensure full relaxation (13C T1 ∼ 15s) and thus warrant quantitative results. SPINAL (63) decoupling at an 1H decoupling strength of 50 kHz was employed during acquisition.
For 1H–13C CP-MAS spectra, rf field strengths were optimized using adamantane (ν (1H) ∼ 60 kHz and ν (13C) ∼ 72 kHz). CP contact times were optimized for each sample resulting in values of 15–50 ms. For such long pulses it is important to carefully obey the power limits of the hardware. Proton decoupling (SPINAL) was employed at a field strength of 50 kHz, the recycle delay was set to 50–70 s (1H T1 ∼ 10–14 s determined by 1H saturation recovery experiments), and an MAS frequency of 12.5 kHz was used.
High-resolution 1H MAS NMR experiments were performed at a magnetic field of 850 MHz and a MAS frequency of 35 kHz. For 1D 1H MAS NMR spectra the recycle delays (65–120 s) were optimized for each sample to reach full relaxation (1H T1 ∼ 13–24 s determined by 1H saturation recovery experiments). 2D 1H−1H DQSQ MAS NMR spectra and 1H DQ buildup curves were recorded using the BABA-xy16 (64) sequence (ν (1H) ∼ 140 kHz) at a MAS rate of 35 kHz. Zero-quantum (ZQ) reference measurements were used for a normalization of the 1H DQ buildup curves: (60,64)
(1)

Molecular Dynamics with Machine-Learning Force Fields

A smoothened machine-learned potential energy surface is modeled by the Gaussian approximation potential (65) with two- and three-body descriptors and kernel function similar to the smooth overlap atomic positions (SOAP) method. (66) The descriptors are defined within a cutoff sphere of 6 or 4 Å for the two or three body term, respectively. They are discretized on radial basis functions (NR = 6 or 7) and, for the three body term, multiplied with spherical harmonics (lmax = 4). The reference structures to train the MLFF are selected on-the-fly during first-principles molecular dynamics calculations under isothermal–isobaric conditions; see refs (57) and (67) for methodological details. This method is integrated in the Vienna ab initio simulation package (VASP) code (68,69) and calculates the potential energy, forces on the atoms, and stress tensor for all the reference structures, which are, by construction, well spread over the available structural phase space. The state-of-the-art meta-gradient corrected functional SCAN (70) is applied in the first-principles (FP) calculations, since it accurately describes the physical interactions in the material. (71) The electronic minimization was performed within the projector augmented wave formalism (72) with a plane wave basis (cutoff 350 eV), a 2 × 2 × 2 k-point grid, and Gaussian smearing (σ = 0.01 eV). For the training, three 2 × 2 × 2 unit cells of MA1–xFAxPbI3 (x = 0, 0.5, 1) each containing eight cations were used. Starting from scratch, we trained the MLFF on FAPbI3 (x = 1) for 100 ps at 400 K with time steps of 3 fs, resulting in 707 included reference structures. Hereafter, training was continued on MAPbI3 (x = 0) for the same time and at the same temperature. The total number of reference structures in the resulting MLFF was only raised to 836. Last, we trained in the same way on MA0.5FA0.5PbI3; this increased the number to a total of 960 structures. These structures supply the finished MLFF with 121, 1432, 201, 244, and 1213 local reference configurations for the Pb, I, C, N, and H atoms, respectively. This MLFF was then used (in production mode, i.e., no more training) for all MD simulations shown in this work.
For the MLFF isothermal and isobaric NPT-MD simulations 4 × 4 × 4 unit cells of MA1–xFAxPbI3 were constructed with x = 0, 1/8, 1/4, ..., 1, where Langevin thermo- and barostats were applied to control the conditions. To study the influence of the spatial distribution of the FA and MA cations, ordered (O) and randomly (R) packed cells were constructed. In the O case, the 4 × 4 × 4 cells are constructed by replicating 2 × 2 × 2 unit cells in which the cations are distributed to maximize the distance to neighboring cations of the same species. In the R cells, the cations are randomly placed. All 4 × 4 × 4 cells were run for 100 ps at 300 and 400 K under 1 bar standard pressure. We calculate the dipolar coupling coefficient between all H–H pairs and divide them in two groups, with the intra- and intermolecular H–H connecting vectors. Applying the ensemble averaging over time and space following the approach by Goc et al. (73−75) (see Supporting Information for details) then gives the average dipolar coupling that can be compared to the value measured by NMR.

Results and Discussion

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Characterization

We prepared three mixed cation perovskites of the form MA1–xFAxPbI3 with x = 0.25, 0.50, 0.75 and a mixed cation and mixed halide composition MA0.15FA0.85PbI2.55Br0.45 (here referred to as double-mixed) by mechanochemical synthesis. The resulting powders were analyzed by powder X-ray diffraction, 207Pb MAS, as well as 13C MAS and high-resolution 1H MAS NMR spectroscopy to determine their crystal structure, exact FA/MA ratio, and possible impurities. The XRD patterns of all samples (Figure 1a) show reflections of a cubic lattice corroborating the stabilization of the cubic lattice upon mixing FA and MA cations. (26−28) The corresponding lattice constants (Table S1) for MA1–xFAxPbI3 increase from 6.31 to 6.34 Å with increasing FA content, while the double-mix shows a smaller lattice constant of 6.30 Å due to incorporation of the smaller Br– ion, consistent with literature observations. (34) All 207Pb MAS NMR spectra of the mixed samples and MAPbI3 (Figure 1b) show a single resonance, which gradually shifts with increasing FA content from 1430 ppm for MAPbI3 to 1490 ppm for α-FAPbI3. (50,76,77) The 207Pb MAS NMR spectrum of the double-mixed sample MA0.15FA0.85PbI2.55Br0.45 (Figure 1b, blue) reveals a broadening of the 207Pb resonance in comparison to the other mixed cation perovskites. In general, multiple effects can play a role in the 207Pb line shape: T2 broadening due to very short spin–spin relaxation, scalar couplings between Pb–X species, or disorder around the lead atoms by halide mixing. (49,76−79) Scalar couplings were found prominent for CsPbX3, while for MA- and FA-based perovskites only Pb–Cl species show features arising from the J-couplings but not for Pb–I or Pb–Br species at room temperature. (78) Therefore, as the observed broadening is slightly asymmetric and the spin–spin relaxation (T2 relaxation) of pure MAPbI3 at room temperature is already very short (∼40 μs), (49) we attribute the observed additional broadening for MA0.15FA0.85PbI2.55Br0.45 to I/Br mixing. This, in combination with the absence of any signal intensity in the chemical shift region for MAPbBr3 and FAPbBr3 (300–600 ppm), (50,76,77,79) corroborates the incorporation of the Br– ions in the lattice.

Figure 1

Figure 1. (a) XRD patterns, (b) 207Pb MAS NMR spectra, (c) 1H–13C CP-MAS NMR, and (d) 1H MAS NMR spectra of the three mixed MA1–xFAxPbI3 samples (x = 0.25, orange; x = 0.5, red; x = 0.75, green), as well as of the double-mixed sample MA0.15FA0.85PbI2.55Br0.45 (blue). (a) The XRD patterns of all samples show reflections of a cubic crystal lattice. The lattice constants are summarized in Table S1. (b) Additionally, a 207Pb MAS NMR spectrum of MAPbI3 (δiso = 1430 ppm) is depicted for comparison and dashed lines indicate chemical shifts for FAPbBr3 and MAPbBr3 from literature. (50,76,77) The 207Pb isotropic chemical shift of α-FAPbI3 is reported to be 1495 ppm. (77) (d) Asterisks in the 1H MAS NMR spectra indicate a small cyclohexane impurity, which is also observed in the 13C SPE MAS NMR spectra (Figure S2).

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Characterization of the cations in terms of types and ratios, as well as the identification of impurities, is achieved by recording single-pulse 13C MAS (Figure S1) and 1H–13C cross-polarization (CP) MAS NMR spectra (Figure 1c), which show the typical resonances at 155.5 ppm for the CH-group of FA and at 31.3 ppm for the CH3-group of the MA cation. Additionally, the direct 13C single-pulse excitation (SPE) NMR spectra of MA0.15FA0.85PbI2.55Br0.45 and MA0.5FA0.5PbI3 (Figure S1) exhibit a sharp resonance at 27.5 ppm, which is absent in the CPMAS NMR spectra, suggesting that the heteronuclear dipolar coupling between 1H and 13C is averaged, indicative of a small, mobile impurity. The high-resolution 1H MAS NMR spectra of all samples (Figure 1d) show four distinct signals, which can readily be assigned to the 1H species of the MA and FA cations. The signals of the CH3-group and the NH3-group of the MA cation occur at chemical shifts of 3.3 and 6.2 ppm, respectively, while the NH2-groups and the CH-group of the FA cation are observed at 7.3 and 8.1 ppm. For MA0.15FA0.85PbI2.55Br0.45, MA0.5FA0.5PbI3, and MA0.75FA0.25PbI3 an additional sharp signal is observed at 1.4 ppm, which together with the 13C NMR signal at 27.5 ppm is assigned to residual cyclohexane, which was used as a milling agent in the mechanochemical synthesis of the powders. The cation ratios obtained from the 13C and 1H NMR spectra are in excellent agreement with the nominal ratios from the synthesis as summarized in Table S2.

Intermolecular Cation Interactions

In order to probe the distribution and mixing behavior of MA and FA cations in the different mixed perovskite systems, we recorded two-dimensional (2D) 1H–1H DQSQ MAS NMR spectra. 1H–1H correlations of protons in close proximity with similar chemical environments result in signals along the diagonal (δDQ = 2δSQ) of the 2D spectra, while off-diagonal resonances stem from correlations between protons of differing chemical groups at the sum of the corresponding chemical shifts (δDQ = δSQ1 + δSQ2).
The experimental 2D 1H–1H DQSQ MAS NMR spectra of the four mixed samples are shown in Figure 2a–d. We observe correlations between the 1H resonances of MA cations (MA–MA; green; δDQ = 6.6, 9.5, and 12.4 ppm), between the 1H resonances of FA cations (FA–FA; blue; δDQ = 14.7, 15.5, and 16.2 ppm), and between the 1H resonances of MA and FA cations (MA–FA; red; δDQ = 10.7, 11.5, 13.6, and 14.4 ppm). The occurrence of MA–MA, FA–FA, and MA–FA correlations indicates the mixing of the cations for all compositions. In contrast, a 2D 1H–1H DQSQ MAS NMR spectrum for a physical mixture of α-FAPbI3 and MAPbI3 (Figure 2e) only shows DQ correlations between MA cations (green), as well as FA cations (blue), but no FA–MA correlations, as expected for a phase-separated system.

Figure 2

Figure 2. 2D 1H–1H DQSQ MAS NMR spectra of the mixed perovskite samples (a–d), as well as of a physical mixture of MAPbI3 and α-FAPbI3 (e) at an excitation time texc of 229 μs. Solid lines between resonances and circles on diagonal signals mark 1H–1H correlations between MA cations (green), FA cations (blue), and MA–FA cations (red). The existence of mixed MA–FA correlations demonstrates a successful mixing of MA and FA on the A site for all mixed perovskite compositions (a–d), while in the case of cation phase segregation the red correlations would diminish as in the case of a physical mixture MAPbI3 and α-FAPbI3 (e).

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After qualitatively determining the 1H–1H correlations from the 2D 1H–1H DQSQ MAS NMR spectra, a quantification of the interaction strength between the coupled 1H species of the FA and MA cations provides further structural information. These can be accessed as the dipolar coupling is proportional to the number of contributing spins, as well as their relative alignment and distance (eq 4). (55,60,80,81) Therefore, 1D 1H DQ buildup curves, which describe the buildup of DQ intensities of coupled spins as a function of excitation time, were recorded for all mixed perovskite samples, as well as the physical mixture of MAPbI3 and α-FAPbI3 (Figure S3). In the latter case, the DQ buildup curves are distinguishable for MA and FA signals (Figures 3a and S3). In contrast, for the mixed MA1–xFAxPbI3 and the double-mixed MA0.15FA0.85PbI2.55Br0.45, the individual DQ buildup curves for each 1H signal corresponding to MACH3, MANH3, FANH2, and FACH show a very similar behavior (Figure S3). Therefore, for each mixed composition, it is reasonable to average the individual DQ buildup curves resulting in the average DQ buildup curves shown in Figure 3b. All experimental DQ buildup curves exhibit the typical shape of a multispin system (Figure S3) with a distribution of dipolar interactions, which can be analyzed using either expensive modeling (55) or a second moment approximation. (60,64) Here, we used the so-called BABA-xy16 pulse sequence, which can be evaluated by the following approach to extract the average dipolar couplings: (64)
(2)
(3)
The average dipolar coupling D̅ in this approach is defined as (60)
(4)

Figure 3

Figure 3. Average 1H DQ buildup curves (a) of MAPbI3 (green) and α-FAPbI3 (blue) and (b) of the mixed perovskite compositions MA1–xFAxPbI3(yellow, red, green), as well as MA0.15FA0.85PbI2.55Br0.45 (blue). The dashed lines are fits of the DQ buildup curves according to eq 2 to extract the average dipolar couplings, which are summarized in Figure 5 and Table S3.

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The extracted average dipolar couplings D̅ from the experimental data for the mixed compositions show a gradual increase with increasing MA content, from about 2800 Hz for pure α-FAPbI3 to ∼3300 Hz for MAPbI3 (Figure 5, pink, Table S3). In contrast, the double-mixed composition MA0.15FA0.85PbI2.55Br0.45 exhibits a significantly larger dipolar coupling of ∼3900 Hz (Figure 5, light blue, Table S3). It is expected that the fast reorientation of the MA and FA cations within their cage in the perovskite lattice (26,43,47) will average the intramolecular dipolar interaction within the cations. Thus, the extracted dipolar couplings are connected to the number of FA and MA cations contributing, as FA has five and MA has six hydrogen atoms, and the average spatial intermolecular distances between neighboring cations. The decrease in D̅ with increasing FA content x could be related to a smaller number of contributing protons or to, on average, longer distances between hydrogens in nearest neighbor cations or a combination thereof.
In order to understand the correlation between the dipolar coupling D̅ and the FA content x (Figure 5), we carry out state-of-the-art MLFF molecular dynamics simulations of MA1–xFAxPbI3 supercells containing a total of 64 MA and/or FA cations with long simulation times (100 ps). The MD trajectories are used to calculate the H–H pair distribution function g(r) (eq 5, Figure S4) that describes the likelihood to find H atoms at distances r:
(5)
Figure 4a depicts the pair distribution function for nearest neighbor coordinations (2–5 Å) for MAPbI3, MA0.5FA0.5PbI3, and α-FAPbI3 (see Figure S4 for full range). The distances resulting from intramolecular H–H pairs are between 1.5 and 4.5 Å depending on the molecular structure of the cations FA and MA (Figure S4). The onset of the intermolecular part of g(r) occurs at larger distances for MA cations (x = 0) than for FA cations (x = 1), and it gradually decreases with increasing x (Figure 4a), as expected considering the different MA and FA cation sizes. (2) As observed above, an opposite trend is needed to explain the decrease of D̅ with increasing x considering only interatomic distances. Evidently, an interpretation of the dipolar couplings in terms of average intermolecular distances between the cations is insufficient.

Figure 4

Figure 4. (a) Close-up of the pair distribution function between 2 and 5 Å for hydrogen atoms in MA1–xFAxPbI3 for x = 0, 0.5, and 1 obtained in the cubic phase at 400 K. The intra- and intermolecular contributions are depicted separately to demonstrate the onset of the intermolecular contributions. The full H–H pair distribution function of the simulation is depicted in the Supporting Information (Figure S4). (b) Intra- (black) and intermolecular (red) contributions to the average dipolar coupling as a function of simulation time for MA0.5FA0.5PbI3. Additionally, the intramolecular term averaged by applying symmetry of the intramolecular H–H vectors is shown in blue.

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To clarify these apparently contradicting results, we calculate the average dipolar coupling (D̅) directly from the MD trajectories following the approach of Goc et al. (73−75) (Supporting Information, section 5). This provides access to the intra- and intermolecular contribution to D̅ as a function of the inverse trajectory length (1/tMD). In Figure 4b the black and red lines show the intra- and intermolecular contribution in MA0.5FA0.5PbI3, respectively. The intramolecular contribution decays only slowly with time, whereas the intermolecular contribution quickly converges and thus appears nearly constant (see Figure 4b and Figure S5). About 100 ps (1/tMD = 0.01 ps–1) of simulation time is needed for the intramolecular contribution to be smaller than the intermolecular contribution. The intramolecular contribution is still noticeably decreasing after these 100 ps. In view of the nearly free rotation of the cations in the cubic perovskite lattice, on longer time scales (1/tMD → 0 ps–1) one would expect a (vanishly) small intramolecular dipolar coupling. This can be demonstrated if costly MD runs are carried out for which several orders of magnitude longer simulation times will be needed. As an alternative, it is possible to significantly reduce the computational effort by considering symmetry within the large supercell (see Supporting Information). Averaging over similar intramolecular H–H vectors results in three remaining inequivalent vectors for MA and six for FA. In this way we can improve the statistics for D̅intra without elongating the trajectory, which causes a drastic reduction of D̅intra (Figure 4b, blue, and Figure S5). These results demonstrate that the average dipolar coupling D̅ is very well approximated by solely considering intermolecular contributions, i.e., D̅intra = 0 on the NMR time scale.
In Figure 5 the calculated D̅ versus perovskite composition x is plotted as well as the experimental values obtained from the 1H DQ buildup curves. The values calculated for the MA1–xFAxPbI3 systems are in excellent agreement with the experiment. The small offset (∼300–400 Hz) of the calculated values is caused by the slightly larger lattice constant (∼0.08 Å) predicted by the MLFF (Figure S1). At 400 K simulation temperature the lattice constants are slightly larger (∼0.02 Å) than at 300 K due to thermal expansion (Figure S1), which results in a decrease of the calculated D̅ (Figure 5). In order to investigate the influence of the packing order on the calculated D̅ values, we also compared two types of homogeneous distributions of FA and MA cations, a random (R) and an ordered (O) packing. The O packing represents FA and MA cations in alternating positions resulting in solely nearest-neighbor MA–FA correlations for x = 0.5. Interestingly, we find that the packing order has no noticeable effect on the average dipolar interaction D̅ between the cations (Figure S6).

Figure 5

Figure 5. Average 1H dipolar couplings for MA1–xFAxPbI3 extracted from 1H DQ buildup curves (pink) and MD simulations at 300 K (blue) and 400 K (red, solid line). Additionally, solely intermolecular contributions to D̅ are shown for the MD run at 400 K (red, dashed lines) revealing minor differences to the full average dipolar coupling (red, solid line). Additionally, linear trends resulting from models, where all H atoms are placed in the center of the lattice A site neglecting dynamics, etc., are depicted in black. The solid line depicts the model with a fixed lattice constant over the whole compositional space resulting in a linear curve with a slope proportional to the hydrogen ratio of FA and MA (y = (√(5/6) – 1)D0 + D0, black solid). The dashed black line is the model using experimental lattice constants of MA1–xFAxPbI3, fitting the experimental data slightly better. This demonstrates that the linear dependence of D̅ on x is dominated by the number of contributing spins. Furthermore, the experimental average dipolar coupling of the double-mixed perovskite composition MA0.15FA0.85PbI2.55Br0.45 is depicted (light blue), revealing a significantly higher average dipolar coupling than the MA1–xFAxPbI3 compositions.

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With these results it becomes clear that the linear dependence of D̅ on x stems from a change of the contributing average amount of hydrogen pairs in the mixed perovskites. As MA possesses six hydrogens, whereas FA has only five, the average dipolar coupling D̅ decreases with increasing FA content x (Figure 5, pink and black solid). Placing all H in the center of the A lattice site is also a good approximate model (Figure 5, black lines). In contrast, the ordering of MA/FA on the grid and the change of the (pseudo)cubic lattice constant have a much smaller effect. As the change of D̅ with x is dominated by the hydrogen content in mixed MA1–xFAxPbI3, we conclude that average intermolecular proton–proton distances in nearest neighbor coordination are rather similar throughout the investigated compositional range.
Figure 5 (light blue diamond) also shows the experimental average dipolar coupling of MA0.15FA0.85PbI2.55Br0.45. At about 3900 Hz it is significantly larger than for the binary MA/FA mixtures. Although the lattice contracts slightly upon Br– incorporation (Table S1), a shrinkage of the pseudocubic lattice constant of about 0.04 Å in comparison to MA0.25FA0.75PbI3 and α-FAPbI3 cannot account for an increase in D̅ of about 1000 Hz. The increase therefore indicates a restriction in cation mobility either by a significant reduction in reorientation frequency or by a restriction in spatial degrees of freedom, i.e., an anisotropic motion over specific orientations. Stronger interactions of the FA and MA cations with the inorganic sublattice, induced by the presence of more electronegative Br– ions (compared to I–), or the lattice contraction itself could cause this. Both these effects will raise the average dipolar couplings D̅ and might give rise to a non-negligible intramolecular contribution to D̅.
These findings fit in a recently proposed scenario of restricted MA cation dynamics upon mixing I– and Br– in the lattice. In this scenario specific hydrogen bonding situations for the MA cations result in a higher activation barrier for rotational jumps in certain directions and thus in their partial immobilization causing an anisotropic dynamical behavior. (82) For FA cations, however, the hydrogen bonds to the inorganic sublattice are much weaker, (26,83) initially resulting in faster reorientations in comparison to MA. Consequently, one would expect less influence of I/Br mixing on the FA dynamics, which was not resolved in our experiments. To fully understand the origin of the increase of D̅ and to characterize the possible dynamical restriction of cations due to interactions with the inorganic sublattice, further MLFF calculations on mixed cation and anion compositions are needed.

Microscopic Cation (Dis)order

The MLFF calculations corroborate that the intramolecular dipolar coupling of the cations is averaged through the rapid reorientation within the A site, and thus only intermolecular dipolar interactions are measured experimentally. Consequently, all 1H–1H correlations measured in the 2D 1H–1H DQSQ MAS NMR spectra (Figure 2) are due to a close proximity of protons on neighboring cations. As we established, the strength of the dipolar interaction only depends on the number of interacting spins and hardly on slight variations of the lattice parameters for the different compositions. Therefore, differences in DQ intensities in the 2D spectra of the different compounds are directly proportional to the number of intercation interactions, i.e., the relative amounts of MA and FA cations, taking the different numbers of protons for MA and FA into account. The quantitative analysis of the DQ signal intensities thus makes it possible to extract the relative occurrence of each of the intercation dipolar contacts MA–MA, MA–FA, and FA–FA (hereafter referred to as MA–MA, MA–FA, and FA–FA contacts). Their population provides a measure for the microscopic order/disorder of the cations within the perovskite lattice.
In the cubic perovskite lattice, each A site cation, MA or FA, is surrounded by six nearest-neighbor A cations. Different ordering of the cations within the cubic lattice, e.g., random mixing, alternating MA and FA ordering, or clustering of MA or FA cations, results in different probabilities for local nearest neighbor coordinations MA[MA6–nFAn] and FA[MA6–nFAn] (n = 1, 2, ..., 6). These are experimentally accessible as the sum of resulting MA–MA, FA–FA, and mixed MA–FA contacts. A random cation distribution can be described by a binomial distribution based on the relative occurrence of MA or FA in the lattice, providing the statistics of the total of MA–MA (Figure 2 and Figure 6, green), FA–FA (Figure 2 and Figure 6, blue), and MA–FA contacts (Figure 2 and Figure 6a, red).

Figure 6

Figure 6. (a) Populations of cation–cation contacts, MA–MA (green), FA–FA (blue), and MA–FA (red), as a function of FA content x. The experimental data are indicated by dots, while the populations according to a random distribution of cations are shown by dashed lines. Dotted lines represent the populations of contacts for a cluster model with an order parameter S of 0.3. (b–e) Calculated populations of cation–cation contacts, MA–MA (green), FA–FA (blue), and MA–FA (red), as a function of order parameter S for the different compositions of the mixed MA1–xFAxPbI3 (b–d), as well as MA0.15FA0.85PbI2.55Br0.45 (e). The horizontal bars indicate the experimental accuracy for the observed populations (dashed lines) of cation–cation correlations in the 2D 1H–1H DQSQ MAS NMR spectra (Figure 2).

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The comparison of the experimentally observed populations (Figure 6a, dots) with the populations resulting for a random distribution (Figure 6a, dashed lines) shows an overall good agreement, with small but systematic deviations especially for the mixed contact MA–FA (red). This indicates a weak tendency for clustering of MA and FA cations, leading to local fluctuations in composition, which can be quantified by introducing an order parameter S, (84−86) in analogy to the analysis of XRD data. (87) For a cluster model, an order parameter of S = 0 corresponds to a random distribution, whereas S = 1 characterizes a complete phase separation. The site occupancies rMA and rFA describing the clustering tendency of the cations and thus the local compositional changes can then be parametrized as
(6)
(7)
With that, the theoretical populations for the three cation–cation contacts are defined as
(8)
(9)
(10)
Parts b–e of Figure 6 depict the calculated populations for the three cation–cation contacts MA–MA (green), FA–FA (blue), and MA–FA (red) as a function of S for different mixed cation compositions MA1–xFAxPbI3 (x = 0.25 (b), x = 0.5 (c), x = 0.75 (d), x = 0.85 (e)). Additionally, the experimentally determined occurrence of each contact for each composition x is depicted as dashed lines, where the width of the bars accounts for the experimental error. The intersection of the observed occurrences with the calculated populations reveals that partial MA–MA and FA–FA clustering with an order parameter S between 0.2 and 0.4 takes place for compositions with x = 0.25 and x = 0.5. For compositions with higher FA contents (x = 0.75, 0.85, Figure 3d,e) the intersection covers a range between S = 0 and S = 0.3 for a composition x = 0.75 and covers a range between S = 0–0.4 for x = 0.85. At low and high values of x the changes in populations are less pronounced, preventing a precise assignment of S within the experimental accuracy. Interestingly, the experimentally determined populations show a similar trend over the entire compositional range.
In order to visualize the effect of cation clustering with S = 0.3 in comparison to a random scenario, the distributions of FA (blue) and MA (red) cations for MA1–xFAxPbI3 compositions on a 2D grid are schematically depicted in Figure 7. The circles labeled rMA and rFA demonstrate the local compositional fluctuations resulting from MA and FA clustering, respectively, within the perovskite particles. The schematic representation illustrates that the nominal overall composition MA1–xFAxPbI3 is heterogeneous with MA and FA-rich regions, where the average compositional fluctuations can be described by rMA and rFA. An upper limit for the size of these clusters is deducted by analyzing the width of the X-ray reflections. Pronounced domains of local compositional fluctuations would lead to the measurement of a distribution of lattice constants and in turn to a broadening of XRD peaks. As no broadening is observed (Figure S7), the cluster domains must be smaller than of the order of 100 nm.

Figure 7

Figure 7. Schematic representation of MA (red)/FA (blue) distributions within MA1–xFAxPbI3 (x = 0.25, 0.50, 0.75) perovskites following random statistics (a) and MA or FA clustering (b) to a degree of S = 0.3 labeled rMA and rFA, respectively (according to eqs 6 and 7). As the experimental NMR data do not provide information about domain sizes of MA-rich and FA-rich regions, arbitrary sized circles were chosen to represent the statistics.

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To be thermodynamically stable, the Gibbs free energy of the clustered structure must be lower than for the random mix (S = 0) structure. In general, the formation of domains results in strain at the domain walls, which is marginal in this particular case, as the pseudocubic lattice constants differ only 0.06 Å between the parent composition MAPbI3 and α-FAPbI3 and 0.03 Å for the mixed compositions x = 0.25 and x = 0.75. Furthermore, if the clusters are very small, i.e., in the range of several nearest neighbor shells, domain walls might not even form. If only gradual compositional changes occur, subtle distortions of the inorganic sublattice will be sufficient to compensate for the compositional fluctuations. In a clustered structure, there are less different ways to distribute the cations over the lattice of A sites, resulting in a lower entropy and thus higher free energy. However, the clustering might raise the entropy in case there is an impact on the cation dynamics. Recently it was discussed that the rotational motion of FA cations is confined upon mixing with MA+ or Cs+ cations because of a preferential orientation of the FA cations. (41,43,88) As the local configuration of neighboring MA+ or Cs+ was important for the ordering of FA, (43) local clustering of MA or FA cations may suppress this reduction of the degrees of motion, thus resulting in a higher dynamical freedom and lowering of the free energy compared to a random mixture.

Conclusion

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We have combined NMR spectroscopy and MLFF MD simulations to study the dynamics and local (dis)order of FA and MA cations in the mixed hybrid perovskite systems MA1–xFAxPbI3 and MA0.15FA0.85PbI2.55Br0.45. On the basis of our results, we can sketch a plausible scenario for an ordering pattern of the cations in MA1–xFAxPbI3 mixed hybrid perovskites. The population analysis of the 1H–1H DQSQ MAS NMR spectra indicates that a microstructure (order parameter S ∼ 0.3) with MA-rich and FA-rich regions occurs. XRD analysis indicates that the average size of the domains is below ∼100 nm. Furthermore, the novel MLFF method has been shown to accurately predict the average dipolar coupling measured in the NMR experiment. Building on this excellent agreement, we can conclude (a) that the average dipolar coupling D̅ is dominated by intermolecular nearest neighbor cation interactions, (b) that it scales with the number of 1H spins on the neighboring cation, which explains its decrease with FA composition x, and (c) that it depends on average composition, i.e., we did not observe changes by short-range compositional fluctuations. While a similar MA and FA ordering was found for the double-mixed MA0.15FA0.85PbI2.55Br0.45 perovskite and the MA1–xFAxPbI3 systems, the average 1H−1H dipolar coupling was observed to be significantly higher in the double-mixed system. This indicates a restriction of the mobility of the organic cations resulting in an anisotropic motion upon incorporation of the smaller Br– ions, possibly induced through the slight lattice contraction. Both these effects will raise the average dipolar coupling D̅.
Heterogeneity in local cation compositions results in a local variation of perovskite lattice constants and in local variations of the electrostatic interaction between cations and inorganic sublattice. (89,90) Both effects cause a distribution of band gap energies of mixed perovskites, as was concluded from the observed distribution of optical properties and ab initio calculations. (89,90) As a consequence, the charge carriers will localize in energetically favorable domains limiting the overall charge transport. Furthermore, it was found that local compositional heterogeneities can cause the formation of clusters of deep traps. (91) These trap clusters in turn appear to be the key factor limiting the optoelectronic properties, (91) ion migration, (92,93) and stability of mixed halide perovskites. On the basis of these considerations, it appears attractive to reduce the degree of mixing while ensuring a robust stabilization of the perovskite lattice. This indeed is in line with the most recent developments in the field of perovskite solar cells, (17) where our results will help to better exploit the full potential of mixed halide perovskites and corresponding optoelectronic devices.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.0c10042.

  • Exact precursor amounts for the syntheses; experimental and calculated average lattice constants of MA1–xFAxPbI3; 13C SPE MAS NMR spectra, individual 1H DQ buildup curves, exact MA/FA ratios and experimental dipolar couplings of MA1–xFAxPbI3 and MA0.15FA0.85PbI2.55Br0.45; full H–H pair distribution function extracted from MD simulations; further details on analyses of the MLFF MD simulations (PDF)

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Author Information

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  • Corresponding Authors
    • Helen Grüninger - Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands;  Orcidhttp://orcid.org/0000-0002-5422-7003;  Email: [email protected]
    • Menno Bokdam - Faculty of Physics and Center for Computational Materials Sciences, University of Vienna, Sensengasse 8/12, 1090 Vienna, Austria;  Faculty of Science and Technology and MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;  Email: [email protected]
    • Arno P. M. Kentgens - Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands;  Orcidhttp://orcid.org/0000-0001-5893-4488;  Email: [email protected]
  • Authors
    • Nico Leupold - Department of Functional Materials, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
    • Paul Tinnemans - Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
    • Ralf Moos - Department of Functional Materials, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany
    • Gilles A. De Wijs - Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands;  Orcidhttp://orcid.org/0000-0002-1818-0738
    • Fabian Panzer - Department of Functional Materials, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany;  Soft Matter Optoelectronics, University of Bayreuth, Universitätsstraße 30, 95447 Bayreuth, Germany;  Orcidhttp://orcid.org/0000-0002-2191-9011
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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We thank NWO for the support of the “Solid-State NMR Facilities for Advanced Materials Science”, which is part of the uNMR-NL ROADMAP facility. The facilities technicians Gerrit Janssen, Hans Janssen, and Ruud Aspers are thanked for their support. H.G. thanks the “Deutsche Forschungsgemeinschaft (DFG)” for funding within Grant GR 5505/1-1. M.B. gratefully thanks Jonathan Lahnsteiner for stimulating discussions on mixed perovskite order. M.B. acknowledges funding by the Austrian Science Fund (FWF): Grant P30316-N27. Computations were partly performed on the Vienna Scientific Cluster VSC3. F.P. and N.L. thank the “Deutsche Forschungsgemeinschaft (DFG)” for funding (Project PA 3373/3-1).

References

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    Here we combine the promising, owing to its comparatively narrow bandgap, but relatively unstable formamidinium lead iodide (FAPbI3) with methylammonium lead bromide (MAPbBr3) as the light-harvesting unit in a bilayer solar cell architecture. We investigated phase stability, morphol. of the perovskite layer, hysteresis in current-voltage characteristics, and overall performance as a function of chem. compn. Our results show that incorporation of MAPbBr3 into FAPbI3 stabilizes the perovskite phase of FAPbI3 and improves the power conversion efficiency of the solar cell to >18% under a std. illumination of 100 mW/cm2. These findings further emphasize the versatility and performance potential of inorg.-org. lead halide perovskite materials for photovoltaic applications.
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  10. 10
    Petrus, M. L.; Schlipf, J.; Li, C.; Gujar, T. P.; Giesbrecht, N.; Müller-Buschbaum, P.; Thelakkat, M.; Bein, T.; Hüttner, S.; Docampo, P. Capturing the Sun: A Review of the Challenges and Perspectives of Perovskite Solar Cells. Adv. Energy Mater. 2017, 7, 1700264,  DOI: 10.1002/aenm.201700264
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  11. 11
    Panzer, F.; Li, C.; Meier, T.; Köhler, A.; Huettner, S. Impact of Structural Dynamics on the Optical Properties of Methylammonium Lead Iodide Perovskites. Adv. Energy Mater. 2017, 7, 1700286,  DOI: 10.1002/aenm.201700286
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    There is no corresponding record for this reference.
  12. 12
    Gao, P.; Grätzel, M.; Nazeeruddin, M. K. Organohalide Lead Perovskites for Photovoltaic Applications. Energy Environ. Sci. 2014, 7, 2448– 2463,  DOI: 10.1039/C4EE00942H
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    12
    Organohalide lead perovskites for photovoltaic applications
    Gao, Peng; Gratzel, Michael; Nazeeruddin, Mohammad K.
    Energy & Environmental Science (2014), 7 (8), 2448-2463CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
    There are only few semiconducting materials that have been shaping the progress of third generation photovoltaic cells as much as perovskites. Although they are deceivingly simple in structure, the archetypal AMX3-type perovskites have built-in potential for complex and surprising discoveries. Since 2009, a small and somewhat exotic class of perovskites, which are quite different from the common rock-solid oxide perovskite, have turned over a new leaf in solar cell research. Highlighted as one of the major scientific breakthroughs of the year 2013, the power conversion efficiency of the title compd. hybrid org.-inorg. perovskite has now exceeded 18%, making it competitive with thin-film PV technol. In this mini-review, a brief history of perovskite materials for photovoltaic applications is reported, the current state-of-the-art is distd. and the basic working mechanisms have been discussed. By analyzing the attainable photocurrent and photovoltage, realizing perovskite solar cells with 20% efficiency for a single junction, and 30% for a tandem configuration on a c-Si solar cell would be realistic.
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  13. 13
    Kazim, S.; Nazeeruddin, M. K.; Grätzel, M.; Ahmad, S. Perovskite as Light Harvester: A Game Changer in Photovoltaics. Angew. Chem., Int. Ed. 2014, 53, 2812– 2824,  DOI: 10.1002/anie.201308719
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    13
    Perovskite as Light Harvester: A Game Changer in Photovoltaics
    Kazim, Samrana; Nazeeruddin, Mohammad Khaja; Graetzel, Michael; Ahmad, Shahzada
    Angewandte Chemie, International Edition (2014), 53 (11), 2812-2824CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    A review; it is not often that the scientific community is blessed with a material, which brings enormous hopes and receives special attention. When it does, it expands at a rapid pace and its every dimension creates curiosity. One such material is perovskite, which has triggered the development of new device architectures in energy conversion. Perovskites are of great interest in photovoltaic devices due to their panchromatic light absorption and ambipolar behavior. Power conversion efficiencies have been doubled in less than a year and over 15 % is being now measured in labs. Every digit increment in efficiency is being celebrated widely in the scientific community and is being discussed in industry. Here we provide a summary on the use of perovskite for inexpensive solar cells fabrication. It will not be unrealistic to speculate that one day perovskite-based solar cells can match the capability and capacity of existing technologies.
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  14. 14
    Park, N.; Grätzel, M.; Miyasaka, T. Organic-Iorganic Halide Perovskite Photovoltaics: From Fundamentals to Devices Architectures; Springer International Publishing: Cham, Switzerland, 2016.
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    There is no corresponding record for this reference.
  15. 15
    Jeon, N. J.; Na, H.; Jung, E. H.; Yang, T.-Y.; Lee, Y. G.; Kim, G.; Shin, H.-W.; Il Seok, S.; Lee, J.; Seo, J. A Fluorene-Terminated Hole-Transporting Material for Highly Efficient and Stable Perovskite Solar Cells. Nat. Energy 2018, 3, 682– 689,  DOI: 10.1038/s41560-018-0200-6
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    15
    A fluorene-terminated hole-transporting material for highly efficient and stable perovskite solar cells
    Jeon, Nam Joong; Na, Hyejin; Jung, Eui Hyuk; Yang, Tae-Youl; Lee, Yong Guk; Kim, Geunjin; Shin, Hee-Won; Il Seok, Sang; Lee, Jaemin; Seo, Jangwon
    Nature Energy (2018), 3 (8), 682-689CODEN: NEANFD; ISSN:2058-7546. (Nature Research)
    Perovskite solar cells (PSCs) require both high efficiency and good long-term stability if they are to be commercialized. It is crucial to finely optimize the energy level matching between the perovskites and hole-transporting materials to achieve better performance. Here, we synthesize a fluorene-terminated hole-transporting material with a fine-tuned energy level and a high glass transition temp. to ensure highly efficient and thermally stable PSCs. We use this material to fabricate photovoltaic devices with 23.2% efficiency (under reverse scanning) with a steady-state efficiency of 22.85% for small-area (∼0.094 cm2) cells and 21.7% efficiency (under reverse scanning) for large-area (∼1 cm2) cells. We also achieve certified efficiencies of 22.6% (small-area cells, ∼0.094 cm2) and 20.9% (large-area, ∼1 cm2). The resultant device shows better thermal stability than the device with spiro-OMeTAD, maintaining almost 95% of its initial performance for more than 500 h after thermal annealing at 60°C.
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  16. 16
    Yang, W. S.; Park, B.; Jung, E. H.; Jeon, N. J.; Kim, Y. C.; Lee, D. U.; Shin, S. S.; Seo, J.; Kim, E. K.; Noh, J. H. Iodide Management in Formamidinium-Lead-Halide-Based Perovskite Layers for Efficient Solar Cells. Science 2017, 356, 1376– 1379,  DOI: 10.1126/science.aan2301
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    16
    Iodide management in formamidinium-lead-halide-based perovskite layers for efficient solar cells
    Yang, Woon Seok; Park, Byung-Wook; Jung, Eui Hyuk; Jeon, Nam Joong; Kim, Young Chan; Lee, Dong Uk; Shin, Seong Sik; Seo, Jangwon; Kim, Eun Kyu; Noh, Jun Hong; Seok, Sang Il
    Science (Washington, DC, United States) (2017), 356 (6345), 1376-1379CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
    The formation of a dense and uniform thin layer on the substrates is crucial for the fabrication of high-performance perovskite solar cells (PSCs) contg. formamidinium with multiple cations and mixed halide anions. The concn. of defect states, which reduce a cell's performance by decreasing the open-circuit voltage and short-circuit c.d., needs to be as low as possible. We show that the introduction of addnl. iodide ions into the org. cation soln., which are used to form the perovskite layers through an intramol. exchanging process, decreases the concn. of deep-level defects. The defect-engineered thin perovskite layers enable the fabrication of PSCs with a certified power conversion efficiency of 22.1% in small cells and 19.7% in 1-square-centimeter cells.
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  17. 17
    Lu, H.; Krishna, A.; Zakeeruddin, S. M.; Grätzel, M.; Hagfeldt, A. Compositional and Interface Engineering of Organic-Inorganic Lead Halide Perovskite Solar Cells. iScience 2020, 23, 101359,  DOI: 10.1016/j.isci.2020.101359
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    17
    Compositional and Interface Engineering of Organic-Inorganic Lead Halide Perovskite Solar Cells
    Lu, Haizhou; Krishna, Anurag; Zakeeruddin, Shaik M.; Gratzel, Michael; Hagfeldt, Anders
    iScience (2020), 23 (8), 101359CODEN: ISCICE; ISSN:2589-0042. (Elsevier B.V.)
    A review. Power conversion efficiency (PCE) of the perovskite solar cells (PSCs) has remarkably been increased from 3.1% to 25.2%. The fast expansion of the PSCs has been along with the development of compositional and interface engineering, which has been playing a crit. role. For the PSCs with record high-efficiency and stability, the perovskite absorber layer has been changed from the initial MAPbI3- to FAPbI3-based compns. Owing to the enormous engineering works, perovskite absorber layers with monolithic grains could be achieved, in which the interior defects are negligible compared with the surface defects. Therefore, interface engineering, which can passivate the surface defects and/or isolate the perovskite from the environmental moistures, has been playing a more and more important role to further boost the PCE and stability of the PSCs. Herein, a compact review study of the compositional and interface engineering is presented and promising strategies and directions of the PSCs are discussed.
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  18. 18
    Hoke, E. T.; Slotcavage, D. J.; Dohner, E. R.; Bowring, A. R.; Karunadasa, H. I.; McGehee, M. D. Reversible Photo-Induced Trap Formation in Mixed-Halide Hybrid Perovskites for Photovoltaics. Chem. Sci. 2015, 6, 613– 617,  DOI: 10.1039/C4SC03141E
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    18
    Reversible photo-induced trap formation in mixed-halide hybrid perovskites for photovoltaics
    Hoke, Eric T.; Slotcavage, Daniel J.; Dohner, Emma R.; Bowring, Andrea R.; Karunadasa, Hemamala I.; McGehee, Michael D.
    Chemical Science (2015), 6 (1), 613-617CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
    We report on reversible, light-induced transformations in (CH3NH3)Pb(BrxI1-x)3. Photoluminescence (PL) spectra of these perovskites develop a new, red-shifted peak at 1.68 eV that grows in intensity under const., 1-sun illumination in less than a minute. This is accompanied by an increase in sub-bandgap absorption at ∼1.7 eV, indicating the formation of luminescent trap states. Light soaking causes a splitting of X-ray diffraction (XRD) peaks, suggesting segregation into two cryst. phases. Surprisingly, these photo-induced changes are fully reversible; the XRD patterns and the PL and absorption spectra revert to their initial states after the materials are left for a few minutes in the dark. We speculate that photoexcitation may cause halide segregation into iodide-rich minority and bromide-enriched majority domains, the former acting as a recombination center trap. This instability may limit achievable voltages from some mixed-halide perovskite solar cells and could have implications for the photostability of halide perovskites used in optoelectronics.
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  19. 19
    Yang, X.; Yan, X.; Wang, W.; Zhu, X.; Li, H.; Ma, W.; Sheng, C. Light Induced Metastable Modification of Optical Properties in CH3NH3PbI3-xBrx Perovskite Films: Two-Step Mechanism. Org. Electron. 2016, 34, 79– 83,  DOI: 10.1016/j.orgel.2016.04.020
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    19
    Light induced metastable modification of optical properties in CH3NH3PbI3-xBrx perovskite films: Two-step mechanism
    Yang, Xiao; Yan, Xiaoliang; Wang, Wei; Zhu, Xiangxiang; Li, Heng; Ma, Wanli; Sheng, ChuanXiang
    Organic Electronics (2016), 34 (), 79-83CODEN: OERLAU; ISSN:1566-1199. (Elsevier B.V.)
    We have used photoluminescence (PL) and photomodulation (PM) spectroscopy to investigate the reversible spectral changes of PL in CH3NH3PbI3-xBrx films, where x is 1.7. In an as-prepd. film, the peak of PL spectra shifts from ∼640 nm near bandedge to ∼750 nm after excitation by a continuous wave (CW) or a pulsed laser with high repetition rate, but keeps at 640 nm excited by same pulsed laser with the repetition rate smaller than 500 Hz. The PM spectroscopy also shows the formation of sub bandgap states after illumination which is responsible for the red shift of PL. The light induced modification of optical properties is reversible after keeping the film out of illumination for several hours at room temp. We analyze the photoinduced modification to be two-steps processes: the temporary sub bandgap states were first photogenerated in perovskite film, if those states interacting with more coming photons within their lifetimes, light induced metastable states responsible for red-shift of PL will be formed. This instability reduces the electronic bandgap and generates more traps which will degrade the performance of the related photovoltaic devices.
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  20. 20
    Knight, A. J.; Herz, L. M. Preventing Phase Segregation in Mixed-Halide Perovskites: A Perspective. Energy Environ. Sci. 2020, 13, 2024– 2046,  DOI: 10.1039/D0EE00788A
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    20
    Preventing phase segregation in mixed-halide perovskites: a perspective
    Knight, Alexander J.; Herz, Laura M.
    Energy & Environmental Science (2020), 13 (7), 2024-2046CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
    Mixed-halide perovskites are ideal materials for the demanding applications of tandem solar cells and emission-tunable light-emitting diodes (LEDs) because of their high compositional flexibility and optoelectronic performance. However, one major obstacle to their use is the compositional instability some mixed-halide perovskites experience under illumination or charge-carrier injection, during which the perovskite material demixes into regions of differing halide content. Such segregation of halide ions adversely affects the electronic properties of the material and severely limits the prospects of mixed-halide perovskite technol. Accordingly, a considerable amt. of research has been performed aiming to uncover the underlying mechanisms and mitigating factors of the halide segregation process. Here we present a perspective of strategies designed to reduce the effects of halide segregation in working mixed-halide perovskite devices, based on recent literature reports. We discuss a multitude of mitigating techniques, and conclude that a combination of stoichiometric engineering, crystallinity control and trap state passivation is clearly imperative for abating halide segregation. In addn., the redn. of halide vacancies and control over illumination and temp. can, to a certain extent, mitigate halide segregation. Less direct approaches, such as a change in atm. environment, perovskite incorporation into a nanocryst. compn., or direct control over the crystallog. structure of the perovskite, may however prove too cumbersome to be of practical use. This perspective paves the way for the design and creation of phase-stable, mixed-halide perovskite materials for photovoltaic and LED applications.
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  21. 21
    Knight, A. J.; Wright, A. D.; Patel, J. B.; McMeekin, D. P.; Snaith, H. J.; Johnston, M. B.; Herz, L. M. Electronic Traps and Phase Segregation in Lead Mixed-Halide Perovskite. ACS Energy Lett. 2019, 4, 75– 84,  DOI: 10.1021/acsenergylett.8b02002
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    21
    Electronic traps and phase segregation in lead mixed-halide perovskite
    Knight, Alexander J.; Wright, Adam D.; Patel, Jay B.; McMeekin, David P.; Snaith, Henry J.; Johnston, Michael B.; Herz, Laura M.
    ACS Energy Letters (2019), 4 (1), 75-84CODEN: AELCCP; ISSN:2380-8195. (American Chemical Society)
    An understanding of the factors driving halide segregation in lead mixed-halide perovskites is required for their implementation in tandem solar cells with existing silicon technol. Here we report that the halide segregation dynamics obsd. in the photoluminescence from CH3NH3Pb(Br0.5I0.5)3 is strongly influenced by the atm. environment, and that encapsulation of films with a layer of poly(Me methacrylate) allows for halide segregation dynamics to be fully reversible and repeatable. The authors further establish an empirical model directly linking the amt. of halide segregation obsd. in the photoluminescence to the fraction of charge carriers recombining through trap-mediated channels, and the photon flux absorbed. From such quant. anal. the authors show that under pulsed illumination, the frequency of the modulation alone has no influence on the segregation dynamics. Addnl., they extrapolate that working CH3NH3Pb(Br0.5I0.5)3 perovskite cells would require a redn. of the trap-related charge carrier recombination rate to .ltorsim.105s-1 in order for halide segregation to be sufficiently suppressed.
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  22. 22
    Jeong, M.; Choi, I. W.; Go, E. M.; Cho, Y.; Kim, M.; Lee, B.; Jeong, S.; Jo, Y.; Choi, H. W.; Lee, J. Stable Perovskite Solar Cells with Efficiency Exceeding 24.8% and 0.3-V Voltage Loss. Science 2020, 369, 1615– 1620,  DOI: 10.1126/science.abb7167
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    22
    Stable perovskite solar cells with efficiency exceeding 24.8% and 0.3-V voltage loss
    Jeong, Mingyu; Choi, In Woo; Go, Eun Min; Cho, Yongjoon; Kim, Minjin; Lee, Byongkyu; Jeong, Seonghun; Jo, Yimhyun; Choi, Hye Won; Lee, Jiyun; Bae, Jin-Hyuk; Kwak, Sang Kyu; Kim, Dong Suk; Yang, Changduk
    Science (Washington, DC, United States) (2020), 369 (6511), 1615-1620CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
    Further improvement and stabilization of perovskite solar cell (PSC) performance are essential to achieve the com. viability of next-generation photovoltaics. Considering the benefits of fluorination to conjugated materials for energy levels, hydrophobicity, and noncovalent interactions, two fluorinated isomeric analogs of the well-known hole-transporting material (HTM) Spiro-OMeTAD are developed and used as HTMs in PSCs. The structure-property relationship induced by constitutional isomerism is investigated through exptl., atomistic, and theor. analyses, and the fabricated PSCs feature high efficiency ≤ 24.82% (certified at 24.64% with 0.3-V voltage loss), along with long-term stability in wet conditions without encapsulation (87% efficiency retention after 500 h). An efficiency of 22.31% is achieved in the large-area cell.
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  23. 23
    Kim, M.; Kim, G.-H.; Lee, T. K.; Choi, I. W.; Choi, H. W.; Jo, Y.; Yoon, Y. J.; Kim, J. W.; Lee, J.; Huh, D. Methylammonium Chloride Induces Intermediate Phase Stabilization for Efficient Perovskite Solar Cells. Joule 2019, 3, 2179– 2192,  DOI: 10.1016/j.joule.2019.06.014
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    23
    Methylammonium Chloride Induces Intermediate Phase Stabilization for Efficient Perovskite Solar Cells
    Kim, Minjin; Kim, Gi-Hwan; Lee, Tae Kyung; Choi, In Woo; Choi, Hye Won; Jo, Yimhyun; Yoon, Yung Jin; Kim, Jae Won; Lee, Jiyun; Huh, Daihong; Lee, Heon; Kwak, Sang Kyu; Kim, Jin Young; Kim, Dong Suk
    Joule (2019), 3 (9), 2179-2192CODEN: JOULBR; ISSN:2542-4351. (Cell Press)
    One of the most effective methods to achieve high-performance perovskite solar cells has been to include additives that serve as dopants, crystn. agents, or passivate defect sites. Cl-based additives are among the most prevalent in literature, yet their exact role is still uncertain. In this work, we systematically study the function of methylammonium chloride (MACl) additive in formamidinium lead iodide (FAPbI3)-based perovskite. Using d. functional theory, we provide a theor. framework for understanding the interaction of MACl with a perovskite. We show that MACl successfully induces an intermediate to the pure FAPbI3 α-phase without annealing. The formation energy is related to the amt. of incorporated MACl. By tuning the incorporation of MACl, the perovskite film quality can be significantly improved, exhibiting a 6× increase in grain size, a 3× increase in phase crystallinity, and a 4.3× increase in photoluminescence lifetime. The optimized solar cells achieved a certified efficiency of 23.48%.
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  24. 24
    Weller, M. T.; Weber, O. J.; Frost, J. M.; Walsh, A. Cubic Perovskite Structure of Black Formamidinium Lead Iodide, α-[HC(NH2)2]PbI3, at 298 K. J. Phys. Chem. Lett. 2015, 6, 3209– 3212,  DOI: 10.1021/acs.jpclett.5b01432
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    24
    Cubic Perovskite Structure of Black Formamidinium Lead Iodide, α-[HC(NH2)2]PbI3, at 298 K
    Weller, Mark T.; Weber, Oliver J.; Frost, Jarvist M.; Walsh, Aron
    Journal of Physical Chemistry Letters (2015), 6 (16), 3209-3212CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    The structure of black formamidinium lead halide, α-[HC(NH2)2]PbI3, at 298 K was refined from high resoln. neutron powder diffraction data and found to adopt a cubic perovskite unit cell, a 6.3620(8) Å. The trigonal planar [HC(NH2)2]+ cations lie in the central mirror plane of the unit cell with the formamidinium cations disordered over 12 possible sites arranged so that the C-H bond is directed into a cube face, whereas the -NH2 groups H bond (NH···I = 2.75-3.00 Å) with the iodide atoms of the [PbI3]- framework. High at. displacement parameters for the formamidinium cation are consistent with rapid mol. rotations at room temp. as evidenced in ab initio mol. dynamic simulations. Crystallog. data and at. coordinates are given.
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  25. 25
    Weber, O. J.; Charles, B.; Weller, M. T. Phase Behaviour and Composition in the Formamidinium-Methylammonium Hybrid Lead Iodide Perovskite Solid Solution. J. Mater. Chem. A 2016, 4, 15375– 15382,  DOI: 10.1039/C6TA06607K
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    25
    Phase behaviour and composition in the formamidinium-methylammonium hybrid lead iodide perovskite solid solution
    Weber, O. J.; Charles, B.; Weller, M. T.
    Journal of Materials Chemistry A: Materials for Energy and Sustainability (2016), 4 (40), 15375-15382CODEN: JMCAET; ISSN:2050-7496. (Royal Society of Chemistry)
    The phase behavior of mixed A-site cation methylammonium (MA)/formamidinium (FA) lead iodide hybrid perovskites FAxMA1-xPbI3 was investigated using powder and variable temp. single crystal x-ray diffraction, with A site compn. detd. by 1H soln. NMR. At room temp., the crystal class is cubic across the compn. range 0.2 ≤ x ≤ 1 but a tetragonal phase is obsd. for x = 0 (MAPbI3) and x = 0.1. Cooling cubic FAxMA1-xPbI3, 0.2 ≤ x ≤ 1, phases below room temp. results in a phase change to a larger unit cell with tilted [PbI6] octahedra and the temp. at which this occurs, TC→T, decreases sharply until x = 0.2 (TC→T = 257 K) before steadily increasing to TC→T = 283 K for FA0.9MA0.1PbI3. The lattice parameters and optical band gap of cubic FAxMA1-xPbI3, 0.2 ≤ x ≤ 1 at 298 K were shown to vary in accordance with Vegard's law, though a larger band gap is obsd. for the tetragonal phases, 0.0 ≤ x ≤ 0.1.
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  26. 26
    Kubicki, D. J.; Prochowicz, D.; Hofstetter, A.; Péchy, P.; Zakeeruddin, S. M.; Grätzel, M.; Emsley, L. Cation Dynamics in Mixed-Cation (MA)x(FA)1-xPbI3 Hybrid Perovskites from Solid-State NMR. J. Am. Chem. Soc. 2017, 139, 10055– 10061,  DOI: 10.1021/jacs.7b04930
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    26
    Cation Dynamics in Mixed-Cation (MA)x(FA)1-xPbI3 Hybrid Perovskites from Solid-State NMR
    Kubicki, Dominik J.; Prochowicz, Daniel; Hofstetter, Albert; Pechy, Peter; Zakeeruddin, Shaik M.; Gratzel, Michael; Emsley, Lyndon
    Journal of the American Chemical Society (2017), 139 (29), 10055-10061CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Mixed-cation org. lead halide perovskites attract unfaltering attention owing to their excellent photovoltaic properties. Currently, the best performing perovskite materials contain multiple cations and provide power conversion efficiencies up to around 22%. Here, the authors report the 1st quant., cation-specific data on cation reorientation dynamics in hybrid mixed-cation formamidinium (FA)/methylammonium (MA) lead halide perovskites. The authors use 14N, 2H, 13C, and 1H solid-state MAS-NMR to elucidate cation reorientation dynamics, microscopic phase compn., and the MA/FA ratio, in (MA)x(FA)1-xPbI3 between 100 and 330 K. The reorientation rates correlate in a striking manner with the carrier lifetimes previously reported for these materials and provide evidence of the polaron nature of charge carriers in PV perovskites.
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  27. 27
    Pellet, N.; Gao, P.; Gregori, G.; Yang, T.-Y.; Nazeeruddin, M. K.; Maier, J.; Grätzel, M. Mixed-Organic-Cation Perovskite Photovoltaics for Enhanced Solar-Light Harvesting. Angew. Chem., Int. Ed. 2014, 53, 3151– 3157,  DOI: 10.1002/anie.201309361
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    27
    Mixed-Organic-Cation Perovskite Photovoltaics for Enhanced Solar-Light Harvesting
    Pellet, Norman; Gao, Peng; Gregori, Giuliano; Yang, Tae-Youl; Nazeeruddin, Mohammad K.; Maier, Joachim; Graetzel, Michael
    Angewandte Chemie, International Edition (2014), 53 (12), 3151-3157CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Hybrid org.-inorg. lead halide perovskite APbX3 pigments, such as methylammonium lead iodide, have recently emerged as excellent light harvesters in solid-state mesoscopic solar cells. An important target for the further improvement of the performance of perovskite-based photovoltaics is to extend their optical-absorption onset further into the red to enhance solar-light harvesting. Herein, this goal can be reached by using a mixt. of formamidinium (HN = CHNH3+, FA) and methylammonium (MeNH3+, MA) cations in the A position of the APbI3 perovskite structure. This combination leads to an enhanced short-circuit current and thus superior devices to those based on only MeNH3+. This concept was not applied previously in perovskite-based solar cells. It shows great potential as a versatile tool to tune the structural, elec., and optoelectronic properties of the light-harvesting materials.
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  28. 28
    Yi, C.; Luo, J.; Meloni, S.; Boziki, A.; Ashari-Astani, N.; Grätzel, C.; Zakeeruddin, S. M.; Röthlisberger, U.; Grätzel, M. Entropic Stabilization of Mixed A-Cation ABX3 Metal Halide Perovskites for High Performance Perovskite Solar Cells. Energy Environ. Sci. 2016, 9, 656– 662,  DOI: 10.1039/C5EE03255E
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    Entropic stabilization of mixed A-cation ABX3 metal halide perovskites for high performance perovskite solar cells
    Yi, Chenyi; Luo, Jingshan; Meloni, Simone; Boziki, Ariadni; Ashari-Astani, Negar; Gratzel, Carole; Zakeeruddin, Shaik M.; Rothlisberger, Ursula; Gratzel, Michael
    Energy & Environmental Science (2016), 9 (2), 656-662CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
    ABX3-type org. lead halide perovskites currently attract broad attention as light harvesters for solar cells due to their high power conversion efficiency (PCE). Mixts. of formamidinium (FA) with methylammonium (MA) as A-cations show currently the best performance. Apart from offering better solar light harvesting in the near IR the addn. of methylammonium stabilizes the perovskite phase of FAPbI3 which in pure form at room temp. converts to the yellow photovoltaically inactive δ-phase. We observe a similar phenomenon upon adding Cs+ cations to FAPbI3. CsPbI3 and FAPbI3 both form the undesirable yellow phase under ambient condition while the mixt. forms the desired black pervoskite. Solar cells employing the compn. Cs0.2FA0.8PbI2.84Br0.16 yield high av. PCEs of over 17% exhibiting negligible hysteresis and excellent long term stability in ambient air. We elucidate here this remarkable behavior using first principle computations. These show that the remarkable stabilization of the perovskite phase by mixing the A-cations stems from entropic gains and the small internal energy input required for the formation of their solid soln. By contrast, the energy of formation of the delta-phase contg. mixed cations is too large to be compensated by this configurational entropy increase. Our calcns. reveal for the first time the optoelectronic properties of such mixed A-cation perovskites and the underlying reasons for their excellent performance and high stability.
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    Goldschmidt, V. M. Die Gesetze Der Krystallochemie. Naturwissenschaften 1926, 14, 477– 485,  DOI: 10.1007/BF01507527
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    Laws of crystal chemistry
    Goldschmidt, V. M.
    Naturwissenschaften (1926), 14 (), 477-85CODEN: NATWAY; ISSN:0028-1042.
    Several laws are cited which govern the relationships between chem. compn. and cryst. form. The crystal structure of a substance is detd. by the size (Bragg's radius) and the polarizability of its components (atoms or atom groups). The at. radius depends on at. no. and "condition" (particularly degree of ionization) of the atom. The polarizability, a function of radius and charge of the atom or ion, increases with increasing radius, decreases with increasing positive charge (cf. Born and Heisenberg). High symmetry of the neighboring atoms tends to diminish it; the polarizing effect of the neighboring atoms depends again on their charge and radius. The distance of 2 polarizable structural units is generally less than the normal distance. The term contrapolarization is used for the dilating influence of strongly polarizing atoms (like Li+ or Zr++++) on such closed groups as ClO4-, CO3--, etc. This influence may even cause these groups to break up entirely. A rule is given for the occurrence of isomorphic crystals: the relative sizes and polarizabilities of the 2 substances must correspond, in order for the chem. formula to be analogous. Isomorphic mixts. will be possible if the radii of the corresponding atoms differ by less than about 15%. For antisomorphic crystals (positive and negative charges reversed) no mixts. are possible. Polymer-isomorphic mixts. occur when a multiple of the crystal unit of one substance is analogous to the unit of the other. If, as a result of thermodynamic influences, a substance ceases to be its own isomorph at different temps. (the polarizability is also a temp. function) polymorphism will appear; the substance undergoes a morphotropic change. Contrapolarization particularly is easily influenced by temp.; it causes such polymorphism as NH4NO3 in its different forms exhibits. At high temps. that cryst. form will be the most stable, which is obtained on substitution of the contrapolarizing cation by a lower homolog. Numerous examples are given.
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  30. 30
    Zhao, J.; Deng, Y.; Wei, H.; Zheng, X.; Yu, Z.; Shao, Y.; Shield, J. E.; Huang, J. Strained Hybrid Perovskite Thin Films and Their Impact on the Intrinsic Stability of Perovskite Solar Cells. Sci. Adv. 2017, 3, eaao5616  DOI: 10.1126/sciadv.aao5616
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    Zhu, C.; Niu, X.; Fu, Y.; Li, N.; Hu, C.; Chen, Y.; He, X.; Na, G.; Liu, P.; Zai, H. Strain Engineering in Perovskite Solar Cells and Its Impacts on Carrier Dynamics. Nat. Commun. 2019, 10, 815,  DOI: 10.1038/s41467-019-08507-4
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    Strain engineering in perovskite solar cells and its impacts on carrier dynamics
    Zhu, Cheng; Niu, Xiuxiu; Fu, Yuhao; Li, Nengxu; Hu, Chen; Chen, Yihua; He, Xin; Na, Guangren; Liu, Pengfei; Zai, Huachao; Ge, Yang; Lu, Yue; Ke, Xiaoxing; Bai, Yang; Yang, Shihe; Chen, Pengwan; Li, Yujing; Sui, Manling; Zhang, Lijun; Zhou, Huanping; Chen, Qi
    Nature Communications (2019), 10 (1), 815CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
    The mixed halide perovskites have emerged as outstanding light absorbers for efficient solar cells. Unfortunately, it reveals inhomogeneity in these polycryst. films due to compn. sepn., which leads to local lattice mismatches and emergent residual strains consequently. Thus far, the understanding of these residual strains and their effects on photovoltaic device performance is absent. Herein we study the evolution of residual strain over the films by depth-dependent grazing incident X-ray diffraction measurements. We identify the gradient distribution of in-plane strain component perpendicular to the substrate. Moreover, we reveal its impacts on the carrier dynamics over corresponding solar cells, which is stemmed from the strain induced energy bands bending of the perovskite absorber as indicated by first-principles calcns. Eventually, we modulate the status of residual strains in a controllable manner, which leads to enhanced PCEs up to 20.7% (certified) in devices via rational strain engineering.
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    Motta, C.; El-Mellouhi, F.; Kais, S.; Tabet, N.; Alharbi, F.; Sanvito, S. Revealing the Role of Organic Cations in Hybrid Halide Perovskite CH3NH3PbI3. Nat. Commun. 2015, 6, 7026,  DOI: 10.1038/ncomms8026
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    Revealing the role of organic cations in hybrid halide perovskite CH3NH3PbI3
    Motta, Carlo; El-Mellouhi, Fedwa; Kais, Sabre; Tabet, Nouar; Alharbi, Fahhad; Sanvito, Stefano
    Nature Communications (2015), 6 (), 7026CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
    The hybrid halide perovskite CH3NH3PbI3 has enabled solar cells to reach an efficiency of about 20%, demonstrating a pace for improvements with no precedents in the solar energy arena. Despite such explosive progress, the microscopic origin behind the success of such material is still debated, with the role played by the org. cations in the light-harvesting process remaining unclear. Here van der Waals-cor. d. functional theory calcns. reveal that the orientation of the org. mols. plays a fundamental role in detg. the material electronic properties. For instance, if CH3NH3 orients along a (011)-like direction, the PbI6 octahedral cage will distort and the bandgap will become indirect. Our results suggest that mol. rotations, with the consequent dynamical change of the band structure, might be at the origin of the slow carrier recombination and the superior conversion efficiency of CH3NH3PbI3.
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  33. 33
    Gong, J.; Yang, M.; Ma, X.; Schaller, R. D.; Liu, G.; Kong, L.; Yang, Y.; Beard, M. C.; Lesslie, M.; Dai, Y. Electron-Rotor Interaction in Organic-Inorganic Lead Iodide Perovskites Discovered by Isotope Effects. J. Phys. Chem. Lett. 2016, 7, 2879– 2887,  DOI: 10.1021/acs.jpclett.6b01199
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    33
    Electron-Rotor Interaction in Organic-Inorganic Lead Iodide Perovskites Discovered by Isotope Effects
    Gong, Jue; Yang, Mengjin; Ma, Xiangchao; Schaller, Richard D.; Liu, Gang; Kong, Lingping; Yang, Ye; Beard, Matthew C.; Lesslie, Michael; Dai, Ying; Huang, Baibiao; Zhu, Kai; Xu, Tao
    Journal of Physical Chemistry Letters (2016), 7 (15), 2879-2887CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    The authors report on the carrier-rotor coupling effect in perovskite org.-inorg. hybrid lead iodide (CH3NH3PbI3) compds. discovered by isotope effects. Deuterated org.-inorg. perovskite compds. including CH3ND3PbI3, CD3NH3PbI3, and CD3ND3PbI3 were synthesized. Devices made from regular CH3NH3PbI3 and deuterated CH3ND3PbI3 exhibit comparable performance in band gap, current-voltage, carrier mobility, and power conversion efficiency. However, a time-resolved photoluminescence (TRPL) study reveals that CH3NH3PbI3 exhibits notably longer carrier lifetime than that of CH3ND3PbI3, in both thin-film and single-crystal formats. Also, the comparison in carrier lifetime between CD3NH3PbI3 and CH3ND3PbI3 single crystals suggests that vibrational modes in methylammonium (MA+) have little impact on carrier lifetime. In contrast, the fully deuterated compd. CD3ND3PbI3 reconfirmed the trend of decreasing carrier lifetime upon the increasing moment of inertia of cationic MA+. Polaron model elucidates the electron-rotor interaction.
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  34. 34
    Jesper Jacobsson, T.; Correa-Baena, J.-P. P.; Pazoki, M.; Saliba, M.; Schenk, K.; Grätzel, M.; Hagfeldt, A. Exploration of the Compositional Space for Mixed Lead Halogen Perovskites for High Efficiency Solar Cells. Energy Environ. Sci. 2016, 9, 1706– 1724,  DOI: 10.1039/C6EE00030D
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    Exploration of the compositional space for mixed lead halogen perovskites for high efficiency solar cells
    Jesper Jacobsson, T.; Correa-Baena, Juan-Pablo; Pazoki, Meysam; Saliba, Michael; Schenk, Kurt; Gratzel, Michael; Hagfeldt, Anders
    Energy & Environmental Science (2016), 9 (5), 1706-1724CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
    Lead halide perovskites have attracted considerable interest as photoabsorbers in PV-applications over the last few years. The most studied perovskite material achieving high photovoltaic performance has been Me ammonium lead iodide, CH3NH3PbI3. Recently the highest solar cell efficiencies have, however, been achieved with mixed perovskites where iodide and Me ammonium partially have been replaced by bromide and formamidinium. In this work, the mixed perovskites were explored in a systematic way by manufg. devices where both iodide and Me ammonium were gradually replaced by bromide and formamidinium. The absorption and the emission behavior as well as the crystallog. properties were explored for the perovskites in this compositional space. The band gaps as well as the crystallog. structures were extd. Small changes in the compn. of the perovskite were found to have a large impact on the properties of the materials and the device performance. In the investigated compositional space, cell efficiencies, for example, vary from a few percent up to 20.7%. From the perspective of applications, exchanging iodide with bromide is esp. interesting as it allows tuning of the band gap from 1.5 to 2.3 eV. This is highly beneficial for tandem applications, and an empirical expression for the band gap as a function of compn. was detd. Exchanging a small amt. of iodide with bromide is found to be highly beneficial, whereas a larger amt. of bromide in the perovskite was found to cause intense sub band gap photoemission with detrimental results for the device performance. This could be caused by the formation of a small amt. of an iodide rich phase with a lower band gap, even though such a phase was not obsd. in diffraction expts. This shows that stabilizing the mixed perovskites will be an important task in order to get the bromide rich perovskites, which has a higher band gap, to reach the same high performance obtained with the best compns.
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    Zheng, X.; Wu, C.; Jha, S. K.; Li, Z.; Zhu, K.; Priya, S. Improved Phase Stability of Formamidinium Lead Triiodide Perovskite by Strain Relaxation. ACS Energy Lett. 2016, 1, 1014– 1020,  DOI: 10.1021/acsenergylett.6b00457
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    Improved Phase Stability of Formamidinium Lead Triiodide Perovskite by Strain Relaxation
    Zheng, Xiaojia; Wu, Congcong; Jha, Shikhar K.; Li, Zhen; Zhu, Kai; Priya, Shashank
    ACS Energy Letters (2016), 1 (5), 1014-1020CODEN: AELCCP; ISSN:2380-8195. (American Chemical Society)
    Though formamidinium lead triiodide (FAPbI3) possesses a suitable band gap and good thermal stability, the phase transition from the pure black perovskite phase (α-phase) to the undesirable yellow nonperovskite polymorph (δ-phase) at room temp., esp. under humid air, hinders its practical application. Here, we investigate the intrinsic instability mechanism of the α-phase at ambient temp. and demonstrate the existence of an anisotropic strained lattice in the (111) plane that drives phase transformation into the δ-phase. Methylammonium bromide (MABr) alloying (or FAPbI3-MABr) was found to cause lattice contraction, thereby balancing the lattice strain. This led to dramatic improvement in the stability of α-FAPbI3. Solar cells fabricated using FAPbI3-MABr demonstrated significantly enhanced stability under the humid air.
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  36. 36
    Xie, L. Q.; Chen, L.; Nan, Z. A.; Lin, H. X.; Wang, T.; Zhan, D. P.; Yan, J. W.; Mao, B. W.; Tian, Z. Q. Understanding the Cubic Phase Stabilization and Crystallization Kinetics in Mixed Cations and Halides Perovskite Single Crystals. J. Am. Chem. Soc. 2017, 139, 3320– 3323,  DOI: 10.1021/jacs.6b12432
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    Understanding the Cubic Phase Stabilization and Crystallization Kinetics in Mixed Cations and Halides Perovskite Single Crystals
    Xie, Li-Qiang; Chen, Liang; Nan, Zi-Ang; Lin, Hai-Xin; Wang, Tan; Zhan, Dong-Ping; Yan, Jia-Wei; Mao, Bing-Wei; Tian, Zhong-Qun
    Journal of the American Chemical Society (2017), 139 (9), 3320-3323CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    The spontaneous α-to-δ phase transition of the formamidinium-based (FA) Pb halide perovskite hinders its large scale application in solar cells. Though this phase transition can be inhibited by alloying with methylammonium-based (MA) perovskite, the underlying mechanism is largely unexplored. We grow high-quality mixed cations and halides perovskite single crystals (FAPbI3)1-x(MAPbBr3)x to understand the principles for maintaining pure perovskite phase, which is essential to device optimization. We demonstrate that the best compn. for a perfect α-phase perovskite without segregation is x =0.1-0.15, and such a mixed perovskite exhibits carrier lifetime as long as 11.0 μs, which is over 20 times of that of FAPbI3 single crystal. Powder XRD, single crystal XRD and FT-IR results reveal that the incorporation of MA+ is crit. for tuning the effective Goldschmidt tolerance factor toward the ideal value of 1 and lowering the Gibbs free energy via unit cell contraction and cation disorder. We find that Br incorporation can effectively control the perovskite crystn. kinetics and reduce defect d. to acquire high-quality single crystals with significant inhibition of δ-phase. These findings benefit the understanding of α-phase stabilization behavior, and have led to fabrication of perovskite solar cells with highest efficiency of 19.9% via solvent management.
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    Tennyson, E. M.; Doherty, T. A. S.; Stranks, S. D. Heterogeneity at Multiple Length Scales in Halide Perovskite Semiconductors. Nat. Rev. Mater. 2019, 4, 573– 587,  DOI: 10.1038/s41578-019-0125-0
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    Heterogeneity at multiple length scales in halide perovskite semiconductors
    Tennyson, Elizabeth M.; Doherty, Tiarnan A. S.; Stranks, Samuel D.
    Nature Reviews Materials (2019), 4 (9), 573-587CODEN: NRMADL; ISSN:2058-8437. (Nature Research)
    A review. Materials with highly cryst. lattice structures and low defect concns. have classically been considered essential for high-performance optoelectronic devices. However, the emergence of high-efficiency devices based on halide perovskites is provoking researchers to rethink this traditional picture, as the heterogeneity in several properties within these materials occurs on a series of length scales. Perovskites are typically fabricated crudely through simple processing techniques, which leads to large local fluctuations in defect d., lattice structure, chem. and bandgap that appear on short length scales (<100 nm) and across long ranges (>10μm). Despite these variable and complex non-uniformities, perovskites maintain exceptional device efficiencies and are, as of 2018, the best-performing polycryst. thin-film solar cell material. In this Review, we highlight the multiple layers of heterogeneity ascertained using high-spatial-resoln. methods that provide access to the relevant length scales. We discuss the impact that the optoelectronic variations have on halide perovskite devices, including the prospect that it is this very disorder that leads to their remarkable power-conversion efficiencies.
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  38. 38
    Alanazi, A. Q.; Kubicki, D. J.; Prochowicz, D.; Alharbi, E. A.; Bouduban, M. E. F.; Jahanbakhshi, F.; Mladenović, M.; Milić, J. V.; Giordano, F.; Ren, D. Atomic-Level Microstructure of Efficient Formamidinium-Based Perovskite Solar Cells Stabilized by 5-Ammonium Valeric Acid Iodide Revealed by Multinuclear and Two-Dimensional Solid-State NMR. J. Am. Chem. Soc. 2019, 141, 17659– 17669,  DOI: 10.1021/jacs.9b07381
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    Atomic-Level Microstructure of Efficient Formamidinium-Based Perovskite Solar Cells Stabilized by 5-Ammonium Valeric Acid Iodide Revealed by Multinuclear and Two-Dimensional Solid-State NMR
    Alanazi, Anwar Q.; Kubicki, Dominik J.; Prochowicz, Daniel; Alharbi, Essa A.; Bouduban, Marine E. F.; Jahanbakhshi, Farzaneh; Mladenovic, Marko; Milic, Jovana V.; Giordano, Fabrizio; Ren, Dan; Alyamani, Ahmed Y.; Albrithen, Hamad; Albadri, Abdulrahman; Alotaibi, Mohammad Hayal; Moser, Jacques-E.; Zakeeruddin, Shaik M.; Rothlisberger, Ursula; Emsley, Lyndon; Gratzel, Michael
    Journal of the American Chemical Society (2019), 141 (44), 17659-17669CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Chem. doping of inorg.-org. hybrid perovskites is an effective way of improving the performance and operational stability of perovskite solar cells (PSCs). Here, we use 5-ammonium valeric acid (AVAI) to chem. stabilize the structure of α-FAPbI3. Using solid-state MAS NMR, we demonstrate the at.-level interaction between the mol. modulator and the perovskite lattice and propose a structural model of the stabilized 3-dimensional structure, further aided by d. functional theory (DFT) calcns. We find that 1-step deposition of the perovskite in the presence of AVAI produces highly cryst. films with large, micrometer-sized grains and enhanced charge-carrier lifetimes, as probed by transient absorption spectroscopy. As a result, we achieve greatly enhanced solar cell performance for the optimized AVA-based devices with a maxi-mum power conversion efficiency (PCE) of 18.94%. The devices retain 90% of the initial efficiency after 300 h under continuous white light illumination and max.-power point-tracking measurement.
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  39. 39
    Kubicki, D. J.; Prochowicz, D.; Hofstetter, A.; Saski, M.; Yadav, P.; Bi, D.; Pellet, N.; Lewiński, J.; Zakeeruddin, S. M.; Grätzel, M. Formation of Stable Mixed Guanidinium-Methylammonium Phases with Exceptionally Long Carrier Lifetimes for High-Efficiency Lead Iodide-Based Perovskite Photovoltaics. J. Am. Chem. Soc. 2018, 140, 3345– 3351,  DOI: 10.1021/jacs.7b12860
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    Formation of Stable Mixed Guanidinium-Methylammonium Phases with Exceptionally Long Carrier Lifetimes for High-Efficiency Lead Iodide-Based Perovskite Photovoltaics
    Kubicki, Dominik J.; Prochowicz, Daniel; Hofstetter, Albert; Saski, Marcin; Yadav, Pankaj; Bi, Dongqin; Pellet, Norman; Lewinski, Janusz; Zakeeruddin, Shaik M.; Gratzel, Michael; Emsley, Lyndon
    Journal of the American Chemical Society (2018), 140 (9), 3345-3351CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Methylammonium (MA)- and formamidinium (FA)-based org.-inorg. lead halide perovskites provide outstanding performance as photovoltaic materials, due to their versatility of fabrication and their power conversion efficiencies reaching over 22%. The proposition of guanidinium (GUA)-doped perovskite materials generated considerable interest due to their potential to increase carrier lifetimes and open-circuit voltages as compared to pure MAPbI3. However, simple size considerations based on the Goldschmidt tolerance factor suggest that guanidinium is too big to completely replace methylammonium as an A cation in the APbI3 perovskite lattice, and its effect was thus ascribed to passivation of surface trap states at grain boundaries. As guanidinium was not thought to incorporate into the MAPbI3 lattice, interest waned since it appeared unlikely that it could be used to modify the intrinsic perovskite properties. Here, using solid-state NMR, we provide for the first time at.-level evidence that GUA is directly incorporated into the MAPbI3 and FAPbI3 lattices, forming pure GUAxMA1-xPbI3 or GUAxFA1-xPbI3 phases, and that it reorients on the picosecond time scale within the perovskite lattice, which explains its superior charge carrier stabilization capacity. Our findings establish a fundamental link between charge carrier lifetimes obsd. in photovoltaic perovskites and the A cation structure in ABX3-type metal halide perovskites.
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  40. 40
    Kubicki, D. J.; Prochowicz, D.; Hofstetter, A.; Zakeeruddin, S. M.; Gratzel, M.; Emsley, L. Phase Segregation in Cs-, Rb- and K-Doped Mixed-Cation (MA)x(FA)1-xPbI3 Hybrid Perovskites from Solid-State NMR. J. Am. Chem. Soc. 2017, 139, 14173– 14180,  DOI: 10.1021/jacs.7b07223
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    Phase Segregation in Cs-, Rb- and K-Doped Mixed-Cation (MA)x(FA)1-xPbI3 Hybrid Perovskites from Solid-State NMR
    Kubicki, Dominik J.; Prochowicz, Daniel; Hofstetter, Albert; Zakeeruddin, Shaik M.; Gratzel, Michael; Emsley, Lyndon
    Journal of the American Chemical Society (2017), 139 (40), 14173-14180CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Hybrid (org.-inorg.) multication lead halide perovskites hold promise for a new generation of easily processable solar cells. Best performing compns. to date are multiple-cation solid alloys of formamidinium (FA), methylammonium (MA), cesium, and rubidium lead halides which provide power conversion efficiencies up to around 22%. Here, we elucidate the at.-level nature of Cs and Rb incorporation into the perovskite lattice of FA-based materials. We use 133Cs, 87Rb, 39K, 13C, and 14N solid-state MAS NMR to probe microscopic compn. of Cs-, Rb-, K-, MA-, and FA-contg. phases in double-, triple-, and quadruple-cation lead halides in bulk and in a thin film. Contrary to previous reports, we have found no proof of Rb or K incorporation into the 3D perovskite lattice in these systems. We also show that the structure of bulk mechanochem. perovskites bears close resemblance to that of thin films, making them a good benchmark for structural studies. These findings provide fundamental understanding of previously reported excellent photovoltaic parameters in these systems and their superior stability.
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  41. 41
    Ghosh, D.; Smith, A. R.; Walker, A. B.; Islam, M. S. Mixed A-Cation Perovskites for Solar Cells: Atomic-Scale Insights into Structural Distortion, Hydrogen Bonding, and Electronic Properties. Chem. Mater. 2018, 30, 5194– 5204,  DOI: 10.1021/acs.chemmater.8b01851
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    41
    Mixed A-Cation Perovskites for Solar Cells: Atomic-Scale Insights Into Structural Distortion, Hydrogen Bonding, and Electronic Properties
    Ghosh, Dibyajyoti; Smith, Alexander R.; Walker, Alison B.; Islam, M. Saiful
    Chemistry of Materials (2018), 30 (15), 5194-5204CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    Hybrid Pb halide perovskites contg. a mixt. of A-site cations such as the formamidinium (CH(NH2)2+, FA) and the smaller Cs+ cations have attracted considerable interest due to their improved stability and solar cell performance. However, the structural changes at the at. scale and modifications to the optoelectronic properties of these mixed cation perovskites are not fully understood. Here, we study the FA1-xCsxPbI3 (x ≤0.25) system using a combination of static and dynamic ab initio computational methods. We find that the incorporation of Cs+ cations into the parent FAPbI3 structure induces a chem. pressure or lattice strain effect through Cs/FA ion size mismatch resulting in structural distortion and stronger FA-iodide (N-H···I) hydrogen bonding interactions. The dynamic tilting of PbI6 octahedra and the rotational motion of FA cations are also suppressed, which leads to symmetry-breaking of the lattice. Such symmetry-breaking distortions of the Pb/I lattice give rise to a Rashba-type effect, which spin-splits the frontier electronic bands making the band gap indirect. Our results suggest that the direct-indirect band gap transition may be a factor in the reduced charge-carrier recombination rate in these mixed cation perovskites.
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  42. 42
    Van Gompel, W. T. M.; Herckens, R.; Reekmans, G.; Ruttens, B.; D’Haen, J.; Adriaensens, P.; Lutsen, L.; Vanderzande, D. Degradation of the Formamidinium Cation and the Quantification of the Formamidinium-Methylammonium Ratio in Lead Iodide Hybrid Perovskites by Nuclear Magnetic Resonance Spectroscopy. J. Phys. Chem. C 2018, 122, 4117– 4124,  DOI: 10.1021/acs.jpcc.7b09805
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    42
    Degradation of the Formamidinium Cation and the Quantification of the Formamidinium-Methylammonium Ratio in Lead Iodide Hybrid Perovskites by Nuclear Magnetic Resonance Spectroscopy
    Van Gompel, Wouter T. M.; Herckens, Roald; Reekmans, Gunter; Ruttens, Bart; DHaen, Jan; Adriaensens, Peter; Lutsen, Laurence; Vanderzande, Dirk
    Journal of Physical Chemistry C (2018), 122 (8), 4117-4124CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
    The highest efficiency in perovskite solar cells is currently achieved with mixed-cation hybrid perovskites. The ratio in which the cations are present in the perovskite structure has an important effect on the optical properties and the stability of these materials. At present, the formamidinium cation is an integral part of many of the highest efficiency perovskite systems. In this work, we introduce an NMR spectroscopy protocol for the identification and differentiation of mixed perovskite phases and of a secondary phase due to formamidinium degrdn. The influence of the cooling rate used in a pptn. method on the FA/MA ratio in formamidinium-methylammonium lead iodide perovskites (FAxMA1-xPbI3) was investigated and compared to the FA/MA ratio in thin films. In order to obtain the FA/MA ratio from fast and accessible liq.-state 1H NMR spectra, the influence of the acidity of the soln. on the line width of the resonances was elucidated. The ratio of the org. cations incorporated into the perovskite structure could be reliably quantified in the presence of the secondary phase through a combination of liq.-state 1H NMR and solid-state 13C NMR spectroscopic anal.
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    Fisicaro, G.; La Magna, A.; Alberti, A.; Smecca, E.; Mannino, G.; Deretzis, I. Local Order and Rotational Dynamics in Mixed A-Cation Lead Iodide Perovskites. J. Phys. Chem. Lett. 2020, 11, 1068– 1074,  DOI: 10.1021/acs.jpclett.9b03763
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    Local Order and Rotational Dynamics in Mixed A-Cation Lead Iodide Perovskites
    Fisicaro, Giuseppe; La Magna, Antonino; Alberti, Alessandra; Smecca, Emanuele; Mannino, Giovanni; Deretzis, Ioannis
    Journal of Physical Chemistry Letters (2020), 11 (3), 1068-1074CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Halide perovskites contg. a mixt. of formamidinium (FA+), methylammonium (MA+) and cesium (Cs+) cations are the actual std. for obtaining record-efficiency perovskite solar cells. Although the compositional tuning that brings to optimal performance of the devices was largely established, little is understood on the role of even small quantities of MA+ or Cs+ in stabilizing the black phase of FAPbI3 while boosting its photovoltaic yield. In this paper, we use Car-Parrinello mol. dynamics in large supercells contg. different ratios of FA+ and either MA+ or Cs+, to study the structural and kinetic features of mixed perovskites at room temp. Our anal. shows that cation mixing relaxes the rotational disorder of FA+ mols. by preferentially aligning their axis toward 〈100〉 cubic directions. The phenomenon stems from the introduction of addnl. local min. in the energetic landscape, which are absent in pure FAPbI3 crystals. As a result, a higher structural order is achieved, characterized by a pronounced octahedral tilting and a lower vibrational activity for the inorg. framework. We show that both MA+ and Cs+ are qualified for this enhancement, with Cs+ being particularly effective when dild. within the FAPbI3 perovskite.
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    Franssen, W. M. J.; Kentgens, A. P. M. Solid - State NMR of Hybrid Halide Perovskites. Solid State Nucl. Magn. Reson. 2019, 100, 36– 44,  DOI: 10.1016/j.ssnmr.2019.03.005
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    Solid-state NMR of hybrid halide perovskites
    Franssen, Wouter M. J.; Kentgens, Arno P. M.
    Solid State Nuclear Magnetic Resonance (2019), 100 (), 36-44CODEN: SSNRE4; ISSN:0926-2040. (Elsevier)
    Recent advances in the development of perovskite based solar cells have increased the demand for in-depth characterization of the perovskite structures and the dynamics of their various constituents in relation to the potential impact on the photovoltaic performance. NMR can play an important role in this respect; NMR has been used to study the incorporation of different ionic species, characterize their internal dynamics and diffusion, and monitor the chem. stability of these technol. relevant materials, including upcoming lower dimensional perovskite materials. Furthermore, the flexibility of NMR allows the study of the materials under relevant conditions e.g. under illumination. Here we present an overview of the recent literature on NMR of (hybrid) halide perovskites, focusing on the insights that NMR can provide.
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    Wasylishen, R. E.; Knop, O.; Macdonald, J. B. Cation Rotation in Methylammonium Lead Halides. Solid State Commun. 1985, 56, 581– 582,  DOI: 10.1016/0038-1098(85)90959-7
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    Cation rotation in methylammonium lead halides
    Wasylishen, R. E.; Knop, Osvald; Macdonald, J. B.
    Solid State Communications (1985), 56 (7), 581-2CODEN: SSCOA4; ISSN:0038-1098.
    2H and 14N NMR spectra of the simple perovskites MeNH3PbX3 (X = Cl, Br, I) reveal the existence of several phases. In the high-temp. phase I the long spin-lattice relaxation times T1 of both nuclei and the absence of quadrupole splitting indicate extremely rapid overall reorientation of the C-N axis of the cation in a potential of cubic symmetry. In phase II of the bromide and iodide, both T1 and the small quadrupole splitting show unusual variation with temp. In the lowest-temp. phase, rotations of the C-N axis are restricted.
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  46. 46
    Knop, O.; Wasylishen, R. E.; White, M. A.; Cameron, T. S.; Van Oort, M. J. M. Alkylammonium Lead Halides. Part 2. CH3NH3PbX3 (X = Cl, Br, I) Perovskites: Cuboctahedral Halide Cages with Isotropic Cation Reorientation. Can. J. Chem. 1990, 68, 412– 422,  DOI: 10.1139/v90-063
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    Alkylammonium lead halides. Part 2. CH3NH3PbX3 (X = chlorine, bromine, iodine) perovskites: cuboctahedral halide cages with isotropic cation reorientation
    Knop, Osvald; Wasylishen, Roderick E.; White, Mary Anne; Cameron, T. Stanley; Van Oort, Michiel J. M.
    Canadian Journal of Chemistry (1990), 68 (3), 412-22CODEN: CJCHAG; ISSN:0008-4042.
    MeNH3PbCl3 (I), MeNH3PbBr3 (II), and MeNH3PbI3 (III) were investigated by single-crystal x-ray diffraction, 2H and 14N NMR, adiabatic calorimetry, and other methods. I has transitions at 171.5 and 177.4 K, II at 148.4, 154.2, and 235.1 K, and III at 162.7 and 326.6 K. The resp. entropies of transition (J K-1 mol-1) are 11.0 and 5.1 for I; 8.7, 3.4, and 5.3 for II; and 16.1 and 1.9 for III. The highest-temp. phase, phase I, of each halide is cubic (Pm3m) perovskite type. The cation in phase I of I and II could not be localized in the electron d. maps; the thermal motion of the halogen atom is highly anisotropic. The ln T1(2H) vs. T-1 plots (N-deuterated samples as well as CD3NH3PbCl3) show significant departures from linearity: the temp. variation of T1(2H) in phase II of II and III can be represented by functions of the type ln T1(H) = k0 - k2T-2, which give adequate anal. representations of T1(2H) and T1(14N) in phase I as well. On cooling, phase II of II and III exhibit small quadrupole splittings QS(2H), which can be represented to a high degree of correlation by QS(2H) = k(Ttr - T)n, i.e. they appear to exhibit crit. behavior with respect to T. The 14N NMR results indicate that the C-N bond in phase I reorients in an isotropic potential at a rate approaching that of the freely rotating methylammonium ion. Below phase I this motion takes place in an increasingly anisotropic potential in phase II of II and III and is essentially arrested in phase II of I and phase III of II and III. The temp. dependence of the activation energy Ea for the cation reorientation and other aspects of the non-Arrhenius behavior are discussed, and the MeNH3PbX3 perovskites are compared with the corresponding (MeNH3)2TeX6 halides, utilizing preliminary 2H NMR results on (CD3ND3)2TeBr6. The elec. cond., between 0 and 95°, of III increases with temp. and exhibits no discontinuity at Ttr = 326.6 K; the activation energy for the conduction process is estd. as ∼0.4 eV.
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  47. 47
    Bernard, G. M.; Wasylishen, R. E.; Ratcliffe, C. I.; Terskikh, V.; Wu, Q.; Buriak, J. M.; Hauger, T. Methylammonium Cation Dynamics in Methylammonium Lead Halide Perovskites: A Solid-State NMR Perspective. J. Phys. Chem. A 2018, 122, 1560– 1573,  DOI: 10.1021/acs.jpca.7b11558
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    Methylammonium Cation Dynamics in Methylammonium Lead Halide Perovskites: A Solid-State NMR Perspective
    Bernard, Guy M.; Wasylishen, Roderick E.; Ratcliffe, Christopher I.; Terskikh, Victor; Wu, Qichao; Buriak, Jillian M.; Hauger, Tate
    Journal of Physical Chemistry A (2018), 122 (6), 1560-1573CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
    In light of the intense recent interest in the methylammonium lead halides, CH3NH3PbX3 (X = Cl, Br, I) as sensitizers for photovoltaic cells, the dynamics of the methylammonium (MA) cation in these perovskite salts has been reinvestigated as a function of temp. via 2H, 14N, and 207Pb NMR spectroscopy. In the cubic phase of all three salts, the MA cation undergoes pseudoisotropic tumbling (picosecond time scale). For example, the correlation time, τ2, for the C-N axis of the iodide salt is 0.85 ± 0.30 ps at 330 K. The dynamics of the MA cation are essentially continuous across the cubic ↔ tetragonal phase transition; however, 2H and 14N NMR line shapes indicate that subtle ordering of the MA cation occurs in the tetragonal phase. The temp. dependence of the cation ordering is rationalized using a six-site model, with two equiv. sites along the c-axis and four equiv. sites either perpendicular or approx. perpendicular to this axis. As the cubic ↔ tetragonal phase transition temp. is approached, the six sites are nearly equally populated. Below the tetragonal ↔ orthorhombic phase transition, 2H NMR line shapes indicate that the C-N axis is essentially frozen.
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  48. 48
    Franssen, W. M. J.; Bruijnaers, B. J.; Portengen, V. H. L.; Kentgens, A. P. M. Dimethylammonium Incorporation in Lead Acetate Based MAPbI3 Perovskite Solar Cells. ChemPhysChem 2018, 19, 3107– 3115,  DOI: 10.1002/cphc.201800732
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    Dimethylammonium Incorporation in Lead Acetate Based MAPbI3 Perovskite Solar Cells
    Franssen, Wouter M. J.; Bruijnaers, Bardo J.; Portengen, Victor H. L.; Kentgens, Arno P. M.
    ChemPhysChem (2018), 19 (22), 3107-3115CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
    Over the last years, several different pathways have been suggested for producing perovskite thin films for solar cell applications. While the merit of these methods with respect to the solar cell efficiency have been shown, the actual compn. of the resulting thin films is often not investigated. Here, we show that methylammonium Pb iodide films produced using lead acetate as a lead source can have ≤15% dimethylammonium incorporated into their crystal structure, even though this ion is often consider to be too large for incorporation. The origin of this ion lies in the precursor soln., where it is formed in a reaction that is facilitated by the basic character of the acetate ions. We further show that these dimethylammonium ions are incorporated in a random fashion throughout the crystal structure, owing to the lack of observable ordered domains.
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    Franssen, W. M. J.; Van Es, S. G. D.; Dervişoǧlu, R.; de Wijs, G. A.; Kentgens, A. P. M. Symmetry, Dynamics, and Defects in Methylammonium Lead Halide Perovskites. J. Phys. Chem. Lett. 2017, 8, 61– 66,  DOI: 10.1021/acs.jpclett.6b02542
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    Symmetry, Dynamics, and Defects in Methylammonium Lead Halide Perovskites
    Franssen, Wouter M. J.; van Es, Sverre G. D.; Dervisoglu, Riza; de Wijs, Gilles A.; Kentgens, Arno P. M.
    Journal of Physical Chemistry Letters (2017), 8 (1), 61-66CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    In order to better understand the structure and dynamics of methylammonium lead halide perovskites, we performed NMR, NQR, and DFT studies of CH3NH3PbI3 in the tetragonal and cubic phase. Our results indicate that the space group of the tetragonal phase is the nonpolar I4/mcm. The highly dynamic methylammonium moiety shows no indication of the occurrence of addnl. orientations of the C-N bond close to the c-axis at temps. approaching the cubic phase. Crystal quality effects are shown to influence the 14N NMR and 127I NQR spectra, and the effects of high-temp. annealing on defects can be obsd. A strong increase in T2 relaxation time of the 207Pb NMR signal on cooling is found, and is an indication of slow motions in the PbI6 octahedra at room temp. These results aid in the understanding of the structure of methylammonium lead halides and enable further studies of defects in these materials.
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    Roiland, C.; Trippé-Allard, G.; Jemli, K.; Alonso, B.; Ameline, J.-C. C.; Gautier, R.; Bataille, T.; Le Pollès, L.; Deleporte, E.; Even, J. Multinuclear NMR as a Tool for Studying Local Order and Dynamics in CH3NH3PbX3 (X = Cl, Br, I) Hybrid Perovskites. Phys. Chem. Chem. Phys. 2016, 18 (39), 27133– 27142,  DOI: 10.1039/C6CP02947G
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    Multinuclear NMR as a tool for studying local order and dynamics in CH3NH3PbX3 (X = Cl, Br, I) hybrid perovskites
    Roiland, Claire; Trippe-Allard, Gaelle; Jemli, Khaoula; Alonso, Bruno; Ameline, Jean-Claude; Gautier, Regis; Bataille, Thierry; Le Polles, Laurent; Deleporte, Emmanuelle; Even, Jacky; Katan, Claudine
    Physical Chemistry Chemical Physics (2016), 18 (39), 27133-27142CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    The authors report on 207Pb, 79Br, 14N, 1H, 13C and 2H NMR expts. for studying the local order and dynamics in hybrid perovskite lattices. 207Pb NMR expts. conducted at room temp. on a series of MAPbX3 compds. (MA = CH3NH3+; X = I (3), Br (4) and Cl (5)) showed that the isotropic 207Pb NMR shift is strongly dependent on the nature of the halogen ions. The other prepd. complexes are CH2ND3Br (1), CH3ND3PbBr3 (2), and CH3NH3PbIBr2 (6). Therefore 207Pb NMR appears to be a very promising tool for the characterization of local order in mixed halogen hybrid perovskites. 207Pb NMR on MAPbBr2I served as a proof of concept. Proton, 13C and 14N NMR expts. confirmed the results previously reported in the literature. Low temp. deuterium NMR measurements, down to 25 K, were carried out to study the structural phase transitions of MAPbBr3. Spectral lineshapes allow following the successive phase transitions of MAPbBr3. Finally, quadrupolar NMR lineshapes recorded in the orthorhombic phase were compared with simulated spectra, using DFT calcd. elec. field gradients (EFG). Computed data do not take into account any temp. effect. Thus, the discrepancy between the calcd. and exptl. EFG evidences the fact that MA cations are still subject to significant dynamics, even at 25 K.
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    Martineau, C.; Senker, J.; Taulelle, F. NMR Crystallography. Annu. Rep. NMR Spectrosc. 2014, 82, 1– 57,  DOI: 10.1016/B978-0-12-800184-4.00001-1
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    Harris, R. K.; Wasylishen, R. E.; Duer, M. J. NMR-Crystallography; Wiley: Chichester, U.K., 2009.
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    Charpentier, T. The PAW/GIPAW Approach for Computing NMR Parameters: A New Dimension Added to NMR Study of Solids. Solid State Nucl. Magn. Reson. 2011, 40, 1– 20,  DOI: 10.1016/j.ssnmr.2011.04.006
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    The PAW/GIPAW approach for computing NMR parameters: A new dimension added to NMR study of solids
    Charpentier, Thibault
    Solid State Nuclear Magnetic Resonance (2011), 40 (1), 1-20CODEN: SSNRE4; ISSN:0926-2040. (Elsevier B.V.)
    A review. In 2001, Mauri and Pickard introduced the gauge including projected augmented wave (GIPAW) method that enabled for the first time the calcn. of all-electron NMR parameters in solids, i.e. accounting for periodic boundary conditions. The GIPAW method roots in the plane wave pseudopotential formalism of the d. functional theory (DFT), and avoids the use of the cluster approxn. This method has undoubtedly revitalized the interest in quantum chem. calcns. in the solid-state NMR community. It has quickly evolved and improved so that the calcn. of the key components of NMR interactions, namely the shielding and elec. field gradient tensors, has now become a routine for most of the common nuclei studied in NMR. Availability of reliable implementations in several software packages (CASTEP, Quantum Espresso, PARATEC) make its usage more and more increasingly popular, maybe indispensable in near future for all material NMR studies. The majority of nuclei of the periodic table have already been investigated by GIPAW, and because of its high accuracy it is quickly becoming an essential tool for interpreting and understanding exptl. NMR spectra, providing reliable assignments of the obsd. resonances to crystallog. sites or enabling a priori prediction of NMR data. The continuous increase of computing power makes ever larger (and thus more realistic) systems amenable to first-principles anal. In the near future perspectives, as the incorporation of dynamical effects and/or disorder are still at their early developments, these areas will certainly be the prime target.
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    Moran, R. F.; Dawson, D. M.; Ashbrook, S. E. Exploiting NMR Spectroscopy for the Study of Disorder in Solids. Int. Rev. Phys. Chem. 2017, 36, 39– 115,  DOI: 10.1080/0144235X.2017.1256604
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    Exploiting NMR spectroscopy for the study of disorder in solids
    Moran, Robert F.; Dawson, Daniel M.; Ashbrook, Sharon E.
    International Reviews in Physical Chemistry (2017), 36 (1), 39-115CODEN: IRPCDL; ISSN:0144-235X. (Taylor & Francis Ltd.)
    Although the solid state is typically characterised by inherent periodicity, many interesting phys. and chem. properties of solids arise from a variation in this, i.e. changes in the nature of the atom occupying a particular site in a crystal structure or variation in the position of an atom (or group of atoms) in different parts of a structure, or variation as a function of time. This lack of long-range order poses significant challenges, not just for the characterization of the structure of disordered materials, but also simply for its description. The sensitivity of NMR (NMR) spectroscopy to the local, at.-scale environment, without the requirement for long-range order, makes it a powerful tool for the study of disorder in the solid state. Information on the no. and type(s) of coordinating atoms or through-space and through-bond connectivity between at. species enables the construction of a detailed picture of the structure. After a brief description of the background theory of NMR spectroscopy, and the exptl. methods employed, we will describe the effects of disorder on NMR spectra and the use of calcns. to help interpret exptl. measurements. We will then review a range of applications to different types of disordered materials, including oxides and ceramics, minerals, porous materials, biomaterials, energy materials, pharmaceuticals, polymers and glasses. We will discuss the most successful approaches for studying different materials, and illustrate the type of information available and the structural insight gained.
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    Grüninger, H.; Schmutzler, A.; Siegel, R.; Armstrong, K.; Frost, D. J.; Senker, J. Quantitative Description of 1H SQ and DQ Coherences for the Hydroxyl Disorder within Hydrous Ringwoodite. Phys. Chem. Chem. Phys. 2018, 20, 15098– 15105,  DOI: 10.1039/C8CP00863A
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    Quantitative description of 1H SQ and DQ coherences for the hydroxyl disorder within hydrous ringwoodite
    Grueninger, Helen; Schmutzler, Adrian; Siegel, Renee; Armstrong, Katherine; Frost, Daniel J.; Senker, Juergen
    Physical Chemistry Chemical Physics (2018), 20 (22), 15098-15105CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    Proton-contg. point defects in solid materials are important for a variety of properties ranging from ionic transport over thermal cond. up to compressibility. Ultrafast magic-angle spinning techniques nowadays offer high-resoln. solid-state NMR spectra, even for 1H, and thus open up possibilities to study the underlying defect chem. Nevertheless, disorder within such defects again leads to heavy spectral overlap of 1H resonances, which prevents quant. anal. of defect concns., if several defect types are present. Here, we present a strategy to overcome this limitation by simulating the 1H lineshape as well as 1H-1H double-quantum buildup curves, which we then validate against the exptl. data in a joint cost function. To mimic the local structural disorder, we use mol. dynamics simulations at the DFT level. It turned out to be advantageous for the joint refinement to put the computational effort into the structural optimization to derive accurate proton positions and to use empirical correlations for the relation between isotropic and anisotropic 1H chem. shifts and structural elements. The expressiveness of this approach is demonstrated on ringwoodite's (γ-Mg2SiO4) OH defect chem. contg. four different defect types in octahedral and tetrahedral voids with both pure Mg and mixed Si and Mg cation environments. Still, we det. the ratio for each defect type with an accuracy of about 5% as a result of the minimization of the joint cost function. We expect that our approach is generally applicable for local proton disorder and might prove to be a valuable alternative to the established AIRSS and Monte Carlo methods, resp.
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    Moran, R. F.; McKay, D.; Pickard, C. J.; Berry, A. J.; Griffin, J. M.; Ashbrook, S. E. Hunting for Hydrogen: Random Structure Searching and Prediction of NMR Parameters of Hydrous Wadsleyite. Phys. Chem. Chem. Phys. 2016, 18, 10173– 10181,  DOI: 10.1039/C6CP01529H
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    Hunting for hydrogen: random structure searching and prediction of NMR parameters of hydrous wadsleyite
    Moran, Robert F.; McKay, David; Pickard, Chris J.; Berry, Andrew J.; Griffin, John M.; Ashbrook, Sharon E.
    Physical Chemistry Chemical Physics (2016), 18 (15), 10173-10181CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    The structural chem. of materials contg. low levels of nonstoichiometric hydrogen is difficult to det., and producing structural models is challenging where hydrogen has no fixed crystallog. site. The authors demonstrated a computational approach employing ab initio random structure searching (AIRSS) to generate a series of candidate structures for hydrous wadsleyite (β-Mg2SiO4 with 1.6 wt% H2O), a high-pressure mineral proposed as a repository for water in the Earth's transition zone. Aligning with previous exptl. work, we solely consider models with Mg3 (over Mg1, Mg2 or Si) vacancies. They adapted the AIRSS method by starting with anhyd. wadsleyite, removing a single Mg2+ and randomly placing two H+ in a unit cell model, generating 819 candidate structures. 103 geometries were then subjected to more accurate optimization under periodic DFT. Using this approach, the authors found the most favorable hydration mechanism involves protonation of two O1 sites around the Mg3 vacancy. The formation of silanol groups on O3 or O4 sites (with loss of stable O1-H hydroxyls) coincides with an increase in total enthalpy. Importantly, the approach the authors employed allows observables such as NMR parameters to be computed for each structure. They consider hydrous wadsleyite (∼1.6 wt%) to be dominated by protonated O1 sites, with O3/O4-H silanol groups present as defects, a model that maps well onto exptl. studies at higher levels of hydration. The AIRSS approach adopted herein provides the crucial link between at.-scale structure and exptl. studies.
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    Jinnouchi, R.; Lahnsteiner, J.; Karsai, F.; Kresse, G.; Bokdam, M. Phase Transitions of Hybrid Perovskites Simulated by Machine-Learning Force Fields Trained on the Fly with Bayesian Inference. Phys. Rev. Lett. 2019, 122, 225701,  DOI: 10.1103/PhysRevLett.122.225701
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    Phase Transitions of Hybrid Perovskites Simulated by Machine-Learning Force Fields Trained on the Fly with Bayesian Inference
    Jinnouchi, Ryosuke; Lahnsteiner, Jonathan; Karsai, Ferenc; Kresse, Georg; Bokdam, Menno
    Physical Review Letters (2019), 122 (22), 225701CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Realistic finite temp. simulations of matter are a formidable challenge for first principles methods. Long simulation times and large length scales are required, demanding years of computing time. Here we present an on-the-fly machine learning scheme that generates force fields automatically during mol. dynamics simulations. This opens up the required time and length scales, while retaining the distinctive chem. precision of first principles methods and minimizing the need for human intervention. The method is widely applicable to multielement complex systems. We demonstrate its predictive power on the entropy driven phase transitions of hybrid perovskites, which have never been accurately described in simulations. Using machine learned potentials, isothermal-isobaric simulations give direct insight into the underlying microscopic mechanisms. Finally, we relate the phase transition temps. of different perovskites to the radii of the involved species, and we det. the order of the transitions in Landau theory.
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    Lahnsteiner, J.; Jinnouchi, R.; Bokdam, M. Long-Range Order Imposed by Short-Range Interactions in Methylammonium Lead Iodide: Comparing Point-Dipole Models to Machine-Learning Force Fields. Phys. Rev. B: Condens. Matter Mater. Phys. 2019, 100, 094106,  DOI: 10.1103/PhysRevB.100.094106
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    Grüninger, H.; Armstrong, K.; Greim, D.; Boffa-Ballaran, T.; Frost, D. J.; Senker, J. Hidden Oceans? Unraveling the Structure of Hydrous Defects in the Earth’s Deep Interior. J. Am. Chem. Soc. 2017, 139 (30), 10499– 10505,  DOI: 10.1021/jacs.7b05432
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    Hidden Oceans? Unraveling the Structure of Hydrous Defects in the Earth's Deep Interior
    Grueninger, Helen; Armstrong, Katherine; Greim, Dominik; Boffa-Ballaran, Tiziana; Frost, Daniel J.; Senker, Juergen
    Journal of the American Chemical Society (2017), 139 (30), 10499-10505CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    High-pressure silicates making up the main proportion of the earth's interior can incorporate a significant amt. of water in the form of OH defects. Generally, they are charge balanced by removing low-valent cations such as Mg2+. By combining high-resoln. multidimensional single- and double-quantum 1H solid-state NMR spectroscopy with d. functional theory calcns., we show that, for ringwoodite (γ-Mg2SiO4), addnl., Si4+ vacancies are formed, even at a water content as low as 0.1 wt. %. They are charge balanced by either four protons or one Mg2+ and two protons. Surprisingly, also a significant proportion of coupled Mg and Si vacancies are present. Furthermore, all defect types feature a pronounced orientational disorder of the OH groups, which results in a significant range of OH···O bond distributions. As such, we are able to present unique insight into the defect chem. of ringwoodite's spinel structure, which not only accounts for a potentially large fraction of the earth's entire water budget, but will also control transport properties in the mantle. We expect that our results will even impact other hydrous spinel-type materials, helping to understand properties such as ion conduction and heterogeneous catalysis.
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    Saalwächter, K. Robust NMR Approaches for the Determination of Homonuclear Dipole-Dipole Coupling Constants in Studies of Solid Materials and Biomolecules. ChemPhysChem 2013, 14, 3000– 3014,  DOI: 10.1002/cphc.201300254
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    Robust NMR approaches for the determination of homonuclear dipole-dipole coupling constants in studies of solid materials and biomolecules
    Saalwachter Kay
    Chemphyschem : a European journal of chemical physics and physical chemistry (2013), 14 (13), 3000-14 ISSN:.
    This review addresses the NMR spectroscopy study of molecular structure and dynamics by way of homonuclear dipole-dipole couplings by relying on their orientation and direct distance dependence. The study of homonuclear couplings as opposed to heteronuclear couplings poses specific challenges. On the one hand, two like spins cannot be independently manipulated easily, which means that simple shift-refocusing concepts by using hard π pulses cannot be used to cope with potentially large chemical-shift dispersions at the high fields used today. On the other hand, the noncommutativity of the different pair Hamiltonians in a multispin system leads to complications associated with the isolation of specific pair couplings while minimizing the influence of the other spins. In particular, the so-called dipolar-truncation effect challenges the observation of weak couplings of interest in the presence of stronger ones. Recent advances in determining homonuclear dipole-dipole coupling constants are reviewed, stressing the use of double-quantum spectroscopy approaches and their similarity to the popular heteronuclear rotational-echo double-resonance experiment. Particular emphasis is put on corrections for the influence of transverse relaxation effects on the measured data, and the handling of distribution effects as well as potential dynamic heterogeneities in complex substances.
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    Brown, S. P. Probing Proton-Proton Proximities in the Solid State. Prog. Nucl. Magn. Reson. Spectrosc. 2007, 50, 199– 251,  DOI: 10.1016/j.pnmrs.2006.10.002
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    Probing proton-proton proximities in the solid state
    Brown, Steven P.
    Progress in Nuclear Magnetic Resonance Spectroscopy (2007), 50 (4), 199-251CODEN: PNMRAT; ISSN:0079-6565. (Elsevier B.V.)
    A review. A review discusses the fast MAS or homonuclear decoupling allowing structurally or dynamically informative high-resoln. 1H-1H correlation expts. to be recorded for an increasing no. and wide range of rigid-solid applications.
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    Leupold, N.; Schötz, K.; Cacovich, S.; Bauer, I.; Schultz, M.; Daubinger, M.; Kaiser, L.; Rebai, A.; Rousset, J.; Köhler, A. High Versatility and Stability of Mechanochemically Synthesized Halide Perovskite Powders for Optoelectronic Devices. ACS Appl. Mater. Interfaces 2019, 11, 30259– 30268,  DOI: 10.1021/acsami.9b09160
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    High Versatility and Stability of Mechanochemically Synthesized Halide Perovskite Powders for Optoelectronic Devices
    Leupold, Nico; Schoetz, Konstantin; Cacovich, Stefania; Bauer, Irene; Schultz, Maximilian; Daubinger, Monika; Kaiser, Leah; Rebai, Amelle; Rousset, Jean; Koehler, Anna; Schulz, Philip; Moos, Ralf; Panzer, Fabian
    ACS Applied Materials & Interfaces (2019), 11 (33), 30259-30268CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
    The authors show that mechanochem. synthesized halide perovskite powders from a ball milling approach can be employed to fabricate a variety of lead halide perovskites with exceptional intrinsic stability. The authors' MAPbI3 powder exhibits higher thermal stability than conventionally processed thin films, without degrdn. after more than two and a half years of storage and only negligible degrdn. after heat treatment at 220°C for 14 h. The authors further show facile recovery strategies of nonphase-pure powders by simple remilling or mild heat treatment. Moreover, the authors demonstrate the mechanochem. synthesis of phase-pure mixed perovskite powders, such as (Cs0.05FA0.95PbI3)0.85(MAPbBr3)0.15, from either the individual metal and org. halides or from readily prepd. ternary perovskites, regardless of the precursor phase purity. Adding potassium iodide (KI) to the milling process successfully passivated the powders. The authors also succeeded in prepg. a precursor soln. on the basis of the powders and obtained uniform thin films for integration into efficient perovskite solar cells from spin-coating this soln. The authors find the KI passivation remains in the devices, leading to improved performance and significantly reduced hysteresis. Their work thus demonstrates the potential of mechanochem. synthesized halide perovskite powders for long-time storage and upscaling, further paving the way toward commercialization of perovskite-based optoelectronic devices.
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    Fung, B. M.; Khitrin, A. K.; Ermolaev, K. An Improved Broadband Decoupling Sequence for Liquid Crystals and Solids. J. Magn. Reson. 2000, 142, 97– 101,  DOI: 10.1006/jmre.1999.1896
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    An Improved Broadband Decoupling Sequence for Liquid Crystals and Solids
    Fung, B. M.; Khitrin, A. K.; Ermolaev, Konstantin
    Journal of Magnetic Resonance (2000), 142 (1), 97-101CODEN: JMARF3; ISSN:1090-7807. (Academic Press)
    Recently the authors developed an efficient broadband decoupling sequence called SPARC-16 for liq. crystals [J. Magn. Reson. 130, 317(1998)]. The sequence is based upon a 16-step phase cycling of the 2-step TPPM decoupling method for solids [J. Chem. Phys. 103, 6951(1995)]. Since then, a stepwise variation of the phase angle in the TPPM sequence offers even better results. The application of this new method to a liq. cryst. compd., 4-n-pentyl-4'-cyanobiphenyl, and a solid, l-tyrosine hydrochloride, is reported. The reason for the improvement is explained by an anal. of the problem in the rotating frame. (c) 2000 Academic Press.
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    Saalwächter, K.; Lange, F.; Matyjaszewski, K.; Huang, C.-F.; Graf, R. BaBa-Xy16: Robust and Broadband Homonuclear DQ Recoupling for Applications in Rigid and Soft Solids up to the Highest MAS Frequencies. J. Magn. Reson. 2011, 212, 204– 215,  DOI: 10.1016/j.jmr.2011.07.001
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    BaBa-xy16: robust and broadband homonuclear DQ recoupling for applications in rigid and soft solids up to the highest MAS frequencies
    Saalwachter Kay; Lange Frank; Matyjaszewski Krzysztof; Huang Chih-Feng; Graf Robert
    Journal of magnetic resonance (San Diego, Calif. : 1997) (2011), 212 (1), 204-15 ISSN:.
    We here present a substantially improved version of the popular Back-to-Back (BaBa) homonuclear double-quantum (DQ) MAS recoupling pulse sequence. By combining the original pulse sequence with a virtual π pulse train with xy-16 phase cycling along with time-reversed DQ reconversion, a truly broadband and exceptionally robust pulse sequence is obtained. The sequence has moderate radio-frequency power requirements, amounting to only one 360° nutation per rotor cycle, it is robust with respect to rf power and tune-up errors, and its broadband performance increases with increasing spinning frequency, here tested up to 63 kHz. The experiment can be applied to many spin-1/2 nuclei in rigid solids with substantial frequency offsets and CSAs, which is demonstrated on the example of 31P NMR of a magnesium ultraphosphate, comparing experimental data with multi-spin simulations, and we also show simulations addressing the performance in 13C NMR of bio(macro)molecules. 1H-based studies of polymer dynamics are highlighted for the example of a rigid solid with strongly anisotropic mobility, represented by a polymer inclusion compound, and for the example of soft materials with weak residual dipole-dipole couplings, represented by homogeneous and inhomogeneous elastomers. We advocate the use of normalized (relaxation-corrected) DQ build-up curves for a quantitative assessment of weak average dipole-dipole couplings and even distributions thereof.
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    Bartók, A. P.; Payne, M. C.; Kondor, R.; Csányi, G. Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons. Phys. Rev. Lett. 2010, 104, 136403,  DOI: 10.1103/PhysRevLett.104.136403
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    Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons
    Bartok, Albert P.; Payne, Mike C.; Kondor, Risi; Csanyi, Gabor
    Physical Review Letters (2010), 104 (13), 136403/1-136403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    We introduce a class of interat. potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, as derived from quantum mech. calcns. The models do not have a fixed functional form and hence are capable of modeling complex potential energy landscapes. They are systematically improvable with more data. We apply the method to bulk crystals, and test it by calcg. properties at high temps. Using the interat. potential to generate the long mol. dynamics trajectories required for such calcns. saves orders of magnitude in computational cost.
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    Bartók, A. P.; Kondor, R.; Csányi, G. On Representing Chemical Environments. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 184115,  DOI: 10.1103/PhysRevB.87.184115
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    On representing chemical environments
    Bartok, Albert P.; Kondor, Risi; Csanyi, Gabor
    Physical Review B: Condensed Matter and Materials Physics (2013), 87 (18), 184115/1-184115/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    We review some recently published methods to represent at. neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave nos. are used to expand the at. neighborhood d. function. Using the example system of small clusters, we quant. show that this expansion needs to be carried to higher and higher wave nos. as the no. of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.
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    Jinnouchi, R.; Karsai, F.; Kresse, G. On-the-Fly Machine Learning Force Field Generation: Application to Melting Points. Phys. Rev. B: Condens. Matter Mater. Phys. 2019, 100, 014105,  DOI: 10.1103/PhysRevB.100.014105
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    Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15– 50,  DOI: 10.1016/0927-0256(96)00008-0
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    Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
    Kresse, G.; Furthmuller, J.
    Computational Materials Science (1996), 6 (1), 15-50CODEN: CMMSEM; ISSN:0927-0256. (Elsevier)
    The authors present a detailed description and comparison of algorithms for performing ab-initio quantum-mech. calcns. using pseudopotentials and a plane-wave basis set. The authors will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temp. d.-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N2atoms scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge d. including a new special preconditioning optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. The authors have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio mol.-dynamics package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
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    Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169– 11186,  DOI: 10.1103/PhysRevB.54.11169
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    Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
    Kresse, G.; Furthmueller, J.
    Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
    The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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    Sun, J.; Ruzsinszky, A.; Perdew, J. P. Strongly Constrained and Appropriately Normed Semilocal Density Functional. Phys. Rev. Lett. 2015, 115, 036402,  DOI: 10.1103/PhysRevLett.115.036402
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    Strongly constrained and appropriately normed semilocal density functional
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    Physical Review Letters (2015), 115 (3), 036402/1-036402/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
    The ground-state energy, electron d., and related properties of ordinary matter can be computed efficiently when the exchange-correlation energy as a functional of the d. is approximated semilocally. We propose the first meta-generalized-gradient approxn. (meta-GGA) that is fully constrained, obeying all 17 known exact constraints that a meta-GGA can. It is also exact or nearly exact for a set of "appropriate norms," including rare-gas atoms and nonbonded interactions. This strongly constrained and appropriately normed meta-GGA achieves remarkable accuracy for systems where the exact exchange-correlation hole is localized near its electron, and esp. for lattice consts. and weak interactions.
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    Bokdam, M.; Lahnsteiner, J.; Ramberger, B.; Schäfer, T.; Kresse, G. Assessing Density Functionals Using Many Body Theory for Hybrid Perovskites. Phys. Rev. Lett. 2017, 119, 145501,  DOI: 10.1103/PhysRevLett.119.145501
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    Assessing density functionals using many body theory for hybrid perovskites
    Bokdam, Menno; Lahnsteiner, Jonathan; Ramberger, Benjamin; Schaefer, Tobias; Kresse, Georg
    Physical Review Letters (2017), 119 (14), 145501/1-145501/5CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    A review. Which d. functional is the "best" for structure simulations of a particular material. A concise, first principles, approach to answer this question is presented. The RPA (RPA)-an accurate many body theory-is used to evaluate various d. functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite MAPbI3, a promising new solar cell material. The evaluation is done by first creating finite temp. ensembles for small supercells using RPA mol. dynamics, and then evaluating the variance between the RPA and various approx. d. functionals for these ensembles. We find that, contrary to recent suggestions, van der Waals functionals do not improve the description of the material, whereas hybrid functionals and the strongly constrained appropriately normed (SCAN) d. functional yield very good agreement with the RPA. Finally, our study shows that in the room temp. tetragonal phase of MAPbI3, the mols. are preferentially parallel to the shorter lattice vectors but reorientation on ps time scales is still possible.
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    Goc, R. Calculation of the NMR Second Moment for Materials with Different Types of Internal Rotation. Solid State Nucl. Magn. Reson. 1998, 13, 55– 61,  DOI: 10.1016/S0926-2040(98)00082-4
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    Calculation of the NMR second moment for materials with different types of internal rotation
    Goc, Roman
    Solid State Nuclear Magnetic Resonance (1998), 13 (1-2), 55-61CODEN: SSNRE4; ISSN:0926-2040. (Elsevier Science B.V.)
    The measurements of the NMR 2nd moment can reveal information about structural and dynamical details of the sample providing that anal. of the exptl. results from the Van Vleck's formula can be performed. The method of calcg. the Van Vleck's 2nd moment for solids with complex internal motions is presented. The method is based on simulating any desired motion of atoms within a block of unit cells large enough to reflect the property of the macroscopic sample and calcg. the 2nd moment value averaged by this motion. The detailed description of this method is given for the case of rotation of mols. or groups of atoms. The algorithm of the computer program which performs calcn. based on the described method is also presented. Examples of application of the described method are listed.
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  75. 75
    Goc, R. Computer Calculation of the Van Vleck Second Moment for Materials with Internal Rotation of Spin Groups. Comput. Phys. Commun. 2004, 162, 102– 112,  DOI: 10.1016/j.cpc.2004.06.071
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    75
    Computer calculation of the Van Vleck second moment for materials with internal rotation of spin groups
    Goc, Roman
    Computer Physics Communications (2004), 162 (2), 102-112CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
    This paper describes m2rc3, a program that calcs. Van Vleck 2nd moments for solids with internal rotation of mols., ions or their structural parts. Only rotations about C3 axes of symmetry are allowed, but up to 15 axes of rotation per crystallog. unit cell are permitted. The program is very useful in interpreting NMR measurements in solids.
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  76. 76
    Karmakar, A.; Askar, A. M.; Bernard, G. M.; Terskikh, V. V.; Ha, M.; Patel, S.; Shankar, K.; Michaelis, V. K. Mechanochemical Synthesis of Methylammonium Lead Mixed-Halide Perovskites: Unraveling the Solid-Solution Behavior Using Solid-State NMR. Chem. Mater. 2018, 30, 2309– 2321,  DOI: 10.1021/acs.chemmater.7b05209
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    76
    Mechanochemical Synthesis of Methylammonium Lead Mixed-Halide Perovskites: Unraveling the Solid-Solution Behavior Using Solid-State NMR
    Karmakar, Abhoy; Askar, Abdelrahman M.; Bernard, Guy M.; Terskikh, Victor V.; Ha, Michelle; Patel, Sahil; Shankar, Karthik; Michaelis, Vladimir K.
    Chemistry of Materials (2018), 30 (7), 2309-2321CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    Mixed-halide lead perovskite (MHP) materials are rapidly advancing as next-generation high-efficiency perovskite solar cells due to enhanced stability and bandgap tunability. Here, we demonstrate the ability to readily and stoichiometrically tune the halide compn. in methylammonium-based MHPs using a mechanochem. synthesis approach. Using this solvent-free protocol we are able to prep. domain-free MHP solid solns. with randomly distributed halide ions about the Pb center. Up to 7 distinct [PbClxBr6-x]4- environments are identified, based on the 207Pb NMR chem. shifts, which are also sensitive to the changes in the unit cell dimensions resulting from the substitution of Br by Cl, obeying Vegard's law. We demonstrate a straightforward and rapid synthetic approach to forming highly tunable stoichiometric MHP solid solns. while avoiding the traditional soln. synthesis method by redirecting the thermodynamically driven compns. We illustrate the importance of complementary characterization methods, obtaining at.-scale structural information from multinuclear, multifield, and multidimensional solid-state magnetic resonance spectroscopy, as well as from quantum chem. calcns. and long-range structural details using powder x-ray diffraction. The solvent-free mechanochem. synthesis approach is also compared to traditional solvent synthesis, revealing identical solid-soln. behavior; however, the mechanochem. approach offers superior control over the stoichiometry of the final mixed-halide compn., which is essential for device engineering.
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  77. 77
    Askar, A. M.; Wiltshire, B. D.; Patel, S.; Fleet, J.; Shankar, K.; Karmakar, A.; Bernard, G. M.; Ha, M.; Michaelis, V. K.; Terskikh, V. V. Composition-Tunable Formamidinium Lead Mixed Halide Perovskites via Solvent-Free Mechanochemical Synthesis: Decoding the Pb Environments Using Solid-State NMR Spectroscopy. J. Phys. Chem. Lett. 2018, 9, 2671– 2677,  DOI: 10.1021/acs.jpclett.8b01084
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    77
    Composition-Tunable Formamidinium Lead Mixed Halide Perovskites via Solvent-Free Mechanochemical Synthesis: Decoding the Pb Environments Using Solid-State NMR Spectroscopy
    Askar, Abdelrahman M.; Karmakar, Abhoy; Bernard, Guy M.; Ha, Michelle; Terskikh, Victor V.; Wiltshire, Benjamin D.; Patel, Sahil; Fleet, Jonathan; Shankar, Karthik; Michaelis, Vladimir K.
    Journal of Physical Chemistry Letters (2018), 9 (10), 2671-2677CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Mixed-halide lead perovskites are becoming of paramount interest in the optoelectronic and photovoltaic research fields, offering band gap tunability, improved efficiency, and enhanced stability compared to their single halide counterparts. Formamidinium-based mixed halide perovskites (FA-MHPs) are crit. to obtaining optimum solar cell performance. Here, the authors report a solvent-free mechanochem. synthesis (MCS) method to prep. FA-MHPs, starting with their parent compds. (FAPbX3; X = Cl, Br, I), achieving compns. not previously accessible through the solvent synthesis (SS) technique. By probing local Pb environments in MCS FA-MHPs using solid-state NMR spectroscopy, along with powder x-ray diffraction for long-range crystallinity and reflectance measurements to det. the optical band gap, MCS FA-MHPs form at.-level solid solns. between Cl/Br and Br/I MHPs. The authors' results pave the way for advanced methods in at.-level structural understanding while offering a 1-pot synthetic approach to prep. MHPs with superior control of stoichiometry.
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  78. 78
    Aebli, M.; Piveteau, L.; Nazarenko, O.; Benin, M. B.; Krieg, F.; Verel, R.; Kovalenko, M. V. Lead-Halide Scalar Couplings in Pb NMR of APbX3 Perovskites (A = Cs, Methylammonium, Formamidinium ; X = Cl, Br, I). Sci. Rep. 2020, 10, 8229,  DOI: 10.1038/s41598-020-65071-4
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    78
    Lead-Halide Scalar Couplings in 207Pb NMR of APbX3 Perovskites (A = Cs, Methylammonium, Formamidinium; X = Cl, Br, I)
    Aebli, Marcel; Piveteau, Laura; Nazarenko, Olga; Benin, Bogdan M.; Krieg, Franziska; Verel, Rene; Kovalenko, Maksym V.
    Scientific Reports (2020), 10 (1), 8229CODEN: SRCEC3; ISSN:2045-2322. (Nature Research)
    Abstr.: Understanding the structure and dynamics of newcomer optoelectronic materials - lead halide perovskites APbX3 [A = Cs, methylammonium (CH3NH3+, MA), formamidinium (CH(NH2)2+, FA); X = Cl, Br, I] - has been a major research thrust. In this work, new insights could be gained by using 207Pb solid-state NMR (NMR) spectroscopy at variable temps. between 100 and 300 K. The existence of scalar couplings 1JPb-Cl of ca. 400 Hz and 1JPb-Br of ca. 2.3 kHz could be confirmed for MAPbX3 and CsPbX3. Diverse and fast structure dynamics, including rotations of A-cations, harmonic and anharmonic vibrations of the lead-halide framework and ionic mobility, affect the resoln. of the coupling pattern. 207Pb NMR can therefore be used to detect the structural disorder and phase transitions. Furthermore, by comparing bulk and nanocryst. CsPbBr3 a greater structural disorder of the PbBr6-octahedra had been confirmed in a nanoscale counterpart, not readily captured by diffraction-based techniques.
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  79. 79
    Rosales, B. A.; Men, L.; Cady, S. D.; Hanrahan, M. P.; Rossini, A. J.; Vela, J. Persistent Dopants and Phase Segregation in Organolead Mixed-Halide Perovskites. Chem. Mater. 2016, 28, 6848– 6859,  DOI: 10.1021/acs.chemmater.6b01874
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    79
    Persistent Dopants and Phase Segregation in Organolead Mixed-Halide Perovskites
    Rosales, Bryan A.; Men, Long; Cady, Sarah D.; Hanrahan, Michael P.; Rossini, Aaron J.; Vela, Javier
    Chemistry of Materials (2016), 28 (19), 6848-6859CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    Organolead mixed-halide perovskites such as CH3NH3PbX3-aX'a (X, X' = I, Br, Cl) are interesting semiconductors because of their low cost, high photovoltaic power conversion efficiencies, enhanced moisture stability, and band gap tunability. Using a combination of optical absorption spectroscopy, powder XRD and, for the 1st time, 207Pb solid state NMR (ssNMR), the authors probe the extent of alloying and phase segregation in these materials. Because 207Pb ssNMR chem. shifts are highly sensitive to local coordination, electronic structure, and vary linearly with halogen electronegativity and band gap, this technique can provide the true chem. speciation and compn. of organolead mixed-halide perovskites. The authors specifically study samples made by three different preparative methods: soln. phase synthesis, thermal annealing, and solid phase synthesis. 207Pb ssNMR reveals that nonstoichiometric dopants and semicryst. phases are prevalent in samples made by soln. phase synthesis. These nanodomains are persistent after thermal annealing up to 200°. Further, a novel solid phase synthesis that starts from the parent, single-halide perovskites can suppress phase segregation but not the formation of dopants. The authors' observations are consistent with the presence of miscibility gaps and spontaneous spinodal decompn. of the mixed-halide perovskites at room temp. This underscores how strongly different synthetic procedures impact the nanostructuring and compn. of organolead halide perovskites. Better optoelectronic properties and improved device stability and performance may be achieved through careful manipulation of the different phases and nanodomains present in these materials.
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  80. 80
    Zorin, V. E.; Brown, S. P.; Hodgkinson, P. Quantification of Homonuclear Dipolar Coupling Networks from Magic-Angle Spinning 1H NMR. Mol. Phys. 2006, 104, 293– 304,  DOI: 10.1080/00268970500351052
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    Quantification of homonuclear dipolar coupling networks from magic-angle spinning 1H NMR
    Zorin, V. E.; Brown, S. P.; Hodgkinson, P.
    Molecular Physics (2006), 104 (2), 293-304CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
    Numerical simulations of magic-angle spinning (MAS) spectra of dipolar-coupled nuclear spins were used to assess different approaches to the quantification of dipolar couplings from 1H solid-state NMR. Exploiting the translational symmetry of periodic spin systems allows extended networks with 'realistic' nos. of spins to be considered. The exptl. accessible parameter is the root-sum-square of the dipolar couplings to a given spin. The effectiveness of either fitting the resulting spinning sideband spectra to small spin system models, or using analyses based on moment expansions, was examd. Fitting of the spinning sideband pattern is considerably more robust with respect to exptl. noise than frequency domain moment anal. The influence of the MAS rate and system geometry on robustness of the quantification is analyzed and discussed.
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  81. 81
    Bradley, J. P.; Tripon, C.; Filip, C.; Brown, S. P. Determining Relative Proton-Proton Proximities from the Build-up of Two-Dimensional Correlation Peaks in 1H Double-Quantum MAS NMR: Insight from Multi-Spin Density-Matrix Simulations. Phys. Chem. Chem. Phys. 2009, 11, 6941– 6952,  DOI: 10.1039/b906400a
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    81
    Determining relative proton-proton proximities from the build-up of two-dimensional correlation peaks in 1H double-quantum MAS NMR: insight from multi-spin density-matrix simulations
    Bradley, Jonathan P.; Tripon, Carmen; Filip, Claudiu; Brown, Steven P.
    Physical Chemistry Chemical Physics (2009), 11 (32), 6941-6952CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    The build-up of intensity-as a function of the no., nrcpl, of POST-C7 elements used for the excitation and reconversion of double-quantum (DQ) coherence (DQC)-is analyzed for the fifteen distinct DQ correlation peaks that are obsd. exptl. for the eight sep. 1H resonances in a 1H (500 MHz) DQ CRAMPS solid-state (12.5 kHz MAS) NMR spectrum of the dipeptide β-AspAla. The simulation in SPINEVOLUTION of t1 (1H DQ evolution) FIDs for clusters of eight dipolar-coupled protons gives sep. simulated 1H DQ build-up curves for the CH2(a), CH2(b), CH(Asp), CH(Ala), NH and OH 1H single-quantum (SQ) 1H resonances. An anal. of both the simulated and exptl. 1H DQ build-up leads to the following general observations: (i) considering the build-up of 1H DQ peaks at a particular SQ frequency, max. intensity is obsd. for the DQC corresponding to the shortest H-H distance; (ii) for the max. intensity 1H DQ peak at a particular SQ frequency, the recoupling time for the obsd. max. intensity depends on the corresponding H-H distance, e.g., max. intensity for the CH2(a)-CH2(b) (H-H distance = 1.55 Å) and OH-CH(Asp) (H-H distance = 2.49 Å) DQ peaks is obsd. at nrcpl = 2 and 3, resp.; (iii) for DQ peaks involving a CH2 proton at a non-CH2 SQ frequency, there is much reduced intensity and a max. intensity at a short recoupling time; (iv) for the other lower intensity 1H DQ peaks at a particular SQ frequency, max. intensity is obsd. for the same (or close to the same) recoupling time, but the relative intensity of the DQ peaks is a reliable indicator of the relative H-H distance-the ratio of the max. intensities for the peaks at the CH(Ala) SQ frequency due to the two DQCs with the NH and OH protons are approx. in the ratio of the squares of the corresponding dipolar coupling consts. While the simulated 1H DQ build-up curves reproduce most of the features of the exptl. curves, max. intensity is often obsd. at a longer recoupling time in simulations. In this respect, simulations for two to eight spins show a trend towards a faster decay for an increasing no. of considered spins. Finally, simulations show that increasing either the Larmor frequency (to 1 GHz) or the MAS frequency (to 125 kHz) does not lead to changes in the marked differences between the 1H DQ build-up curves at the CH(Asp) SQ frequency for DQCs to the CH2(a) and OH protons that correspond to similar H-H distances (2.39 Å and 2.49 Å, resp.).
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  82. 82
    Selig, O.; Sadhanala, A.; Müller, C.; Lovrincic, R.; Chen, Z.; Rezus, Y. L. A.; Frost, J. M.; Jansen, T. L. C.; Bakulin, A. A. Organic Cation Rotation and Immobilization in Pure and Mixed Methylammonium Lead-Halide Perovskites. J. Am. Chem. Soc. 2017, 139, 4068– 4074,  DOI: 10.1021/jacs.6b12239
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    82
    Organic Cation Rotation and Immobilization in Pure and Mixed Methylammonium Lead-Halide Perovskites
    Selig, Oleg; Sadhanala, Aditya; Mueller, Christian; Lovrincic, Robert; Chen, Zhuoying; Rezus, Yves L. A.; Frost, Jarvist M.; Jansen, Thomas L. C.; Bakulin, Artem A.
    Journal of the American Chemical Society (2017), 139 (11), 4068-4074CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
    Three-dimensional lead-halide perovskites have attracted a lot of attention due to their ability to combine soln. processing with outstanding optoelectronic properties. Despite their soft ionic nature these materials demonstrate a surprisingly low level of electronic disorder resulting in sharp band edges and narrow distributions of the electronic energies. Understanding how structural and dynamic disorder impacts the optoelectronic properties of these perovskites is important for many applications. Here the authors combine ultrafast two-dimensional vibrational spectroscopy and mol. dynamics simulations to study the dynamics of the org. methylammonium (MA) cation orientation in a range of pure and mixed trihalide perovskite materials. For pure MAPbX3 (X = I, Br, Cl) perovskite films, the cation dynamics accelerate with decreasing size of the halide atom. This acceleration is surprising given the expected strengthening of the hydrogen bonds between the MA and the smaller halide anions, but can be explained by the increase in the polarizability with the size of halide. Much slower dynamics, up to partial immobilization of the org. cation, are obsd. in the mixed MAPb(ClxBr1-x)3 and MAPb(BrxI1-x)3 alloys, which the authors assoc. with symmetry breaking within the perovskite unit cell. The obsd. dynamics are essential for understanding the effects of structural and dynamical disorder in perovskite-based optoelectronic systems.
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  83. 83
    Svane, K. L.; Forse, A. C.; Grey, C. P.; Kieslich, G.; Cheetham, A. K.; Walsh, A.; Butler, K. T. How Strong Is the Hydrogen Bond in Hybrid Perovskites?. J. Phys. Chem. Lett. 2017, 8, 6154– 6159,  DOI: 10.1021/acs.jpclett.7b03106
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    83
    How Strong Is the Hydrogen Bond in Hybrid Perovskites?
    Svane, Katrine L.; Forse, Alexander C.; Grey, Clare P.; Kieslich, Gregor; Cheetham, Anthony K.; Walsh, Aron; Butler, Keith T.
    Journal of Physical Chemistry Letters (2017), 8 (24), 6154-6159CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
    Hybrid org.-inorg. perovskites represent a special class of metal-org. framework where a mol. cation is encased in an anionic cage. The mol.-cage interaction influences phase stability, phase transformations, and the mol. dynamics. We examine the hydrogen bonding in four AmBX3 formate perovskites: [Am]Zn(HCOO)3, with Am+ = hydrazinium (NH2NH3+), guanidinium (C(NH2)3+), dimethylammonium (CH3)2NH2+, and azetidinium (CH2)3NH2+. We develop a scheme to quantify the strength of hydrogen bonding in these systems from first-principles, which separates the electrostatic interactions between the amine (Am+) and the BX3- cage. The hydrogen-bonding strengths of formate perovskites range from 0.36 to 1.40 eV/cation (8-32 kcalmol-1). Complementary solid-state NMR spectroscopy confirms that strong hydrogen bonding hinders cation mobility. Application of the procedure to hybrid lead halide perovskites (X = Cl, Br, I, Am+ = CH3NH3+, CH(NH2)2+) shows that these compds. have significantly weaker hydrogen-bonding energies of 0.09 to 0.27 eV/cation (2-6 kcalmol-1), correlating with lower order-disorder transition temps.
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  84. 84
    Knijn, P. J.; van Bentum, P. J. M.; van Eck, E. R. H.; Fang, C.; Grimminck, D. L. A. G.; de Groot, R. A.; Havenith, R. W. A.; Marsman, M.; Meerts, W. L.; De Wijs, G. A. A Solid-State NMR and DFT Study of Compositional Modulations in AlxGa1-xAs. Phys. Chem. Chem. Phys. 2010, 12, 11517– 11535,  DOI: 10.1039/c003624b
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    A solid-state NMR and DFT study of compositional modulations in AlxGa1-xAs
    Knijn, Paulus J.; van Bentum, P. Jan M.; van Eck, Ernst R. H.; Fang, Changming; Grimminck, Dennis L. A. G.; de Groot, Robert A.; Havenith, Remco W. A.; Marsman, Martijn; Meerts, W. Leo; de Wijs, Gilles A.; Kentgens, Arno P. M.
    Physical Chemistry Chemical Physics (2010), 12 (37), 11517-11535CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
    The authors have conducted 75As and 69Ga NMR expts. to study order/disorder in AlxGa1-xAs lift-off films with x ∼ 0.297 and 0.489. The authors were able to identify all possible As(AlnGa4-n) sites with n = 0-4 coordinations in 75As NMR spectra using spin-echo expts. at 18.8 T. This was achieved by employing high radiofrequency field strengths using a small solenoid coil and an NMR probe specifically designed for this purpose. Spectral deconvolution, using an evolutionary algorithm, complies with the absence of long-range order if a CuAu based order parameter is imposed. An unconstrained fit shows a deviation of the statistics imposed by this type of ordering. The occupational disorder in the Ga and Al positions is reflected in a distribution of the Elec. Field Gradients (EFGs) experienced at the different arsenic sites. This can be modeled by summing the effects of the 1st coordination sphere and a Czjzek type distribution resulting from the compositional variation in the Al/Ga sub-lattice in the higher coordination spheres. 69Ga 3QMAS and nutation data exclude the presence of highly sym. sites and also show a distribution in EFG. The exptl. obtained quadrupolar interactions are in good agreement with calcns. based on D. Functional Theory (DFT). Using additivity of EFG tensors arising from distant charge perturbations, the authors could use DFT to model the EFG distributions of the n = 0-4 sites, reproducing the Czjzek and extended Czjzek distributions that were found exptl. From these calcns. the 75As quadrupolar interaction is sensitive to compositional modulations up to the 7th coordination shell in these systems.
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    Tycko, R.; Dabbagh, G.; Kurtz, S. R.; Goral, J. P. Quantitative Study of Atomic Ordering in Ga0.5In0.5P Thin Films by P31 Nuclear Magnetic Resonance. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13452– 13457,  DOI: 10.1103/PhysRevB.45.13452
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    Quantitative study of atomic ordering in gallium indium phosphide (Ga0.5In0.5P) thin films by phosphorus-31 nuclear magnetic resonance
    Tycko, Robert; Dabbagh, Gary; Kurtz, Sarah R.; Goral, John P.
    Physical Review B: Condensed Matter and Materials Physics (1992), 45 (23), 13452-7CODEN: PRBMDO; ISSN:0163-1829.
    Phosphorus-31 NMR spectra were used to measure the degree of cation ordering in thin films of the semiconductor alloy Ga0.5In0.5P grown by organometallic VPE. The 5 possible GanIn4-nP clusters in GxIn1-xP give rise to resolved NMR lines under magic-angle spinning, allowing a detn. of the degree of cation ordering from the relative areas of the 5 lines. The ordering is weak (order parameter ≤0.6) even in films that appear highly ordered in TEM.
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    Degen, C.; Tomaselli, M.; Meier, B. H.; Voncken, M. M. A. J.; Kentgens, A. P. M. NMR Investigation of Atomic Ordering in AlxGa1-xAs Thin Films. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 1– 4,  DOI: 10.1103/PhysRevB.69.193303
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    Mozur, E. M.; Hope, M. A.; Trowbridge, J. C.; Halat, D. M.; Daemen, L. L.; Maughan, A. E.; Prisk, T. R.; Grey, C. P.; Neilson, J. R. Cesium Substitution Disrupts Concerted Cation Dynamics in Formamidinium Hybrid Perovskites. Chem. Mater. 2020, 32, 6266– 6277,  DOI: 10.1021/acs.chemmater.0c01862
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    Cesium substitution disrupts concerted cation dynamics in formamidinium hybrid perovskites
    Mozur, Eve M.; Hope, Michael A.; Trowbridge, Julia C.; Halat, David M.; Daemen, Luke L.; Maughan, Annalise E.; Prisk, Timothy R.; Grey, Clare P.; Neilson, James R.
    Chemistry of Materials (2020), 32 (14), 6266-6277CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
    Although initial studies on hybrid perovskites for photovoltaic applications focused on simple compns., the most technol. relevant perovskites are heavily substituted. The influence of chem. substitution on the general phase behavior and specific phys. properties remains ambiguous. The hybrid perovskite formamidinium lead bromide, CH(NH2)2PbBr3, exhibits complex phase behavior manifesting in a series of crystallog. unresolvable phase transitions assocd. with changes in the cation dynamics. Here, we characterize the mol. and lattice dynamics of CH(NH2)2PbBr3 as a function of temp. and their evolution upon chem. substitution of CH(NH2)2+ for cesium (Cs+) with crystallog., neutron scattering, 1H and 14N NMR spectroscopy, and 79Br nuclear quadrupolar spectroscopy. Cs+ substitution suppresses the four low-temp. phase transitions of CH(NH2)2PbBr3, which propagate through concerted changes in the dynamic degrees of freedom of the org. sublattice and local or long-range distortions of the octahedral framework. We propose that cesium substitution suppresses the phase transitions through the relief of geometric frustration assocd. with the orientations of CH(NH2)2+ mols., which retain their local dynamical degrees of freedom.
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    Chatterjee, R.; Pavlovetc, I. M.; Aleshire, K.; Hartland, G. V.; Kuno, M. Subdiffraction Infrared Imaging of Mixed Cation Perovskites: Probing Local Cation Heterogeneities. ACS Energy Lett. 2018, 3, 469– 475,  DOI: 10.1021/acsenergylett.7b01306
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    Subdiffraction Infrared Imaging of Mixed Cation Perovskites: Probing Local Cation Heterogeneities
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    ACS Energy Letters (2018), 3 (2), 469-475CODEN: AELCCP; ISSN:2380-8195. (American Chemical Society)
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    We present ab initio calcns. (DFT and SOC-G0W0) of the optoelectronic properties of different hybrid-halide perovskites, namely X-PbI3 (X = methylammonium, formamidinium, guanidinium, hydrazinium, and hydroxylammonium). These calcns. shed new light on how the substitution of different org. cations in the material influences its optoelectronic properties. Our simulations show a significant modification of the lattice parameter and band gap of the material upon cation substitution. These modifications are not only due to steric effects but also due to electrostatic interactions between the org. and inorg. parts of the material. In addn. to this, we demonstrate how the relative orientations of neighboring cations in the material modify the local electrostatic potential of the system and its fundamental band gap. This change in the band gap is accompanied by the formation of localized and spatially sepd. electronic states. These localized states modify the carrier mobility in the materials and can be a reason for the formation and recombination of the charge carriers in these very promising materials.
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    ACS Energy Letters (2017), 2 (9), 1997-2004CODEN: AELCCP; ISSN:2380-8195. (American Chemical Society)
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    Intrinsic properties of FA(1-x)MAxPbI3 perovskite single crystals
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    Org.-inorg. hybrid perovskites with mixed org. cations and/or halides have attracted increasing attention due to their superior optoelectronic properties, which are tailorable for different applications. To obtain a deeper understanding of materials properties, single crystals are regarded as the best platform among various building blocks for fundamental study. Here, we synthesized a series of perovskite single crystals with mixed org. cations (APbI3, A = CH3NH3+, MA+; or CH(NH2)2+, FA+) along the compositional space, and conducted a systematic investigation to correlate the carrier behavior with the org. cations. The single crystals were synthesized via inverse temp. crystn. assisted by hydroiodic acid, where the quality of the crystals could be judiciously controlled by the thermodn. process. It is found that the substitution of 15% MA+ in FAPbI3 single crystals stabilizes the phase with the best charge transport characteristics. Both photodetector and J-V measurements suggested that FA0.85MA0.15PbI3 single crystal exhibits suppressed ion migration compared with the counterpart FA0.15MA0.85PbI3 single crystal. These results represent an important step to highlight the role of org. cations in hybrid perovskite materials, which will further benefit fundamental understanding of materials and device optimization.
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  • Abstract

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    Figure 1

    Figure 1. (a) XRD patterns, (b) 207Pb MAS NMR spectra, (c) 1H–13C CP-MAS NMR, and (d) 1H MAS NMR spectra of the three mixed MA1–xFAxPbI3 samples (x = 0.25, orange; x = 0.5, red; x = 0.75, green), as well as of the double-mixed sample MA0.15FA0.85PbI2.55Br0.45 (blue). (a) The XRD patterns of all samples show reflections of a cubic crystal lattice. The lattice constants are summarized in Table S1. (b) Additionally, a 207Pb MAS NMR spectrum of MAPbI3 (δiso = 1430 ppm) is depicted for comparison and dashed lines indicate chemical shifts for FAPbBr3 and MAPbBr3 from literature. (50,76,77) The 207Pb isotropic chemical shift of α-FAPbI3 is reported to be 1495 ppm. (77) (d) Asterisks in the 1H MAS NMR spectra indicate a small cyclohexane impurity, which is also observed in the 13C SPE MAS NMR spectra (Figure S2).

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    Figure 2

    Figure 2. 2D 1H–1H DQSQ MAS NMR spectra of the mixed perovskite samples (a–d), as well as of a physical mixture of MAPbI3 and α-FAPbI3 (e) at an excitation time texc of 229 μs. Solid lines between resonances and circles on diagonal signals mark 1H–1H correlations between MA cations (green), FA cations (blue), and MA–FA cations (red). The existence of mixed MA–FA correlations demonstrates a successful mixing of MA and FA on the A site for all mixed perovskite compositions (a–d), while in the case of cation phase segregation the red correlations would diminish as in the case of a physical mixture MAPbI3 and α-FAPbI3 (e).

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    Figure 3

    Figure 3. Average 1H DQ buildup curves (a) of MAPbI3 (green) and α-FAPbI3 (blue) and (b) of the mixed perovskite compositions MA1–xFAxPbI3(yellow, red, green), as well as MA0.15FA0.85PbI2.55Br0.45 (blue). The dashed lines are fits of the DQ buildup curves according to eq 2 to extract the average dipolar couplings, which are summarized in Figure 5 and Table S3.

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    Figure 4

    Figure 4. (a) Close-up of the pair distribution function between 2 and 5 Å for hydrogen atoms in MA1–xFAxPbI3 for x = 0, 0.5, and 1 obtained in the cubic phase at 400 K. The intra- and intermolecular contributions are depicted separately to demonstrate the onset of the intermolecular contributions. The full H–H pair distribution function of the simulation is depicted in the Supporting Information (Figure S4). (b) Intra- (black) and intermolecular (red) contributions to the average dipolar coupling as a function of simulation time for MA0.5FA0.5PbI3. Additionally, the intramolecular term averaged by applying symmetry of the intramolecular H–H vectors is shown in blue.

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    Figure 5

    Figure 5. Average 1H dipolar couplings for MA1–xFAxPbI3 extracted from 1H DQ buildup curves (pink) and MD simulations at 300 K (blue) and 400 K (red, solid line). Additionally, solely intermolecular contributions to D̅ are shown for the MD run at 400 K (red, dashed lines) revealing minor differences to the full average dipolar coupling (red, solid line). Additionally, linear trends resulting from models, where all H atoms are placed in the center of the lattice A site neglecting dynamics, etc., are depicted in black. The solid line depicts the model with a fixed lattice constant over the whole compositional space resulting in a linear curve with a slope proportional to the hydrogen ratio of FA and MA (y = (√(5/6) – 1)D0 + D0, black solid). The dashed black line is the model using experimental lattice constants of MA1–xFAxPbI3, fitting the experimental data slightly better. This demonstrates that the linear dependence of D̅ on x is dominated by the number of contributing spins. Furthermore, the experimental average dipolar coupling of the double-mixed perovskite composition MA0.15FA0.85PbI2.55Br0.45 is depicted (light blue), revealing a significantly higher average dipolar coupling than the MA1–xFAxPbI3 compositions.

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    Figure 6

    Figure 6. (a) Populations of cation–cation contacts, MA–MA (green), FA–FA (blue), and MA–FA (red), as a function of FA content x. The experimental data are indicated by dots, while the populations according to a random distribution of cations are shown by dashed lines. Dotted lines represent the populations of contacts for a cluster model with an order parameter S of 0.3. (b–e) Calculated populations of cation–cation contacts, MA–MA (green), FA–FA (blue), and MA–FA (red), as a function of order parameter S for the different compositions of the mixed MA1–xFAxPbI3 (b–d), as well as MA0.15FA0.85PbI2.55Br0.45 (e). The horizontal bars indicate the experimental accuracy for the observed populations (dashed lines) of cation–cation correlations in the 2D 1H–1H DQSQ MAS NMR spectra (Figure 2).

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    Figure 7

    Figure 7. Schematic representation of MA (red)/FA (blue) distributions within MA1–xFAxPbI3 (x = 0.25, 0.50, 0.75) perovskites following random statistics (a) and MA or FA clustering (b) to a degree of S = 0.3 labeled rMA and rFA, respectively (according to eqs 6 and 7). As the experimental NMR data do not provide information about domain sizes of MA-rich and FA-rich regions, arbitrary sized circles were chosen to represent the statistics.

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      Lin, Kebin; Xing, Jun; Quan, Li Na; de Arquer, F. Pelayo Garcia; Gong, Xiwen; Lu, Jianxun; Xie, Liqiang; Zhao, Weijie; Zhang, Di; Yan, Chuanzhong; Li, Wenqiang; Liu, Xinyi; Lu, Yan; Kirman, Jeffrey; Sargent, Edward H.; Xiong, Qihua; Wei, Zhanhua
      Nature (London, United Kingdom) (2018), 562 (7726), 245-248CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
      Metal halide perovskite materials are an emerging class of soln.-processable semiconductors with considerable potential for use in optoelectronic devices1-3. For example, light-emitting diodes (LEDs) based on these materials could see application in flat-panel displays and solid-state lighting, owing to their potential to be made at low cost via facile soln. processing, and could provide tunable colors and narrow emission line widths at high photoluminescence quantum yields4-8. However, the highest reported external quantum efficiencies of green- and red-light-emitting perovskite LEDs are around 14 per cent7,9 and 12 per cent8, resp.-still well behind the performance of org. LEDs10-12 and inorg. quantum dot LEDs13. Here we describe visible-light-emitting perovskite LEDs that surpass the quantum efficiency milestone of 20 per cent. This achievement stems from a new strategy for managing the compositional distribution in the device-an approach that simultaneously provides high luminescence and balanced charge injection. Specifically, we mixed a presynthesized CsPbBr3 perovskite with a MABr additive (where MA is CH3NH3), the differing solubilities of which yield sequential crystn. into a CsPbBr3/MABr quasi-core/shell structure. The MABr shell passivates the nonradiative defects that would otherwise be present in CsPbBr3 crystals, boosting the photoluminescence quantum efficiency, while the MABr capping layer enables balanced charge injection. The resulting 20.3 per cent external quantum efficiency represents a substantial step towards the practical application of perovskite LEDs in lighting and display.
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    4. 4
      Cho, C.; Zhao, B.; Tainter, G. D.; Lee, J.-Y.; Friend, R. H.; Di, D.; Deschler, F.; Greenham, N. C. The Role of Photon Recycling in Perovskite Light-Emitting Diodes. Nat. Commun. 2020, 11, 611,  DOI: 10.1038/s41467-020-14401-1
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      4
      The role of photon recycling in perovskite light-emitting diodes
      Cho, Changsoon; Zhao, Baodan; Tainter, Gregory D.; Lee, Jung-Yong; Friend, Richard H.; Di, Dawei; Deschler, Felix; Greenham, Neil C.
      Nature Communications (2020), 11 (1), 611CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
      Abstr.: Perovskite light-emitting diodes have recently broken the 20% barrier for external quantum efficiency. These values cannot be explained with classical models for optical outcoupling. Here, we analyze the role of photon recycling (PR) in assisting light extn. from perovskite light-emitting diodes. Spatially-resolved photoluminescence and electroluminescence measurements combined with optical modeling show that repetitive re-absorption and re-emission of photons trapped in substrate and waveguide modes significantly enhance light extn. when the radiation efficiency is sufficiently high. In this manner, PR can contribute more than 70% to the overall emission, in agreement with recently-reported high efficiencies. While an outcoupling efficiency of 100% is theor. possible with PR, parasitic absorption losses due to absorption from the electrodes are shown to limit practical efficiencies in current device architectures. To overcome the present limits, we propose a future configuration with a reduced injection electrode area to drive the efficiency toward 100%.
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    5. 5
      Gao, L.; Yan, Q. Recent Advances in Lead Halide Perovskites for Radiation Detectors. Sol. RRL 2020, 4, 1900210,  DOI: 10.1002/solr.201900210
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      There is no corresponding record for this reference.
    6. 6
      Wei, H.; Huang, J. Halide Lead Perovskites for Ionizing Radiation Detection. Nat. Commun. 2019, 10, 1066,  DOI: 10.1038/s41467-019-08981-w
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      6
      Halide lead perovskites for ionizing radiation detection
      Wei Haotong; Huang Jinsong
      Nature communications (2019), 10 (1), 1066 ISSN:.
      Halide lead perovskites have attracted increasing attention in recent years for ionizing radiation detection due to their strong stopping power, defect-tolerance, large mobility-lifetime (μτ) product, tunable bandgap and simple single crystal growth from low-cost solution processes. In this review, we start with the requirement of material properties for high performance ionizing radiation detection based on direct detection mechanisms for applications in X-ray imaging and γ-ray energy spectroscopy. By comparing the performances of halide perovskites radiation detectors with current state-of-the-art ionizing radiation detectors, we show the promising features and challenges of halide perovskites as promising radiation detectors.
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    7. 7
      Chen, Y.; Yi, H. T.; Wu, X.; Haroldson, R.; Gartstein, Y. N.; Rodionov, Y. I.; Tikhonov, K. S.; Zakhidov, A.; Zhu, X. Y.; Podzorov, V. Extended Carrier Lifetimes and Diffusion in Hybrid Perovskites Revealed by Hall Effect and Photoconductivity Measurements. Nat. Commun. 2016, 7, 12253,  DOI: 10.1038/ncomms12253
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      7
      Extended carrier lifetimes and diffusion in hybrid perovskites revealed by Hall effect and photoconductivity measurements
      Chen, Y.; Yi, H. T.; Wu, X.; Haroldson, R.; Gartstein, Y. N.; Rodionov, Y. I.; Tikhonov, K. S.; Zakhidov, A.; Zhu, X.-Y.; Podzorov, V.
      Nature Communications (2016), 7 (), 12253CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      Impressive performance of hybrid perovskite solar cells reported in recent years still awaits a comprehensive understanding of its microscopic origins. In this work, the intrinsic Hall mobility and photocarrier recombination coeff. are directly measured in these materials in steady-state transport studies. The results show that electron-hole recombination and carrier trapping rates in hybrid perovskites are very low. The bimol. recombination coeff. (10-11 to 10-10 cm3 s-1) is found to be on par with that in the best direct-band inorg. semiconductors, even though the intrinsic Hall mobility in hybrid perovskites is considerably lower (up to 60 cm2 V-1 s-1). Measured here, steady-state carrier lifetimes (of up to 3 ms) and diffusion lengths (as long as 650 μm) are significantly longer than those in high-purity cryst. inorg. semiconductors. We suggest that these exptl. findings are consistent with the polaronic nature of charge carriers, resulting from an interaction of charges with methylammonium dipoles.
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    8. 8
      Walsh, A. Principles of Chemical Bonding and Band Gap Engineering in Hybrid Organic-Inorganic Halide Perovskites. J. Phys. Chem. C 2015, 119, 5755– 5760,  DOI: 10.1021/jp512420b
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      8
      Principles of Chemical Bonding and Band Gap Engineering in Hybrid Organic-Inorganic Halide Perovskites
      Walsh, Aron
      Journal of Physical Chemistry C (2015), 119 (11), 5755-5760CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      A review. The performance of solar cells based on hybrid halide perovskites has seen an unparalleled rate of progress, while our understanding of the underlying phys. chem. of these materials trails behind. Superficially, CH3NH3PbI3 is similar to other thin-film photovoltaic materials: a semiconductor with an optical band gap in the optimal region of the electromagnetic spectrum. Microscopically, the material is more unconventional. Progress in our understanding of the local and long-range chem. bonding of hybrid perovskites is discussed here, drawing from a series of computational studies involving electronic structure, mol. dynamics, and Monte Carlo simulation techniques. The orientational freedom of the dipolar methylammonium ion gives rise to temp.-dependent dielec. screening and the possibility for the formation of polar (ferroelec.) domains. The ability to independently substitute on the A, B, and X lattice sites provides the means to tune the optoelectronic properties. Finally, ten crit. challenges and opportunities for phys. chemists are highlighted.
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    9. 9
      Jeon, N. J.; Noh, J. H.; Yang, W. S.; Kim, Y. C.; Ryu, S.; Seo, J.; Seok, S. Il. Compositional Engineering of Perovskite Materials for High-Performance Solar Cells. Nature 2015, 517, 476– 480,  DOI: 10.1038/nature14133
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      9
      Compositional engineering of perovskite materials for high-performance solar cells
      Jeon, Nam Joong; Noh, Jun Hong; Yang, Woon Seok; Kim, Young Chan; Ryu, Seungchan; Seo, Jangwon; Seok, Sang Il
      Nature (London, United Kingdom) (2015), 517 (7535), 476-480CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      Here we combine the promising, owing to its comparatively narrow bandgap, but relatively unstable formamidinium lead iodide (FAPbI3) with methylammonium lead bromide (MAPbBr3) as the light-harvesting unit in a bilayer solar cell architecture. We investigated phase stability, morphol. of the perovskite layer, hysteresis in current-voltage characteristics, and overall performance as a function of chem. compn. Our results show that incorporation of MAPbBr3 into FAPbI3 stabilizes the perovskite phase of FAPbI3 and improves the power conversion efficiency of the solar cell to >18% under a std. illumination of 100 mW/cm2. These findings further emphasize the versatility and performance potential of inorg.-org. lead halide perovskite materials for photovoltaic applications.
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    10. 10
      Petrus, M. L.; Schlipf, J.; Li, C.; Gujar, T. P.; Giesbrecht, N.; Müller-Buschbaum, P.; Thelakkat, M.; Bein, T.; Hüttner, S.; Docampo, P. Capturing the Sun: A Review of the Challenges and Perspectives of Perovskite Solar Cells. Adv. Energy Mater. 2017, 7, 1700264,  DOI: 10.1002/aenm.201700264
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      There is no corresponding record for this reference.
    11. 11
      Panzer, F.; Li, C.; Meier, T.; Köhler, A.; Huettner, S. Impact of Structural Dynamics on the Optical Properties of Methylammonium Lead Iodide Perovskites. Adv. Energy Mater. 2017, 7, 1700286,  DOI: 10.1002/aenm.201700286
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      There is no corresponding record for this reference.
    12. 12
      Gao, P.; Grätzel, M.; Nazeeruddin, M. K. Organohalide Lead Perovskites for Photovoltaic Applications. Energy Environ. Sci. 2014, 7, 2448– 2463,  DOI: 10.1039/C4EE00942H
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      12
      Organohalide lead perovskites for photovoltaic applications
      Gao, Peng; Gratzel, Michael; Nazeeruddin, Mohammad K.
      Energy & Environmental Science (2014), 7 (8), 2448-2463CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      There are only few semiconducting materials that have been shaping the progress of third generation photovoltaic cells as much as perovskites. Although they are deceivingly simple in structure, the archetypal AMX3-type perovskites have built-in potential for complex and surprising discoveries. Since 2009, a small and somewhat exotic class of perovskites, which are quite different from the common rock-solid oxide perovskite, have turned over a new leaf in solar cell research. Highlighted as one of the major scientific breakthroughs of the year 2013, the power conversion efficiency of the title compd. hybrid org.-inorg. perovskite has now exceeded 18%, making it competitive with thin-film PV technol. In this mini-review, a brief history of perovskite materials for photovoltaic applications is reported, the current state-of-the-art is distd. and the basic working mechanisms have been discussed. By analyzing the attainable photocurrent and photovoltage, realizing perovskite solar cells with 20% efficiency for a single junction, and 30% for a tandem configuration on a c-Si solar cell would be realistic.
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    13. 13
      Kazim, S.; Nazeeruddin, M. K.; Grätzel, M.; Ahmad, S. Perovskite as Light Harvester: A Game Changer in Photovoltaics. Angew. Chem., Int. Ed. 2014, 53, 2812– 2824,  DOI: 10.1002/anie.201308719
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      13
      Perovskite as Light Harvester: A Game Changer in Photovoltaics
      Kazim, Samrana; Nazeeruddin, Mohammad Khaja; Graetzel, Michael; Ahmad, Shahzada
      Angewandte Chemie, International Edition (2014), 53 (11), 2812-2824CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      A review; it is not often that the scientific community is blessed with a material, which brings enormous hopes and receives special attention. When it does, it expands at a rapid pace and its every dimension creates curiosity. One such material is perovskite, which has triggered the development of new device architectures in energy conversion. Perovskites are of great interest in photovoltaic devices due to their panchromatic light absorption and ambipolar behavior. Power conversion efficiencies have been doubled in less than a year and over 15 % is being now measured in labs. Every digit increment in efficiency is being celebrated widely in the scientific community and is being discussed in industry. Here we provide a summary on the use of perovskite for inexpensive solar cells fabrication. It will not be unrealistic to speculate that one day perovskite-based solar cells can match the capability and capacity of existing technologies.
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    14. 14
      Park, N.; Grätzel, M.; Miyasaka, T. Organic-Iorganic Halide Perovskite Photovoltaics: From Fundamentals to Devices Architectures; Springer International Publishing: Cham, Switzerland, 2016.
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      There is no corresponding record for this reference.
    15. 15
      Jeon, N. J.; Na, H.; Jung, E. H.; Yang, T.-Y.; Lee, Y. G.; Kim, G.; Shin, H.-W.; Il Seok, S.; Lee, J.; Seo, J. A Fluorene-Terminated Hole-Transporting Material for Highly Efficient and Stable Perovskite Solar Cells. Nat. Energy 2018, 3, 682– 689,  DOI: 10.1038/s41560-018-0200-6
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      15
      A fluorene-terminated hole-transporting material for highly efficient and stable perovskite solar cells
      Jeon, Nam Joong; Na, Hyejin; Jung, Eui Hyuk; Yang, Tae-Youl; Lee, Yong Guk; Kim, Geunjin; Shin, Hee-Won; Il Seok, Sang; Lee, Jaemin; Seo, Jangwon
      Nature Energy (2018), 3 (8), 682-689CODEN: NEANFD; ISSN:2058-7546. (Nature Research)
      Perovskite solar cells (PSCs) require both high efficiency and good long-term stability if they are to be commercialized. It is crucial to finely optimize the energy level matching between the perovskites and hole-transporting materials to achieve better performance. Here, we synthesize a fluorene-terminated hole-transporting material with a fine-tuned energy level and a high glass transition temp. to ensure highly efficient and thermally stable PSCs. We use this material to fabricate photovoltaic devices with 23.2% efficiency (under reverse scanning) with a steady-state efficiency of 22.85% for small-area (∼0.094 cm2) cells and 21.7% efficiency (under reverse scanning) for large-area (∼1 cm2) cells. We also achieve certified efficiencies of 22.6% (small-area cells, ∼0.094 cm2) and 20.9% (large-area, ∼1 cm2). The resultant device shows better thermal stability than the device with spiro-OMeTAD, maintaining almost 95% of its initial performance for more than 500 h after thermal annealing at 60°C.
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    16. 16
      Yang, W. S.; Park, B.; Jung, E. H.; Jeon, N. J.; Kim, Y. C.; Lee, D. U.; Shin, S. S.; Seo, J.; Kim, E. K.; Noh, J. H. Iodide Management in Formamidinium-Lead-Halide-Based Perovskite Layers for Efficient Solar Cells. Science 2017, 356, 1376– 1379,  DOI: 10.1126/science.aan2301
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      16
      Iodide management in formamidinium-lead-halide-based perovskite layers for efficient solar cells
      Yang, Woon Seok; Park, Byung-Wook; Jung, Eui Hyuk; Jeon, Nam Joong; Kim, Young Chan; Lee, Dong Uk; Shin, Seong Sik; Seo, Jangwon; Kim, Eun Kyu; Noh, Jun Hong; Seok, Sang Il
      Science (Washington, DC, United States) (2017), 356 (6345), 1376-1379CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      The formation of a dense and uniform thin layer on the substrates is crucial for the fabrication of high-performance perovskite solar cells (PSCs) contg. formamidinium with multiple cations and mixed halide anions. The concn. of defect states, which reduce a cell's performance by decreasing the open-circuit voltage and short-circuit c.d., needs to be as low as possible. We show that the introduction of addnl. iodide ions into the org. cation soln., which are used to form the perovskite layers through an intramol. exchanging process, decreases the concn. of deep-level defects. The defect-engineered thin perovskite layers enable the fabrication of PSCs with a certified power conversion efficiency of 22.1% in small cells and 19.7% in 1-square-centimeter cells.
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    17. 17
      Lu, H.; Krishna, A.; Zakeeruddin, S. M.; Grätzel, M.; Hagfeldt, A. Compositional and Interface Engineering of Organic-Inorganic Lead Halide Perovskite Solar Cells. iScience 2020, 23, 101359,  DOI: 10.1016/j.isci.2020.101359
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      17
      Compositional and Interface Engineering of Organic-Inorganic Lead Halide Perovskite Solar Cells
      Lu, Haizhou; Krishna, Anurag; Zakeeruddin, Shaik M.; Gratzel, Michael; Hagfeldt, Anders
      iScience (2020), 23 (8), 101359CODEN: ISCICE; ISSN:2589-0042. (Elsevier B.V.)
      A review. Power conversion efficiency (PCE) of the perovskite solar cells (PSCs) has remarkably been increased from 3.1% to 25.2%. The fast expansion of the PSCs has been along with the development of compositional and interface engineering, which has been playing a crit. role. For the PSCs with record high-efficiency and stability, the perovskite absorber layer has been changed from the initial MAPbI3- to FAPbI3-based compns. Owing to the enormous engineering works, perovskite absorber layers with monolithic grains could be achieved, in which the interior defects are negligible compared with the surface defects. Therefore, interface engineering, which can passivate the surface defects and/or isolate the perovskite from the environmental moistures, has been playing a more and more important role to further boost the PCE and stability of the PSCs. Herein, a compact review study of the compositional and interface engineering is presented and promising strategies and directions of the PSCs are discussed.
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    18. 18
      Hoke, E. T.; Slotcavage, D. J.; Dohner, E. R.; Bowring, A. R.; Karunadasa, H. I.; McGehee, M. D. Reversible Photo-Induced Trap Formation in Mixed-Halide Hybrid Perovskites for Photovoltaics. Chem. Sci. 2015, 6, 613– 617,  DOI: 10.1039/C4SC03141E
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      18
      Reversible photo-induced trap formation in mixed-halide hybrid perovskites for photovoltaics
      Hoke, Eric T.; Slotcavage, Daniel J.; Dohner, Emma R.; Bowring, Andrea R.; Karunadasa, Hemamala I.; McGehee, Michael D.
      Chemical Science (2015), 6 (1), 613-617CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)
      We report on reversible, light-induced transformations in (CH3NH3)Pb(BrxI1-x)3. Photoluminescence (PL) spectra of these perovskites develop a new, red-shifted peak at 1.68 eV that grows in intensity under const., 1-sun illumination in less than a minute. This is accompanied by an increase in sub-bandgap absorption at ∼1.7 eV, indicating the formation of luminescent trap states. Light soaking causes a splitting of X-ray diffraction (XRD) peaks, suggesting segregation into two cryst. phases. Surprisingly, these photo-induced changes are fully reversible; the XRD patterns and the PL and absorption spectra revert to their initial states after the materials are left for a few minutes in the dark. We speculate that photoexcitation may cause halide segregation into iodide-rich minority and bromide-enriched majority domains, the former acting as a recombination center trap. This instability may limit achievable voltages from some mixed-halide perovskite solar cells and could have implications for the photostability of halide perovskites used in optoelectronics.
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    19. 19
      Yang, X.; Yan, X.; Wang, W.; Zhu, X.; Li, H.; Ma, W.; Sheng, C. Light Induced Metastable Modification of Optical Properties in CH3NH3PbI3-xBrx Perovskite Films: Two-Step Mechanism. Org. Electron. 2016, 34, 79– 83,  DOI: 10.1016/j.orgel.2016.04.020
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      19
      Light induced metastable modification of optical properties in CH3NH3PbI3-xBrx perovskite films: Two-step mechanism
      Yang, Xiao; Yan, Xiaoliang; Wang, Wei; Zhu, Xiangxiang; Li, Heng; Ma, Wanli; Sheng, ChuanXiang
      Organic Electronics (2016), 34 (), 79-83CODEN: OERLAU; ISSN:1566-1199. (Elsevier B.V.)
      We have used photoluminescence (PL) and photomodulation (PM) spectroscopy to investigate the reversible spectral changes of PL in CH3NH3PbI3-xBrx films, where x is 1.7. In an as-prepd. film, the peak of PL spectra shifts from ∼640 nm near bandedge to ∼750 nm after excitation by a continuous wave (CW) or a pulsed laser with high repetition rate, but keeps at 640 nm excited by same pulsed laser with the repetition rate smaller than 500 Hz. The PM spectroscopy also shows the formation of sub bandgap states after illumination which is responsible for the red shift of PL. The light induced modification of optical properties is reversible after keeping the film out of illumination for several hours at room temp. We analyze the photoinduced modification to be two-steps processes: the temporary sub bandgap states were first photogenerated in perovskite film, if those states interacting with more coming photons within their lifetimes, light induced metastable states responsible for red-shift of PL will be formed. This instability reduces the electronic bandgap and generates more traps which will degrade the performance of the related photovoltaic devices.
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    20. 20
      Knight, A. J.; Herz, L. M. Preventing Phase Segregation in Mixed-Halide Perovskites: A Perspective. Energy Environ. Sci. 2020, 13, 2024– 2046,  DOI: 10.1039/D0EE00788A
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      20
      Preventing phase segregation in mixed-halide perovskites: a perspective
      Knight, Alexander J.; Herz, Laura M.
      Energy & Environmental Science (2020), 13 (7), 2024-2046CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      Mixed-halide perovskites are ideal materials for the demanding applications of tandem solar cells and emission-tunable light-emitting diodes (LEDs) because of their high compositional flexibility and optoelectronic performance. However, one major obstacle to their use is the compositional instability some mixed-halide perovskites experience under illumination or charge-carrier injection, during which the perovskite material demixes into regions of differing halide content. Such segregation of halide ions adversely affects the electronic properties of the material and severely limits the prospects of mixed-halide perovskite technol. Accordingly, a considerable amt. of research has been performed aiming to uncover the underlying mechanisms and mitigating factors of the halide segregation process. Here we present a perspective of strategies designed to reduce the effects of halide segregation in working mixed-halide perovskite devices, based on recent literature reports. We discuss a multitude of mitigating techniques, and conclude that a combination of stoichiometric engineering, crystallinity control and trap state passivation is clearly imperative for abating halide segregation. In addn., the redn. of halide vacancies and control over illumination and temp. can, to a certain extent, mitigate halide segregation. Less direct approaches, such as a change in atm. environment, perovskite incorporation into a nanocryst. compn., or direct control over the crystallog. structure of the perovskite, may however prove too cumbersome to be of practical use. This perspective paves the way for the design and creation of phase-stable, mixed-halide perovskite materials for photovoltaic and LED applications.
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    21. 21
      Knight, A. J.; Wright, A. D.; Patel, J. B.; McMeekin, D. P.; Snaith, H. J.; Johnston, M. B.; Herz, L. M. Electronic Traps and Phase Segregation in Lead Mixed-Halide Perovskite. ACS Energy Lett. 2019, 4, 75– 84,  DOI: 10.1021/acsenergylett.8b02002
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      21
      Electronic traps and phase segregation in lead mixed-halide perovskite
      Knight, Alexander J.; Wright, Adam D.; Patel, Jay B.; McMeekin, David P.; Snaith, Henry J.; Johnston, Michael B.; Herz, Laura M.
      ACS Energy Letters (2019), 4 (1), 75-84CODEN: AELCCP; ISSN:2380-8195. (American Chemical Society)
      An understanding of the factors driving halide segregation in lead mixed-halide perovskites is required for their implementation in tandem solar cells with existing silicon technol. Here we report that the halide segregation dynamics obsd. in the photoluminescence from CH3NH3Pb(Br0.5I0.5)3 is strongly influenced by the atm. environment, and that encapsulation of films with a layer of poly(Me methacrylate) allows for halide segregation dynamics to be fully reversible and repeatable. The authors further establish an empirical model directly linking the amt. of halide segregation obsd. in the photoluminescence to the fraction of charge carriers recombining through trap-mediated channels, and the photon flux absorbed. From such quant. anal. the authors show that under pulsed illumination, the frequency of the modulation alone has no influence on the segregation dynamics. Addnl., they extrapolate that working CH3NH3Pb(Br0.5I0.5)3 perovskite cells would require a redn. of the trap-related charge carrier recombination rate to .ltorsim.105s-1 in order for halide segregation to be sufficiently suppressed.
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    22. 22
      Jeong, M.; Choi, I. W.; Go, E. M.; Cho, Y.; Kim, M.; Lee, B.; Jeong, S.; Jo, Y.; Choi, H. W.; Lee, J. Stable Perovskite Solar Cells with Efficiency Exceeding 24.8% and 0.3-V Voltage Loss. Science 2020, 369, 1615– 1620,  DOI: 10.1126/science.abb7167
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      Stable perovskite solar cells with efficiency exceeding 24.8% and 0.3-V voltage loss
      Jeong, Mingyu; Choi, In Woo; Go, Eun Min; Cho, Yongjoon; Kim, Minjin; Lee, Byongkyu; Jeong, Seonghun; Jo, Yimhyun; Choi, Hye Won; Lee, Jiyun; Bae, Jin-Hyuk; Kwak, Sang Kyu; Kim, Dong Suk; Yang, Changduk
      Science (Washington, DC, United States) (2020), 369 (6511), 1615-1620CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)
      Further improvement and stabilization of perovskite solar cell (PSC) performance are essential to achieve the com. viability of next-generation photovoltaics. Considering the benefits of fluorination to conjugated materials for energy levels, hydrophobicity, and noncovalent interactions, two fluorinated isomeric analogs of the well-known hole-transporting material (HTM) Spiro-OMeTAD are developed and used as HTMs in PSCs. The structure-property relationship induced by constitutional isomerism is investigated through exptl., atomistic, and theor. analyses, and the fabricated PSCs feature high efficiency ≤ 24.82% (certified at 24.64% with 0.3-V voltage loss), along with long-term stability in wet conditions without encapsulation (87% efficiency retention after 500 h). An efficiency of 22.31% is achieved in the large-area cell.
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    23. 23
      Kim, M.; Kim, G.-H.; Lee, T. K.; Choi, I. W.; Choi, H. W.; Jo, Y.; Yoon, Y. J.; Kim, J. W.; Lee, J.; Huh, D. Methylammonium Chloride Induces Intermediate Phase Stabilization for Efficient Perovskite Solar Cells. Joule 2019, 3, 2179– 2192,  DOI: 10.1016/j.joule.2019.06.014
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      23
      Methylammonium Chloride Induces Intermediate Phase Stabilization for Efficient Perovskite Solar Cells
      Kim, Minjin; Kim, Gi-Hwan; Lee, Tae Kyung; Choi, In Woo; Choi, Hye Won; Jo, Yimhyun; Yoon, Yung Jin; Kim, Jae Won; Lee, Jiyun; Huh, Daihong; Lee, Heon; Kwak, Sang Kyu; Kim, Jin Young; Kim, Dong Suk
      Joule (2019), 3 (9), 2179-2192CODEN: JOULBR; ISSN:2542-4351. (Cell Press)
      One of the most effective methods to achieve high-performance perovskite solar cells has been to include additives that serve as dopants, crystn. agents, or passivate defect sites. Cl-based additives are among the most prevalent in literature, yet their exact role is still uncertain. In this work, we systematically study the function of methylammonium chloride (MACl) additive in formamidinium lead iodide (FAPbI3)-based perovskite. Using d. functional theory, we provide a theor. framework for understanding the interaction of MACl with a perovskite. We show that MACl successfully induces an intermediate to the pure FAPbI3 α-phase without annealing. The formation energy is related to the amt. of incorporated MACl. By tuning the incorporation of MACl, the perovskite film quality can be significantly improved, exhibiting a 6× increase in grain size, a 3× increase in phase crystallinity, and a 4.3× increase in photoluminescence lifetime. The optimized solar cells achieved a certified efficiency of 23.48%.
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    24. 24
      Weller, M. T.; Weber, O. J.; Frost, J. M.; Walsh, A. Cubic Perovskite Structure of Black Formamidinium Lead Iodide, α-[HC(NH2)2]PbI3, at 298 K. J. Phys. Chem. Lett. 2015, 6, 3209– 3212,  DOI: 10.1021/acs.jpclett.5b01432
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      24
      Cubic Perovskite Structure of Black Formamidinium Lead Iodide, α-[HC(NH2)2]PbI3, at 298 K
      Weller, Mark T.; Weber, Oliver J.; Frost, Jarvist M.; Walsh, Aron
      Journal of Physical Chemistry Letters (2015), 6 (16), 3209-3212CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      The structure of black formamidinium lead halide, α-[HC(NH2)2]PbI3, at 298 K was refined from high resoln. neutron powder diffraction data and found to adopt a cubic perovskite unit cell, a 6.3620(8) Å. The trigonal planar [HC(NH2)2]+ cations lie in the central mirror plane of the unit cell with the formamidinium cations disordered over 12 possible sites arranged so that the C-H bond is directed into a cube face, whereas the -NH2 groups H bond (NH···I = 2.75-3.00 Å) with the iodide atoms of the [PbI3]- framework. High at. displacement parameters for the formamidinium cation are consistent with rapid mol. rotations at room temp. as evidenced in ab initio mol. dynamic simulations. Crystallog. data and at. coordinates are given.
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    25. 25
      Weber, O. J.; Charles, B.; Weller, M. T. Phase Behaviour and Composition in the Formamidinium-Methylammonium Hybrid Lead Iodide Perovskite Solid Solution. J. Mater. Chem. A 2016, 4, 15375– 15382,  DOI: 10.1039/C6TA06607K
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      25
      Phase behaviour and composition in the formamidinium-methylammonium hybrid lead iodide perovskite solid solution
      Weber, O. J.; Charles, B.; Weller, M. T.
      Journal of Materials Chemistry A: Materials for Energy and Sustainability (2016), 4 (40), 15375-15382CODEN: JMCAET; ISSN:2050-7496. (Royal Society of Chemistry)
      The phase behavior of mixed A-site cation methylammonium (MA)/formamidinium (FA) lead iodide hybrid perovskites FAxMA1-xPbI3 was investigated using powder and variable temp. single crystal x-ray diffraction, with A site compn. detd. by 1H soln. NMR. At room temp., the crystal class is cubic across the compn. range 0.2 ≤ x ≤ 1 but a tetragonal phase is obsd. for x = 0 (MAPbI3) and x = 0.1. Cooling cubic FAxMA1-xPbI3, 0.2 ≤ x ≤ 1, phases below room temp. results in a phase change to a larger unit cell with tilted [PbI6] octahedra and the temp. at which this occurs, TC→T, decreases sharply until x = 0.2 (TC→T = 257 K) before steadily increasing to TC→T = 283 K for FA0.9MA0.1PbI3. The lattice parameters and optical band gap of cubic FAxMA1-xPbI3, 0.2 ≤ x ≤ 1 at 298 K were shown to vary in accordance with Vegard's law, though a larger band gap is obsd. for the tetragonal phases, 0.0 ≤ x ≤ 0.1.
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    26. 26
      Kubicki, D. J.; Prochowicz, D.; Hofstetter, A.; Péchy, P.; Zakeeruddin, S. M.; Grätzel, M.; Emsley, L. Cation Dynamics in Mixed-Cation (MA)x(FA)1-xPbI3 Hybrid Perovskites from Solid-State NMR. J. Am. Chem. Soc. 2017, 139, 10055– 10061,  DOI: 10.1021/jacs.7b04930
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      26
      Cation Dynamics in Mixed-Cation (MA)x(FA)1-xPbI3 Hybrid Perovskites from Solid-State NMR
      Kubicki, Dominik J.; Prochowicz, Daniel; Hofstetter, Albert; Pechy, Peter; Zakeeruddin, Shaik M.; Gratzel, Michael; Emsley, Lyndon
      Journal of the American Chemical Society (2017), 139 (29), 10055-10061CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Mixed-cation org. lead halide perovskites attract unfaltering attention owing to their excellent photovoltaic properties. Currently, the best performing perovskite materials contain multiple cations and provide power conversion efficiencies up to around 22%. Here, the authors report the 1st quant., cation-specific data on cation reorientation dynamics in hybrid mixed-cation formamidinium (FA)/methylammonium (MA) lead halide perovskites. The authors use 14N, 2H, 13C, and 1H solid-state MAS-NMR to elucidate cation reorientation dynamics, microscopic phase compn., and the MA/FA ratio, in (MA)x(FA)1-xPbI3 between 100 and 330 K. The reorientation rates correlate in a striking manner with the carrier lifetimes previously reported for these materials and provide evidence of the polaron nature of charge carriers in PV perovskites.
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    27. 27
      Pellet, N.; Gao, P.; Gregori, G.; Yang, T.-Y.; Nazeeruddin, M. K.; Maier, J.; Grätzel, M. Mixed-Organic-Cation Perovskite Photovoltaics for Enhanced Solar-Light Harvesting. Angew. Chem., Int. Ed. 2014, 53, 3151– 3157,  DOI: 10.1002/anie.201309361
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      27
      Mixed-Organic-Cation Perovskite Photovoltaics for Enhanced Solar-Light Harvesting
      Pellet, Norman; Gao, Peng; Gregori, Giuliano; Yang, Tae-Youl; Nazeeruddin, Mohammad K.; Maier, Joachim; Graetzel, Michael
      Angewandte Chemie, International Edition (2014), 53 (12), 3151-3157CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Hybrid org.-inorg. lead halide perovskite APbX3 pigments, such as methylammonium lead iodide, have recently emerged as excellent light harvesters in solid-state mesoscopic solar cells. An important target for the further improvement of the performance of perovskite-based photovoltaics is to extend their optical-absorption onset further into the red to enhance solar-light harvesting. Herein, this goal can be reached by using a mixt. of formamidinium (HN = CHNH3+, FA) and methylammonium (MeNH3+, MA) cations in the A position of the APbI3 perovskite structure. This combination leads to an enhanced short-circuit current and thus superior devices to those based on only MeNH3+. This concept was not applied previously in perovskite-based solar cells. It shows great potential as a versatile tool to tune the structural, elec., and optoelectronic properties of the light-harvesting materials.
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    28. 28
      Yi, C.; Luo, J.; Meloni, S.; Boziki, A.; Ashari-Astani, N.; Grätzel, C.; Zakeeruddin, S. M.; Röthlisberger, U.; Grätzel, M. Entropic Stabilization of Mixed A-Cation ABX3 Metal Halide Perovskites for High Performance Perovskite Solar Cells. Energy Environ. Sci. 2016, 9, 656– 662,  DOI: 10.1039/C5EE03255E
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      Entropic stabilization of mixed A-cation ABX3 metal halide perovskites for high performance perovskite solar cells
      Yi, Chenyi; Luo, Jingshan; Meloni, Simone; Boziki, Ariadni; Ashari-Astani, Negar; Gratzel, Carole; Zakeeruddin, Shaik M.; Rothlisberger, Ursula; Gratzel, Michael
      Energy & Environmental Science (2016), 9 (2), 656-662CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      ABX3-type org. lead halide perovskites currently attract broad attention as light harvesters for solar cells due to their high power conversion efficiency (PCE). Mixts. of formamidinium (FA) with methylammonium (MA) as A-cations show currently the best performance. Apart from offering better solar light harvesting in the near IR the addn. of methylammonium stabilizes the perovskite phase of FAPbI3 which in pure form at room temp. converts to the yellow photovoltaically inactive δ-phase. We observe a similar phenomenon upon adding Cs+ cations to FAPbI3. CsPbI3 and FAPbI3 both form the undesirable yellow phase under ambient condition while the mixt. forms the desired black pervoskite. Solar cells employing the compn. Cs0.2FA0.8PbI2.84Br0.16 yield high av. PCEs of over 17% exhibiting negligible hysteresis and excellent long term stability in ambient air. We elucidate here this remarkable behavior using first principle computations. These show that the remarkable stabilization of the perovskite phase by mixing the A-cations stems from entropic gains and the small internal energy input required for the formation of their solid soln. By contrast, the energy of formation of the delta-phase contg. mixed cations is too large to be compensated by this configurational entropy increase. Our calcns. reveal for the first time the optoelectronic properties of such mixed A-cation perovskites and the underlying reasons for their excellent performance and high stability.
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      Goldschmidt, V. M. Die Gesetze Der Krystallochemie. Naturwissenschaften 1926, 14, 477– 485,  DOI: 10.1007/BF01507527
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      Laws of crystal chemistry
      Goldschmidt, V. M.
      Naturwissenschaften (1926), 14 (), 477-85CODEN: NATWAY; ISSN:0028-1042.
      Several laws are cited which govern the relationships between chem. compn. and cryst. form. The crystal structure of a substance is detd. by the size (Bragg's radius) and the polarizability of its components (atoms or atom groups). The at. radius depends on at. no. and "condition" (particularly degree of ionization) of the atom. The polarizability, a function of radius and charge of the atom or ion, increases with increasing radius, decreases with increasing positive charge (cf. Born and Heisenberg). High symmetry of the neighboring atoms tends to diminish it; the polarizing effect of the neighboring atoms depends again on their charge and radius. The distance of 2 polarizable structural units is generally less than the normal distance. The term contrapolarization is used for the dilating influence of strongly polarizing atoms (like Li+ or Zr++++) on such closed groups as ClO4-, CO3--, etc. This influence may even cause these groups to break up entirely. A rule is given for the occurrence of isomorphic crystals: the relative sizes and polarizabilities of the 2 substances must correspond, in order for the chem. formula to be analogous. Isomorphic mixts. will be possible if the radii of the corresponding atoms differ by less than about 15%. For antisomorphic crystals (positive and negative charges reversed) no mixts. are possible. Polymer-isomorphic mixts. occur when a multiple of the crystal unit of one substance is analogous to the unit of the other. If, as a result of thermodynamic influences, a substance ceases to be its own isomorph at different temps. (the polarizability is also a temp. function) polymorphism will appear; the substance undergoes a morphotropic change. Contrapolarization particularly is easily influenced by temp.; it causes such polymorphism as NH4NO3 in its different forms exhibits. At high temps. that cryst. form will be the most stable, which is obtained on substitution of the contrapolarizing cation by a lower homolog. Numerous examples are given.
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    30. 30
      Zhao, J.; Deng, Y.; Wei, H.; Zheng, X.; Yu, Z.; Shao, Y.; Shield, J. E.; Huang, J. Strained Hybrid Perovskite Thin Films and Their Impact on the Intrinsic Stability of Perovskite Solar Cells. Sci. Adv. 2017, 3, eaao5616  DOI: 10.1126/sciadv.aao5616
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      Zhu, C.; Niu, X.; Fu, Y.; Li, N.; Hu, C.; Chen, Y.; He, X.; Na, G.; Liu, P.; Zai, H. Strain Engineering in Perovskite Solar Cells and Its Impacts on Carrier Dynamics. Nat. Commun. 2019, 10, 815,  DOI: 10.1038/s41467-019-08507-4
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      Strain engineering in perovskite solar cells and its impacts on carrier dynamics
      Zhu, Cheng; Niu, Xiuxiu; Fu, Yuhao; Li, Nengxu; Hu, Chen; Chen, Yihua; He, Xin; Na, Guangren; Liu, Pengfei; Zai, Huachao; Ge, Yang; Lu, Yue; Ke, Xiaoxing; Bai, Yang; Yang, Shihe; Chen, Pengwan; Li, Yujing; Sui, Manling; Zhang, Lijun; Zhou, Huanping; Chen, Qi
      Nature Communications (2019), 10 (1), 815CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
      The mixed halide perovskites have emerged as outstanding light absorbers for efficient solar cells. Unfortunately, it reveals inhomogeneity in these polycryst. films due to compn. sepn., which leads to local lattice mismatches and emergent residual strains consequently. Thus far, the understanding of these residual strains and their effects on photovoltaic device performance is absent. Herein we study the evolution of residual strain over the films by depth-dependent grazing incident X-ray diffraction measurements. We identify the gradient distribution of in-plane strain component perpendicular to the substrate. Moreover, we reveal its impacts on the carrier dynamics over corresponding solar cells, which is stemmed from the strain induced energy bands bending of the perovskite absorber as indicated by first-principles calcns. Eventually, we modulate the status of residual strains in a controllable manner, which leads to enhanced PCEs up to 20.7% (certified) in devices via rational strain engineering.
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    32. 32
      Motta, C.; El-Mellouhi, F.; Kais, S.; Tabet, N.; Alharbi, F.; Sanvito, S. Revealing the Role of Organic Cations in Hybrid Halide Perovskite CH3NH3PbI3. Nat. Commun. 2015, 6, 7026,  DOI: 10.1038/ncomms8026
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      Revealing the role of organic cations in hybrid halide perovskite CH3NH3PbI3
      Motta, Carlo; El-Mellouhi, Fedwa; Kais, Sabre; Tabet, Nouar; Alharbi, Fahhad; Sanvito, Stefano
      Nature Communications (2015), 6 (), 7026CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      The hybrid halide perovskite CH3NH3PbI3 has enabled solar cells to reach an efficiency of about 20%, demonstrating a pace for improvements with no precedents in the solar energy arena. Despite such explosive progress, the microscopic origin behind the success of such material is still debated, with the role played by the org. cations in the light-harvesting process remaining unclear. Here van der Waals-cor. d. functional theory calcns. reveal that the orientation of the org. mols. plays a fundamental role in detg. the material electronic properties. For instance, if CH3NH3 orients along a (011)-like direction, the PbI6 octahedral cage will distort and the bandgap will become indirect. Our results suggest that mol. rotations, with the consequent dynamical change of the band structure, might be at the origin of the slow carrier recombination and the superior conversion efficiency of CH3NH3PbI3.
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    33. 33
      Gong, J.; Yang, M.; Ma, X.; Schaller, R. D.; Liu, G.; Kong, L.; Yang, Y.; Beard, M. C.; Lesslie, M.; Dai, Y. Electron-Rotor Interaction in Organic-Inorganic Lead Iodide Perovskites Discovered by Isotope Effects. J. Phys. Chem. Lett. 2016, 7, 2879– 2887,  DOI: 10.1021/acs.jpclett.6b01199
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      Electron-Rotor Interaction in Organic-Inorganic Lead Iodide Perovskites Discovered by Isotope Effects
      Gong, Jue; Yang, Mengjin; Ma, Xiangchao; Schaller, Richard D.; Liu, Gang; Kong, Lingping; Yang, Ye; Beard, Matthew C.; Lesslie, Michael; Dai, Ying; Huang, Baibiao; Zhu, Kai; Xu, Tao
      Journal of Physical Chemistry Letters (2016), 7 (15), 2879-2887CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      The authors report on the carrier-rotor coupling effect in perovskite org.-inorg. hybrid lead iodide (CH3NH3PbI3) compds. discovered by isotope effects. Deuterated org.-inorg. perovskite compds. including CH3ND3PbI3, CD3NH3PbI3, and CD3ND3PbI3 were synthesized. Devices made from regular CH3NH3PbI3 and deuterated CH3ND3PbI3 exhibit comparable performance in band gap, current-voltage, carrier mobility, and power conversion efficiency. However, a time-resolved photoluminescence (TRPL) study reveals that CH3NH3PbI3 exhibits notably longer carrier lifetime than that of CH3ND3PbI3, in both thin-film and single-crystal formats. Also, the comparison in carrier lifetime between CD3NH3PbI3 and CH3ND3PbI3 single crystals suggests that vibrational modes in methylammonium (MA+) have little impact on carrier lifetime. In contrast, the fully deuterated compd. CD3ND3PbI3 reconfirmed the trend of decreasing carrier lifetime upon the increasing moment of inertia of cationic MA+. Polaron model elucidates the electron-rotor interaction.
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    34. 34
      Jesper Jacobsson, T.; Correa-Baena, J.-P. P.; Pazoki, M.; Saliba, M.; Schenk, K.; Grätzel, M.; Hagfeldt, A. Exploration of the Compositional Space for Mixed Lead Halogen Perovskites for High Efficiency Solar Cells. Energy Environ. Sci. 2016, 9, 1706– 1724,  DOI: 10.1039/C6EE00030D
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      Exploration of the compositional space for mixed lead halogen perovskites for high efficiency solar cells
      Jesper Jacobsson, T.; Correa-Baena, Juan-Pablo; Pazoki, Meysam; Saliba, Michael; Schenk, Kurt; Gratzel, Michael; Hagfeldt, Anders
      Energy & Environmental Science (2016), 9 (5), 1706-1724CODEN: EESNBY; ISSN:1754-5706. (Royal Society of Chemistry)
      Lead halide perovskites have attracted considerable interest as photoabsorbers in PV-applications over the last few years. The most studied perovskite material achieving high photovoltaic performance has been Me ammonium lead iodide, CH3NH3PbI3. Recently the highest solar cell efficiencies have, however, been achieved with mixed perovskites where iodide and Me ammonium partially have been replaced by bromide and formamidinium. In this work, the mixed perovskites were explored in a systematic way by manufg. devices where both iodide and Me ammonium were gradually replaced by bromide and formamidinium. The absorption and the emission behavior as well as the crystallog. properties were explored for the perovskites in this compositional space. The band gaps as well as the crystallog. structures were extd. Small changes in the compn. of the perovskite were found to have a large impact on the properties of the materials and the device performance. In the investigated compositional space, cell efficiencies, for example, vary from a few percent up to 20.7%. From the perspective of applications, exchanging iodide with bromide is esp. interesting as it allows tuning of the band gap from 1.5 to 2.3 eV. This is highly beneficial for tandem applications, and an empirical expression for the band gap as a function of compn. was detd. Exchanging a small amt. of iodide with bromide is found to be highly beneficial, whereas a larger amt. of bromide in the perovskite was found to cause intense sub band gap photoemission with detrimental results for the device performance. This could be caused by the formation of a small amt. of an iodide rich phase with a lower band gap, even though such a phase was not obsd. in diffraction expts. This shows that stabilizing the mixed perovskites will be an important task in order to get the bromide rich perovskites, which has a higher band gap, to reach the same high performance obtained with the best compns.
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    35. 35
      Zheng, X.; Wu, C.; Jha, S. K.; Li, Z.; Zhu, K.; Priya, S. Improved Phase Stability of Formamidinium Lead Triiodide Perovskite by Strain Relaxation. ACS Energy Lett. 2016, 1, 1014– 1020,  DOI: 10.1021/acsenergylett.6b00457
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      Improved Phase Stability of Formamidinium Lead Triiodide Perovskite by Strain Relaxation
      Zheng, Xiaojia; Wu, Congcong; Jha, Shikhar K.; Li, Zhen; Zhu, Kai; Priya, Shashank
      ACS Energy Letters (2016), 1 (5), 1014-1020CODEN: AELCCP; ISSN:2380-8195. (American Chemical Society)
      Though formamidinium lead triiodide (FAPbI3) possesses a suitable band gap and good thermal stability, the phase transition from the pure black perovskite phase (α-phase) to the undesirable yellow nonperovskite polymorph (δ-phase) at room temp., esp. under humid air, hinders its practical application. Here, we investigate the intrinsic instability mechanism of the α-phase at ambient temp. and demonstrate the existence of an anisotropic strained lattice in the (111) plane that drives phase transformation into the δ-phase. Methylammonium bromide (MABr) alloying (or FAPbI3-MABr) was found to cause lattice contraction, thereby balancing the lattice strain. This led to dramatic improvement in the stability of α-FAPbI3. Solar cells fabricated using FAPbI3-MABr demonstrated significantly enhanced stability under the humid air.
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    36. 36
      Xie, L. Q.; Chen, L.; Nan, Z. A.; Lin, H. X.; Wang, T.; Zhan, D. P.; Yan, J. W.; Mao, B. W.; Tian, Z. Q. Understanding the Cubic Phase Stabilization and Crystallization Kinetics in Mixed Cations and Halides Perovskite Single Crystals. J. Am. Chem. Soc. 2017, 139, 3320– 3323,  DOI: 10.1021/jacs.6b12432
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      36
      Understanding the Cubic Phase Stabilization and Crystallization Kinetics in Mixed Cations and Halides Perovskite Single Crystals
      Xie, Li-Qiang; Chen, Liang; Nan, Zi-Ang; Lin, Hai-Xin; Wang, Tan; Zhan, Dong-Ping; Yan, Jia-Wei; Mao, Bing-Wei; Tian, Zhong-Qun
      Journal of the American Chemical Society (2017), 139 (9), 3320-3323CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      The spontaneous α-to-δ phase transition of the formamidinium-based (FA) Pb halide perovskite hinders its large scale application in solar cells. Though this phase transition can be inhibited by alloying with methylammonium-based (MA) perovskite, the underlying mechanism is largely unexplored. We grow high-quality mixed cations and halides perovskite single crystals (FAPbI3)1-x(MAPbBr3)x to understand the principles for maintaining pure perovskite phase, which is essential to device optimization. We demonstrate that the best compn. for a perfect α-phase perovskite without segregation is x =0.1-0.15, and such a mixed perovskite exhibits carrier lifetime as long as 11.0 μs, which is over 20 times of that of FAPbI3 single crystal. Powder XRD, single crystal XRD and FT-IR results reveal that the incorporation of MA+ is crit. for tuning the effective Goldschmidt tolerance factor toward the ideal value of 1 and lowering the Gibbs free energy via unit cell contraction and cation disorder. We find that Br incorporation can effectively control the perovskite crystn. kinetics and reduce defect d. to acquire high-quality single crystals with significant inhibition of δ-phase. These findings benefit the understanding of α-phase stabilization behavior, and have led to fabrication of perovskite solar cells with highest efficiency of 19.9% via solvent management.
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    37. 37
      Tennyson, E. M.; Doherty, T. A. S.; Stranks, S. D. Heterogeneity at Multiple Length Scales in Halide Perovskite Semiconductors. Nat. Rev. Mater. 2019, 4, 573– 587,  DOI: 10.1038/s41578-019-0125-0
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      37
      Heterogeneity at multiple length scales in halide perovskite semiconductors
      Tennyson, Elizabeth M.; Doherty, Tiarnan A. S.; Stranks, Samuel D.
      Nature Reviews Materials (2019), 4 (9), 573-587CODEN: NRMADL; ISSN:2058-8437. (Nature Research)
      A review. Materials with highly cryst. lattice structures and low defect concns. have classically been considered essential for high-performance optoelectronic devices. However, the emergence of high-efficiency devices based on halide perovskites is provoking researchers to rethink this traditional picture, as the heterogeneity in several properties within these materials occurs on a series of length scales. Perovskites are typically fabricated crudely through simple processing techniques, which leads to large local fluctuations in defect d., lattice structure, chem. and bandgap that appear on short length scales (<100 nm) and across long ranges (>10μm). Despite these variable and complex non-uniformities, perovskites maintain exceptional device efficiencies and are, as of 2018, the best-performing polycryst. thin-film solar cell material. In this Review, we highlight the multiple layers of heterogeneity ascertained using high-spatial-resoln. methods that provide access to the relevant length scales. We discuss the impact that the optoelectronic variations have on halide perovskite devices, including the prospect that it is this very disorder that leads to their remarkable power-conversion efficiencies.
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    38. 38
      Alanazi, A. Q.; Kubicki, D. J.; Prochowicz, D.; Alharbi, E. A.; Bouduban, M. E. F.; Jahanbakhshi, F.; Mladenović, M.; Milić, J. V.; Giordano, F.; Ren, D. Atomic-Level Microstructure of Efficient Formamidinium-Based Perovskite Solar Cells Stabilized by 5-Ammonium Valeric Acid Iodide Revealed by Multinuclear and Two-Dimensional Solid-State NMR. J. Am. Chem. Soc. 2019, 141, 17659– 17669,  DOI: 10.1021/jacs.9b07381
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      Atomic-Level Microstructure of Efficient Formamidinium-Based Perovskite Solar Cells Stabilized by 5-Ammonium Valeric Acid Iodide Revealed by Multinuclear and Two-Dimensional Solid-State NMR
      Alanazi, Anwar Q.; Kubicki, Dominik J.; Prochowicz, Daniel; Alharbi, Essa A.; Bouduban, Marine E. F.; Jahanbakhshi, Farzaneh; Mladenovic, Marko; Milic, Jovana V.; Giordano, Fabrizio; Ren, Dan; Alyamani, Ahmed Y.; Albrithen, Hamad; Albadri, Abdulrahman; Alotaibi, Mohammad Hayal; Moser, Jacques-E.; Zakeeruddin, Shaik M.; Rothlisberger, Ursula; Emsley, Lyndon; Gratzel, Michael
      Journal of the American Chemical Society (2019), 141 (44), 17659-17669CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Chem. doping of inorg.-org. hybrid perovskites is an effective way of improving the performance and operational stability of perovskite solar cells (PSCs). Here, we use 5-ammonium valeric acid (AVAI) to chem. stabilize the structure of α-FAPbI3. Using solid-state MAS NMR, we demonstrate the at.-level interaction between the mol. modulator and the perovskite lattice and propose a structural model of the stabilized 3-dimensional structure, further aided by d. functional theory (DFT) calcns. We find that 1-step deposition of the perovskite in the presence of AVAI produces highly cryst. films with large, micrometer-sized grains and enhanced charge-carrier lifetimes, as probed by transient absorption spectroscopy. As a result, we achieve greatly enhanced solar cell performance for the optimized AVA-based devices with a maxi-mum power conversion efficiency (PCE) of 18.94%. The devices retain 90% of the initial efficiency after 300 h under continuous white light illumination and max.-power point-tracking measurement.
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    39. 39
      Kubicki, D. J.; Prochowicz, D.; Hofstetter, A.; Saski, M.; Yadav, P.; Bi, D.; Pellet, N.; Lewiński, J.; Zakeeruddin, S. M.; Grätzel, M. Formation of Stable Mixed Guanidinium-Methylammonium Phases with Exceptionally Long Carrier Lifetimes for High-Efficiency Lead Iodide-Based Perovskite Photovoltaics. J. Am. Chem. Soc. 2018, 140, 3345– 3351,  DOI: 10.1021/jacs.7b12860
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      Formation of Stable Mixed Guanidinium-Methylammonium Phases with Exceptionally Long Carrier Lifetimes for High-Efficiency Lead Iodide-Based Perovskite Photovoltaics
      Kubicki, Dominik J.; Prochowicz, Daniel; Hofstetter, Albert; Saski, Marcin; Yadav, Pankaj; Bi, Dongqin; Pellet, Norman; Lewinski, Janusz; Zakeeruddin, Shaik M.; Gratzel, Michael; Emsley, Lyndon
      Journal of the American Chemical Society (2018), 140 (9), 3345-3351CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Methylammonium (MA)- and formamidinium (FA)-based org.-inorg. lead halide perovskites provide outstanding performance as photovoltaic materials, due to their versatility of fabrication and their power conversion efficiencies reaching over 22%. The proposition of guanidinium (GUA)-doped perovskite materials generated considerable interest due to their potential to increase carrier lifetimes and open-circuit voltages as compared to pure MAPbI3. However, simple size considerations based on the Goldschmidt tolerance factor suggest that guanidinium is too big to completely replace methylammonium as an A cation in the APbI3 perovskite lattice, and its effect was thus ascribed to passivation of surface trap states at grain boundaries. As guanidinium was not thought to incorporate into the MAPbI3 lattice, interest waned since it appeared unlikely that it could be used to modify the intrinsic perovskite properties. Here, using solid-state NMR, we provide for the first time at.-level evidence that GUA is directly incorporated into the MAPbI3 and FAPbI3 lattices, forming pure GUAxMA1-xPbI3 or GUAxFA1-xPbI3 phases, and that it reorients on the picosecond time scale within the perovskite lattice, which explains its superior charge carrier stabilization capacity. Our findings establish a fundamental link between charge carrier lifetimes obsd. in photovoltaic perovskites and the A cation structure in ABX3-type metal halide perovskites.
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    40. 40
      Kubicki, D. J.; Prochowicz, D.; Hofstetter, A.; Zakeeruddin, S. M.; Gratzel, M.; Emsley, L. Phase Segregation in Cs-, Rb- and K-Doped Mixed-Cation (MA)x(FA)1-xPbI3 Hybrid Perovskites from Solid-State NMR. J. Am. Chem. Soc. 2017, 139, 14173– 14180,  DOI: 10.1021/jacs.7b07223
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      40
      Phase Segregation in Cs-, Rb- and K-Doped Mixed-Cation (MA)x(FA)1-xPbI3 Hybrid Perovskites from Solid-State NMR
      Kubicki, Dominik J.; Prochowicz, Daniel; Hofstetter, Albert; Zakeeruddin, Shaik M.; Gratzel, Michael; Emsley, Lyndon
      Journal of the American Chemical Society (2017), 139 (40), 14173-14180CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Hybrid (org.-inorg.) multication lead halide perovskites hold promise for a new generation of easily processable solar cells. Best performing compns. to date are multiple-cation solid alloys of formamidinium (FA), methylammonium (MA), cesium, and rubidium lead halides which provide power conversion efficiencies up to around 22%. Here, we elucidate the at.-level nature of Cs and Rb incorporation into the perovskite lattice of FA-based materials. We use 133Cs, 87Rb, 39K, 13C, and 14N solid-state MAS NMR to probe microscopic compn. of Cs-, Rb-, K-, MA-, and FA-contg. phases in double-, triple-, and quadruple-cation lead halides in bulk and in a thin film. Contrary to previous reports, we have found no proof of Rb or K incorporation into the 3D perovskite lattice in these systems. We also show that the structure of bulk mechanochem. perovskites bears close resemblance to that of thin films, making them a good benchmark for structural studies. These findings provide fundamental understanding of previously reported excellent photovoltaic parameters in these systems and their superior stability.
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      Ghosh, D.; Smith, A. R.; Walker, A. B.; Islam, M. S. Mixed A-Cation Perovskites for Solar Cells: Atomic-Scale Insights into Structural Distortion, Hydrogen Bonding, and Electronic Properties. Chem. Mater. 2018, 30, 5194– 5204,  DOI: 10.1021/acs.chemmater.8b01851
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      Mixed A-Cation Perovskites for Solar Cells: Atomic-Scale Insights Into Structural Distortion, Hydrogen Bonding, and Electronic Properties
      Ghosh, Dibyajyoti; Smith, Alexander R.; Walker, Alison B.; Islam, M. Saiful
      Chemistry of Materials (2018), 30 (15), 5194-5204CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      Hybrid Pb halide perovskites contg. a mixt. of A-site cations such as the formamidinium (CH(NH2)2+, FA) and the smaller Cs+ cations have attracted considerable interest due to their improved stability and solar cell performance. However, the structural changes at the at. scale and modifications to the optoelectronic properties of these mixed cation perovskites are not fully understood. Here, we study the FA1-xCsxPbI3 (x ≤0.25) system using a combination of static and dynamic ab initio computational methods. We find that the incorporation of Cs+ cations into the parent FAPbI3 structure induces a chem. pressure or lattice strain effect through Cs/FA ion size mismatch resulting in structural distortion and stronger FA-iodide (N-H···I) hydrogen bonding interactions. The dynamic tilting of PbI6 octahedra and the rotational motion of FA cations are also suppressed, which leads to symmetry-breaking of the lattice. Such symmetry-breaking distortions of the Pb/I lattice give rise to a Rashba-type effect, which spin-splits the frontier electronic bands making the band gap indirect. Our results suggest that the direct-indirect band gap transition may be a factor in the reduced charge-carrier recombination rate in these mixed cation perovskites.
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    42. 42
      Van Gompel, W. T. M.; Herckens, R.; Reekmans, G.; Ruttens, B.; D’Haen, J.; Adriaensens, P.; Lutsen, L.; Vanderzande, D. Degradation of the Formamidinium Cation and the Quantification of the Formamidinium-Methylammonium Ratio in Lead Iodide Hybrid Perovskites by Nuclear Magnetic Resonance Spectroscopy. J. Phys. Chem. C 2018, 122, 4117– 4124,  DOI: 10.1021/acs.jpcc.7b09805
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      42
      Degradation of the Formamidinium Cation and the Quantification of the Formamidinium-Methylammonium Ratio in Lead Iodide Hybrid Perovskites by Nuclear Magnetic Resonance Spectroscopy
      Van Gompel, Wouter T. M.; Herckens, Roald; Reekmans, Gunter; Ruttens, Bart; DHaen, Jan; Adriaensens, Peter; Lutsen, Laurence; Vanderzande, Dirk
      Journal of Physical Chemistry C (2018), 122 (8), 4117-4124CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
      The highest efficiency in perovskite solar cells is currently achieved with mixed-cation hybrid perovskites. The ratio in which the cations are present in the perovskite structure has an important effect on the optical properties and the stability of these materials. At present, the formamidinium cation is an integral part of many of the highest efficiency perovskite systems. In this work, we introduce an NMR spectroscopy protocol for the identification and differentiation of mixed perovskite phases and of a secondary phase due to formamidinium degrdn. The influence of the cooling rate used in a pptn. method on the FA/MA ratio in formamidinium-methylammonium lead iodide perovskites (FAxMA1-xPbI3) was investigated and compared to the FA/MA ratio in thin films. In order to obtain the FA/MA ratio from fast and accessible liq.-state 1H NMR spectra, the influence of the acidity of the soln. on the line width of the resonances was elucidated. The ratio of the org. cations incorporated into the perovskite structure could be reliably quantified in the presence of the secondary phase through a combination of liq.-state 1H NMR and solid-state 13C NMR spectroscopic anal.
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    43. 43
      Fisicaro, G.; La Magna, A.; Alberti, A.; Smecca, E.; Mannino, G.; Deretzis, I. Local Order and Rotational Dynamics in Mixed A-Cation Lead Iodide Perovskites. J. Phys. Chem. Lett. 2020, 11, 1068– 1074,  DOI: 10.1021/acs.jpclett.9b03763
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      Local Order and Rotational Dynamics in Mixed A-Cation Lead Iodide Perovskites
      Fisicaro, Giuseppe; La Magna, Antonino; Alberti, Alessandra; Smecca, Emanuele; Mannino, Giovanni; Deretzis, Ioannis
      Journal of Physical Chemistry Letters (2020), 11 (3), 1068-1074CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Halide perovskites contg. a mixt. of formamidinium (FA+), methylammonium (MA+) and cesium (Cs+) cations are the actual std. for obtaining record-efficiency perovskite solar cells. Although the compositional tuning that brings to optimal performance of the devices was largely established, little is understood on the role of even small quantities of MA+ or Cs+ in stabilizing the black phase of FAPbI3 while boosting its photovoltaic yield. In this paper, we use Car-Parrinello mol. dynamics in large supercells contg. different ratios of FA+ and either MA+ or Cs+, to study the structural and kinetic features of mixed perovskites at room temp. Our anal. shows that cation mixing relaxes the rotational disorder of FA+ mols. by preferentially aligning their axis toward 〈100〉 cubic directions. The phenomenon stems from the introduction of addnl. local min. in the energetic landscape, which are absent in pure FAPbI3 crystals. As a result, a higher structural order is achieved, characterized by a pronounced octahedral tilting and a lower vibrational activity for the inorg. framework. We show that both MA+ and Cs+ are qualified for this enhancement, with Cs+ being particularly effective when dild. within the FAPbI3 perovskite.
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      Franssen, W. M. J.; Kentgens, A. P. M. Solid - State NMR of Hybrid Halide Perovskites. Solid State Nucl. Magn. Reson. 2019, 100, 36– 44,  DOI: 10.1016/j.ssnmr.2019.03.005
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      Solid-state NMR of hybrid halide perovskites
      Franssen, Wouter M. J.; Kentgens, Arno P. M.
      Solid State Nuclear Magnetic Resonance (2019), 100 (), 36-44CODEN: SSNRE4; ISSN:0926-2040. (Elsevier)
      Recent advances in the development of perovskite based solar cells have increased the demand for in-depth characterization of the perovskite structures and the dynamics of their various constituents in relation to the potential impact on the photovoltaic performance. NMR can play an important role in this respect; NMR has been used to study the incorporation of different ionic species, characterize their internal dynamics and diffusion, and monitor the chem. stability of these technol. relevant materials, including upcoming lower dimensional perovskite materials. Furthermore, the flexibility of NMR allows the study of the materials under relevant conditions e.g. under illumination. Here we present an overview of the recent literature on NMR of (hybrid) halide perovskites, focusing on the insights that NMR can provide.
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      Wasylishen, R. E.; Knop, O.; Macdonald, J. B. Cation Rotation in Methylammonium Lead Halides. Solid State Commun. 1985, 56, 581– 582,  DOI: 10.1016/0038-1098(85)90959-7
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      Cation rotation in methylammonium lead halides
      Wasylishen, R. E.; Knop, Osvald; Macdonald, J. B.
      Solid State Communications (1985), 56 (7), 581-2CODEN: SSCOA4; ISSN:0038-1098.
      2H and 14N NMR spectra of the simple perovskites MeNH3PbX3 (X = Cl, Br, I) reveal the existence of several phases. In the high-temp. phase I the long spin-lattice relaxation times T1 of both nuclei and the absence of quadrupole splitting indicate extremely rapid overall reorientation of the C-N axis of the cation in a potential of cubic symmetry. In phase II of the bromide and iodide, both T1 and the small quadrupole splitting show unusual variation with temp. In the lowest-temp. phase, rotations of the C-N axis are restricted.
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      Knop, O.; Wasylishen, R. E.; White, M. A.; Cameron, T. S.; Van Oort, M. J. M. Alkylammonium Lead Halides. Part 2. CH3NH3PbX3 (X = Cl, Br, I) Perovskites: Cuboctahedral Halide Cages with Isotropic Cation Reorientation. Can. J. Chem. 1990, 68, 412– 422,  DOI: 10.1139/v90-063
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      Alkylammonium lead halides. Part 2. CH3NH3PbX3 (X = chlorine, bromine, iodine) perovskites: cuboctahedral halide cages with isotropic cation reorientation
      Knop, Osvald; Wasylishen, Roderick E.; White, Mary Anne; Cameron, T. Stanley; Van Oort, Michiel J. M.
      Canadian Journal of Chemistry (1990), 68 (3), 412-22CODEN: CJCHAG; ISSN:0008-4042.
      MeNH3PbCl3 (I), MeNH3PbBr3 (II), and MeNH3PbI3 (III) were investigated by single-crystal x-ray diffraction, 2H and 14N NMR, adiabatic calorimetry, and other methods. I has transitions at 171.5 and 177.4 K, II at 148.4, 154.2, and 235.1 K, and III at 162.7 and 326.6 K. The resp. entropies of transition (J K-1 mol-1) are 11.0 and 5.1 for I; 8.7, 3.4, and 5.3 for II; and 16.1 and 1.9 for III. The highest-temp. phase, phase I, of each halide is cubic (Pm3m) perovskite type. The cation in phase I of I and II could not be localized in the electron d. maps; the thermal motion of the halogen atom is highly anisotropic. The ln T1(2H) vs. T-1 plots (N-deuterated samples as well as CD3NH3PbCl3) show significant departures from linearity: the temp. variation of T1(2H) in phase II of II and III can be represented by functions of the type ln T1(H) = k0 - k2T-2, which give adequate anal. representations of T1(2H) and T1(14N) in phase I as well. On cooling, phase II of II and III exhibit small quadrupole splittings QS(2H), which can be represented to a high degree of correlation by QS(2H) = k(Ttr - T)n, i.e. they appear to exhibit crit. behavior with respect to T. The 14N NMR results indicate that the C-N bond in phase I reorients in an isotropic potential at a rate approaching that of the freely rotating methylammonium ion. Below phase I this motion takes place in an increasingly anisotropic potential in phase II of II and III and is essentially arrested in phase II of I and phase III of II and III. The temp. dependence of the activation energy Ea for the cation reorientation and other aspects of the non-Arrhenius behavior are discussed, and the MeNH3PbX3 perovskites are compared with the corresponding (MeNH3)2TeX6 halides, utilizing preliminary 2H NMR results on (CD3ND3)2TeBr6. The elec. cond., between 0 and 95°, of III increases with temp. and exhibits no discontinuity at Ttr = 326.6 K; the activation energy for the conduction process is estd. as ∼0.4 eV.
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      Bernard, G. M.; Wasylishen, R. E.; Ratcliffe, C. I.; Terskikh, V.; Wu, Q.; Buriak, J. M.; Hauger, T. Methylammonium Cation Dynamics in Methylammonium Lead Halide Perovskites: A Solid-State NMR Perspective. J. Phys. Chem. A 2018, 122, 1560– 1573,  DOI: 10.1021/acs.jpca.7b11558
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      Methylammonium Cation Dynamics in Methylammonium Lead Halide Perovskites: A Solid-State NMR Perspective
      Bernard, Guy M.; Wasylishen, Roderick E.; Ratcliffe, Christopher I.; Terskikh, Victor; Wu, Qichao; Buriak, Jillian M.; Hauger, Tate
      Journal of Physical Chemistry A (2018), 122 (6), 1560-1573CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
      In light of the intense recent interest in the methylammonium lead halides, CH3NH3PbX3 (X = Cl, Br, I) as sensitizers for photovoltaic cells, the dynamics of the methylammonium (MA) cation in these perovskite salts has been reinvestigated as a function of temp. via 2H, 14N, and 207Pb NMR spectroscopy. In the cubic phase of all three salts, the MA cation undergoes pseudoisotropic tumbling (picosecond time scale). For example, the correlation time, τ2, for the C-N axis of the iodide salt is 0.85 ± 0.30 ps at 330 K. The dynamics of the MA cation are essentially continuous across the cubic ↔ tetragonal phase transition; however, 2H and 14N NMR line shapes indicate that subtle ordering of the MA cation occurs in the tetragonal phase. The temp. dependence of the cation ordering is rationalized using a six-site model, with two equiv. sites along the c-axis and four equiv. sites either perpendicular or approx. perpendicular to this axis. As the cubic ↔ tetragonal phase transition temp. is approached, the six sites are nearly equally populated. Below the tetragonal ↔ orthorhombic phase transition, 2H NMR line shapes indicate that the C-N axis is essentially frozen.
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    48. 48
      Franssen, W. M. J.; Bruijnaers, B. J.; Portengen, V. H. L.; Kentgens, A. P. M. Dimethylammonium Incorporation in Lead Acetate Based MAPbI3 Perovskite Solar Cells. ChemPhysChem 2018, 19, 3107– 3115,  DOI: 10.1002/cphc.201800732
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      Dimethylammonium Incorporation in Lead Acetate Based MAPbI3 Perovskite Solar Cells
      Franssen, Wouter M. J.; Bruijnaers, Bardo J.; Portengen, Victor H. L.; Kentgens, Arno P. M.
      ChemPhysChem (2018), 19 (22), 3107-3115CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
      Over the last years, several different pathways have been suggested for producing perovskite thin films for solar cell applications. While the merit of these methods with respect to the solar cell efficiency have been shown, the actual compn. of the resulting thin films is often not investigated. Here, we show that methylammonium Pb iodide films produced using lead acetate as a lead source can have ≤15% dimethylammonium incorporated into their crystal structure, even though this ion is often consider to be too large for incorporation. The origin of this ion lies in the precursor soln., where it is formed in a reaction that is facilitated by the basic character of the acetate ions. We further show that these dimethylammonium ions are incorporated in a random fashion throughout the crystal structure, owing to the lack of observable ordered domains.
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      Franssen, W. M. J.; Van Es, S. G. D.; Dervişoǧlu, R.; de Wijs, G. A.; Kentgens, A. P. M. Symmetry, Dynamics, and Defects in Methylammonium Lead Halide Perovskites. J. Phys. Chem. Lett. 2017, 8, 61– 66,  DOI: 10.1021/acs.jpclett.6b02542
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      Symmetry, Dynamics, and Defects in Methylammonium Lead Halide Perovskites
      Franssen, Wouter M. J.; van Es, Sverre G. D.; Dervisoglu, Riza; de Wijs, Gilles A.; Kentgens, Arno P. M.
      Journal of Physical Chemistry Letters (2017), 8 (1), 61-66CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      In order to better understand the structure and dynamics of methylammonium lead halide perovskites, we performed NMR, NQR, and DFT studies of CH3NH3PbI3 in the tetragonal and cubic phase. Our results indicate that the space group of the tetragonal phase is the nonpolar I4/mcm. The highly dynamic methylammonium moiety shows no indication of the occurrence of addnl. orientations of the C-N bond close to the c-axis at temps. approaching the cubic phase. Crystal quality effects are shown to influence the 14N NMR and 127I NQR spectra, and the effects of high-temp. annealing on defects can be obsd. A strong increase in T2 relaxation time of the 207Pb NMR signal on cooling is found, and is an indication of slow motions in the PbI6 octahedra at room temp. These results aid in the understanding of the structure of methylammonium lead halides and enable further studies of defects in these materials.
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    50. 50
      Roiland, C.; Trippé-Allard, G.; Jemli, K.; Alonso, B.; Ameline, J.-C. C.; Gautier, R.; Bataille, T.; Le Pollès, L.; Deleporte, E.; Even, J. Multinuclear NMR as a Tool for Studying Local Order and Dynamics in CH3NH3PbX3 (X = Cl, Br, I) Hybrid Perovskites. Phys. Chem. Chem. Phys. 2016, 18 (39), 27133– 27142,  DOI: 10.1039/C6CP02947G
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      50
      Multinuclear NMR as a tool for studying local order and dynamics in CH3NH3PbX3 (X = Cl, Br, I) hybrid perovskites
      Roiland, Claire; Trippe-Allard, Gaelle; Jemli, Khaoula; Alonso, Bruno; Ameline, Jean-Claude; Gautier, Regis; Bataille, Thierry; Le Polles, Laurent; Deleporte, Emmanuelle; Even, Jacky; Katan, Claudine
      Physical Chemistry Chemical Physics (2016), 18 (39), 27133-27142CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The authors report on 207Pb, 79Br, 14N, 1H, 13C and 2H NMR expts. for studying the local order and dynamics in hybrid perovskite lattices. 207Pb NMR expts. conducted at room temp. on a series of MAPbX3 compds. (MA = CH3NH3+; X = I (3), Br (4) and Cl (5)) showed that the isotropic 207Pb NMR shift is strongly dependent on the nature of the halogen ions. The other prepd. complexes are CH2ND3Br (1), CH3ND3PbBr3 (2), and CH3NH3PbIBr2 (6). Therefore 207Pb NMR appears to be a very promising tool for the characterization of local order in mixed halogen hybrid perovskites. 207Pb NMR on MAPbBr2I served as a proof of concept. Proton, 13C and 14N NMR expts. confirmed the results previously reported in the literature. Low temp. deuterium NMR measurements, down to 25 K, were carried out to study the structural phase transitions of MAPbBr3. Spectral lineshapes allow following the successive phase transitions of MAPbBr3. Finally, quadrupolar NMR lineshapes recorded in the orthorhombic phase were compared with simulated spectra, using DFT calcd. elec. field gradients (EFG). Computed data do not take into account any temp. effect. Thus, the discrepancy between the calcd. and exptl. EFG evidences the fact that MA cations are still subject to significant dynamics, even at 25 K.
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      Martineau, C.; Senker, J.; Taulelle, F. NMR Crystallography. Annu. Rep. NMR Spectrosc. 2014, 82, 1– 57,  DOI: 10.1016/B978-0-12-800184-4.00001-1
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      Harris, R. K.; Wasylishen, R. E.; Duer, M. J. NMR-Crystallography; Wiley: Chichester, U.K., 2009.
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      Charpentier, T. The PAW/GIPAW Approach for Computing NMR Parameters: A New Dimension Added to NMR Study of Solids. Solid State Nucl. Magn. Reson. 2011, 40, 1– 20,  DOI: 10.1016/j.ssnmr.2011.04.006
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      The PAW/GIPAW approach for computing NMR parameters: A new dimension added to NMR study of solids
      Charpentier, Thibault
      Solid State Nuclear Magnetic Resonance (2011), 40 (1), 1-20CODEN: SSNRE4; ISSN:0926-2040. (Elsevier B.V.)
      A review. In 2001, Mauri and Pickard introduced the gauge including projected augmented wave (GIPAW) method that enabled for the first time the calcn. of all-electron NMR parameters in solids, i.e. accounting for periodic boundary conditions. The GIPAW method roots in the plane wave pseudopotential formalism of the d. functional theory (DFT), and avoids the use of the cluster approxn. This method has undoubtedly revitalized the interest in quantum chem. calcns. in the solid-state NMR community. It has quickly evolved and improved so that the calcn. of the key components of NMR interactions, namely the shielding and elec. field gradient tensors, has now become a routine for most of the common nuclei studied in NMR. Availability of reliable implementations in several software packages (CASTEP, Quantum Espresso, PARATEC) make its usage more and more increasingly popular, maybe indispensable in near future for all material NMR studies. The majority of nuclei of the periodic table have already been investigated by GIPAW, and because of its high accuracy it is quickly becoming an essential tool for interpreting and understanding exptl. NMR spectra, providing reliable assignments of the obsd. resonances to crystallog. sites or enabling a priori prediction of NMR data. The continuous increase of computing power makes ever larger (and thus more realistic) systems amenable to first-principles anal. In the near future perspectives, as the incorporation of dynamical effects and/or disorder are still at their early developments, these areas will certainly be the prime target.
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    54. 54
      Moran, R. F.; Dawson, D. M.; Ashbrook, S. E. Exploiting NMR Spectroscopy for the Study of Disorder in Solids. Int. Rev. Phys. Chem. 2017, 36, 39– 115,  DOI: 10.1080/0144235X.2017.1256604
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      Exploiting NMR spectroscopy for the study of disorder in solids
      Moran, Robert F.; Dawson, Daniel M.; Ashbrook, Sharon E.
      International Reviews in Physical Chemistry (2017), 36 (1), 39-115CODEN: IRPCDL; ISSN:0144-235X. (Taylor & Francis Ltd.)
      Although the solid state is typically characterised by inherent periodicity, many interesting phys. and chem. properties of solids arise from a variation in this, i.e. changes in the nature of the atom occupying a particular site in a crystal structure or variation in the position of an atom (or group of atoms) in different parts of a structure, or variation as a function of time. This lack of long-range order poses significant challenges, not just for the characterization of the structure of disordered materials, but also simply for its description. The sensitivity of NMR (NMR) spectroscopy to the local, at.-scale environment, without the requirement for long-range order, makes it a powerful tool for the study of disorder in the solid state. Information on the no. and type(s) of coordinating atoms or through-space and through-bond connectivity between at. species enables the construction of a detailed picture of the structure. After a brief description of the background theory of NMR spectroscopy, and the exptl. methods employed, we will describe the effects of disorder on NMR spectra and the use of calcns. to help interpret exptl. measurements. We will then review a range of applications to different types of disordered materials, including oxides and ceramics, minerals, porous materials, biomaterials, energy materials, pharmaceuticals, polymers and glasses. We will discuss the most successful approaches for studying different materials, and illustrate the type of information available and the structural insight gained.
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    55. 55
      Grüninger, H.; Schmutzler, A.; Siegel, R.; Armstrong, K.; Frost, D. J.; Senker, J. Quantitative Description of 1H SQ and DQ Coherences for the Hydroxyl Disorder within Hydrous Ringwoodite. Phys. Chem. Chem. Phys. 2018, 20, 15098– 15105,  DOI: 10.1039/C8CP00863A
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      55
      Quantitative description of 1H SQ and DQ coherences for the hydroxyl disorder within hydrous ringwoodite
      Grueninger, Helen; Schmutzler, Adrian; Siegel, Renee; Armstrong, Katherine; Frost, Daniel J.; Senker, Juergen
      Physical Chemistry Chemical Physics (2018), 20 (22), 15098-15105CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      Proton-contg. point defects in solid materials are important for a variety of properties ranging from ionic transport over thermal cond. up to compressibility. Ultrafast magic-angle spinning techniques nowadays offer high-resoln. solid-state NMR spectra, even for 1H, and thus open up possibilities to study the underlying defect chem. Nevertheless, disorder within such defects again leads to heavy spectral overlap of 1H resonances, which prevents quant. anal. of defect concns., if several defect types are present. Here, we present a strategy to overcome this limitation by simulating the 1H lineshape as well as 1H-1H double-quantum buildup curves, which we then validate against the exptl. data in a joint cost function. To mimic the local structural disorder, we use mol. dynamics simulations at the DFT level. It turned out to be advantageous for the joint refinement to put the computational effort into the structural optimization to derive accurate proton positions and to use empirical correlations for the relation between isotropic and anisotropic 1H chem. shifts and structural elements. The expressiveness of this approach is demonstrated on ringwoodite's (γ-Mg2SiO4) OH defect chem. contg. four different defect types in octahedral and tetrahedral voids with both pure Mg and mixed Si and Mg cation environments. Still, we det. the ratio for each defect type with an accuracy of about 5% as a result of the minimization of the joint cost function. We expect that our approach is generally applicable for local proton disorder and might prove to be a valuable alternative to the established AIRSS and Monte Carlo methods, resp.
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    56. 56
      Moran, R. F.; McKay, D.; Pickard, C. J.; Berry, A. J.; Griffin, J. M.; Ashbrook, S. E. Hunting for Hydrogen: Random Structure Searching and Prediction of NMR Parameters of Hydrous Wadsleyite. Phys. Chem. Chem. Phys. 2016, 18, 10173– 10181,  DOI: 10.1039/C6CP01529H
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      56
      Hunting for hydrogen: random structure searching and prediction of NMR parameters of hydrous wadsleyite
      Moran, Robert F.; McKay, David; Pickard, Chris J.; Berry, Andrew J.; Griffin, John M.; Ashbrook, Sharon E.
      Physical Chemistry Chemical Physics (2016), 18 (15), 10173-10181CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The structural chem. of materials contg. low levels of nonstoichiometric hydrogen is difficult to det., and producing structural models is challenging where hydrogen has no fixed crystallog. site. The authors demonstrated a computational approach employing ab initio random structure searching (AIRSS) to generate a series of candidate structures for hydrous wadsleyite (β-Mg2SiO4 with 1.6 wt% H2O), a high-pressure mineral proposed as a repository for water in the Earth's transition zone. Aligning with previous exptl. work, we solely consider models with Mg3 (over Mg1, Mg2 or Si) vacancies. They adapted the AIRSS method by starting with anhyd. wadsleyite, removing a single Mg2+ and randomly placing two H+ in a unit cell model, generating 819 candidate structures. 103 geometries were then subjected to more accurate optimization under periodic DFT. Using this approach, the authors found the most favorable hydration mechanism involves protonation of two O1 sites around the Mg3 vacancy. The formation of silanol groups on O3 or O4 sites (with loss of stable O1-H hydroxyls) coincides with an increase in total enthalpy. Importantly, the approach the authors employed allows observables such as NMR parameters to be computed for each structure. They consider hydrous wadsleyite (∼1.6 wt%) to be dominated by protonated O1 sites, with O3/O4-H silanol groups present as defects, a model that maps well onto exptl. studies at higher levels of hydration. The AIRSS approach adopted herein provides the crucial link between at.-scale structure and exptl. studies.
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    57. 57
      Jinnouchi, R.; Lahnsteiner, J.; Karsai, F.; Kresse, G.; Bokdam, M. Phase Transitions of Hybrid Perovskites Simulated by Machine-Learning Force Fields Trained on the Fly with Bayesian Inference. Phys. Rev. Lett. 2019, 122, 225701,  DOI: 10.1103/PhysRevLett.122.225701
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      Phase Transitions of Hybrid Perovskites Simulated by Machine-Learning Force Fields Trained on the Fly with Bayesian Inference
      Jinnouchi, Ryosuke; Lahnsteiner, Jonathan; Karsai, Ferenc; Kresse, Georg; Bokdam, Menno
      Physical Review Letters (2019), 122 (22), 225701CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      Realistic finite temp. simulations of matter are a formidable challenge for first principles methods. Long simulation times and large length scales are required, demanding years of computing time. Here we present an on-the-fly machine learning scheme that generates force fields automatically during mol. dynamics simulations. This opens up the required time and length scales, while retaining the distinctive chem. precision of first principles methods and minimizing the need for human intervention. The method is widely applicable to multielement complex systems. We demonstrate its predictive power on the entropy driven phase transitions of hybrid perovskites, which have never been accurately described in simulations. Using machine learned potentials, isothermal-isobaric simulations give direct insight into the underlying microscopic mechanisms. Finally, we relate the phase transition temps. of different perovskites to the radii of the involved species, and we det. the order of the transitions in Landau theory.
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    58. 58
      Lahnsteiner, J.; Jinnouchi, R.; Bokdam, M. Long-Range Order Imposed by Short-Range Interactions in Methylammonium Lead Iodide: Comparing Point-Dipole Models to Machine-Learning Force Fields. Phys. Rev. B: Condens. Matter Mater. Phys. 2019, 100, 094106,  DOI: 10.1103/PhysRevB.100.094106
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      Grüninger, H.; Armstrong, K.; Greim, D.; Boffa-Ballaran, T.; Frost, D. J.; Senker, J. Hidden Oceans? Unraveling the Structure of Hydrous Defects in the Earth’s Deep Interior. J. Am. Chem. Soc. 2017, 139 (30), 10499– 10505,  DOI: 10.1021/jacs.7b05432
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      Hidden Oceans? Unraveling the Structure of Hydrous Defects in the Earth's Deep Interior
      Grueninger, Helen; Armstrong, Katherine; Greim, Dominik; Boffa-Ballaran, Tiziana; Frost, Daniel J.; Senker, Juergen
      Journal of the American Chemical Society (2017), 139 (30), 10499-10505CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      High-pressure silicates making up the main proportion of the earth's interior can incorporate a significant amt. of water in the form of OH defects. Generally, they are charge balanced by removing low-valent cations such as Mg2+. By combining high-resoln. multidimensional single- and double-quantum 1H solid-state NMR spectroscopy with d. functional theory calcns., we show that, for ringwoodite (γ-Mg2SiO4), addnl., Si4+ vacancies are formed, even at a water content as low as 0.1 wt. %. They are charge balanced by either four protons or one Mg2+ and two protons. Surprisingly, also a significant proportion of coupled Mg and Si vacancies are present. Furthermore, all defect types feature a pronounced orientational disorder of the OH groups, which results in a significant range of OH···O bond distributions. As such, we are able to present unique insight into the defect chem. of ringwoodite's spinel structure, which not only accounts for a potentially large fraction of the earth's entire water budget, but will also control transport properties in the mantle. We expect that our results will even impact other hydrous spinel-type materials, helping to understand properties such as ion conduction and heterogeneous catalysis.
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      Saalwächter, K. Robust NMR Approaches for the Determination of Homonuclear Dipole-Dipole Coupling Constants in Studies of Solid Materials and Biomolecules. ChemPhysChem 2013, 14, 3000– 3014,  DOI: 10.1002/cphc.201300254
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      Robust NMR approaches for the determination of homonuclear dipole-dipole coupling constants in studies of solid materials and biomolecules
      Saalwachter Kay
      Chemphyschem : a European journal of chemical physics and physical chemistry (2013), 14 (13), 3000-14 ISSN:.
      This review addresses the NMR spectroscopy study of molecular structure and dynamics by way of homonuclear dipole-dipole couplings by relying on their orientation and direct distance dependence. The study of homonuclear couplings as opposed to heteronuclear couplings poses specific challenges. On the one hand, two like spins cannot be independently manipulated easily, which means that simple shift-refocusing concepts by using hard π pulses cannot be used to cope with potentially large chemical-shift dispersions at the high fields used today. On the other hand, the noncommutativity of the different pair Hamiltonians in a multispin system leads to complications associated with the isolation of specific pair couplings while minimizing the influence of the other spins. In particular, the so-called dipolar-truncation effect challenges the observation of weak couplings of interest in the presence of stronger ones. Recent advances in determining homonuclear dipole-dipole coupling constants are reviewed, stressing the use of double-quantum spectroscopy approaches and their similarity to the popular heteronuclear rotational-echo double-resonance experiment. Particular emphasis is put on corrections for the influence of transverse relaxation effects on the measured data, and the handling of distribution effects as well as potential dynamic heterogeneities in complex substances.
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      Brown, S. P. Probing Proton-Proton Proximities in the Solid State. Prog. Nucl. Magn. Reson. Spectrosc. 2007, 50, 199– 251,  DOI: 10.1016/j.pnmrs.2006.10.002
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      Probing proton-proton proximities in the solid state
      Brown, Steven P.
      Progress in Nuclear Magnetic Resonance Spectroscopy (2007), 50 (4), 199-251CODEN: PNMRAT; ISSN:0079-6565. (Elsevier B.V.)
      A review. A review discusses the fast MAS or homonuclear decoupling allowing structurally or dynamically informative high-resoln. 1H-1H correlation expts. to be recorded for an increasing no. and wide range of rigid-solid applications.
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    62. 62
      Leupold, N.; Schötz, K.; Cacovich, S.; Bauer, I.; Schultz, M.; Daubinger, M.; Kaiser, L.; Rebai, A.; Rousset, J.; Köhler, A. High Versatility and Stability of Mechanochemically Synthesized Halide Perovskite Powders for Optoelectronic Devices. ACS Appl. Mater. Interfaces 2019, 11, 30259– 30268,  DOI: 10.1021/acsami.9b09160
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      High Versatility and Stability of Mechanochemically Synthesized Halide Perovskite Powders for Optoelectronic Devices
      Leupold, Nico; Schoetz, Konstantin; Cacovich, Stefania; Bauer, Irene; Schultz, Maximilian; Daubinger, Monika; Kaiser, Leah; Rebai, Amelle; Rousset, Jean; Koehler, Anna; Schulz, Philip; Moos, Ralf; Panzer, Fabian
      ACS Applied Materials & Interfaces (2019), 11 (33), 30259-30268CODEN: AAMICK; ISSN:1944-8244. (American Chemical Society)
      The authors show that mechanochem. synthesized halide perovskite powders from a ball milling approach can be employed to fabricate a variety of lead halide perovskites with exceptional intrinsic stability. The authors' MAPbI3 powder exhibits higher thermal stability than conventionally processed thin films, without degrdn. after more than two and a half years of storage and only negligible degrdn. after heat treatment at 220°C for 14 h. The authors further show facile recovery strategies of nonphase-pure powders by simple remilling or mild heat treatment. Moreover, the authors demonstrate the mechanochem. synthesis of phase-pure mixed perovskite powders, such as (Cs0.05FA0.95PbI3)0.85(MAPbBr3)0.15, from either the individual metal and org. halides or from readily prepd. ternary perovskites, regardless of the precursor phase purity. Adding potassium iodide (KI) to the milling process successfully passivated the powders. The authors also succeeded in prepg. a precursor soln. on the basis of the powders and obtained uniform thin films for integration into efficient perovskite solar cells from spin-coating this soln. The authors find the KI passivation remains in the devices, leading to improved performance and significantly reduced hysteresis. Their work thus demonstrates the potential of mechanochem. synthesized halide perovskite powders for long-time storage and upscaling, further paving the way toward commercialization of perovskite-based optoelectronic devices.
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      Fung, B. M.; Khitrin, A. K.; Ermolaev, K. An Improved Broadband Decoupling Sequence for Liquid Crystals and Solids. J. Magn. Reson. 2000, 142, 97– 101,  DOI: 10.1006/jmre.1999.1896
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      An Improved Broadband Decoupling Sequence for Liquid Crystals and Solids
      Fung, B. M.; Khitrin, A. K.; Ermolaev, Konstantin
      Journal of Magnetic Resonance (2000), 142 (1), 97-101CODEN: JMARF3; ISSN:1090-7807. (Academic Press)
      Recently the authors developed an efficient broadband decoupling sequence called SPARC-16 for liq. crystals [J. Magn. Reson. 130, 317(1998)]. The sequence is based upon a 16-step phase cycling of the 2-step TPPM decoupling method for solids [J. Chem. Phys. 103, 6951(1995)]. Since then, a stepwise variation of the phase angle in the TPPM sequence offers even better results. The application of this new method to a liq. cryst. compd., 4-n-pentyl-4'-cyanobiphenyl, and a solid, l-tyrosine hydrochloride, is reported. The reason for the improvement is explained by an anal. of the problem in the rotating frame. (c) 2000 Academic Press.
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    64. 64
      Saalwächter, K.; Lange, F.; Matyjaszewski, K.; Huang, C.-F.; Graf, R. BaBa-Xy16: Robust and Broadband Homonuclear DQ Recoupling for Applications in Rigid and Soft Solids up to the Highest MAS Frequencies. J. Magn. Reson. 2011, 212, 204– 215,  DOI: 10.1016/j.jmr.2011.07.001
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      BaBa-xy16: robust and broadband homonuclear DQ recoupling for applications in rigid and soft solids up to the highest MAS frequencies
      Saalwachter Kay; Lange Frank; Matyjaszewski Krzysztof; Huang Chih-Feng; Graf Robert
      Journal of magnetic resonance (San Diego, Calif. : 1997) (2011), 212 (1), 204-15 ISSN:.
      We here present a substantially improved version of the popular Back-to-Back (BaBa) homonuclear double-quantum (DQ) MAS recoupling pulse sequence. By combining the original pulse sequence with a virtual π pulse train with xy-16 phase cycling along with time-reversed DQ reconversion, a truly broadband and exceptionally robust pulse sequence is obtained. The sequence has moderate radio-frequency power requirements, amounting to only one 360° nutation per rotor cycle, it is robust with respect to rf power and tune-up errors, and its broadband performance increases with increasing spinning frequency, here tested up to 63 kHz. The experiment can be applied to many spin-1/2 nuclei in rigid solids with substantial frequency offsets and CSAs, which is demonstrated on the example of 31P NMR of a magnesium ultraphosphate, comparing experimental data with multi-spin simulations, and we also show simulations addressing the performance in 13C NMR of bio(macro)molecules. 1H-based studies of polymer dynamics are highlighted for the example of a rigid solid with strongly anisotropic mobility, represented by a polymer inclusion compound, and for the example of soft materials with weak residual dipole-dipole couplings, represented by homogeneous and inhomogeneous elastomers. We advocate the use of normalized (relaxation-corrected) DQ build-up curves for a quantitative assessment of weak average dipole-dipole couplings and even distributions thereof.
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      Bartók, A. P.; Payne, M. C.; Kondor, R.; Csányi, G. Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons. Phys. Rev. Lett. 2010, 104, 136403,  DOI: 10.1103/PhysRevLett.104.136403
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      Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons
      Bartok, Albert P.; Payne, Mike C.; Kondor, Risi; Csanyi, Gabor
      Physical Review Letters (2010), 104 (13), 136403/1-136403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      We introduce a class of interat. potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, as derived from quantum mech. calcns. The models do not have a fixed functional form and hence are capable of modeling complex potential energy landscapes. They are systematically improvable with more data. We apply the method to bulk crystals, and test it by calcg. properties at high temps. Using the interat. potential to generate the long mol. dynamics trajectories required for such calcns. saves orders of magnitude in computational cost.
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      Bartók, A. P.; Kondor, R.; Csányi, G. On Representing Chemical Environments. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 184115,  DOI: 10.1103/PhysRevB.87.184115
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      On representing chemical environments
      Bartok, Albert P.; Kondor, Risi; Csanyi, Gabor
      Physical Review B: Condensed Matter and Materials Physics (2013), 87 (18), 184115/1-184115/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      We review some recently published methods to represent at. neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave nos. are used to expand the at. neighborhood d. function. Using the example system of small clusters, we quant. show that this expansion needs to be carried to higher and higher wave nos. as the no. of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.
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    67. 67
      Jinnouchi, R.; Karsai, F.; Kresse, G. On-the-Fly Machine Learning Force Field Generation: Application to Melting Points. Phys. Rev. B: Condens. Matter Mater. Phys. 2019, 100, 014105,  DOI: 10.1103/PhysRevB.100.014105
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      Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15– 50,  DOI: 10.1016/0927-0256(96)00008-0
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      68
      Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
      Kresse, G.; Furthmuller, J.
      Computational Materials Science (1996), 6 (1), 15-50CODEN: CMMSEM; ISSN:0927-0256. (Elsevier)
      The authors present a detailed description and comparison of algorithms for performing ab-initio quantum-mech. calcns. using pseudopotentials and a plane-wave basis set. The authors will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temp. d.-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N2atoms scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge d. including a new special preconditioning optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. The authors have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio mol.-dynamics package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.
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    69. 69
      Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169– 11186,  DOI: 10.1103/PhysRevB.54.11169
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      69
      Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
      Kresse, G.; Furthmueller, J.
      Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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    70. 70
      Sun, J.; Ruzsinszky, A.; Perdew, J. P. Strongly Constrained and Appropriately Normed Semilocal Density Functional. Phys. Rev. Lett. 2015, 115, 036402,  DOI: 10.1103/PhysRevLett.115.036402
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      70
      Strongly constrained and appropriately normed semilocal density functional
      Sun, Jianwei; Ruzsinszky, Adrienn; Perdew, John P.
      Physical Review Letters (2015), 115 (3), 036402/1-036402/6CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The ground-state energy, electron d., and related properties of ordinary matter can be computed efficiently when the exchange-correlation energy as a functional of the d. is approximated semilocally. We propose the first meta-generalized-gradient approxn. (meta-GGA) that is fully constrained, obeying all 17 known exact constraints that a meta-GGA can. It is also exact or nearly exact for a set of "appropriate norms," including rare-gas atoms and nonbonded interactions. This strongly constrained and appropriately normed meta-GGA achieves remarkable accuracy for systems where the exact exchange-correlation hole is localized near its electron, and esp. for lattice consts. and weak interactions.
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    71. 71
      Bokdam, M.; Lahnsteiner, J.; Ramberger, B.; Schäfer, T.; Kresse, G. Assessing Density Functionals Using Many Body Theory for Hybrid Perovskites. Phys. Rev. Lett. 2017, 119, 145501,  DOI: 10.1103/PhysRevLett.119.145501
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      71
      Assessing density functionals using many body theory for hybrid perovskites
      Bokdam, Menno; Lahnsteiner, Jonathan; Ramberger, Benjamin; Schaefer, Tobias; Kresse, Georg
      Physical Review Letters (2017), 119 (14), 145501/1-145501/5CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      A review. Which d. functional is the "best" for structure simulations of a particular material. A concise, first principles, approach to answer this question is presented. The RPA (RPA)-an accurate many body theory-is used to evaluate various d. functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite MAPbI3, a promising new solar cell material. The evaluation is done by first creating finite temp. ensembles for small supercells using RPA mol. dynamics, and then evaluating the variance between the RPA and various approx. d. functionals for these ensembles. We find that, contrary to recent suggestions, van der Waals functionals do not improve the description of the material, whereas hybrid functionals and the strongly constrained appropriately normed (SCAN) d. functional yield very good agreement with the RPA. Finally, our study shows that in the room temp. tetragonal phase of MAPbI3, the mols. are preferentially parallel to the shorter lattice vectors but reorientation on ps time scales is still possible.
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    72. 72
      Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953– 17979,  DOI: 10.1103/PhysRevB.50.17953
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      Projector augmented-wave method
      Blochl
      Physical review. B, Condensed matter (1994), 50 (24), 17953-17979 ISSN:0163-1829.
      There is no expanded citation for this reference.
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    73. 73
      Goc, R. Effective Spatial Averaging for NMR Second Moment Calculation. J. Magn. Reson. 1998, 132, 78– 80,  DOI: 10.1006/jmre.1998.1384
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      Goc, R. Calculation of the NMR Second Moment for Materials with Different Types of Internal Rotation. Solid State Nucl. Magn. Reson. 1998, 13, 55– 61,  DOI: 10.1016/S0926-2040(98)00082-4
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      Calculation of the NMR second moment for materials with different types of internal rotation
      Goc, Roman
      Solid State Nuclear Magnetic Resonance (1998), 13 (1-2), 55-61CODEN: SSNRE4; ISSN:0926-2040. (Elsevier Science B.V.)
      The measurements of the NMR 2nd moment can reveal information about structural and dynamical details of the sample providing that anal. of the exptl. results from the Van Vleck's formula can be performed. The method of calcg. the Van Vleck's 2nd moment for solids with complex internal motions is presented. The method is based on simulating any desired motion of atoms within a block of unit cells large enough to reflect the property of the macroscopic sample and calcg. the 2nd moment value averaged by this motion. The detailed description of this method is given for the case of rotation of mols. or groups of atoms. The algorithm of the computer program which performs calcn. based on the described method is also presented. Examples of application of the described method are listed.
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    75. 75
      Goc, R. Computer Calculation of the Van Vleck Second Moment for Materials with Internal Rotation of Spin Groups. Comput. Phys. Commun. 2004, 162, 102– 112,  DOI: 10.1016/j.cpc.2004.06.071
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      Computer calculation of the Van Vleck second moment for materials with internal rotation of spin groups
      Goc, Roman
      Computer Physics Communications (2004), 162 (2), 102-112CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
      This paper describes m2rc3, a program that calcs. Van Vleck 2nd moments for solids with internal rotation of mols., ions or their structural parts. Only rotations about C3 axes of symmetry are allowed, but up to 15 axes of rotation per crystallog. unit cell are permitted. The program is very useful in interpreting NMR measurements in solids.
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    76. 76
      Karmakar, A.; Askar, A. M.; Bernard, G. M.; Terskikh, V. V.; Ha, M.; Patel, S.; Shankar, K.; Michaelis, V. K. Mechanochemical Synthesis of Methylammonium Lead Mixed-Halide Perovskites: Unraveling the Solid-Solution Behavior Using Solid-State NMR. Chem. Mater. 2018, 30, 2309– 2321,  DOI: 10.1021/acs.chemmater.7b05209
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      76
      Mechanochemical Synthesis of Methylammonium Lead Mixed-Halide Perovskites: Unraveling the Solid-Solution Behavior Using Solid-State NMR
      Karmakar, Abhoy; Askar, Abdelrahman M.; Bernard, Guy M.; Terskikh, Victor V.; Ha, Michelle; Patel, Sahil; Shankar, Karthik; Michaelis, Vladimir K.
      Chemistry of Materials (2018), 30 (7), 2309-2321CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      Mixed-halide lead perovskite (MHP) materials are rapidly advancing as next-generation high-efficiency perovskite solar cells due to enhanced stability and bandgap tunability. Here, we demonstrate the ability to readily and stoichiometrically tune the halide compn. in methylammonium-based MHPs using a mechanochem. synthesis approach. Using this solvent-free protocol we are able to prep. domain-free MHP solid solns. with randomly distributed halide ions about the Pb center. Up to 7 distinct [PbClxBr6-x]4- environments are identified, based on the 207Pb NMR chem. shifts, which are also sensitive to the changes in the unit cell dimensions resulting from the substitution of Br by Cl, obeying Vegard's law. We demonstrate a straightforward and rapid synthetic approach to forming highly tunable stoichiometric MHP solid solns. while avoiding the traditional soln. synthesis method by redirecting the thermodynamically driven compns. We illustrate the importance of complementary characterization methods, obtaining at.-scale structural information from multinuclear, multifield, and multidimensional solid-state magnetic resonance spectroscopy, as well as from quantum chem. calcns. and long-range structural details using powder x-ray diffraction. The solvent-free mechanochem. synthesis approach is also compared to traditional solvent synthesis, revealing identical solid-soln. behavior; however, the mechanochem. approach offers superior control over the stoichiometry of the final mixed-halide compn., which is essential for device engineering.
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    77. 77
      Askar, A. M.; Wiltshire, B. D.; Patel, S.; Fleet, J.; Shankar, K.; Karmakar, A.; Bernard, G. M.; Ha, M.; Michaelis, V. K.; Terskikh, V. V. Composition-Tunable Formamidinium Lead Mixed Halide Perovskites via Solvent-Free Mechanochemical Synthesis: Decoding the Pb Environments Using Solid-State NMR Spectroscopy. J. Phys. Chem. Lett. 2018, 9, 2671– 2677,  DOI: 10.1021/acs.jpclett.8b01084
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      77
      Composition-Tunable Formamidinium Lead Mixed Halide Perovskites via Solvent-Free Mechanochemical Synthesis: Decoding the Pb Environments Using Solid-State NMR Spectroscopy
      Askar, Abdelrahman M.; Karmakar, Abhoy; Bernard, Guy M.; Ha, Michelle; Terskikh, Victor V.; Wiltshire, Benjamin D.; Patel, Sahil; Fleet, Jonathan; Shankar, Karthik; Michaelis, Vladimir K.
      Journal of Physical Chemistry Letters (2018), 9 (10), 2671-2677CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Mixed-halide lead perovskites are becoming of paramount interest in the optoelectronic and photovoltaic research fields, offering band gap tunability, improved efficiency, and enhanced stability compared to their single halide counterparts. Formamidinium-based mixed halide perovskites (FA-MHPs) are crit. to obtaining optimum solar cell performance. Here, the authors report a solvent-free mechanochem. synthesis (MCS) method to prep. FA-MHPs, starting with their parent compds. (FAPbX3; X = Cl, Br, I), achieving compns. not previously accessible through the solvent synthesis (SS) technique. By probing local Pb environments in MCS FA-MHPs using solid-state NMR spectroscopy, along with powder x-ray diffraction for long-range crystallinity and reflectance measurements to det. the optical band gap, MCS FA-MHPs form at.-level solid solns. between Cl/Br and Br/I MHPs. The authors' results pave the way for advanced methods in at.-level structural understanding while offering a 1-pot synthetic approach to prep. MHPs with superior control of stoichiometry.
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    78. 78
      Aebli, M.; Piveteau, L.; Nazarenko, O.; Benin, M. B.; Krieg, F.; Verel, R.; Kovalenko, M. V. Lead-Halide Scalar Couplings in Pb NMR of APbX3 Perovskites (A = Cs, Methylammonium, Formamidinium ; X = Cl, Br, I). Sci. Rep. 2020, 10, 8229,  DOI: 10.1038/s41598-020-65071-4
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      78
      Lead-Halide Scalar Couplings in 207Pb NMR of APbX3 Perovskites (A = Cs, Methylammonium, Formamidinium; X = Cl, Br, I)
      Aebli, Marcel; Piveteau, Laura; Nazarenko, Olga; Benin, Bogdan M.; Krieg, Franziska; Verel, Rene; Kovalenko, Maksym V.
      Scientific Reports (2020), 10 (1), 8229CODEN: SRCEC3; ISSN:2045-2322. (Nature Research)
      Abstr.: Understanding the structure and dynamics of newcomer optoelectronic materials - lead halide perovskites APbX3 [A = Cs, methylammonium (CH3NH3+, MA), formamidinium (CH(NH2)2+, FA); X = Cl, Br, I] - has been a major research thrust. In this work, new insights could be gained by using 207Pb solid-state NMR (NMR) spectroscopy at variable temps. between 100 and 300 K. The existence of scalar couplings 1JPb-Cl of ca. 400 Hz and 1JPb-Br of ca. 2.3 kHz could be confirmed for MAPbX3 and CsPbX3. Diverse and fast structure dynamics, including rotations of A-cations, harmonic and anharmonic vibrations of the lead-halide framework and ionic mobility, affect the resoln. of the coupling pattern. 207Pb NMR can therefore be used to detect the structural disorder and phase transitions. Furthermore, by comparing bulk and nanocryst. CsPbBr3 a greater structural disorder of the PbBr6-octahedra had been confirmed in a nanoscale counterpart, not readily captured by diffraction-based techniques.
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    79. 79
      Rosales, B. A.; Men, L.; Cady, S. D.; Hanrahan, M. P.; Rossini, A. J.; Vela, J. Persistent Dopants and Phase Segregation in Organolead Mixed-Halide Perovskites. Chem. Mater. 2016, 28, 6848– 6859,  DOI: 10.1021/acs.chemmater.6b01874
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      Persistent Dopants and Phase Segregation in Organolead Mixed-Halide Perovskites
      Rosales, Bryan A.; Men, Long; Cady, Sarah D.; Hanrahan, Michael P.; Rossini, Aaron J.; Vela, Javier
      Chemistry of Materials (2016), 28 (19), 6848-6859CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      Organolead mixed-halide perovskites such as CH3NH3PbX3-aX'a (X, X' = I, Br, Cl) are interesting semiconductors because of their low cost, high photovoltaic power conversion efficiencies, enhanced moisture stability, and band gap tunability. Using a combination of optical absorption spectroscopy, powder XRD and, for the 1st time, 207Pb solid state NMR (ssNMR), the authors probe the extent of alloying and phase segregation in these materials. Because 207Pb ssNMR chem. shifts are highly sensitive to local coordination, electronic structure, and vary linearly with halogen electronegativity and band gap, this technique can provide the true chem. speciation and compn. of organolead mixed-halide perovskites. The authors specifically study samples made by three different preparative methods: soln. phase synthesis, thermal annealing, and solid phase synthesis. 207Pb ssNMR reveals that nonstoichiometric dopants and semicryst. phases are prevalent in samples made by soln. phase synthesis. These nanodomains are persistent after thermal annealing up to 200°. Further, a novel solid phase synthesis that starts from the parent, single-halide perovskites can suppress phase segregation but not the formation of dopants. The authors' observations are consistent with the presence of miscibility gaps and spontaneous spinodal decompn. of the mixed-halide perovskites at room temp. This underscores how strongly different synthetic procedures impact the nanostructuring and compn. of organolead halide perovskites. Better optoelectronic properties and improved device stability and performance may be achieved through careful manipulation of the different phases and nanodomains present in these materials.
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    80. 80
      Zorin, V. E.; Brown, S. P.; Hodgkinson, P. Quantification of Homonuclear Dipolar Coupling Networks from Magic-Angle Spinning 1H NMR. Mol. Phys. 2006, 104, 293– 304,  DOI: 10.1080/00268970500351052
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      Quantification of homonuclear dipolar coupling networks from magic-angle spinning 1H NMR
      Zorin, V. E.; Brown, S. P.; Hodgkinson, P.
      Molecular Physics (2006), 104 (2), 293-304CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
      Numerical simulations of magic-angle spinning (MAS) spectra of dipolar-coupled nuclear spins were used to assess different approaches to the quantification of dipolar couplings from 1H solid-state NMR. Exploiting the translational symmetry of periodic spin systems allows extended networks with 'realistic' nos. of spins to be considered. The exptl. accessible parameter is the root-sum-square of the dipolar couplings to a given spin. The effectiveness of either fitting the resulting spinning sideband spectra to small spin system models, or using analyses based on moment expansions, was examd. Fitting of the spinning sideband pattern is considerably more robust with respect to exptl. noise than frequency domain moment anal. The influence of the MAS rate and system geometry on robustness of the quantification is analyzed and discussed.
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    81. 81
      Bradley, J. P.; Tripon, C.; Filip, C.; Brown, S. P. Determining Relative Proton-Proton Proximities from the Build-up of Two-Dimensional Correlation Peaks in 1H Double-Quantum MAS NMR: Insight from Multi-Spin Density-Matrix Simulations. Phys. Chem. Chem. Phys. 2009, 11, 6941– 6952,  DOI: 10.1039/b906400a
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      81
      Determining relative proton-proton proximities from the build-up of two-dimensional correlation peaks in 1H double-quantum MAS NMR: insight from multi-spin density-matrix simulations
      Bradley, Jonathan P.; Tripon, Carmen; Filip, Claudiu; Brown, Steven P.
      Physical Chemistry Chemical Physics (2009), 11 (32), 6941-6952CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The build-up of intensity-as a function of the no., nrcpl, of POST-C7 elements used for the excitation and reconversion of double-quantum (DQ) coherence (DQC)-is analyzed for the fifteen distinct DQ correlation peaks that are obsd. exptl. for the eight sep. 1H resonances in a 1H (500 MHz) DQ CRAMPS solid-state (12.5 kHz MAS) NMR spectrum of the dipeptide β-AspAla. The simulation in SPINEVOLUTION of t1 (1H DQ evolution) FIDs for clusters of eight dipolar-coupled protons gives sep. simulated 1H DQ build-up curves for the CH2(a), CH2(b), CH(Asp), CH(Ala), NH and OH 1H single-quantum (SQ) 1H resonances. An anal. of both the simulated and exptl. 1H DQ build-up leads to the following general observations: (i) considering the build-up of 1H DQ peaks at a particular SQ frequency, max. intensity is obsd. for the DQC corresponding to the shortest H-H distance; (ii) for the max. intensity 1H DQ peak at a particular SQ frequency, the recoupling time for the obsd. max. intensity depends on the corresponding H-H distance, e.g., max. intensity for the CH2(a)-CH2(b) (H-H distance = 1.55 Å) and OH-CH(Asp) (H-H distance = 2.49 Å) DQ peaks is obsd. at nrcpl = 2 and 3, resp.; (iii) for DQ peaks involving a CH2 proton at a non-CH2 SQ frequency, there is much reduced intensity and a max. intensity at a short recoupling time; (iv) for the other lower intensity 1H DQ peaks at a particular SQ frequency, max. intensity is obsd. for the same (or close to the same) recoupling time, but the relative intensity of the DQ peaks is a reliable indicator of the relative H-H distance-the ratio of the max. intensities for the peaks at the CH(Ala) SQ frequency due to the two DQCs with the NH and OH protons are approx. in the ratio of the squares of the corresponding dipolar coupling consts. While the simulated 1H DQ build-up curves reproduce most of the features of the exptl. curves, max. intensity is often obsd. at a longer recoupling time in simulations. In this respect, simulations for two to eight spins show a trend towards a faster decay for an increasing no. of considered spins. Finally, simulations show that increasing either the Larmor frequency (to 1 GHz) or the MAS frequency (to 125 kHz) does not lead to changes in the marked differences between the 1H DQ build-up curves at the CH(Asp) SQ frequency for DQCs to the CH2(a) and OH protons that correspond to similar H-H distances (2.39 Å and 2.49 Å, resp.).
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    82. 82
      Selig, O.; Sadhanala, A.; Müller, C.; Lovrincic, R.; Chen, Z.; Rezus, Y. L. A.; Frost, J. M.; Jansen, T. L. C.; Bakulin, A. A. Organic Cation Rotation and Immobilization in Pure and Mixed Methylammonium Lead-Halide Perovskites. J. Am. Chem. Soc. 2017, 139, 4068– 4074,  DOI: 10.1021/jacs.6b12239
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      82
      Organic Cation Rotation and Immobilization in Pure and Mixed Methylammonium Lead-Halide Perovskites
      Selig, Oleg; Sadhanala, Aditya; Mueller, Christian; Lovrincic, Robert; Chen, Zhuoying; Rezus, Yves L. A.; Frost, Jarvist M.; Jansen, Thomas L. C.; Bakulin, Artem A.
      Journal of the American Chemical Society (2017), 139 (11), 4068-4074CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
      Three-dimensional lead-halide perovskites have attracted a lot of attention due to their ability to combine soln. processing with outstanding optoelectronic properties. Despite their soft ionic nature these materials demonstrate a surprisingly low level of electronic disorder resulting in sharp band edges and narrow distributions of the electronic energies. Understanding how structural and dynamic disorder impacts the optoelectronic properties of these perovskites is important for many applications. Here the authors combine ultrafast two-dimensional vibrational spectroscopy and mol. dynamics simulations to study the dynamics of the org. methylammonium (MA) cation orientation in a range of pure and mixed trihalide perovskite materials. For pure MAPbX3 (X = I, Br, Cl) perovskite films, the cation dynamics accelerate with decreasing size of the halide atom. This acceleration is surprising given the expected strengthening of the hydrogen bonds between the MA and the smaller halide anions, but can be explained by the increase in the polarizability with the size of halide. Much slower dynamics, up to partial immobilization of the org. cation, are obsd. in the mixed MAPb(ClxBr1-x)3 and MAPb(BrxI1-x)3 alloys, which the authors assoc. with symmetry breaking within the perovskite unit cell. The obsd. dynamics are essential for understanding the effects of structural and dynamical disorder in perovskite-based optoelectronic systems.
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    83. 83
      Svane, K. L.; Forse, A. C.; Grey, C. P.; Kieslich, G.; Cheetham, A. K.; Walsh, A.; Butler, K. T. How Strong Is the Hydrogen Bond in Hybrid Perovskites?. J. Phys. Chem. Lett. 2017, 8, 6154– 6159,  DOI: 10.1021/acs.jpclett.7b03106
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      How Strong Is the Hydrogen Bond in Hybrid Perovskites?
      Svane, Katrine L.; Forse, Alexander C.; Grey, Clare P.; Kieslich, Gregor; Cheetham, Anthony K.; Walsh, Aron; Butler, Keith T.
      Journal of Physical Chemistry Letters (2017), 8 (24), 6154-6159CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
      Hybrid org.-inorg. perovskites represent a special class of metal-org. framework where a mol. cation is encased in an anionic cage. The mol.-cage interaction influences phase stability, phase transformations, and the mol. dynamics. We examine the hydrogen bonding in four AmBX3 formate perovskites: [Am]Zn(HCOO)3, with Am+ = hydrazinium (NH2NH3+), guanidinium (C(NH2)3+), dimethylammonium (CH3)2NH2+, and azetidinium (CH2)3NH2+. We develop a scheme to quantify the strength of hydrogen bonding in these systems from first-principles, which separates the electrostatic interactions between the amine (Am+) and the BX3- cage. The hydrogen-bonding strengths of formate perovskites range from 0.36 to 1.40 eV/cation (8-32 kcalmol-1). Complementary solid-state NMR spectroscopy confirms that strong hydrogen bonding hinders cation mobility. Application of the procedure to hybrid lead halide perovskites (X = Cl, Br, I, Am+ = CH3NH3+, CH(NH2)2+) shows that these compds. have significantly weaker hydrogen-bonding energies of 0.09 to 0.27 eV/cation (2-6 kcalmol-1), correlating with lower order-disorder transition temps.
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    84. 84
      Knijn, P. J.; van Bentum, P. J. M.; van Eck, E. R. H.; Fang, C.; Grimminck, D. L. A. G.; de Groot, R. A.; Havenith, R. W. A.; Marsman, M.; Meerts, W. L.; De Wijs, G. A. A Solid-State NMR and DFT Study of Compositional Modulations in AlxGa1-xAs. Phys. Chem. Chem. Phys. 2010, 12, 11517– 11535,  DOI: 10.1039/c003624b
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      A solid-state NMR and DFT study of compositional modulations in AlxGa1-xAs
      Knijn, Paulus J.; van Bentum, P. Jan M.; van Eck, Ernst R. H.; Fang, Changming; Grimminck, Dennis L. A. G.; de Groot, Robert A.; Havenith, Remco W. A.; Marsman, Martijn; Meerts, W. Leo; de Wijs, Gilles A.; Kentgens, Arno P. M.
      Physical Chemistry Chemical Physics (2010), 12 (37), 11517-11535CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      The authors have conducted 75As and 69Ga NMR expts. to study order/disorder in AlxGa1-xAs lift-off films with x ∼ 0.297 and 0.489. The authors were able to identify all possible As(AlnGa4-n) sites with n = 0-4 coordinations in 75As NMR spectra using spin-echo expts. at 18.8 T. This was achieved by employing high radiofrequency field strengths using a small solenoid coil and an NMR probe specifically designed for this purpose. Spectral deconvolution, using an evolutionary algorithm, complies with the absence of long-range order if a CuAu based order parameter is imposed. An unconstrained fit shows a deviation of the statistics imposed by this type of ordering. The occupational disorder in the Ga and Al positions is reflected in a distribution of the Elec. Field Gradients (EFGs) experienced at the different arsenic sites. This can be modeled by summing the effects of the 1st coordination sphere and a Czjzek type distribution resulting from the compositional variation in the Al/Ga sub-lattice in the higher coordination spheres. 69Ga 3QMAS and nutation data exclude the presence of highly sym. sites and also show a distribution in EFG. The exptl. obtained quadrupolar interactions are in good agreement with calcns. based on D. Functional Theory (DFT). Using additivity of EFG tensors arising from distant charge perturbations, the authors could use DFT to model the EFG distributions of the n = 0-4 sites, reproducing the Czjzek and extended Czjzek distributions that were found exptl. From these calcns. the 75As quadrupolar interaction is sensitive to compositional modulations up to the 7th coordination shell in these systems.
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    85. 85
      Tycko, R.; Dabbagh, G.; Kurtz, S. R.; Goral, J. P. Quantitative Study of Atomic Ordering in Ga0.5In0.5P Thin Films by P31 Nuclear Magnetic Resonance. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 13452– 13457,  DOI: 10.1103/PhysRevB.45.13452
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      Quantitative study of atomic ordering in gallium indium phosphide (Ga0.5In0.5P) thin films by phosphorus-31 nuclear magnetic resonance
      Tycko, Robert; Dabbagh, Gary; Kurtz, Sarah R.; Goral, John P.
      Physical Review B: Condensed Matter and Materials Physics (1992), 45 (23), 13452-7CODEN: PRBMDO; ISSN:0163-1829.
      Phosphorus-31 NMR spectra were used to measure the degree of cation ordering in thin films of the semiconductor alloy Ga0.5In0.5P grown by organometallic VPE. The 5 possible GanIn4-nP clusters in GxIn1-xP give rise to resolved NMR lines under magic-angle spinning, allowing a detn. of the degree of cation ordering from the relative areas of the 5 lines. The ordering is weak (order parameter ≤0.6) even in films that appear highly ordered in TEM.
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      Degen, C.; Tomaselli, M.; Meier, B. H.; Voncken, M. M. A. J.; Kentgens, A. P. M. NMR Investigation of Atomic Ordering in AlxGa1-xAs Thin Films. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 1– 4,  DOI: 10.1103/PhysRevB.69.193303
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      Cullity, B. D. Elements of X-Ray Diffraction, 2nd ed.; Addison Wesley: Reading, MA, 1978.
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      Mozur, E. M.; Hope, M. A.; Trowbridge, J. C.; Halat, D. M.; Daemen, L. L.; Maughan, A. E.; Prisk, T. R.; Grey, C. P.; Neilson, J. R. Cesium Substitution Disrupts Concerted Cation Dynamics in Formamidinium Hybrid Perovskites. Chem. Mater. 2020, 32, 6266– 6277,  DOI: 10.1021/acs.chemmater.0c01862
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      Cesium substitution disrupts concerted cation dynamics in formamidinium hybrid perovskites
      Mozur, Eve M.; Hope, Michael A.; Trowbridge, Julia C.; Halat, David M.; Daemen, Luke L.; Maughan, Annalise E.; Prisk, Timothy R.; Grey, Clare P.; Neilson, James R.
      Chemistry of Materials (2020), 32 (14), 6266-6277CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
      Although initial studies on hybrid perovskites for photovoltaic applications focused on simple compns., the most technol. relevant perovskites are heavily substituted. The influence of chem. substitution on the general phase behavior and specific phys. properties remains ambiguous. The hybrid perovskite formamidinium lead bromide, CH(NH2)2PbBr3, exhibits complex phase behavior manifesting in a series of crystallog. unresolvable phase transitions assocd. with changes in the cation dynamics. Here, we characterize the mol. and lattice dynamics of CH(NH2)2PbBr3 as a function of temp. and their evolution upon chem. substitution of CH(NH2)2+ for cesium (Cs+) with crystallog., neutron scattering, 1H and 14N NMR spectroscopy, and 79Br nuclear quadrupolar spectroscopy. Cs+ substitution suppresses the four low-temp. phase transitions of CH(NH2)2PbBr3, which propagate through concerted changes in the dynamic degrees of freedom of the org. sublattice and local or long-range distortions of the octahedral framework. We propose that cesium substitution suppresses the phase transitions through the relief of geometric frustration assocd. with the orientations of CH(NH2)2+ mols., which retain their local dynamical degrees of freedom.
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    89. 89
      Chatterjee, R.; Pavlovetc, I. M.; Aleshire, K.; Hartland, G. V.; Kuno, M. Subdiffraction Infrared Imaging of Mixed Cation Perovskites: Probing Local Cation Heterogeneities. ACS Energy Lett. 2018, 3, 469– 475,  DOI: 10.1021/acsenergylett.7b01306
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      89
      Subdiffraction Infrared Imaging of Mixed Cation Perovskites: Probing Local Cation Heterogeneities
      Chatterjee, Rusha; Pavlovetc, Ilia M.; Aleshire, Kyle; Hartland, Gregory V.; Kuno, Masaru
      ACS Energy Letters (2018), 3 (2), 469-475CODEN: AELCCP; ISSN:2380-8195. (American Chemical Society)
      Compositional engineering has led to dramatic improvements in hybrid perovskite-based solar cell stabilities and performance. Mixed cation perovskites have emerged as champion photovoltaic materials with power conversion efficiencies exceeding 22%. However, there has been relatively little work done to explore local cation-related compositional inhomogeneities in mixed cation perovskite films. Such studies are necessary because hybrid perovskite optical properties and, consequently, their photovoltaic performance strongly depend on compn. Here, we perform spatially resolved, subdiffraction IR photothermal heterodyne imaging measurements to probe cation-specific compositional distributions within FAxMA1-xPbI3 perovskite films. Our measurements reveal that these perovskites possess large compositional spatial heterogeneities with cation distributions varying on av. ∼20% from expected ensemble stoichiometries. Correlated emission measurements show intrafilm emission energies differing by over 30 meV due to these compositional differences. These measurements thus reveal cation stoichiometric heterogeneities and their direct impact on local photovoltaic response-detg. optical properties of mixed cation perovskites.
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    90. 90
      Maheshwari, S.; Patwardhan, S.; Schatz, G. C.; Renaud, N.; Grozema, F. C. The Effect of the Magnitude and Direction of the Dipoles of Organic Cations on the Electronic Structure of Hybrid Halide Perovskites. Phys. Chem. Chem. Phys. 2019, 21, 16564– 16572,  DOI: 10.1039/C9CP02866H
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      90
      The effect of the magnitude and direction of the dipoles of organic cations on the electronic structure of hybrid halide perovskites
      Maheshwari, Sudeep; Patwardhan, Sameer; Schatz, George C.; Renaud, Nicolas; Grozema, Ferdinand C.
      Physical Chemistry Chemical Physics (2019), 21 (30), 16564-16572CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
      We present ab initio calcns. (DFT and SOC-G0W0) of the optoelectronic properties of different hybrid-halide perovskites, namely X-PbI3 (X = methylammonium, formamidinium, guanidinium, hydrazinium, and hydroxylammonium). These calcns. shed new light on how the substitution of different org. cations in the material influences its optoelectronic properties. Our simulations show a significant modification of the lattice parameter and band gap of the material upon cation substitution. These modifications are not only due to steric effects but also due to electrostatic interactions between the org. and inorg. parts of the material. In addn. to this, we demonstrate how the relative orientations of neighboring cations in the material modify the local electrostatic potential of the system and its fundamental band gap. This change in the band gap is accompanied by the formation of localized and spatially sepd. electronic states. These localized states modify the carrier mobility in the materials and can be a reason for the formation and recombination of the charge carriers in these very promising materials.
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    91. 91
      Doherty, T. A. S.; Winchester, A. J.; Macpherson, S.; Johnstone, D. N.; Pareek, V.; Tennyson, E. M.; Kosar, S.; Kosasih, F. U.; Anaya, M.; Abdi-Jalebi, M. Performance-Limiting Nanoscale Trap Clusters at Grain Junctions in Halide Perovskites. Nature 2020, 580, 360– 366,  DOI: 10.1038/s41586-020-2184-1
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      91
      Performance-limiting nanoscale trap clusters at grain junctions in halide perovskites
      Doherty, Tiarnan A. S.; Winchester, Andrew J.; MacPherson, Stuart; Johnstone, Duncan N.; Pareek, Vivek; Tennyson, Elizabeth M.; Kosar, Sofiia; Kosasih, Felix U.; Anaya, Miguel; Abdi-Jalebi, Mojtaba; Andaji-Garmaroudi, Zahra; Wong, E. Laine; Madeo, Julien; Chiang, Yu-Hsien; Park, Ji-Sang; Jung, Young-Kwang; Petoukhoff, Christopher E.; Divitini, Giorgio; Man, Michael K. L.; Ducati, Caterina; Walsh, Aron; Midgley, Paul A.; Dani, Keshav M.; Stranks, Samuel D.
      Nature (London, United Kingdom) (2020), 580 (7803), 360-366CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
      Photoemission electron microscopy was used to image the trap distribution in state-of-the-art halide perovskite films. Instead of a relatively uniform distribution within regions of poor luminescence efficiency, discrete, nanoscale trap clusters were obsd. By correlating microscopy measurements with scanning electron anal. techniques, these trap clusters appear at the interfaces between crystallog. and compositionally distinct entities. By generating time-resolved photoemission sequences of the photoexcited carrier trapping process, a hole-trapping character with the kinetics limited by diffusion of holes to the local trap clusters was revealed. Managing structure and compn. on the nanoscale will be essential for optimal performance of halide perovskite devices.
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    92. 92
      Tong, C.-J.; Geng, W.; Prezhdo, O. V.; Liu, L.-M. Role of Methylammonium Orientation in Ion Diffusion and Current-Voltage Hysteresis in the CH3NH3PbI3 Perovskite. ACS Energy Lett. 2017, 2, 1997– 2004,  DOI: 10.1021/acsenergylett.7b00659
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      92
      Role of methylammonium orientation in ion diffusion and current-voltage hysteresis in the CH3NH3PbI3 perovskite
      Tong, Chuan-Jia; Geng, Wei; Prezhdo, Oleg V.; Liu, Li-Min
      ACS Energy Letters (2017), 2 (9), 1997-2004CODEN: AELCCP; ISSN:2380-8195. (American Chemical Society)
      Hybrid org.-inorg. perovskites, and particularly CH3NH3PbI3 (MAPbI3), have emerged as a new generation of photovoltaic devices due to low cost and superior performance. The performance is strongly influenced by current-voltage hysteresis that arises due to ion migration, and the challenge remains how to suppress the ion migration and hysteresis. Our first-principles calcns. demonstrate that the energy barriers to diffusion of the I-, MA+, and Pb2+ ions are greatly affected by dipole moments of the MA species. The energy barriers of the most mobile I- ion range from 0.06 to 0.65 eV, depending on MA orientation. The pos. charged MA+ and Pb2+ ions diffuse along the dipole direction, while the neg. charged I- ion strongly prefers to diffuse against the dipole direction. By influencing ion migration, the arrangement of MA mols. can effectively modulate the current-voltage hysteresis intensity. The current work contributes to the fundamental understanding of the microscopic mechanism of ion migration in MAPbI3 and suggests means to suppress the hysteresis effect and optimize perovskite performance. By demonstrating in detail how the arrangement of the org. mols. can efficiently influence ion migration and, hence, amplitude of the current-voltage hysteresis, our results suggest that the hysteresis effect can be suppressed and the long-term performance of perovskites can be improved, if the org. mols. are arranged and stabilized in an antiferroelec. order.
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    93. 93
      Huang, Y.; Li, L.; Liu, Z.; Jiao, H.; He, Y.; Wang, X.; Zhu, R.; Wang, D.; Sun, J.; Chen, Q. The Intrinsic Properties of FA(1-x)MAxPbI3 Perovskite Single Crystals. J. Mater. Chem. A 2017, 5 (18), 8537– 8544,  DOI: 10.1039/C7TA01441D
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      93
      Intrinsic properties of FA(1-x)MAxPbI3 perovskite single crystals
      Huang, Yuan; Li, Liang; Liu, Zonghao; Jiao, Haoyang; He, Yuqing; Wang, Xiaoge; Zhu, Rui; Wang, Dong; Sun, Junliang; Chen, Qi; Zhou, Huanping
      Journal of Materials Chemistry A: Materials for Energy and Sustainability (2017), 5 (18), 8537-8544CODEN: JMCAET; ISSN:2050-7496. (Royal Society of Chemistry)
      Org.-inorg. hybrid perovskites with mixed org. cations and/or halides have attracted increasing attention due to their superior optoelectronic properties, which are tailorable for different applications. To obtain a deeper understanding of materials properties, single crystals are regarded as the best platform among various building blocks for fundamental study. Here, we synthesized a series of perovskite single crystals with mixed org. cations (APbI3, A = CH3NH3+, MA+; or CH(NH2)2+, FA+) along the compositional space, and conducted a systematic investigation to correlate the carrier behavior with the org. cations. The single crystals were synthesized via inverse temp. crystn. assisted by hydroiodic acid, where the quality of the crystals could be judiciously controlled by the thermodn. process. It is found that the substitution of 15% MA+ in FAPbI3 single crystals stabilizes the phase with the best charge transport characteristics. Both photodetector and J-V measurements suggested that FA0.85MA0.15PbI3 single crystal exhibits suppressed ion migration compared with the counterpart FA0.15MA0.85PbI3 single crystal. These results represent an important step to highlight the role of org. cations in hybrid perovskite materials, which will further benefit fundamental understanding of materials and device optimization.
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    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.0c10042.

    • Exact precursor amounts for the syntheses; experimental and calculated average lattice constants of MA1–xFAxPbI3; 13C SPE MAS NMR spectra, individual 1H DQ buildup curves, exact MA/FA ratios and experimental dipolar couplings of MA1–xFAxPbI3 and MA0.15FA0.85PbI2.55Br0.45; full H–H pair distribution function extracted from MD simulations; further details on analyses of the MLFF MD simulations (PDF)


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