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Functional Inorganic Materials and DevicesNovember 9, 2023

Combined Theoretical and Experimental Study of the Moiré Dislocation Network at the SrTiO₃-(La,Sr)(Al,Ta)O₃ Interface
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Chiara Ricca
Chiara Ricca
Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
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Elizabeth Skoropata
Elizabeth Skoropata
Swiss Light Source, Paul Scherrer Institut, Forschungsstrasse 111, 5232 Villigen PSI, Switzerland
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Marta D. Rossell
Marta D. Rossell
Electron Microscopy Center, Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
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https://orcid.org/0000-0001-8610-8853
Rolf Erni
Rolf Erni
Electron Microscopy Center, Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland
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https://orcid.org/0000-0003-2391-5943
Urs Staub
Urs Staub
Swiss Light Source, Paul Scherrer Institut, Forschungsstrasse 111, 5232 Villigen PSI, Switzerland
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https://orcid.org/0000-0003-2035-3367
Ulrich Aschauer*
Ulrich Aschauer
Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
Department of Chemistry and Physics of Materials, University of Salzburg, Jakob-Haringer-Street 2A, A-5020 Salzburg, Austria
*Email: [email protected]
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https://orcid.org/0000-0002-1165-6377

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ACS Applied Materials & Interfaces

Cite this: ACS Appl. Mater. Interfaces 2023, 15, 46, 53678–53687

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https://doi.org/10.1021/acsami.3c10958

Published November 9, 2023

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Abstract

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Recently, a highly ordered Moiré dislocation lattice was identified at the interface between a SrTiO₃ (STO) thin film and the (LaAlO₃)_0.3(Sr₂TaAlO₆)_0.7 (LSAT) substrate. A fundamental understanding of the local ionic and electronic structures around the dislocation cores is crucial to further engineer the properties of these complex multifunctional heterostructures. Here, we combine experimental characterization via analytical scanning transmission electron microscopy with results of molecular dynamics and density functional theory calculations to gain insights into the structure and defect chemistry of these dislocation arrays. Our results show that these dislocations lead to undercoordinated Ta/Al cations at the dislocation core, where oxygen vacancies can easily be formed, further facilitated by the presence of cation vacancies. The reduced Ti³⁺ observed experimentally at the dislocations by electron energy-loss spectroscopy is a consequence of both the structure of the dislocation itself and of the electron doping due to oxygen vacancy formation. Finally, the experimentally observed Ti diffusion into the LSAT around the dislocation core occurs only together with cation vacancy formation in the LSAT or Ta diffusion into STO.

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1. Introduction

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Complex transition metal perovskite oxides are a versatile class of materials with a wide spectrum of functional properties. They can be insulating, semiconducting, or metallic and show technologically relevant phenomena such as magnetism, ferroelectricity, or the more exotic high-temperature superconductivity and colossal magnetoresistance. (1−4) These properties are the result of a complex interplay of charge, orbital, spin, and lattice degrees of freedom (1) and depend strongly on strain and the defect chemistry. (5−7) The structural compatibility between different perovskites allows them to be stacked on top of each other, and the advances in deposition techniques enabled the fabrication of complex multifunctional heterostructures with relative ease. These heterostructures often give rise to interesting, novel, and unexpected physical phenomena emerging at the interface where materials with different structural and electronic properties meet: quasi-two-dimensional (2D) electron gas, colossal ionic conductivity, giant thermoelectric effect, or resistance switching. (1,3,8−12)

Recently, a highly ordered Moiré lattice has been identified at the interface between SrTiO₃ (STO) and (LaAlO₃)_0.3(Sr₂TaAlO₆)_0.7 (LSAT) by high-resolution X-ray diffraction reciprocal space mapping. (13) A 30 nm thick film of STO was grown on LSAT (001) by pulsed laser deposition, followed by 12 h of annealing at 1200 °C and ambient pressure. STO (a_STO = 3.905 Å) and LSAT (a_LSAT = 3.869 Å) both have a cubic lattice with a small mismatch of 0.93%. The high-temperature annealing allows the almost complete relaxation of the STO film, which results in the appearance of the Moiré pattern. This newly formed 2D pattern has a Moiré lattice constant of approximately 40 nm, corresponding to 106/107 unit cells of STO/LSAT, necessary to compensate for the small lattice mismatch between the two materials. Scanning transmission electron microscopy (STEM) images suggest that this periodicity is related to the appearance of a network of edge dislocations at the interface that has the same periodicity as the Moiré pattern.

The ability to form such ordered superlattices with a 2D network of line defects at complex perovskite oxide interfaces could be an emerging avenue to induce new interfacial functionalities with unforeseen potential applications, such as 2D ferroics, 2D grid conductivity along the defect lines, or ferroelectric three-dimensional (3D) vortex structures. These interfacial phenomena are a consequence of spin and charge interactions at the interface, which are in turn controlled by the local atomic arrangement. Hence, a detailed understanding of the atomic structure and electronic properties of the STO/LSAT interface in the presence of dislocations is key to interpreting the behavior of this heterostructure and to enhance its functional properties.

Given that the oxide defect chemistry and diffusion are known to be heavily affected by strain (14−17) and since dislocations are surrounded by strong strain fields, one would expect preferential defect formation and segregation around dislocations. Indeed, recent computational studies have focused not only on describing the structure of interfacial misfit dislocations (18,19) but also on their interaction with dopants, defects, and defect clusters. (20−22) These classical potential-based calculations, however, always treat charged point defects since whole ions are removed. Electronic structure density functional theory (DFT) calculations would be necessary to account for the formation of neutral or not fully ionic defects. In the present case, DFT is, however, limited by the large size of the supercells required to describe the periodicity of the Moiré lattice and misfit dislocations. In addition, the huge configurational space of point defects and point-defect clusters in the symmetry-broken environment represents a challenge, given the computational cost of DFT.

To overcome these challenges, we use classical molecular dynamics (MD) to obtain a dislocation structure with the correct long-range strain field of the Moiré interface with misfit dislocations and combine it with DFT calculations on cluster models extracted from these classically relaxed structures. The space of possible defects and their location around the dislocation are reduced by experimental information obtained from chemical mapping by electron energy-loss (EELS) and energy-dispersive X-ray (EDX) spectroscopies. The results lead to a detailed understanding of the atomic-scale defect structure and the resulting electronic properties around the interfacial dislocation network that will guide the design and optimization of these promising heterostructures.

2. Methods

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2.1. Computational Details

2.1.1. Dislocation Models

The simulation of these dislocation arrays is complicated by their nonperiodic nature along the interface normal and by their large ordering period along the interface. An appropriate description along both of these directions is, however, crucial to accurately determine the long-range strain field associated with the dislocation. The interfacial Moiré periodicity can be determined by X-ray diffraction experiments (see Figure 1a–c for a plane-view and line cuts through the reciprocal space volume) and best fits simulated diffraction patterns for a 106/107 type Moiré motif. (13) This periodicity with a Moiré lattice constant of 40.8 nm also compensates for the 0.93% lattice mismatch between the STO film and the LSAT substrate. The associated interfacial dislocation structure matches this periodicity as shown by the high-angle annular dark-field (HAADF)-STEM image and associated strain map in Figure 1d,e.

Figure 1. (a) In-plane projection of the X-ray diffraction of the (22̅4) reflection of SrTiO₃/LSAT thin films with a Moiré lattice. Line cuts through the (b) film (L = 4.000) and (c) substrate (L = 4.034) reflections show the periodicity of the Moiré lattice. (d) HAADF-STEM image of a STO thin film grown on a LSAT (001) substrate and (e) corresponding strain map along the x direction calculated by geometric phase analysis. The misfit dislocations appear as butterflylike features at the STO/LSAT interface with a compression region (in blue) and a tensile region (in yellow). (f) Structure of the periodically repeated relaxed MD model of the dislocation array at the SrTiO₃/LSAT interface with the dislocations and the (2 × 107 × 60) simulation cell highlighted. Only the B–O bonding network and the A-site atoms are shown for clarity. Insets show the initial unrelaxed part of the structure with the removed STO plane and the extracted DFT cluster model, respectively. In the DFT model, the faded-out atoms are fixed during DFT geometry optimization to impose elastic boundary conditions.

In order to obtain a reliable computational description of the 2D Moiré pattern at the interface of a thin film of STO on LSAT (001), we employed the simulation setup schematically shown in Figure 1f, which is a combination of the simulation approaches suggested in refs (20), (23), and (24). We started by creating two dislocations with opposite Burgers vectors in a simulation box with dimensions ∼0.75 nm × 41.50 nm × 23.51 nm (approximately 64,000 atoms) corresponding to a 2 × 107 × 60 supercell of a 5-atom cubic perovskite unit cell. The number of cells along the y axis allows us to reproduce the observed periodicity of the Moiré superlattice, while along the z axis, we stacked 30 STO on 30 LSAT layers. This means that the two dislocation cores are separated by about 11.76 nm along the z axis, which is sufficient to significantly suppress interactions between them. A missing plane is then created in the middle of the cell by removing one SrO and one TiO₂ plane (see Figure 1f). The system is relaxed via classical MD (see below for details), during which the missing plane heals, forming two dislocations with opposite Burgers vectors at the upper and lower interfaces.

DFT calculations (see below for details) are then performed on a cluster model created from the final MD structure by extracting a section of 2 × 10 × 10 STO/LSAT unit cells around the bottom dislocation core (Figure 1f). This cell contains 950 atoms and 5 STO and 5 LSAT layers along the z axis. For the LSAT substrate, 18 La and 82 Sr, as well as 59 Al and 41 Ta atoms, were randomly introduced at the A and B sites, respectively, to obtain a charge-neutral LSAT layer with a composition (La_0.2Sr_0.8Al_0.4Ta_0.6O₆) similar to that of the experiment (La_0.3Sr_0.7Al_0.3Ta_0.7O₆). The cluster was periodically repeated along the dislocation line only (x axis), while in the perpendicular directions, only the periodicity of the electrostatic potential was imposed. Furthermore, atoms in the boundary region were kept fixed throughout the simulation to impose the elastic boundary conditions of the interface and dislocation environment. Within this approach, it is possible to avoid artifacts due to the interaction of the dislocation with its images in neighboring cells, thus isolating the dislocation core. The dislocation core is embedded in the correct long-range elastic field, allowing, at the same time, to minimize any spurious effect due to long-range electrostatic fields. (23)

Neutral vacancies (V_X) were created by removing one X (X = O, La, Al, and Ta) atom from the DFT dislocation model. Ti-substitution at Al (Ti_Al) or Ta (Ti_Ta) sites and Ta-substitution of Ti atoms (Ta_Ti) were also taken into account. Different possible vacancies and substitutional defect configurations involving different sites around the dislocation were considered. All data are available on the Materials Cloud Archive. (25)

2.1.2. Molecular Dynamics

The LAMMPS (26) code was used to perform the classical MD simulations. Interatomic interactions were described using a nonpolarizable rigid-ion model consisting of long-range electrostatic interactions between the nuclei and a short-range Buckingham potential with a cutoff radius of 12 Å

V_{i j} = \frac{q_{i} q_{j}}{4 π ϵ_{0} r_{i j}} + A_{i j} e^{- r_{i j} / ρ_{i j}} - \frac{C_{i j}}{r_{i j}^{6}}

(1)

where q_i/j is the atomic charge, r_ij is their separation, and A_ij, ρ_ij, and C_ij are the parameters of the short-range potential as reported in Table 1. The short-range parameters were derived by starting from the Lewis and Catlow (27) set and using the GULP code (28−30) to fit lattice parameters and elastic constants of STO and LSAT derived from DFT calculations (see below). For LSAT, we chose to describe the interaction between the O and A/B dummy atoms representing the average properties of the La/Sr and Al/Ta atoms occupying the A and B sites, respectively. MD simulations were performed in the canonical (NVT) ensemble with a Nose–Hoover thermostat and barostat. The system was allowed to relax first at 50 K for 50 ps and then at 1473 K for 130 ps before the temperature was reduced again to 50 K over 120 ps. In order to drain the kinetic energy released during closing the missing plane in a controlled way, a viscous damping force with a coefficient γ = 1.0 eV·ps/Å² is applied to all atoms.

Table 1. Parameters of the Coulomb–Buckingham Potentials for STO and LSAT

i	j	q_i (e)	A_ij (eV)	ρ_ij (Å)	C_ij (eV/Å^–⁶)
Sr	O	2.00	1324.77	0.3008	0.00
Ti	O	4.00	762.26	0.4014	0.00
A	O	2.18	2018.14	0.2876	0.00
B	O	3.82	867.03	0.3828	0.00
O	O	–2.00	22764.30	0.1490	31.15

DFT calculations to determine lattice parameters and elastic constants used in potential fitting were performed with the VASP code. (31−34) We used the PBE (35) exchange-correction functional together with PAW (36,37) potentials with La(5s, 5d, 5p, and 6s), Sr(4s, 4p, and 5s), Al(3s and 3p), Ta(5p, 5d, and 6s), and O(2s and 2p) valence electrons and a plane-wave cutoff of 550 eV. For LSAT, we used a

7.76 Å \times 10.97 Å \times 10.97 Å 2 \times 2 \sqrt{2} \times 2 \sqrt{2}

supercell of the 5-atom cubic unit cell with composition La₃Sr₁₃Al₉Ta₇O₄₈, the reciprocal space of which was sampled with a 4 × 4 × 4 Monkhorst–Pack (38) mesh, while a 8 × 8 × 8 mesh was used for the 5-atom STO unit cell (3.90 Å × 3.90 Å × 3.90 Å). Structures were relaxed until forces converged below 10^–4 eV/Å before elastic constants were determined using a central finite-differences approach with a step size of 0.015 Å.

2.1.3. DFT Calculations

The DFT calculations on the cluster model were performed with the CP2K program package (39) using the PBE (35) exchange–correlation functional. The norm-conserving Goedecker–Teter–Hutter (GTH) pseudopotentials (40) together with the GTH double-ζ polarized molecularly optimized basis sets (41) and an energy cutoff of 750 Ry were applied. The convergence criterion for the self-consistent field method was set to 1 × 10^–6 Ha, while atomic positions were relaxed within a force threshold of 10^–3 eV/Å.

The defect formation energy (E_f) of a neutral defect was calculated as described in ref (42)

E_{f} (μ_{i}) = E_{t o t, def} - E_{t o t, s t o i c} - \sum_{i} n_{i} μ_{i}

(2)

where E_tot,def and E_tot,stoic are the DFT total energies of the defective system and of the stoichiometric cell, respectively. n_i indicates the number of atoms of a certain species i that is added (n_i > 0) or removed (n_i < 0) from the supercell to form the defect, while μ_i is the species’ chemical potential. For simplicity, we used the atomic energy of the corresponding reference phase for each element (metal La, Ta, Ti, Al, and molecular O₂) as the chemical potential.

2.2. Experimental Methods

2.2.1. X-ray Diffraction

X-ray diffraction was measured at the surface diffraction endstation of the materials science beamline at the Swiss Light Source. X-rays of 12.65 keV were focused with a beam size of 500 × 500 μm on the sample at room temperature. The (22̅4) reflection was measured with an area detector after alignment of the UB matrix with 3 orthogonal and 2 nonorthogonal reflections. The detector images were converted to reciprocal space according to Schlepütz et al., (43) and the data were analyzed using the xrayutilities package. (44)

2.2.2. Scanning Transmission Electron Microscopy

Electron-transparent samples for STEM investigations were produced in a cross-section geometry using an FEI Helios 660 G3 UC dual-beam focused (Ga) ion beam instrument operated at 30 and 5 kV, after the deposition of C and Pt protective layers. HAADF STEM, EELS, and EDX were carried out using a probe aberration-corrected FEI Titan Themis microscope operated at 300 kV and equipped with a SuperX EDX system and a CEFID energy filter in combination with an ELA direct electron detector (for details, see ref (45)). For the HAADF-STEM data acquisition, a probe convergence semiangle of 26 mrad was set, and the inner angle of the annular semidetection range was 171 mrad. The EELS data were obtained with a collection semiangle of 35 mrad yielding an effective collection angle of about 29.5 mrad considering the energy range of the spectra.

A quantitative analysis of the lattice distortions at the dislocation cores was performed by means of peak-pair analysis (PPA), fitting the peaks corresponding to the atomic columns in the high-resolution HAADF-STEM images as described in ref (46). In particular, we analyzed the structural distortions by measuring the distance between the peaks corresponding to the atomic columns of the A sublattice.

3. Results and Discussion

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3.1. Structure and Strain Field at the Dislocation Core

As already discussed in ref (13), high-resolution STEM images of the annealed STO/LSAT samples reveal the presence of a highly ordered arrangement of edge dislocations with periodicity equivalent to the one of the Moiré lattice observed by high-resolution X-ray diffraction reciprocal space mapping. These dislocations form where the local structural mismatch between the two materials is the largest (see Figure 2b). In the present work, the HAADF-STEM images have been used to map the strain field around the dislocation core, as reported in Figure 2a. The strain field is, indeed, highly localized around the dislocation core, where two different strain regions can be identified: a tensile strain region in the STO film and a compressive strain region in the LSAT layer.

Figure 2. (a) Map of the interatomic distances (in Å) for the A sublattice along the horizontal direction as obtained by PPA from the HAADF-STEM image in (b). (c) Map of horizontal interatomic A–A distances extracted from the DFT-relaxed dislocation core structure shown in (d). Circles are located at the midpoint of A–A pairs and are color-coded according to the distance between that pair. (e) Electronic density of states (DOS) projected on the atoms at the dislocation core for the stoichiometric dislocation model. The vertical dashed line indicates the position of the Fermi level. (f) Charge density isosurface (10^–2 e/Å³) in the energy range highlighted in red in (e).

Figure 2d shows the final structure of the dislocation core obtained after DFT geometry optimization starting from the structure extracted from the MD simulations. The strain field associated with this model was computed by extracting A–A distances parallel to the interface, as shown in Figure 2c. In this case, the largest strains are also observed at the dislocation core with an average tensile/compressive strain in the STO/LSAT layer, respectively. Overall, the strain-field maps derived from experiments and DFT calculations show a qualitative agreement, allowing us to confidently use the DFT model to understand the structural properties of the dislocation core at the atomic level.

As shown in Figure 2d, highly strained Ti–O–Ti bonds are established across the missing planes, leaving the B cations of the extra Ta/AlO₂ plane undercoordinated at the dislocation core. The missing Al–O bonds at the STO/LSAT interface induce hole doping of the system, as can be seen from the DOS projected on the atoms at the dislocation core (Figure 2e), where the Fermi level crosses the top of the valence band, which is formed by the O-2p states of the O atoms bonded to the undercoordinated B cations at the dislocation core (Figure 2f).

Despite the overall qualitative agreement, the dislocation core imaged by STEM shows contrast differences larger than expected from the structural and electronic changes in the DFT model, which could result from the DFT model being constructed with stoichiometric STO and LSAT, while point defects, such as oxygen and cation vacancies or substitutional defects, may be present in experiment.

3.2. Defect Chemistry of the Dislocation Core

3.2.1. Oxygen Vacancies

EELS applied to the STO/LSAT interface can be used to obtain information on both the O and Ti states from the O–K (O 1s → 2p) and Ti–L_3,2 (Ti 2p → 3d) core edges and could thus provide information about the presence of oxygen vacancies at the interface between the two oxides. The O–K edge map of Figure 3b appears to be darker at the dislocation core, pointing to the presence of oxygen vacancies in this region. At the O–K edge, the unoccupied O p-DOS in the presence of a core hole is probed, and thus, its intensity is expected to be reduced in the presence of oxygen vacancies that are, generally, electron donors in transition metal oxides. (47)

Figure 3. (a) HAADF-STEM image of a dislocation at the STO/LSAT interface and corresponding atomic-resolution maps of the (b) O–K and (c) Ti–L_3,2 excitation edges. The scale bar is 1 nm. (d) Representative Ti–L_3,2 EELS spectra of the STO film and the surroundings of the dislocation core. The spectra have been normalized to the L₂ e_g peak height for clarity.

To investigate the formation of oxygen vacancies (V_O) around the dislocation using DFT, we considered, for simplicity, a single neutral V_O created at different oxygen sites in our STO/LSAT dislocation model. The map reported in Figure 4a is color-coded according to the V_O formation energy of each V_O site relative to that of the most stable site (ΔE_f). The energetically most favorable site to form a V_O is at the dislocation core for the O atoms of the extra Ta/AlO₂ plane closest to the STO/LSAT interface. This can be ascribed to the removal of an undercoordinated O atom to form this defect. It was already observed that similar to what happens at surfaces and grain boundaries, also at the dislocation core, undercoordination can result in a lowering of E_f. (20) Furthermore, as seen above, the DOS of the stoichiometric dislocation model is characterized by hole states right above the Fermi level and localized on the undercoordinated O atoms at the dislocation core (Figure 2e). These hole states can be filled by the two extra electrons left in the lattice upon the formation of a neutral V_O (Figure 4b). The formation energy gradually increases with increasing distance from the dislocation core, with larger values in LSAT compared to those in STO, which is easier to reduce, as shown by the computed V_O formation energies in the two bulk materials (STO: 3.90 eV and LSAT: 5.04 eV). It also agrees with tensile strain, as in the STO layer, favoring neutral V_O formation based on chemical expansion arguments. (48) These results suggest that V_O has the tendency to segregate to the dislocation core and, in particular, to the STO side of the interface, in agreement with information obtained from the O–K edge EELS spectral map.

Figure 4. (a) Color map of the relative V_O formation energy (ΔE_f) around the dislocation core. Electronic DOS projected on the atoms at the dislocation core for the STO/LSAT interface model containing (b) one, (c) two, and (d) three V_O in the most stable configurations. The vertical dashed line indicates the position of the Fermi level.

The Ti-L_3,2 map of Figure 3c shows that Ti atoms tend to diffuse into the LSAT. Interestingly, the Ti-L_3,2 EELS spectra acquired in the STO film far away from the interface and around the dislocation core show striking differences (Figure 3d). Both spectra are composed of two main features, namely, the L₃ and L₂ edges, separated by about ∼5.5 eV due to the spin–orbit splitting of the Ti 2p core hole into 2p_3/2 and 2p_1/2 states. Besides, these edges are further subdivided into two peaks, the t_2g and e_g peaks, by the strong octahedral crystal-field splitting arising from the surrounding oxygen atoms. In particular, the spectrum acquired at the dislocation is characterized by a relative increase in the spectral weight of the Ti-L_3,2 t_2g peaks, especially in the higher-energy L₂ edge, compared with the spectrum of the STO film. Previously, such spectral changes were related to the presence of Ti³⁺ in nominally Ti⁴⁺-based perovskite oxides. (49) Aside from this, the energy shift to lower energies of the Ti-L_3,2 edge observed in the dislocation spectrum with respect to the spectra obtained in the STO film suggests the presence of reduced Ti³⁺ species in the dislocation core compared to Ti⁴⁺ in the STO film. (47)

This change in the oxidation state is consistent with electron doping due to neutral V_O at the dislocation core. Unfortunately, our DFT results did not show a complete reduction of Ti atoms at or around the dislocation core. Indeed, the DOS in Figure 4b–d do not show any filled localized state with Ti-3d character, inherent with reduction of Ti atoms to Ti³⁺ even in the presence of three V_O, positioned, for simplicity, at the most stable sites according to Figure 4a. The absence of DOS features related to Ti reduction could be due to the limitations of our DFT method. It is well known that standard semilocal DFT functionals, such as PBE, fail in localizing the charge on Ti atoms neighboring a V_O for small bulk STO cells. (50) Test calculations using a Hubbard-corrected PBE + U functional did not yield localized Ti³⁺ either. We note that hybrid functionals have shown promise in obtaining these excess charge locations in STO. (51−53) Apart from being too computationally intensive for our simulation cells, these functionals may, due to the slight overestimation of the band gap, result in states that are too deep in the gap and, given the underestimation of the crystal field splitting, may have an e_g rather than a t_2g character. (54,55) The position of the defect states is, however, improved for very large cell sizes, where oxygen vacancy defect states become shallower. (54)

However, with increasing the number of V_O, we observe a small peak with Ti-3d character at the bottom of the CB (see the arrow in Figure 4b) that is present for a single V_O to disappear, while the states with O-2p character at the top of the valence band are lowered in energy. This suggests a filling of Ti states for an increasing number of V_O and hence an increase in electron doping. This is supported by an analysis of the Mulliken charges for Ti atoms. Already in the stoichiometric dislocation model, Ti ions close to the dislocation core are more reduced compared to the rest of the Ti sites in STO (Figure 5a). The creation of the first V_O at the dislocation core, when the dislocation hole state is only partially filled, does not significantly alter the charge of these Ti atoms. These charges, however, increase for 2 or 3 V_O in STO around the dislocation (Figures 5b–d). These results suggest that the Ti³⁺ detected by EELS in the vicinity of the dislocation stems from both the presence of the dislocation and the formation of V_O.

Figure 5. Mulliken charges for the Ti atoms in (a) the stoichiometric dislocation model and in the presence of (b) one, (c) two, and (d) three V_O. The black squares indicate the position of the V_O.

3.2.2. Cation Vacancies

To further characterize the defect chemistry of the STO/LSAT interface, we performed chemical mapping with atomic resolution using EDX. The positions of the atomic columns visualized in the EDX maps, shown in Figure 6b–g for Sr, Ti, O, La, Al, and Ta, reveal the chemical structure at the STO/LSAT interface at and around the dislocation core: cation vacancies (especially V_Al, V_La, and V_Ta) are formed around the dislocation core, which are (partially) filled by Ti diffusing from STO into LSAT. At the same time, a partial substitution of Ti by Ta takes place in the STO film above the dislocation.

Figure 6. (a) HAADF-STEM image of a misfit dislocation at the STO/LSAT interface and (b–g) corresponding elemental maps of Sr, Ti, O, La, Al, and Ta calculated from an EDX spectrum image using the Sr–K, Ti–K, O–K1, La–L, Al–K1, and Ta–L lines, respectively. The scale bar is 1 nm.

EDX mapping suggests that a combination of different defects accompanies dislocation formation that is driven by strain relaxation. It is, however, impractical to compute these defects simultaneously due to the size of the model and the large number of defect types and configurations that would have to be taken into account. We thus try to identify guiding rules for point defect formation in the vicinity of the dislocation core at the STO/LSAT interface by considering the most relevant defect types separately.

We start by investigating the formation of a single neutral Ta (V_Ta) and Al (V_Al) vacancy, for which the experiment shows Ta atoms to diffuse into STO, while Al diffuses out of dislocation cores that appear elementally hollow. The map of relative formation energies in Figure 7a indicates that one of the most stable V_Ta configurations is at the STO/LSAT interface, closest to the dislocation core. Interestingly, all other V_Ta molecules have much larger formation energies (by 1.2 eV) and are thus much less favorable to form. More generally, we observe that V_Ta positions with low E_f values are located in a trapezoidal area below the dislocation core (see Figure 7a). This peculiar profile matches with the magnitude of the compressive strain in the LSAT region (Figure 2c), which is known to lower the formation of cation vacancies. (48) This result suggests that V_Ta strongly favors a trapezoidal area below the dislocation core, in agreement with the EDX maps and the STEM image contrast (Figure 2b). Instead, V_Al formation is less sensitive to strain, consistent with the smaller radius of Al³⁺, favorable sites being both at the STO/LSAT interface close to the dislocation core as well as further into the LSAT substrate, in agreement with EDX mapping.

Figure 7. Color map of the relative (a) V_Ta and (b) V_Al formation energy (ΔE_f) around the dislocation core. The energy of the most stable defect is used as a reference in each plot. The shaded trapezoidal area in (a) indicates where V_Ta tends to form/segregate. Electronic DOS projected on the atoms at the dislocation core containing (c) one V_Al and (d) one V_Ta, each at the most stable site at the STO/LSAT interface or (e) away from the interface in LSAT. (f–h) show charge density isosurfaces (10^–2 e/Å³) in the energy range of the defect states highlighted in brown or orange in the DOS.

As expected, the formation of both V_Ta and V_Al leads to the creation of holes, as shown by the empty peaks with an O character above the Fermi level in Figures 7c–e. These states are localized on O atoms at the dislocation core when the vacancy is formed close to the core or on O atoms adjacent to the defect when the vacancy is further from the core (Figures 7f–h). Filling of these defect states at the dislocation core by electron doping, for example, due to oxygen vacancies, could further favor V_O formation at the dislocation core and result in conductivity along the dislocation line. For these reasons, we re-evaluated the formation of a V_O in the presence of a V_Ta. The comparison of Figures 8a and 4a suggests that E_f for a V_O is lowered due to the V_Ta, with a reduction of up to 3 eV for O positions close to the V_Ta and both in LSAT and STO. For neighboring V_Ta and V_O at the dislocation core, the excess electrons due to V_O formation partially heal the V_Ta hole state, as can be seen by comparing Figure 8b,c with Figure 7b,e.

Figure 8. (a) Color map of the relative V_O formation energy (ΔE_f) around the dislocation core in the presence of a V_Ta, indicated by the orange square. (b) DOS projected on the atoms at the dislocation core containing one V_Ta at the dislocation core and one V_O at a neighboring site. (c) Charge density isosurfaces (10^–2 e/Å³) in the energy range of the defect state highlighted orange in the DOS.

3.2.3. Substitutional Defects

Since the interdiffusion of B-site cations, namely, Ti, Al, and Ta, between LSAT and STO is clearly visible in the EDX maps (Figure 6), we also considered the possibility of Ti substituting Al (Ti_Al) or Ta (Ti_Ta) in the LSAT substrate and of Ta substituting Ti (Ta_Ti) in the STO film. When Ta_Ti is formed in STO (Figure 9c), we observe fairly strong variations in the formation energy for the explored configurations, with low values at the interface adjacent to the dislocation core but also further up in STO, in line with EDX maps showing Ta diffusion to 3 or even more Ti layers from the interface. Results for Ti diffusion into LSAT, forming Ti_Ta or Ti_Al (Figure 9a,b) are, instead, at odds with experiments and suggest that Ti should not be mainly located at the dislocation core, contrary to what is shown in Figure 6c.

Figure 9. Color map of the relative (a) Ti_Al, (b) Ti_Ta, and (c) Ta_Ti formation energy (ΔE_f) around the dislocation core. The energy of the most stable defect is used in each plot as a reference.

This result suggests that the Ti/Ta/Al intermixing observed experimentally could be the result of a complex interplay between different defect types, some of which can lead to excess charges. To further investigate the effect of electron or hole doping on the cation interdiffusion, we select the two example defects, Ta_Ti and V_Ta, that result in electron and hole doping, respectively, and reevaluate Ti_Al and Ti_Ta formation in LSAT in the presence of these defects. Figure 10 reports the average Mulliken charges for Ti atoms in STO (Ti_bulk) or at the dislocation core (Ti_core) for different single defects in the dislocation model. This data shows, indeed, that while Ti_bulk stays unaltered, Ti_core is oxidized/reduced in the presence of a Ta_Ti/V_Ta compared to the stoichiometric model. Instead, Ti-substitution in LSAT (Ti_Ta or Ti_Al) does not significantly alter the charges of Ti_bulk or Ti_core, but instead the substitutional Ti atom (Ti_sub) is oxidized compared to Ti_bulk, especially when substitution takes place at the Ta site. Comparison of Figures 9 and 11 indicates that reducing Ta_Ti leading to electron doping at the dislocation core favors Ti-substitution around the dislocation at less oxidizing Al³⁺ sites, while hole doping by V_Ta at the dislocation core increases Ti-substitution at the more oxidizing Ta⁵⁺ site due to charge compensation reasons. In summary, these data show that while Ti diffusion into LSAT is unlikely without other defects, it is facilitated by the simultaneous presence of V_Ta or by Ta diffusion into STO (Ta_Ti).

Figure 10. Average Mulliken charges for Ti atoms in STO far from the dislocation core (Ti_bulk), Ti atoms close to the dislocation core (Ti_core), and substitutional Ti atoms in LSAT (Ti_sub).

Figure 11. Color map of the relative formation energy (ΔE_f) of a Ti_Al in the presence of one (a) Ta_Ti or (b) V_Ta and of a Ti_Ta in the presence of one (c) Ta_Ti or (d) V_Ta. The energy of the most stable defect is used in each plot as a reference. The black square indicates the position of the Ta_Ti or V_Ta defect.

4. Conclusions

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In this work, we investigated the atomic structure and defect chemistry of the highly ordered Moiré network of dislocations formed at the interface between an STO thin film grown on an LSAT substrate, combining experimental and theoretical techniques. Combined MD and DFT calculations lead to an atomic-scale model of the dislocation core that features undercoordinated Ta/Al cations at the interface and has a strain field in nice agreement with the one derived from high-resolution STEM data.

Both EELS and DFT results indicate that oxygen vacancies (V_O) easily form at the dislocation core and in the STO above the dislocation core. Furthermore, DFT calculations show that the experimentally observed Ti³⁺ around the dislocation core is due to both the dislocation structure itself and the presence of V_O.

EDX mapping suggests that cation vacancies form at the dislocation core in LSAT: Ti substitutes Al and Ta around the dislocation core in LSAT, and a partial substitution of Ta by Ti takes place in the STO film above the dislocation core. DFT calculations confirm that cation vacancies are favored to form in a compressively strained region below the dislocation core, leading to hole doping that, in turn, further favors V_O formation at the core. Finally, we show that Ti diffusion into the LSAT substrate below the dislocation core only occurs in the presence of cation vacancies (favoring substitutions at Ta sites) or concurrently with the diffusion of Ta into STO (favoring substitution at the Al site).

Even though additional defect combinations and sites further from the dislocation core could be explored, the present DFT results and their good agreement with the experiment lead to a deeper understanding of the structure and electronic properties of these systems. Our results show, in particular, the predominance of p-type 1D conductivity along the dislocations, depending on the defects present also with shallow acceptor states. These results will be instrumental in further engineering the functional properties of these systems.

Author Information

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Corresponding Author
- Ulrich Aschauer - Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland; Department of Chemistry and Physics of Materials, University of Salzburg, Jakob-Haringer-Street 2A, A-5020 Salzburg, Austria; https://orcid.org/0000-0002-1165-6377; Email: [email protected]
Authors
- Chiara Ricca - Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
- Elizabeth Skoropata - Swiss Light Source, Paul Scherrer Institut, Forschungsstrasse 111, 5232 Villigen PSI, Switzerland
- Marta D. Rossell - Electron Microscopy Center, Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland; https://orcid.org/0000-0001-8610-8853
- Rolf Erni - Electron Microscopy Center, Empa, Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, 8600 Dübendorf, Switzerland; https://orcid.org/0000-0003-2391-5943
- Urs Staub - Swiss Light Source, Paul Scherrer Institut, Forschungsstrasse 111, 5232 Villigen PSI, Switzerland; https://orcid.org/0000-0003-2035-3367
Notes
The authors declare no competing financial interest.

Acknowledgments

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C.R. and E.S. were supported by the NCCR MARVEL, a National Centre of Competence in Research, funded by the Swiss National Science Foundation (grant number 182892). E.S. was also supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement no 884104 (PSI-FELLOW-III-3i). Computational resources were provided by the University of Bern (on the HPC cluster UBELIX, http://www.id.unibe.ch/hpc) and by the Swiss National Supercomputing Center (CSCS) under project ID mr26.

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Nano Letters (2017), 17 (11), 7062-7066CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
Polar discontinuities and redox reactions provide alternative paths to create two-dimensional electron liqs. (2DELs) at oxide interfaces. Herein, we report high mobility 2DELs at interfaces involving SrTiO3 (STO) achieved using polar La7/8Sr1/8MnO3 (LSMO) buffer layers to manipulate both polarities and redox reactions from disordered overlayers grown at room temp. Using resonant X-ray reflectometry expts., we quantify redox reactions from oxide overlayers on STO as well as polarity induced electronic reconstruction at epitaxial LSMO/STO interfaces. The anal. reveals how these effects can be combined in a STO/LSMO/disordered film trilayer system to yield high mobility modulation doped 2DELs, where the buffer layer undergoes a partial transformation from perovskite to brownmillerite structure. This uncovered interplay between polar discontinuities and redox reactions via buffer layers provides a new approach for the design of functional oxide interfaces.
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Burian, M.; Pedrini, B. F.; Ortiz Hernandez, N.; Ueda, H.; Vaz, C. A. F.; Caputo, M.; Radovic, M.; Staub, U. Buried Moiré Supercells Through SrTiO₃ Nanolayer Relaxation. Phys. Rev. Res. 2021, 3, 013225, DOI: 10.1103/PhysRevResearch.3.013225
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Buried moire supercells through SrTiO3 nanolayer relaxation
Burian, Max; Pedrini, Bill Francesco; Ortiz Hernandez, Nazaret; Ueda, Hiroki; Vaz, C. A. F.; Caputo, Marco; Radovic, Milan; Staub, Urs
Physical Review Research (2021), 3 (1), 013225CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)
We identified a highly ordered moire lattice at the buried SrTiO3 (STO)-(La,Sr)(Al,Ta)-oxide (LSAT) interface by high-resoln. x-ray diffraction reciprocal space mapping. We found long-ranged ordered supercells of 106/107 unit cells of unstrained STO-LSAT caused by complete lattice relaxation through high-temp. annealing. Transmission electron microscopy images show that this periodicity is based on line dislocations at the interface region. The presence of such ordered superstructures in such widely used complex oxides sets the ideal conditions for moire-tuned interfacial electronic modifications and ferroelec. supercrystallinity, opening the possibility for interface functionalities and impacting findings on vortex structured multilayers systems.
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Adler, S. B. Chemical Expansivity of Electrochemical Ceramics. J. Am. Ceram. Soc. 2004, 84, 2117– 2119, DOI: 10.1111/j.1151-2916.2001.tb00968.x
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Aschauer, U.; Pfenninger, R.; Selbach, S. M.; Grande, T.; Spaldin, N. A. Strain-Controlled Oxygen Vacancy Formation and Ordering in CaMnO₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 054111, DOI: 10.1103/PhysRevB.88.054111
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Strain-controlled oxygen vacancy formation and ordering in CaMnO3
Aschauer, Ulrich; Pfenninger, Reto; Selbach, Sverre M.; Grande, Tor; Spaldin, Nicola A.
Physical Review B: Condensed Matter and Materials Physics (2013), 88 (5), 054111/1-054111/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
We use 1st-principles calcns. to investigate the stability of biaxially strained Pnma perovskite CaMnO3 towards the formation of O vacancies. Our motivation is provided by promising indications that novel material properties can be engineered by application of strain through coherent heteroepitaxy in thin films. While it is usually assumed that such epitaxial strain is accommodated primarily by changes in intrinsic lattice consts., point defect formation is also a likely strain-relaxation mechanism. Our 1st-principles calcns. of O vacancy defect formation energy indeed show a strong strain dependence: We find that tensile strain lowers the formation energy, consistent with the established chem. expansion concept that O deficiency increases the molar volume in oxides. In addn., we find that strain differentiates the formation energy for different lattice sites, suggesting its use as a route to engineering vacancy ordering in epitaxial thin films.
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Aidhy, D. S.; Liu, B.; Zhang, Y.; Weber, W. J. Strain-Induced Phase and Oxygen-Vacancy Stability in Ionic Interfaces From First-Principles Calculations. J. Phys. Chem. C 2014, 118, 30139– 30144, DOI: 10.1021/jp507876m
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Strain-Induced Phase and Oxygen-Vacancy Stability in Ionic Interfaces from First-Principles Calculations
Aidhy, Dilpuneet S.; Liu, Bin; Zhang, Yanwen; Weber, William J.
Journal of Physical Chemistry C (2014), 118 (51), 30139-30144CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
Understanding interfacial chem. is becoming crucial in materials design for heterointerfaces. Using d. functional theory, the authors elucidate the effect of strained interfaces on phase and oxygen-vacancy stability for CeO2|ZrO2, ThO2|ZrO2 and CeO2|ThO2 interfaces. The calcns. show that ZrO2 transforms from cubic fluorite to the orthorhombic columbite under tensile strain providing evidence of a previous exptl. speculation of an unrecognized ZrO2 phase. The authors also show oxygen vacancy formation energy decreases in the presence of tensile strain. As a result, the interfacial strain could be used as a knob to stabilize oxygen vacancies on either side of the interface, and control their concn. for fast-ion conductor applications.
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Yildiz, B. Stretching” the Energy Landscape of Oxides - Effects on Electrocatalysis and Diffusion. MRS Bull. 2014, 39, 147– 156, DOI: 10.1557/mrs.2014.8
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"Stretching" the energy landscape of oxides-Effects on electrocatalysis and diffusion
Yildiz, Bilge
MRS Bulletin (2014), 39 (2), 147-156CODEN: MRSBEA; ISSN:0883-7694. (Cambridge University Press)
A review; elastic strain engineering offers a new route to enable high-performance catalysts, electrochem. energy conversion devices, sepn. membranes and memristors. By applying mech. stress, the inherent energy landscape of reactions involved in the material can be altered. This is the so-called mechano-chem. coupling. Here we discuss how elastic strain activates reactions on metals and oxides. We also present analogies to strained polymer reactions. A rich set of investigations have been performed on strained metal surfaces over the last 15 years, and the mechanistic reasons behind strain-induced reactivity are explained by an electronic structure model. On the other hand, the potential of strain engineering of oxides for catalytic and energy applications has been largely underexplored. In oxides, mech. stress couples to reaction and diffusion kinetics by altering the oxygen defect formation enthalpy, migration energy barrier, adsorption energy, dissocn. barrier, and charge transfer barrier. A generalization of the principles for stress activated reactions from polymers to metals to oxides is offered, and the prospect of using elastic strain to tune reaction and diffusion kinetics in functional oxides is discussed.
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Choudhury, S.; Morgan, D.; Uberuaga, B. P. Massive Interfacial Reconstruction at Misfit Dislocations in Metal/Oxide Interfaces. Sci. Rep. 2014, 4, 6533, DOI: 10.1038/srep06533
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Massive Interfacial Reconstruction at Misfit Dislocations in Metal/Oxide Interfaces
Choudhury, Samrat; Morgan, Dane; Uberuaga, Blas Pedro
Scientific Reports (2014), 4 (), 6533CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)
Electronic structure calcns. were performed to study the role of misfit dislocations on the structure and chem. of a metal/oxide interface. We found that a chem. imbalance exists at the misfit dislocation which leads to dramatic changes in the point defect content at the interface - stabilizing the structure requires removing as much as 50% of the metal atoms and insertion of a large no. of oxygen interstitials. The exact defect compn. that stabilizes the interface is sensitive to the external oxygen partial pressure. We relate the preferred defect structure at the interface to a competition between chem. and strain energies as defects are introduced.
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Dholabhai, P. P.; Uberuaga, B. P. Beyond Coherent Oxide Heterostructures: Atomic-Scale Structure of Misfit Dislocations. Adv. Theory Simul. 2019, 2, 1900078, DOI: 10.1002/adts.201900078
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Beyond Coherent Oxide Heterostructures: Atomic-Scale Structure of Misfit Dislocations
Dholabhai, Pratik P.; Uberuaga, Blas P.
Advanced Theory and Simulations (2019), 2 (9), n/a1900078CODEN: ATSDCW; ISSN:2513-0390. (Wiley-VCH Verlag GmbH & Co. KGaA)
A review. Nanoscale design of complex oxide heterostructures and thin films is imperative as they have significant promise in novel technol. applications. A coherent interface is formed in oxide heterostructures with small mismatches, and the lattice mismatch is completely compensated by elastic strain. In semi-coherent oxide heterostructures, when an epitaxial layer is grown on the substrate above the crit. thickness of the film, misfit dislocations are formed to mitigate the strain between the two materials with dissimilar lattice consts. Key properties of semi-coherent oxide heterostructures are influenced or even controlled by the presence of misfit dislocations. Therefore, it is crit. to understand the at.-scale structure of semi-coherent oxide heterostructures, specifically the structure of misfit dislocations that are ubiquitous at such heterointerfaces. Numerous state-of-the-art expts. have reported emergent phenomena at semi-coherent oxide heterostructures, wherein misfit dislocations play a crucial role. However, their at.-scale and nanoscale structure is not always discernable from expts. Due to large system sizes, computational studies dedicated to examg. misfit dislocations in semi-coherent oxide heterostructures are still in their infancy. This review aims to summarize the recent advancements and challenges involved in computational studies elucidating the at.-scale structure of misfit dislocations in semi-coherent oxide heterostructures and motivate future computational efforts.
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Marrocchelli, D.; Sun, L.; Yildiz, B. Dislocations in SrTiO₃: Easy to Reduce but Not So Fast for Oxygen Transport. J. Am. Chem. Soc. 2015, 137, 4735– 4748, DOI: 10.1021/ja513176u
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Dislocations in SrTiO3: Easy To Reduce but Not so Fast for Oxygen Transport
Marrocchelli, Dario; Sun, Lixin; Yildiz, Bilge
Journal of the American Chemical Society (2015), 137 (14), 4735-4748CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
The effect of dislocations on the chem., elec. and transport properties in oxide materials is important for electrochem. devices, such as fuel cells and resistive switches, but these effects have remained largely unexplored at the at. level. By using large-scale atomistic simulations, the authors uncover how a 〈100〉{011} edge dislocation in SrTiO3, a prototypical perovskite oxide, impacts the local defect chem. and oxide ion transport. In the dil. limit, oxygen vacancy formation energy in SrTiO3 is lower at sites close to the dislocation core, by ≤2 eV compared to that in the bulk. The formation of a space-charge zone based on the redistribution of charged oxygen vacancies can be captured quant. at atomistic level by mapping the vacancy formation energies around the dislocation. Oxide-ion diffusion was studied for a low vacancy concn. regime (ppm level) and a high vacancy concn. regime (up to 2.5%). In both cases, no evidence of pipe-diffusion, i.e., significantly enhanced mobility of oxide ions, was found as detd. from the calcd. migration barriers, contrary to the case in metals. However, in the low vacancy concn. regime, the vacancy accumulation at the dislocation core gives rise to a higher diffusion coeff., even though the oxide-ion mobility itself is lower than that in the bulk. The authors' findings have important implications for applications of perovskite oxides for information and energy technologies. The obsd. lower oxygen vacancy formation energy at the dislocation core provides a quant. and direct explanation for the electronic cond. of dislocations in SrTiO3 and related oxides studied for red-ox based resistive switching. Reducibility and electronic transport at dislocations can also be quant. engineered into active materials for fuel cells, catalysis, and electronics.
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Dholabhai, P. P.; Martinez, E.; Uberuaga, B. P. Influence of Chemistry and Misfit Dislocation Structure on Dopant Segregation at Complex Oxide Heterointerfaces. Adv. Theory Simul. 2019, 2, 1800095, DOI: 10.1002/adts.201800095
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Influence of Chemistry and Misfit Dislocation Structure on Dopant Segregation at Complex Oxide Heterointerfaces
Dholabhai, Pratik P.; Martinez, Enrique; Uberuaga, Blas P.
Advanced Theory and Simulations (2019), 2 (1), 1800095/1-1800095/10CODEN: ATSDCW; ISSN:2513-0390. (Wiley-VCH Verlag GmbH & Co. KGaA)
Complex oxide heterostructures and thin films have emerged as promising candidates for diverse applications. Lattice mismatch between the two oxides lead to the formation of misfit dislocations, which influence vital material features. Trivalent dopant segregation to misfit dislocations at semi-coherent oxide heterointerfaces, while not well understood, is anticipated to impact interface-governed properties. Here, atomistic simulations elucidating the influence of misfit dislocations on dopant segregation at SrTiO3/MgO heterointerfaces are reported. SrO- and TiO2-terminated interfaces that have differing misfit dislocation structure were considered for trivalent dopants segregation. At SrO-terminated interface, dopants tend to segregate toward but not precisely to the heterointerface, whereas at TiO2-terminated interface, dopants exhibit a thermodn. preference to accumulate at the heterointerface. Most favorable segregation sites at SrO-terminated interface are located within the coherent terrace, whereas those at TiO2-terminated interface are at misfit dislocation intersections. Atomic layer chem. and the resulting misfit dislocation structure at the heterointerface, along with concomitant strain at the heterointerface due to mismatched dopants, play a crit. role in influencing the obsd. trends for dopant segregation. Overall, the present results offer a fundamental at. scale perspective of dopant behavior at semi-coherent complex oxide heterointerfaces and the interplay between dopant chem., interface chem., and misfit dislocation structure.
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Marzano, C.; Dholabhai, P. P. High-Throughput Prediction of Thermodynamic Stabilities of Dopant-Defect Clusters at Misfit Dislocations in Perovskite Oxide Heterostructures. J. Phys. Chem. C 2023, 127, 15988– 15999, DOI: 10.1021/acs.jpcc.3c02367
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High-Throughput Prediction of Thermodynamic Stabilities of Dopant-Defect Clusters at Misfit Dislocations in Perovskite Oxide Heterostructures
Marzano, Chloe; Dholabhai, Pratik P.
Journal of Physical Chemistry C (2023), 127 (32), 15988-15999CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
Complex oxide heterostructures and thin films have emerged as promising candidates for diverse applications, wherein interfaces formed by joining two different oxides play a central role in novel properties that are not present in the individual components. Lattice mismatch between the two oxides leads to the formation of misfit dislocations, which often influence vital material properties. In oxides, doping is used as a strategy to improve properties, wherein inclusion of aliovalent dopants leads to formation of oxygen vacancy defects. At low temps., these dopants and defects often form stable clusters. In semicoherent perovskite oxide heterostructures, the stability of such clusters at misfit dislocations, while not well understood, is anticipated to impact interface-governed properties. Herein, we report atomistic simulations elucidating the influence of misfit dislocations on the stability of dopant-defect clusters in SrTiO3/BaZrO3 heterostructures. SrO-BaO, SrO-ZrO2, BaO-TiO2, and ZrO2-TiO2 interfaces having dissimilar misfit dislocation structures were considered. High-throughput computing was implemented to predict the thermodn. stabilities of 275,610 dopant-defect clusters in the vicinity of misfit dislocations. The misfit dislocation structure of the given interface and corresponding at. layer chem. play a fundamental role in influencing the thermodn. stability of geometrically diverse clusters. A stark difference in cluster stability is obsd. at misfit dislocation lines and intersections as compared to the coherent terraces. These results offer an at. scale perspective of the complex interplay between dopants, point defects, and extended defects, which is necessary to comprehend the functionalities of the perovskite oxide heterostructures.
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Hirel, P.; Mrovec, M.; Elsässer, C. Atomistic Simulation Study of (110) Dislocations in Strontium Titanate. Acta Mater. 2012, 60, 329– 338, DOI: 10.1016/j.actamat.2011.09.049
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Atomistic simulation study of <110> dislocations in strontium titanate
Hirel, P.; Mrovec, M.; Elsaesser, C.
Acta Materialia (2012), 60 (1), 329-338CODEN: ACMAFD; ISSN:1359-6454. (Elsevier Ltd.)
The core structures of glide-dissocd. screw and edge <110>{1‾10} dislocations in strontium titanate were investigated by using atomistic simulations. For both dislocations the Sr, Ti and O sublattices follow different patterns of elastic displacements, and the partial dislocations have extended core structures. Dissocn. distances in the range of exptl. results are obtained, and a long-standing discrepancy between theor. and exptl. predictions of the anti-phase boundary energy is resolved. Studies of dislocations under applied load reveal marked difference in mobilities of the screw and edge dislocations that are consistent with exptl. observations.
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Sun, L.; Marrocchelli, D.; Yildiz, B. Edge Dislocation Slows Down Oxide Ion Diffusion in Doped CeO₂ by Segregation of Charged Defects. Nat. Commun. 2015, 6, 6294, DOI: 10.1038/ncomms7294
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Edge dislocation slows down oxide ion diffusion in doped CeO2 by segregation of charged defects
Sun, Lixin; Marrocchelli, Dario; Yildiz, Bilge
Nature Communications (2015), 6 (), 6294CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
Strained oxide thin films are of interest for accelerating oxide ion conduction in electrochem. devices. Although the effect of elastic strain has been uncovered theor., the effect of dislocations on the diffusion kinetics in such strained oxides is yet unclear. Here we investigate a 1/2<110>{100} edge dislocation by performing atomistic simulations in 4-12% doped CeO2 as a model fast ion conductor. At equil., depending on the size of the dopant, trivalent cations and oxygen vacancies are found to simultaneously enrich or deplete either in the compressive or in the tensile strain fields around the dislocation. The associative interactions among the point defects in the enrichment zone and the lack of oxygen vacancies in the depletion zone slow down oxide ion transport. This finding is contrary to the fast diffusion of atoms along the dislocations in metals and should be considered when assessing the effects of strain on oxide ion cond.
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Ricca, C.; Skoropata, E.; Rossell, M. D.; Erni, R.; Staub, U.; Aschauer, U. Combined Theoretical and Experimental Study of the Moiré Dislocation Network at the SrTiO₃-(La,Sr)(Al,Ta)O₃ Interface. 2023, arXiv:2307.12572.
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Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1– 19, DOI: 10.1006/jcph.1995.1039
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Fast parallel algorithms for short-range molecular dynamics
Plimpton, Steve
Journal of Computational Physics (1995), 117 (1), 1-19CODEN: JCTPAH; ISSN:0021-9991.
Three parallel algorithms for classical mol. dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-at. forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for mol. dynamics models which can be difficult to parallelize efficiently - those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a std. Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers - the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C90 processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex mol. dynamics simulations are also discussed.
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Lewis, G. V.; Catlow, C. R. A. Potential Models for Ionic Oxides. J. Phys. C: Solid State Phys. 1985, 18, 1149– 1161, DOI: 10.1088/0022-3719/18/6/010
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Potential models for ionic oxides
Lewis, G. V.; Catlow, C. R. A.
Journal of Physics C: Solid State Physics (1985), 18 (6), 1149-61CODEN: JPSOAW; ISSN:0022-3719.
A method for calcg. empirical potential parameters for binary oxides is given, and their modification for use in mixed oxide systems is discussed. Shell-model potentials are used, but, unlike the case for the alkali halides within which polarizability and short-range interaction parameters can be transferred, modifications must be introduced when transferring potential parameters between different oxides. The anion polarizability varies with structure and with the nature of the host cation; changes in cation coordination are reflected in the short- range repulsive cation-anion interaction. Parameters were derived for a range of oxides, and trends in these parameters are discussed. Applications of the potentials to the calcn. of perfect lattice properties are discussed, as well as when defect and surface properties are considered. Calcns. were done on the activation energies for dopant diffusion in NiO, and the surface rumpling of MgO.
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Gale, J. D. GULP: A Computer Program for the Symmetry-Adapted Simulation of Solids. J. Chem. Soc., Faraday Trans. 1997, 93, 629– 637, DOI: 10.1039/a606455h
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GULP: a computer program for the symmetry-adapted simulation of solids
Gale, Julian D.
Journal of the Chemical Society, Faraday Transactions (1997), 93 (4), 629-637CODEN: JCFTEV; ISSN:0956-5000. (Royal Society of Chemistry)
Algorithms for the symmetry-adapted energy minimization of solids using anal. first and second derivs. have been devised and implemented in a new computer program GULP. These new methods are found to lead to an improvement in computational efficiency of up to an order of magnitude over the std. algorithm, which takes no account of symmetry, the largest improvement being obtained from the use of symmetry in the generation of the Hessian. Accelerated convergence techniques for the dispersion energy are found to be beneficial in improving the precision at little extra computational cost, particularly when a one center decompn. is possible or the Ewald sum weighting towards real-space is increased.
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Gale, J. D.; Rohl, A. L. The General Utility Lattice Program (GULP). Mol. Simul. 2003, 29, 291– 341, DOI: 10.1080/0892702031000104887
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The General Utility Lattice Program (GULP)
Gale, Julian D.; Rohl, Andrew L.
Molecular Simulation (2003), 29 (5), 291-341CODEN: MOSIEA; ISSN:0892-7022. (Taylor & Francis Ltd.)
The General Utility Lattice Program (gulp) has been extended to include the ability to simulate polymers and surfaces, as well as adding many other new features, and the current status of the program is fully documented. Both the background theory is described, as well as providing a concise review of some of the previous applications in order to demonstrate the range of its use. Examples are presented of work performed using the new compatibilities of the software, including the calcn. of Born effective charges, mech. properties as a function of applied pressure, calcn. of frequency-dependent dielec. data, surface reconstructions of calcite and the performance of a linear-scaling algorithm for bond-order potentials.
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Gale, J. D. GULP: Capabilities and Prospects. Z. für Kristallogr. - Cryst. Mater. 2005, 220, 552– 554, DOI: 10.1524/zkri.220.5.552.65070
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GULP: Capabilities and prospects
Gale, Julian D.
Zeitschrift fuer Kristallographie (2005), 220 (5-6), 552-554CODEN: ZEKRDZ; ISSN:0044-2968. (Oldenbourg Wissenschaftsverlag GmbH)
The current status and capabilities of the atomistic simulation code GULP are described. In particular, the differences between versions 1.3.2 and 3.0 are detailed, as well as a concise pointer to applications in computational crystallog.
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Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558– 561, DOI: 10.1103/PhysRevB.47.558
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Ab initio molecular dynamics of liquid metals
Kresse, G.; Hafner, J.
Physical Review B: Condensed Matter and Materials Physics (1993), 47 (1), 558-61CODEN: PRBMDO; ISSN:0163-1829.
The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.
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Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal - Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 14251– 14269, DOI: 10.1103/PhysRevB.49.14251
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Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium
Kresse, G.; Hafner, J.
Physical Review B: Condensed Matter and Materials Physics (1994), 49 (20), 14251-69CODEN: PRBMDO; ISSN:0163-1829.
The authors present ab initio quantum-mech. mol.-dynamics simulations of the liq.-metal-amorphous-semiconductor transition in Ge. The simulations are based on (a) finite-temp. d.-functional theory of the 1-electron states, (b) exact energy minimization and hence calcn. of the exact Hellmann-Feynman forces after each mol.-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nose' dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows the authors to perform simulations over >30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liq. and amorphous Ge in very good agreement with expt.. The simulation allows the authors to study in detail the changes in the structure-property relation through the metal-semiconductor transition. The authors report a detailed anal. of the local structural properties and their changes induced by an annealing process. The geometrical, bounding, and spectral properties of defects in the disordered tetrahedral network are studied and compared with expt.
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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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Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865– 3868, DOI: 10.1103/PhysRevLett.77.3865
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Generalized gradient approximation made simple
Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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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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Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758– 1775, DOI: 10.1103/PhysRevB.59.1758
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From ultrasoft pseudopotentials to the projector augmented-wave method
Kresse, G.; Joubert, D.
Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B: Solid State 1976, 13, 5188– 5192, DOI: 10.1103/PhysRevB.13.5188
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Kühne, T. D.; Iannuzzi, M.; Del Ben, M.; Rybkin, V. V.; Seewald, P.; Stein, F.; Laino, T.; Khaliullin, R. Z.; Schütt, O.; Schiffmann, F. CP2K: An Electronic Structure and Molecular Dynamics Software Package - Quickstep: Efficient and Accurate Electronic Structure Calculations. J. Chem. Phys. 2020, 152, 194103, DOI: 10.1063/5.0007045
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CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations
Kuehne, Thomas D.; Iannuzzi, Marcella; Del Ben, Mauro; Rybkin, Vladimir V.; Seewald, Patrick; Stein, Frederick; Laino, Teodoro; Khaliullin, Rustam Z.; Schuett, Ole; Schiffmann, Florian; Golze, Dorothea; Wilhelm, Jan; Chulkov, Sergey; Bani-Hashemian, Mohammad Hossein; Weber, Valery; Borstnik, Urban; Taillefumier, Mathieu; Jakobovits, Alice Shoshana; Lazzaro, Alfio; Pabst, Hans; Mueller, Tiziano; Schade, Robert; Guidon, Manuel; Andermatt, Samuel; Holmberg, Nico; Schenter, Gregory K.; Hehn, Anna; Bussy, Augustin; Belleflamme, Fabian; Tabacchi, Gloria; Gloess, Andreas; Lass, Michael; Bethune, Iain; Mundy, Christopher J.; Plessl, Christian; Watkins, Matt; VandeVondele, Joost; Krack, Matthias; Hutter, Juerg
Journal of Chemical Physics (2020), 152 (19), 194103CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A review. CP2K is an open source electronic structure and mol. dynamics software package to perform atomistic simulations of solid-state, liq., mol., and biol. systems. It is esp. aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio mol. dynamics simulations. Excellent performance for electronic structure calcns. is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on d. functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension. (c) 2020 American Institute of Physics.
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Goedecker, S.; Teter, M.; Hutter, J. Separable Dual-Space Gaussian Pseudopotentials. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 1703– 1710, DOI: 10.1103/PhysRevB.54.1703
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Separable dual-space Gaussian pseudopotentials
Goedecker, S.; Teter, M.; Hutter, J.
Physical Review B: Condensed Matter (1996), 54 (3), 1703-1710CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
We present pseudopotential coeffs. for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, even coeffs. are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive at. and mol. test calcns.
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VandeVondele, J.; Hutter, J. Gaussian Basis Sets for Accurate Calculations on Molecular Systems in Gas and Condensed Phases. J. Chem. Phys. 2007, 127, 114105, DOI: 10.1063/1.2770708
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Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases
VandeVondele, Joost; Hutter, Jurg
Journal of Chemical Physics (2007), 127 (11), 114105/1-114105/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We present a library of Gaussian basis sets that has been specifically optimized to perform accurate mol. calcns. based on d. functional theory. It targets a wide range of chem. environments, including the gas phase, interfaces, and the condensed phase. These generally contracted basis sets, which include diffuse primitives, are obtained minimizing a linear combination of the total energy and the condition no. of the overlap matrix for a set of mols. with respect to the exponents and contraction coeffs. of the full basis. Typically, for a given accuracy in the total energy, significantly fewer basis functions are needed in this scheme than in the usual split valence scheme, leading to a speedup for systems where the computational cost is dominated by diagonalization. More importantly, binding energies of hydrogen bonded complexes are of similar quality as the ones obtained with augmented basis sets, i.e., have a small (down to 0.2 kcal/mol) basis set superposition error, and the monomers have dipoles within 0.1 D of the basis set limit. However, contrary to typical augmented basis sets, there are no near linear dependencies in the basis, so that the overlap matrix is always well conditioned, also, in the condensed phase. The basis can therefore be used in first principles mol. dynamics simulations and is well suited for linear scaling calcns.
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Freysoldt, C.; Grabowski, B.; Hickel, T.; Neugebauer, J.; Kresse, G.; Janotti, A.; Van de Walle, C. G. First-Principles Calculations for Point Defects in Solids. Rev. Mod. Phys. 2014, 86, 253– 305, DOI: 10.1103/RevModPhys.86.253
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Schlepütz, C. M.; Mariager, S. O.; Pauli, S. A.; Feidenhans’l, R.; Willmott, P. R. Angle Calculations for a (2 + 3)-Type Diffractometer: Focus on Area Detectors. J. Appl. Crystallogr. 2011, 44, 73– 83, DOI: 10.1107/S0021889810048922
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Angle calculations for a (2+3)-type diffractometer. Focus on area detectors
Schlepuetz, Christian M.; Mariager, Simon O.; Pauli, Stephan A.; Feidenhans'l, Robert; Willmott, Philip R.
Journal of Applied Crystallography (2011), 44 (1), 73-83CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
Angle calcns. for a (2+3)-type diffractometer are presented with comprehensive derivations for both cases of either a vertical or horizontal sample configuration. This work focuses on some particular aspects of using area detectors in surface x-ray diffraction, namely the role of the detector rotation and the direct conversion of the angle-resolved diffraction signal recorded by the detector into a 2D slice through reciprocal space.
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Kriegner, D.; Wintersberger, E.; Stangl, J. xrayutilities: A Versatile Tool for Reciprocal Space Conversion of Scattering Data Recorded With Linear and Area Detectors. J. Appl. Crystallogr. 2013, 46, 1162– 1170, DOI: 10.1107/S0021889813017214
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xrayutilities: a versatile tool for reciprocal space conversion of scattering data recorded with linear and area detectors
Kriegner, Dominik; Wintersberger, Eugen; Stangl, Julian
Journal of Applied Crystallography (2013), 46 (4), 1162-1170CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
General algorithms to convert scattering data of linear and area detectors recorded in various scattering geometries to reciprocal space coordinates are presented. These algorithms work for any goniometer configuration including popular four-circle, six-circle and kappa goniometers. The use of commonly employed approxns. is avoided and therefore the algorithms work also for large detectors at small sample-detector distances. A recipe for detg. the necessary detector parameters including mostly ignored misalignments is given. The algorithms are implemented in a freely available open-source package.
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Ruiz Caridad, A.; Erni, R.; Vogel, A.; Rossell, M. D. Applications of a Novel Electron Energy Filter Combined With a Hybrid-Pixel Direct Electron Detector for the Analysis of Functional Oxides by STEM-EELS and Energy-Filtered Imaging. Micron 2022, 160, 103331, DOI: 10.1016/j.micron.2022.103331
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Applications of a novel electron energy filter combined with a hybrid-pixel direct electron detector for the analysis of functional oxides by STEM/EELS and energy-filtered imaging
Ruiz Caridad, Alicia; Erni, Rolf; Vogel, Alexander; Rossell, Marta D.
Micron (2022), 160 (), 103331CODEN: MCONEN; ISSN:0968-4328. (Elsevier Ltd.)
The performance and suitability of a new electron energy filter in combination with a hybrid pixel, direct electron detector for anal. (scanning) transmission electron microscopy are demonstrated using four examples. The STEM-EELS capabilities of the CEOS Energy Filtering and Imaging Device (CEFID) were tested with focus on weak signals and high spatio-temporal resoln. A multiferroic, multilayer structure of REMnO3 (RE = Yb, Er, Tb, Y), grown on yttria-stabilized zirconia (YSZ), is used to exemplify that this new instrumental setup produces valuable electron energy-loss spectroscopy (EELS) data at high energy losses even when using short acquisition times, providing detailed chem. information about the interfaces in this complex multilayer sample. Another functional oxide, namely a ferromagnetic La2NiMnO6 thin film grown on SrTiO3, demonstrates that atomically resolved spectrum images can be recorded, using short dwell times and moderate beam currents in order to warrant the integrity of the sample. In a third example, inhomogeneously Er-doped YSZ shows by EELS spectrum imaging that elements at low concns. can be detected semi-quant., uncovering the expected layered Er distribution but revealing substantial interdiffusion. In a final example, we simply demonstrate that the hybrid pixel detector in combination with the energy filter can also be used for energy-filtered imaging and thus for elemental mapping complementary to EELS in scanning transmission mode.
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Campanini, M.; Erni, R.; Yang, C.-H.; Ramesh, R.; Rossell, M. D. Periodic Giant Polarization Gradients in Doped BiFeO₃ Thin Films. Nano Lett. 2018, 18, 717– 724, DOI: 10.1021/acs.nanolett.7b03817
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Periodic Giant Polarization Gradients in Doped BiFeO3 Thin Films
Campanini, Marco; Erni, Rolf; Yang, Chan-Ho; Ramesh, Ramamoorthy; Rossell, Marta D.
Nano Letters (2018), 18 (2), 717-724CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
The ultimate challenge for the development of new multiferroics with enhanced properties lies in achieving nanoscale control of the coupling between different ordering parameters. In oxide-based multiferroics, substitutional cation dopants offer the unparalleled possibility to modify both the elec. and magnetic properties at a local scale. Herein it is demonstrated the formation of a dopant-controlled polar pattern in BiFeO3 leading to the spontaneous instauration of periodic polarization waves. In particular, nonpolar Ca-doped rich regions act as spacers between consecutive dopant-depleted regions displaying coupled ferroelec. states. n. This alternation of layers with different ferroelec. state creates a novel vertical polar structure exhibiting giant polarization gradients as large as 70 μC cm-2 across 30 Å thick domains. The drastic change in the polar state of the film is visualized using high-resoln. differential phase-contrast imaging able to map changes in ferroelec. polarization at at. scale. Also, a periodic distortion in the Fe-O-Fe bonding angle suggests a local variation in the magnetic ordering. The findings provide a new insight into the role of doping and reveal hitherto unexplored means to tailor the functional properties of multiferroics by doping engineering.
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Muller, D. A.; Nakagawa, N.; Ohtomo, A.; Grazul, J. L.; Hwang, H. Y. Atomic-Scale Imaging of Nanoengineered Oxygen Vacancy Profiles in SrTiO₃. Nature 2004, 430, 657– 661, DOI: 10.1038/nature02756
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Atomic-scale imaging of nanoengineered oxygen vacancy profiles in SrTiO3
Muller, David A.; Nakagawa, Naoyuki; Ohtomo, Akira; Grazul, John L.; Hwang, Harold Y.
Nature (London, United Kingdom) (2004), 430 (7000), 657-661CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
At the heart of modern oxide chem. lies the recognition that beneficial (as well as deleterious) materials properties can be obtained by deliberate deviations of oxygen atom occupancy from the ideal stoichiometry. Conversely, the capability to control and confine oxygen vacancies will be important to realize the full potential of perovskite ferroelec. materials, varistors and field-effect devices. In transition metal oxides, oxygen vacancies are generally electron donors, and in strontium titanate (SrTiO3) thin films, oxygen vacancies (unlike impurity dopants) are particularly important because they tend to retain high carrier mobilities, even at high carrier densities. Here the authors report the successful fabrication, using a pulsed laser deposition technique, of SrTiO3 superlattice films with oxygen doping profiles that exhibit subnanometre abruptness. The authors profile the vacancy concns. on an at. scale using annular-dark-field electron microscopy and core-level spectroscopy, and demonstrate abs. detection sensitivities of one to four oxygen vacancies. The authors' findings open a pathway to the microscopic study of individual vacancies and their clustering, not only in oxides, but in cryst. materials more generally.
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Aschauer, U.; Vonrüti, N.; Spaldin, N. A. Effect of Epitaxial Strain on Cation and Anion Vacancy Formation in MnO. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 054103, DOI: 10.1103/PhysRevB.92.054103
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Effect of epitaxial strain on cation and anion vacancy formation in MnO
Aschauer, Ulrich; Vonruti, Nathalie; Spaldin, Nicola A.
Physical Review B: Condensed Matter and Materials Physics (2015), 92 (5), 054103/1-054103/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
Biaxial strain in coherent epitaxial thin films can have a pronounced effect on the point-defect profile in the films' material. Detailed fundamental knowledge of the interaction of strain with point defects is crucial to understanding the stoichiometry and resulting properties of strained thin films. Here we investigate the effect of biaxial strain on the formation energy of cation and anion vacancies using MnO as a model system. Our d.-functional-theory calcns. show that, as expected from local vol. arguments, compressive strain favors the formation of cation vacancies. Interestingly, we find that small compressive and tensile strains lead to ordering of the resulting holes along the in-plane and normal direction, resp., which should manifest in different anisotropic properties in the two strain states.
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Abbate, M.; de Groot, F. M. F.; Fuggle, J. C.; Fujimori, A.; Tokura, Y.; Fujishima, Y.; Strebel, O.; Domke, M.; Kaindl, G.; van Elp, J.; Thole, B. T.; Sawatzky, G. A.; Sacchi, M.; Tsuda, N. Soft-X-Ray-Absorption Studies of the Location of Extra Charges Induced by Substitution in Controlled-Valence Materials. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 44, 5419– 5422, DOI: 10.1103/PhysRevB.44.5419
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Soft-x-ray-absorption studies of the location of extra charges induced by substitution in controlled-valence materials
Abbate, M.; De Groot, F. M. F.; Fuggle, J. C.; Fujimori, A.; Tokura, Y.; Fujishima, Y.; Strebel, O.; Domke, M.; Kaindl, G.; et al.
Physical Review B: Condensed Matter and Materials Physics (1991), 44 (11), 5419-22CODEN: PRBMDO; ISSN:0163-1829.
High-resoln. 2p x-ray-absorption spectra are presented from 3d transition metals M in three series of pseudobinary and pseudoternary oxides. The detailed shape of the multiplet within the spectra can be used to det. the valence of the M ions. The spectra of the early-transition-metal compds. show dramatic changes as a function of substitution due to changes in the M 3d occupancy, indicating that the extra holes or electrons are located predominantly at the 3d-metal sites. This contrasts strongly with the behavior of the spectra of late-transition-metal compds., for which the extra charges induced by substitution go to oxygen states.
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Ricca, C.; Timrov, I.; Cococcioni, M.; Marzari, N.; Aschauer, U. Self-Consistent DFT+U+V Study of Oxygen Vacancies in SrTiO₃. Phys. Rev. Res. 2020, 2, 023313, DOI: 10.1103/PhysRevResearch.2.023313
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Self-consistent DFT+U+V study of oxygen vacancies in SrTiO3
Ricca, Chiara; Timrov, Iurii; Cococcioni, Matteo; Marzari, Nicola; Aschauer, Ulrich
Physical Review Research (2020), 2 (2), 023313CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)
Contradictory theor. results for oxygen vacancies in SrTiO3 (STO) were often related to the peculiar properties of STO, which is a d0 transition metal oxide with mixed ionic-covalent bonding. Here, we apply, for the first time, d. functional theory (DFT) within the extended Hubbard DFT+U+V approach, including onsite as well as intersite electronic interactions, to study oxygen-deficient STO with Hubbard U and V parameters computed self-consistently via d.-functional perturbation theory. Our results demonstrate that the extended Hubbard functional is a promising approach to study defects in materials with electronic properties similar to STO. Indeed, DFT+U+V provides a better description of stoichiometric STO compared to std. DFT or DFT+U, the band gap and crystal field splitting being in good agreement with expts. In turn, also the description of the electronic properties of oxygen vacancies in STO is improved, with formation energies in excellent agreement with expts. as well as results obtained with the most frequently used hybrid functionals, however, at a fraction of the computational cost. While our results do not fully resolve the contradictory findings reported in literature, our systematic approach leads to a deeper understanding of their origin, which stems from different cell sizes, STO phases, the exchange-correlation functional, and the treatment of structural relaxations and spin-polarization.
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Ricci, D.; Bano, G.; Pacchioni, G.; Illas, F. Electronic Structure of a Neutral Oxygen Vacancy in SrTiO₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 224105, DOI: 10.1103/PhysRevB.68.224105
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Electronic structure of a neutral oxygen vacancy in SrTiO3
Ricci, Davide; Bano, Giuseppe; Pacchioni, Gianfranco; Illas, Francesc
Physical Review B: Condensed Matter and Materials Physics (2003), 68 (22), 224105/1-224105/9CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The electronic structure of an isolated oxygen vacancy in SrTiO3 has been investigated with a variety of ab initio quantum mech. approaches. In particular we compared pure d. functional theory (DFT) approaches with the Hartree-Fock method, and with hybrid methods where the exchange term is treated in a mixed way. Both local cluster models and periodic calcns. with large supercells contg. up to 80 atoms have been performed. Both diamagnetic (singlet state) and paramagnetic (triplet state) solns. have been considered. We found that the formation of an O vacancy is accompanied by the transfer of two electrons to the 3d(z2) orbitals of the two Ti atoms along the Ti-Vac-Ti axis. The two electrons are spin coupled and the ground state is diamagnetic. New states assocd. with the defect center appear in the gap just below the conduction band edge. The formation energy computed with respect to an isolated oxygen atom in the triplet state is 9.4 eV.
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Evarestov, R. A.; Kotomin, E. A.; Zhukovskii, Y. F. DFT Study of a Single F Center in Cubic SrTiO₃ Perovskite. Int. J. Quantum Chem. 2006, 106, 2173– 2183, DOI: 10.1002/qua.20855
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DFT study of a single F center in cubic SrTiO3 perovskite
Evarestov, R. A.; Kotomin, E. A.; Zhukovskii, Yu. F.
International Journal of Quantum Chemistry (2006), 106 (10), 2173-2183CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)
Various properties of a cubic phase of SrTiO3 perovskite contg. single F centers (neutral oxygen vacancies), including energies of their formation and migration, were simulated using different formalisms of d. functional theory (DFT) as implemented into CRYSTAL-2003 and VASP computer codes. The lattice relaxation around the F center was found to be sensitive to both shape and size of supercells used. The larger the supercell, the closer the defect energy level in the bandgap lies to the conduction band bottom. It approaches the optical ionization energy of 0.49 eV for 270- and 320-atom supercells, where the distance between neighboring defects increases up to four lattice consts. The defect bandwidth decreases for these supercells down to 0.02 eV, i.e., the defect-defect interaction becomes negligible. Thus, the two different first-principles periodic approaches combined provide results that are converged with respect to the supercell size and correspond to a single defect limit.
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Zhukovskii, Y. F.; Kotomin, E. A.; Piskunov, S.; Ellis, D. A Comparative Ab Initio Study of Bulk and Surface Oxygen Vacancies in PbTiO₃, PbZrO₃ and SrTiO₃ Perovskites. Solid State Commun. 2009, 149, 1359– 1362, DOI: 10.1016/j.ssc.2009.05.023
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A comparative ab initio study of bulk and surface oxygen vacancies in PbTiO3, PbZrO3 and SrTiO3 perovskites
Zhukovskii, Yu. F.; Kotomin, E. A.; Piskunov, S.; Ellis, D. E.
Solid State Communications (2009), 149 (33-34), 1359-1362CODEN: SSCOA4; ISSN:0038-1098. (Elsevier Ltd.)
Using the DFT-HF hybrid LCAO approach as implemented in the CRYSTAL computer code, we have performed large supercell comparative calcns. of neutral O vacancies (F centers) in the bulk and on the (001) surface of three cubic perovskite crystals (SrTiO3, PbTiO3, and PbZrO3). The local lattice relaxation, charge redistribution, and positions of defect energy levels within the band gap are compared. The difference in the chem. compn. of host materials leads to quite different defect properties.
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Mitra, C.; Lin, C.; Robertson, J.; Demkov, A. A. Electronic Structure of Oxygen Vacancies in SrTiO₃ and LaAlO₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 155105, DOI: 10.1103/PhysRevB.86.155105
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Electronic structure of oxygen vacancies in SrTiO3 and LaAlO3
Mitra, C.; Lin, C.; Robertson, J.; Demkov, Alexander A.
Physical Review B: Condensed Matter and Materials Physics (2012), 86 (15), 155105/1-155105/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
The electronic structure of oxygen vacancies in bulk perovskite oxides SrTiO3 and LaAlO3 is studied using the Heyd, Scuseria, Ernzerhof (HSE) hybrid d. functional. In SrTiO3 the oxygen vacancy defect introduces a localized state comprised of 3dz2 and 4pz orbitals of the adjacent Ti atoms. This results in a bound state 0.7 eV below the conduction band edge. For LaAlO3, the oxygen vacancy creates a deep state 2.19 eV below the conduction band edge. The defect state is a hybrid of the adjacent La 5d and the Al 3p states. We compute the formation energies of the neutral oxygen vacancy defect V0 in bulk SrTiO3 and LaAlO3 to be 6.0 and 8.3 eV, resp.
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Lin, C.; Mitra, C.; Demkov, A. A. Orbital Ordering Under Reduced Symmetry in Transition Metal Perovskites: Oxygen Vacancy in SrTiO₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 161102, DOI: 10.1103/physrevb.86.161102
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Orbital ordering under reduced symmetry in transition metal perovskites: oxygen vacancy in SrTiO3
Lin, Chungwei; Mitra, Chandrima; Demkov, Alexander A.
Physical Review B: Condensed Matter and Materials Physics (2012), 86 (16), 161102/1-161102/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
By using a combination of d. function theory and model Hamiltonian anal., we explain the general electronic structure features induced by an oxygen vacancy (OV) in SrTiO3. We show that the most important effect caused by an oxygen vacancy is the direct on-site coupling between the 3d3z2-r2 and 4s,4p orbitals of Ti atoms adjacent to the vacancy caused by lifting of the local cubic symmetry. This would be the case for any transition metal perovskite under symmetry-reduced environments such as an interface, surface, or a defect. We find that the OV-induced localized state is highly one dimensional and is mainly composed of Ti 3d3z2-r2 orbitals along the Ti-OV-Ti axis (defined as the z axis) and Ti 4s,4p orbitals at the OV site. The oxygen vacancy does not lead to Ti t2g-based localized states.
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Abstract
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Figure 1
Figure 1. (a) In-plane projection of the X-ray diffraction of the (22̅4) reflection of SrTiO₃/LSAT thin films with a Moiré lattice. Line cuts through the (b) film (L = 4.000) and (c) substrate (L = 4.034) reflections show the periodicity of the Moiré lattice. (d) HAADF-STEM image of a STO thin film grown on a LSAT (001) substrate and (e) corresponding strain map along the x direction calculated by geometric phase analysis. The misfit dislocations appear as butterflylike features at the STO/LSAT interface with a compression region (in blue) and a tensile region (in yellow). (f) Structure of the periodically repeated relaxed MD model of the dislocation array at the SrTiO₃/LSAT interface with the dislocations and the (2 × 107 × 60) simulation cell highlighted. Only the B–O bonding network and the A-site atoms are shown for clarity. Insets show the initial unrelaxed part of the structure with the removed STO plane and the extracted DFT cluster model, respectively. In the DFT model, the faded-out atoms are fixed during DFT geometry optimization to impose elastic boundary conditions.
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Figure 2
Figure 2. (a) Map of the interatomic distances (in Å) for the A sublattice along the horizontal direction as obtained by PPA from the HAADF-STEM image in (b). (c) Map of horizontal interatomic A–A distances extracted from the DFT-relaxed dislocation core structure shown in (d). Circles are located at the midpoint of A–A pairs and are color-coded according to the distance between that pair. (e) Electronic density of states (DOS) projected on the atoms at the dislocation core for the stoichiometric dislocation model. The vertical dashed line indicates the position of the Fermi level. (f) Charge density isosurface (10^–2 e/Å³) in the energy range highlighted in red in (e).
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Figure 3
Figure 3. (a) HAADF-STEM image of a dislocation at the STO/LSAT interface and corresponding atomic-resolution maps of the (b) O–K and (c) Ti–L_3,2 excitation edges. The scale bar is 1 nm. (d) Representative Ti–L_3,2 EELS spectra of the STO film and the surroundings of the dislocation core. The spectra have been normalized to the L₂ e_g peak height for clarity.
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Figure 4
Figure 4. (a) Color map of the relative V_O formation energy (ΔE_f) around the dislocation core. Electronic DOS projected on the atoms at the dislocation core for the STO/LSAT interface model containing (b) one, (c) two, and (d) three V_O in the most stable configurations. The vertical dashed line indicates the position of the Fermi level.
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Figure 5
Figure 5. Mulliken charges for the Ti atoms in (a) the stoichiometric dislocation model and in the presence of (b) one, (c) two, and (d) three V_O. The black squares indicate the position of the V_O.
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Figure 6
Figure 6. (a) HAADF-STEM image of a misfit dislocation at the STO/LSAT interface and (b–g) corresponding elemental maps of Sr, Ti, O, La, Al, and Ta calculated from an EDX spectrum image using the Sr–K, Ti–K, O–K1, La–L, Al–K1, and Ta–L lines, respectively. The scale bar is 1 nm.
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Figure 7
Figure 7. Color map of the relative (a) V_Ta and (b) V_Al formation energy (ΔE_f) around the dislocation core. The energy of the most stable defect is used as a reference in each plot. The shaded trapezoidal area in (a) indicates where V_Ta tends to form/segregate. Electronic DOS projected on the atoms at the dislocation core containing (c) one V_Al and (d) one V_Ta, each at the most stable site at the STO/LSAT interface or (e) away from the interface in LSAT. (f–h) show charge density isosurfaces (10^–2 e/Å³) in the energy range of the defect states highlighted in brown or orange in the DOS.
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Figure 8
Figure 8. (a) Color map of the relative V_O formation energy (ΔE_f) around the dislocation core in the presence of a V_Ta, indicated by the orange square. (b) DOS projected on the atoms at the dislocation core containing one V_Ta at the dislocation core and one V_O at a neighboring site. (c) Charge density isosurfaces (10^–2 e/Å³) in the energy range of the defect state highlighted orange in the DOS.
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Figure 9
Figure 9. Color map of the relative (a) Ti_Al, (b) Ti_Ta, and (c) Ta_Ti formation energy (ΔE_f) around the dislocation core. The energy of the most stable defect is used in each plot as a reference.
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Figure 10
Figure 10. Average Mulliken charges for Ti atoms in STO far from the dislocation core (Ti_bulk), Ti atoms close to the dislocation core (Ti_core), and substitutional Ti atoms in LSAT (Ti_sub).
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Figure 11
Figure 11. Color map of the relative formation energy (ΔE_f) of a Ti_Al in the presence of one (a) Ta_Ti or (b) V_Ta and of a Ti_Ta in the presence of one (c) Ta_Ti or (d) V_Ta. The energy of the most stable defect is used in each plot as a reference. The black square indicates the position of the Ta_Ti or V_Ta defect.
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  Ohta, Hiromichi; Kim, SungWng; Mune, Yoriko; Mizoguchi, Teruyasu; Nomura, Kenji; Ohta, Shingo; Nomura, Takashi; Nakanishi, Yuki; Ikuhara, Yuichi; Hirano, Masahiro; Hosono, Hideo; Koumoto, Kunihito
  Nature Materials (2007), 6 (2), 129-134CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
  Enhancement of the Seebeck coeff. (S ) without reducing the elec. cond. (σ) is essential to realize practical thermoelec. materials exhibiting a dimensionless figure of merit (ZT=S2·σ·T·κ-1) exceeding 2, where T is the abs. temp. and κ is the thermal cond. Here, a high-d. two-dimensional electron gas (2DEG) confined within a unit cell layer thickness in SrTiO3 yields unusually large |S|, approx. five times larger than that of SrTiO3 bulks, while maintaining a high σ2DEG. In the best case, the authors observe |S|=850 μV K-1 and σ2DEG = 1.4×103 S cm-1. By using the κ of bulk single-crystal SrTiO3 at room temp., the authors est. ZT∼2.4 for the 2DEG, corresponding to ZT∼0.24 for a complete device having the 2DEG as the active region. The present approach using a 2DEG provides a new route to realize practical thermoelec. materials without the use of toxic heavy elements.
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9. 9
  Garcia-Barriocanal, J.; Rivera-Calzada, A.; Varela, M.; Sefrioui, Z.; Iborra, E.; Leon, C.; Pennycook, S. J.; Santamaria, J. Colossal Ionic Conductivity at Interfaces of Epitaxial ZrO₂:Y₂O₃/SrTiO₃ Heterostructures. Science 2008, 321, 676– 680, DOI: 10.1126/science.1156393
  9
  Colossal Ionic Conductivity at Interfaces of Epitaxial ZrO2:Y2O3/SrTiO3 Heterostructures
  Garcia-Barriocanal, J.; Rivera-Calzada, A.; Varela, M.; Sefrioui, Z.; Iborra, E.; Leon, C.; Pennycook, S. J.; Santamaria, J.
  Science (Washington, DC, United States) (2008), 321 (5889), 676-680CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
  We report a high lateral ionic cond., showing up to eight orders of magnitude enhancement near room temp., in yttria-stabilized zirconia (YSZ)/strontium titanate epitaxial heterostructures. The enhancement of the cond. is obsd., along with a YSZ layer thickness-independent conductance, showing that it is an interface process. We propose that the at. reconstruction at the interface between highly dissimilar structures (such as fluorite and perovskite) provides both a large no. of carriers and a high-mobility plane, yielding colossal values of the ionic cond.
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10. 10
  Mannhart, J.; Schlom, D. G. Oxide Interfaces-An Opportunity for Electronics. Science 2010, 327, 1607– 1611, DOI: 10.1126/science.1181862
  10
  Oxide Interfaces-An Opportunity for Electronics
  Mannhart, J.; Schlom, D. G.
  Science (Washington, DC, United States) (2010), 327 (5973), 1607-1611CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
  A review. Extraordinary electron systems can be generated at well-defined interfaces between complex oxides. In recent years, progress was achieved in exploring and making use of the fundamental properties of such interfaces, and it has become clear that these electron systems offer the potential for possible future devices. The authors trace the state of the art of this emerging field of electronics and discuss some of the challenges and pitfalls that may lie ahead.
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11. 11
  Zubko, P.; Jecklin, N.; Torres-Pardo, A.; Aguado-Puente, P.; Gloter, A.; Lichtensteiger, C.; Junquera, J.; Stéphan, O.; Triscone, J.-M. Electrostatic Coupling and Local Structural Distortions at Interfaces in Ferroelectric/Paraelectric Superlattices. Nano Lett. 2012, 12, 2846– 2851, DOI: 10.1021/nl3003717
  11
  Electrostatic Coupling and Local Structural Distortions at Interfaces in Ferroelectric/Paraelectric Superlattices
  Zubko, P.; Jecklin, N.; Torres-Pardo, A.; Aguado-Puente, P.; Gloter, A.; Lichtensteiger, C.; Junquera, J.; Stephan, O.; Triscone, J.-M.
  Nano Letters (2012), 12 (6), 2846-2851CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
  The performance of ferroelec. devices is intimately entwined with the structure and dynamics of ferroelec. domains. In ultrathin ferroelecs., ordered nanodomains arise naturally in response to the presence of a depolarizing field and give rise to highly inhomogeneous polarization and structural profiles. Ferroelec. superlattices offer a unique way of engineering the desired nanodomain structure by modifying the strength of the electrostatic interactions between different ferroelec. layers. Through a combination of x-ray diffraction, TEM, and 1st-principles calcns., the electrostatic coupling between ferroelec. layers was studied, revealing the existence of interfacial layers of reduced tetragonality attributed to inhomogeneous strain and polarization profiles assocd. with the domain structure.
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12. 12
  Chen, Y.; Green, R. J.; Sutarto, R.; He, F.; Linderoth, S.; Sawatzky, G. A.; Pryds, N. Tuning the Two-Dimensional Electron Liquid at Oxide Interfaces by Buffer-Layer-Engineered Redox Reactions. Nano Lett. 2017, 17, 7062– 7066, DOI: 10.1021/acs.nanolett.7b03744
  12
  Tuning the two-dimensional electron liquid at oxide interfaces by buffer-layer-engineered redox reactions
  Chen, Yunzhong; Green, Robert J.; Sutarto, Ronny; He, Feizhou; Linderoth, Soeren; Sawatzky, George A.; Pryds, Nini
  Nano Letters (2017), 17 (11), 7062-7066CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
  Polar discontinuities and redox reactions provide alternative paths to create two-dimensional electron liqs. (2DELs) at oxide interfaces. Herein, we report high mobility 2DELs at interfaces involving SrTiO3 (STO) achieved using polar La7/8Sr1/8MnO3 (LSMO) buffer layers to manipulate both polarities and redox reactions from disordered overlayers grown at room temp. Using resonant X-ray reflectometry expts., we quantify redox reactions from oxide overlayers on STO as well as polarity induced electronic reconstruction at epitaxial LSMO/STO interfaces. The anal. reveals how these effects can be combined in a STO/LSMO/disordered film trilayer system to yield high mobility modulation doped 2DELs, where the buffer layer undergoes a partial transformation from perovskite to brownmillerite structure. This uncovered interplay between polar discontinuities and redox reactions via buffer layers provides a new approach for the design of functional oxide interfaces.
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13. 13
  Burian, M.; Pedrini, B. F.; Ortiz Hernandez, N.; Ueda, H.; Vaz, C. A. F.; Caputo, M.; Radovic, M.; Staub, U. Buried Moiré Supercells Through SrTiO₃ Nanolayer Relaxation. Phys. Rev. Res. 2021, 3, 013225, DOI: 10.1103/PhysRevResearch.3.013225
  13
  Buried moire supercells through SrTiO3 nanolayer relaxation
  Burian, Max; Pedrini, Bill Francesco; Ortiz Hernandez, Nazaret; Ueda, Hiroki; Vaz, C. A. F.; Caputo, Marco; Radovic, Milan; Staub, Urs
  Physical Review Research (2021), 3 (1), 013225CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)
  We identified a highly ordered moire lattice at the buried SrTiO3 (STO)-(La,Sr)(Al,Ta)-oxide (LSAT) interface by high-resoln. x-ray diffraction reciprocal space mapping. We found long-ranged ordered supercells of 106/107 unit cells of unstrained STO-LSAT caused by complete lattice relaxation through high-temp. annealing. Transmission electron microscopy images show that this periodicity is based on line dislocations at the interface region. The presence of such ordered superstructures in such widely used complex oxides sets the ideal conditions for moire-tuned interfacial electronic modifications and ferroelec. supercrystallinity, opening the possibility for interface functionalities and impacting findings on vortex structured multilayers systems.
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14. 14
  Adler, S. B. Chemical Expansivity of Electrochemical Ceramics. J. Am. Ceram. Soc. 2004, 84, 2117– 2119, DOI: 10.1111/j.1151-2916.2001.tb00968.x
  There is no corresponding record for this reference.
15. 15
  Aschauer, U.; Pfenninger, R.; Selbach, S. M.; Grande, T.; Spaldin, N. A. Strain-Controlled Oxygen Vacancy Formation and Ordering in CaMnO₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 054111, DOI: 10.1103/PhysRevB.88.054111
  15
  Strain-controlled oxygen vacancy formation and ordering in CaMnO3
  Aschauer, Ulrich; Pfenninger, Reto; Selbach, Sverre M.; Grande, Tor; Spaldin, Nicola A.
  Physical Review B: Condensed Matter and Materials Physics (2013), 88 (5), 054111/1-054111/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We use 1st-principles calcns. to investigate the stability of biaxially strained Pnma perovskite CaMnO3 towards the formation of O vacancies. Our motivation is provided by promising indications that novel material properties can be engineered by application of strain through coherent heteroepitaxy in thin films. While it is usually assumed that such epitaxial strain is accommodated primarily by changes in intrinsic lattice consts., point defect formation is also a likely strain-relaxation mechanism. Our 1st-principles calcns. of O vacancy defect formation energy indeed show a strong strain dependence: We find that tensile strain lowers the formation energy, consistent with the established chem. expansion concept that O deficiency increases the molar volume in oxides. In addn., we find that strain differentiates the formation energy for different lattice sites, suggesting its use as a route to engineering vacancy ordering in epitaxial thin films.
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16. 16
  Aidhy, D. S.; Liu, B.; Zhang, Y.; Weber, W. J. Strain-Induced Phase and Oxygen-Vacancy Stability in Ionic Interfaces From First-Principles Calculations. J. Phys. Chem. C 2014, 118, 30139– 30144, DOI: 10.1021/jp507876m
  16
  Strain-Induced Phase and Oxygen-Vacancy Stability in Ionic Interfaces from First-Principles Calculations
  Aidhy, Dilpuneet S.; Liu, Bin; Zhang, Yanwen; Weber, William J.
  Journal of Physical Chemistry C (2014), 118 (51), 30139-30144CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  Understanding interfacial chem. is becoming crucial in materials design for heterointerfaces. Using d. functional theory, the authors elucidate the effect of strained interfaces on phase and oxygen-vacancy stability for CeO2|ZrO2, ThO2|ZrO2 and CeO2|ThO2 interfaces. The calcns. show that ZrO2 transforms from cubic fluorite to the orthorhombic columbite under tensile strain providing evidence of a previous exptl. speculation of an unrecognized ZrO2 phase. The authors also show oxygen vacancy formation energy decreases in the presence of tensile strain. As a result, the interfacial strain could be used as a knob to stabilize oxygen vacancies on either side of the interface, and control their concn. for fast-ion conductor applications.
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17. 17
  Yildiz, B. Stretching” the Energy Landscape of Oxides - Effects on Electrocatalysis and Diffusion. MRS Bull. 2014, 39, 147– 156, DOI: 10.1557/mrs.2014.8
  17
  "Stretching" the energy landscape of oxides-Effects on electrocatalysis and diffusion
  Yildiz, Bilge
  MRS Bulletin (2014), 39 (2), 147-156CODEN: MRSBEA; ISSN:0883-7694. (Cambridge University Press)
  A review; elastic strain engineering offers a new route to enable high-performance catalysts, electrochem. energy conversion devices, sepn. membranes and memristors. By applying mech. stress, the inherent energy landscape of reactions involved in the material can be altered. This is the so-called mechano-chem. coupling. Here we discuss how elastic strain activates reactions on metals and oxides. We also present analogies to strained polymer reactions. A rich set of investigations have been performed on strained metal surfaces over the last 15 years, and the mechanistic reasons behind strain-induced reactivity are explained by an electronic structure model. On the other hand, the potential of strain engineering of oxides for catalytic and energy applications has been largely underexplored. In oxides, mech. stress couples to reaction and diffusion kinetics by altering the oxygen defect formation enthalpy, migration energy barrier, adsorption energy, dissocn. barrier, and charge transfer barrier. A generalization of the principles for stress activated reactions from polymers to metals to oxides is offered, and the prospect of using elastic strain to tune reaction and diffusion kinetics in functional oxides is discussed.
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18. 18
  Choudhury, S.; Morgan, D.; Uberuaga, B. P. Massive Interfacial Reconstruction at Misfit Dislocations in Metal/Oxide Interfaces. Sci. Rep. 2014, 4, 6533, DOI: 10.1038/srep06533
  18
  Massive Interfacial Reconstruction at Misfit Dislocations in Metal/Oxide Interfaces
  Choudhury, Samrat; Morgan, Dane; Uberuaga, Blas Pedro
  Scientific Reports (2014), 4 (), 6533CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)
  Electronic structure calcns. were performed to study the role of misfit dislocations on the structure and chem. of a metal/oxide interface. We found that a chem. imbalance exists at the misfit dislocation which leads to dramatic changes in the point defect content at the interface - stabilizing the structure requires removing as much as 50% of the metal atoms and insertion of a large no. of oxygen interstitials. The exact defect compn. that stabilizes the interface is sensitive to the external oxygen partial pressure. We relate the preferred defect structure at the interface to a competition between chem. and strain energies as defects are introduced.
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19. 19
  Dholabhai, P. P.; Uberuaga, B. P. Beyond Coherent Oxide Heterostructures: Atomic-Scale Structure of Misfit Dislocations. Adv. Theory Simul. 2019, 2, 1900078, DOI: 10.1002/adts.201900078
  19
  Beyond Coherent Oxide Heterostructures: Atomic-Scale Structure of Misfit Dislocations
  Dholabhai, Pratik P.; Uberuaga, Blas P.
  Advanced Theory and Simulations (2019), 2 (9), n/a1900078CODEN: ATSDCW; ISSN:2513-0390. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A review. Nanoscale design of complex oxide heterostructures and thin films is imperative as they have significant promise in novel technol. applications. A coherent interface is formed in oxide heterostructures with small mismatches, and the lattice mismatch is completely compensated by elastic strain. In semi-coherent oxide heterostructures, when an epitaxial layer is grown on the substrate above the crit. thickness of the film, misfit dislocations are formed to mitigate the strain between the two materials with dissimilar lattice consts. Key properties of semi-coherent oxide heterostructures are influenced or even controlled by the presence of misfit dislocations. Therefore, it is crit. to understand the at.-scale structure of semi-coherent oxide heterostructures, specifically the structure of misfit dislocations that are ubiquitous at such heterointerfaces. Numerous state-of-the-art expts. have reported emergent phenomena at semi-coherent oxide heterostructures, wherein misfit dislocations play a crucial role. However, their at.-scale and nanoscale structure is not always discernable from expts. Due to large system sizes, computational studies dedicated to examg. misfit dislocations in semi-coherent oxide heterostructures are still in their infancy. This review aims to summarize the recent advancements and challenges involved in computational studies elucidating the at.-scale structure of misfit dislocations in semi-coherent oxide heterostructures and motivate future computational efforts.
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20. 20
  Marrocchelli, D.; Sun, L.; Yildiz, B. Dislocations in SrTiO₃: Easy to Reduce but Not So Fast for Oxygen Transport. J. Am. Chem. Soc. 2015, 137, 4735– 4748, DOI: 10.1021/ja513176u
  20
  Dislocations in SrTiO3: Easy To Reduce but Not so Fast for Oxygen Transport
  Marrocchelli, Dario; Sun, Lixin; Yildiz, Bilge
  Journal of the American Chemical Society (2015), 137 (14), 4735-4748CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  The effect of dislocations on the chem., elec. and transport properties in oxide materials is important for electrochem. devices, such as fuel cells and resistive switches, but these effects have remained largely unexplored at the at. level. By using large-scale atomistic simulations, the authors uncover how a 〈100〉{011} edge dislocation in SrTiO3, a prototypical perovskite oxide, impacts the local defect chem. and oxide ion transport. In the dil. limit, oxygen vacancy formation energy in SrTiO3 is lower at sites close to the dislocation core, by ≤2 eV compared to that in the bulk. The formation of a space-charge zone based on the redistribution of charged oxygen vacancies can be captured quant. at atomistic level by mapping the vacancy formation energies around the dislocation. Oxide-ion diffusion was studied for a low vacancy concn. regime (ppm level) and a high vacancy concn. regime (up to 2.5%). In both cases, no evidence of pipe-diffusion, i.e., significantly enhanced mobility of oxide ions, was found as detd. from the calcd. migration barriers, contrary to the case in metals. However, in the low vacancy concn. regime, the vacancy accumulation at the dislocation core gives rise to a higher diffusion coeff., even though the oxide-ion mobility itself is lower than that in the bulk. The authors' findings have important implications for applications of perovskite oxides for information and energy technologies. The obsd. lower oxygen vacancy formation energy at the dislocation core provides a quant. and direct explanation for the electronic cond. of dislocations in SrTiO3 and related oxides studied for red-ox based resistive switching. Reducibility and electronic transport at dislocations can also be quant. engineered into active materials for fuel cells, catalysis, and electronics.
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21. 21
  Dholabhai, P. P.; Martinez, E.; Uberuaga, B. P. Influence of Chemistry and Misfit Dislocation Structure on Dopant Segregation at Complex Oxide Heterointerfaces. Adv. Theory Simul. 2019, 2, 1800095, DOI: 10.1002/adts.201800095
  21
  Influence of Chemistry and Misfit Dislocation Structure on Dopant Segregation at Complex Oxide Heterointerfaces
  Dholabhai, Pratik P.; Martinez, Enrique; Uberuaga, Blas P.
  Advanced Theory and Simulations (2019), 2 (1), 1800095/1-1800095/10CODEN: ATSDCW; ISSN:2513-0390. (Wiley-VCH Verlag GmbH & Co. KGaA)
  Complex oxide heterostructures and thin films have emerged as promising candidates for diverse applications. Lattice mismatch between the two oxides lead to the formation of misfit dislocations, which influence vital material features. Trivalent dopant segregation to misfit dislocations at semi-coherent oxide heterointerfaces, while not well understood, is anticipated to impact interface-governed properties. Here, atomistic simulations elucidating the influence of misfit dislocations on dopant segregation at SrTiO3/MgO heterointerfaces are reported. SrO- and TiO2-terminated interfaces that have differing misfit dislocation structure were considered for trivalent dopants segregation. At SrO-terminated interface, dopants tend to segregate toward but not precisely to the heterointerface, whereas at TiO2-terminated interface, dopants exhibit a thermodn. preference to accumulate at the heterointerface. Most favorable segregation sites at SrO-terminated interface are located within the coherent terrace, whereas those at TiO2-terminated interface are at misfit dislocation intersections. Atomic layer chem. and the resulting misfit dislocation structure at the heterointerface, along with concomitant strain at the heterointerface due to mismatched dopants, play a crit. role in influencing the obsd. trends for dopant segregation. Overall, the present results offer a fundamental at. scale perspective of dopant behavior at semi-coherent complex oxide heterointerfaces and the interplay between dopant chem., interface chem., and misfit dislocation structure.
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22. 22
  Marzano, C.; Dholabhai, P. P. High-Throughput Prediction of Thermodynamic Stabilities of Dopant-Defect Clusters at Misfit Dislocations in Perovskite Oxide Heterostructures. J. Phys. Chem. C 2023, 127, 15988– 15999, DOI: 10.1021/acs.jpcc.3c02367
  22
  High-Throughput Prediction of Thermodynamic Stabilities of Dopant-Defect Clusters at Misfit Dislocations in Perovskite Oxide Heterostructures
  Marzano, Chloe; Dholabhai, Pratik P.
  Journal of Physical Chemistry C (2023), 127 (32), 15988-15999CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
  Complex oxide heterostructures and thin films have emerged as promising candidates for diverse applications, wherein interfaces formed by joining two different oxides play a central role in novel properties that are not present in the individual components. Lattice mismatch between the two oxides leads to the formation of misfit dislocations, which often influence vital material properties. In oxides, doping is used as a strategy to improve properties, wherein inclusion of aliovalent dopants leads to formation of oxygen vacancy defects. At low temps., these dopants and defects often form stable clusters. In semicoherent perovskite oxide heterostructures, the stability of such clusters at misfit dislocations, while not well understood, is anticipated to impact interface-governed properties. Herein, we report atomistic simulations elucidating the influence of misfit dislocations on the stability of dopant-defect clusters in SrTiO3/BaZrO3 heterostructures. SrO-BaO, SrO-ZrO2, BaO-TiO2, and ZrO2-TiO2 interfaces having dissimilar misfit dislocation structures were considered. High-throughput computing was implemented to predict the thermodn. stabilities of 275,610 dopant-defect clusters in the vicinity of misfit dislocations. The misfit dislocation structure of the given interface and corresponding at. layer chem. play a fundamental role in influencing the thermodn. stability of geometrically diverse clusters. A stark difference in cluster stability is obsd. at misfit dislocation lines and intersections as compared to the coherent terraces. These results offer an at. scale perspective of the complex interplay between dopants, point defects, and extended defects, which is necessary to comprehend the functionalities of the perovskite oxide heterostructures.
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23. 23
  Hirel, P.; Mrovec, M.; Elsässer, C. Atomistic Simulation Study of (110) Dislocations in Strontium Titanate. Acta Mater. 2012, 60, 329– 338, DOI: 10.1016/j.actamat.2011.09.049
  23
  Atomistic simulation study of <110> dislocations in strontium titanate
  Hirel, P.; Mrovec, M.; Elsaesser, C.
  Acta Materialia (2012), 60 (1), 329-338CODEN: ACMAFD; ISSN:1359-6454. (Elsevier Ltd.)
  The core structures of glide-dissocd. screw and edge <110>{1‾10} dislocations in strontium titanate were investigated by using atomistic simulations. For both dislocations the Sr, Ti and O sublattices follow different patterns of elastic displacements, and the partial dislocations have extended core structures. Dissocn. distances in the range of exptl. results are obtained, and a long-standing discrepancy between theor. and exptl. predictions of the anti-phase boundary energy is resolved. Studies of dislocations under applied load reveal marked difference in mobilities of the screw and edge dislocations that are consistent with exptl. observations.
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24. 24
  Sun, L.; Marrocchelli, D.; Yildiz, B. Edge Dislocation Slows Down Oxide Ion Diffusion in Doped CeO₂ by Segregation of Charged Defects. Nat. Commun. 2015, 6, 6294, DOI: 10.1038/ncomms7294
  24
  Edge dislocation slows down oxide ion diffusion in doped CeO2 by segregation of charged defects
  Sun, Lixin; Marrocchelli, Dario; Yildiz, Bilge
  Nature Communications (2015), 6 (), 6294CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
  Strained oxide thin films are of interest for accelerating oxide ion conduction in electrochem. devices. Although the effect of elastic strain has been uncovered theor., the effect of dislocations on the diffusion kinetics in such strained oxides is yet unclear. Here we investigate a 1/2<110>{100} edge dislocation by performing atomistic simulations in 4-12% doped CeO2 as a model fast ion conductor. At equil., depending on the size of the dopant, trivalent cations and oxygen vacancies are found to simultaneously enrich or deplete either in the compressive or in the tensile strain fields around the dislocation. The associative interactions among the point defects in the enrichment zone and the lack of oxygen vacancies in the depletion zone slow down oxide ion transport. This finding is contrary to the fast diffusion of atoms along the dislocations in metals and should be considered when assessing the effects of strain on oxide ion cond.
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25. 25
  Ricca, C.; Skoropata, E.; Rossell, M. D.; Erni, R.; Staub, U.; Aschauer, U. Combined Theoretical and Experimental Study of the Moiré Dislocation Network at the SrTiO₃-(La,Sr)(Al,Ta)O₃ Interface. 2023, arXiv:2307.12572.
  There is no corresponding record for this reference.
26. 26
  Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1– 19, DOI: 10.1006/jcph.1995.1039
  26
  Fast parallel algorithms for short-range molecular dynamics
  Plimpton, Steve
  Journal of Computational Physics (1995), 117 (1), 1-19CODEN: JCTPAH; ISSN:0021-9991.
  Three parallel algorithms for classical mol. dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-at. forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for mol. dynamics models which can be difficult to parallelize efficiently - those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a std. Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers - the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C90 processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex mol. dynamics simulations are also discussed.
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27. 27
  Lewis, G. V.; Catlow, C. R. A. Potential Models for Ionic Oxides. J. Phys. C: Solid State Phys. 1985, 18, 1149– 1161, DOI: 10.1088/0022-3719/18/6/010
  27
  Potential models for ionic oxides
  Lewis, G. V.; Catlow, C. R. A.
  Journal of Physics C: Solid State Physics (1985), 18 (6), 1149-61CODEN: JPSOAW; ISSN:0022-3719.
  A method for calcg. empirical potential parameters for binary oxides is given, and their modification for use in mixed oxide systems is discussed. Shell-model potentials are used, but, unlike the case for the alkali halides within which polarizability and short-range interaction parameters can be transferred, modifications must be introduced when transferring potential parameters between different oxides. The anion polarizability varies with structure and with the nature of the host cation; changes in cation coordination are reflected in the short- range repulsive cation-anion interaction. Parameters were derived for a range of oxides, and trends in these parameters are discussed. Applications of the potentials to the calcn. of perfect lattice properties are discussed, as well as when defect and surface properties are considered. Calcns. were done on the activation energies for dopant diffusion in NiO, and the surface rumpling of MgO.
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28. 28
  Gale, J. D. GULP: A Computer Program for the Symmetry-Adapted Simulation of Solids. J. Chem. Soc., Faraday Trans. 1997, 93, 629– 637, DOI: 10.1039/a606455h
  28
  GULP: a computer program for the symmetry-adapted simulation of solids
  Gale, Julian D.
  Journal of the Chemical Society, Faraday Transactions (1997), 93 (4), 629-637CODEN: JCFTEV; ISSN:0956-5000. (Royal Society of Chemistry)
  Algorithms for the symmetry-adapted energy minimization of solids using anal. first and second derivs. have been devised and implemented in a new computer program GULP. These new methods are found to lead to an improvement in computational efficiency of up to an order of magnitude over the std. algorithm, which takes no account of symmetry, the largest improvement being obtained from the use of symmetry in the generation of the Hessian. Accelerated convergence techniques for the dispersion energy are found to be beneficial in improving the precision at little extra computational cost, particularly when a one center decompn. is possible or the Ewald sum weighting towards real-space is increased.
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29. 29
  Gale, J. D.; Rohl, A. L. The General Utility Lattice Program (GULP). Mol. Simul. 2003, 29, 291– 341, DOI: 10.1080/0892702031000104887
  29
  The General Utility Lattice Program (GULP)
  Gale, Julian D.; Rohl, Andrew L.
  Molecular Simulation (2003), 29 (5), 291-341CODEN: MOSIEA; ISSN:0892-7022. (Taylor & Francis Ltd.)
  The General Utility Lattice Program (gulp) has been extended to include the ability to simulate polymers and surfaces, as well as adding many other new features, and the current status of the program is fully documented. Both the background theory is described, as well as providing a concise review of some of the previous applications in order to demonstrate the range of its use. Examples are presented of work performed using the new compatibilities of the software, including the calcn. of Born effective charges, mech. properties as a function of applied pressure, calcn. of frequency-dependent dielec. data, surface reconstructions of calcite and the performance of a linear-scaling algorithm for bond-order potentials.
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30. 30
  Gale, J. D. GULP: Capabilities and Prospects. Z. für Kristallogr. - Cryst. Mater. 2005, 220, 552– 554, DOI: 10.1524/zkri.220.5.552.65070
  30
  GULP: Capabilities and prospects
  Gale, Julian D.
  Zeitschrift fuer Kristallographie (2005), 220 (5-6), 552-554CODEN: ZEKRDZ; ISSN:0044-2968. (Oldenbourg Wissenschaftsverlag GmbH)
  The current status and capabilities of the atomistic simulation code GULP are described. In particular, the differences between versions 1.3.2 and 3.0 are detailed, as well as a concise pointer to applications in computational crystallog.
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31. 31
  Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558– 561, DOI: 10.1103/PhysRevB.47.558
  31
  Ab initio molecular dynamics of liquid metals
  Kresse, G.; Hafner, J.
  Physical Review B: Condensed Matter and Materials Physics (1993), 47 (1), 558-61CODEN: PRBMDO; ISSN:0163-1829.
  The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.
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32. 32
  Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal - Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 14251– 14269, DOI: 10.1103/PhysRevB.49.14251
  32
  Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium
  Kresse, G.; Hafner, J.
  Physical Review B: Condensed Matter and Materials Physics (1994), 49 (20), 14251-69CODEN: PRBMDO; ISSN:0163-1829.
  The authors present ab initio quantum-mech. mol.-dynamics simulations of the liq.-metal-amorphous-semiconductor transition in Ge. The simulations are based on (a) finite-temp. d.-functional theory of the 1-electron states, (b) exact energy minimization and hence calcn. of the exact Hellmann-Feynman forces after each mol.-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nose' dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows the authors to perform simulations over >30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liq. and amorphous Ge in very good agreement with expt.. The simulation allows the authors to study in detail the changes in the structure-property relation through the metal-semiconductor transition. The authors report a detailed anal. of the local structural properties and their changes induced by an annealing process. The geometrical, bounding, and spectral properties of defects in the disordered tetrahedral network are studied and compared with expt.
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33. 33
  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
  33
  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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34. 34
  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
  34
  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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35. 35
  Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865– 3868, DOI: 10.1103/PhysRevLett.77.3865
  35
  Generalized gradient approximation made simple
  Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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36. 36
  Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953– 17979, DOI: 10.1103/PhysRevB.50.17953
  36
  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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37. 37
  Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758– 1775, DOI: 10.1103/PhysRevB.59.1758
  37
  From ultrasoft pseudopotentials to the projector augmented-wave method
  Kresse, G.; Joubert, D.
  Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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38. 38
  Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B: Solid State 1976, 13, 5188– 5192, DOI: 10.1103/PhysRevB.13.5188
  There is no corresponding record for this reference.
39. 39
  Kühne, T. D.; Iannuzzi, M.; Del Ben, M.; Rybkin, V. V.; Seewald, P.; Stein, F.; Laino, T.; Khaliullin, R. Z.; Schütt, O.; Schiffmann, F. CP2K: An Electronic Structure and Molecular Dynamics Software Package - Quickstep: Efficient and Accurate Electronic Structure Calculations. J. Chem. Phys. 2020, 152, 194103, DOI: 10.1063/5.0007045
  39
  CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations
  Kuehne, Thomas D.; Iannuzzi, Marcella; Del Ben, Mauro; Rybkin, Vladimir V.; Seewald, Patrick; Stein, Frederick; Laino, Teodoro; Khaliullin, Rustam Z.; Schuett, Ole; Schiffmann, Florian; Golze, Dorothea; Wilhelm, Jan; Chulkov, Sergey; Bani-Hashemian, Mohammad Hossein; Weber, Valery; Borstnik, Urban; Taillefumier, Mathieu; Jakobovits, Alice Shoshana; Lazzaro, Alfio; Pabst, Hans; Mueller, Tiziano; Schade, Robert; Guidon, Manuel; Andermatt, Samuel; Holmberg, Nico; Schenter, Gregory K.; Hehn, Anna; Bussy, Augustin; Belleflamme, Fabian; Tabacchi, Gloria; Gloess, Andreas; Lass, Michael; Bethune, Iain; Mundy, Christopher J.; Plessl, Christian; Watkins, Matt; VandeVondele, Joost; Krack, Matthias; Hutter, Juerg
  Journal of Chemical Physics (2020), 152 (19), 194103CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A review. CP2K is an open source electronic structure and mol. dynamics software package to perform atomistic simulations of solid-state, liq., mol., and biol. systems. It is esp. aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio mol. dynamics simulations. Excellent performance for electronic structure calcns. is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on d. functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension. (c) 2020 American Institute of Physics.
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40. 40
  Goedecker, S.; Teter, M.; Hutter, J. Separable Dual-Space Gaussian Pseudopotentials. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 1703– 1710, DOI: 10.1103/PhysRevB.54.1703
  40
  Separable dual-space Gaussian pseudopotentials
  Goedecker, S.; Teter, M.; Hutter, J.
  Physical Review B: Condensed Matter (1996), 54 (3), 1703-1710CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  We present pseudopotential coeffs. for the first two rows of the Periodic Table. The pseudopotential is of an analytic form that gives optimal efficiency in numerical calculations using plane waves as a basis set. At most, even coeffs. are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudopotential to a wave function can be done efficiently on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space, since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudopotentials by extensive at. and mol. test calcns.
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41. 41
  VandeVondele, J.; Hutter, J. Gaussian Basis Sets for Accurate Calculations on Molecular Systems in Gas and Condensed Phases. J. Chem. Phys. 2007, 127, 114105, DOI: 10.1063/1.2770708
  41
  Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases
  VandeVondele, Joost; Hutter, Jurg
  Journal of Chemical Physics (2007), 127 (11), 114105/1-114105/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We present a library of Gaussian basis sets that has been specifically optimized to perform accurate mol. calcns. based on d. functional theory. It targets a wide range of chem. environments, including the gas phase, interfaces, and the condensed phase. These generally contracted basis sets, which include diffuse primitives, are obtained minimizing a linear combination of the total energy and the condition no. of the overlap matrix for a set of mols. with respect to the exponents and contraction coeffs. of the full basis. Typically, for a given accuracy in the total energy, significantly fewer basis functions are needed in this scheme than in the usual split valence scheme, leading to a speedup for systems where the computational cost is dominated by diagonalization. More importantly, binding energies of hydrogen bonded complexes are of similar quality as the ones obtained with augmented basis sets, i.e., have a small (down to 0.2 kcal/mol) basis set superposition error, and the monomers have dipoles within 0.1 D of the basis set limit. However, contrary to typical augmented basis sets, there are no near linear dependencies in the basis, so that the overlap matrix is always well conditioned, also, in the condensed phase. The basis can therefore be used in first principles mol. dynamics simulations and is well suited for linear scaling calcns.
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42. 42
  Freysoldt, C.; Grabowski, B.; Hickel, T.; Neugebauer, J.; Kresse, G.; Janotti, A.; Van de Walle, C. G. First-Principles Calculations for Point Defects in Solids. Rev. Mod. Phys. 2014, 86, 253– 305, DOI: 10.1103/RevModPhys.86.253
  There is no corresponding record for this reference.
43. 43
  Schlepütz, C. M.; Mariager, S. O.; Pauli, S. A.; Feidenhans’l, R.; Willmott, P. R. Angle Calculations for a (2 + 3)-Type Diffractometer: Focus on Area Detectors. J. Appl. Crystallogr. 2011, 44, 73– 83, DOI: 10.1107/S0021889810048922
  43
  Angle calculations for a (2+3)-type diffractometer. Focus on area detectors
  Schlepuetz, Christian M.; Mariager, Simon O.; Pauli, Stephan A.; Feidenhans'l, Robert; Willmott, Philip R.
  Journal of Applied Crystallography (2011), 44 (1), 73-83CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
  Angle calcns. for a (2+3)-type diffractometer are presented with comprehensive derivations for both cases of either a vertical or horizontal sample configuration. This work focuses on some particular aspects of using area detectors in surface x-ray diffraction, namely the role of the detector rotation and the direct conversion of the angle-resolved diffraction signal recorded by the detector into a 2D slice through reciprocal space.
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44. 44
  Kriegner, D.; Wintersberger, E.; Stangl, J. xrayutilities: A Versatile Tool for Reciprocal Space Conversion of Scattering Data Recorded With Linear and Area Detectors. J. Appl. Crystallogr. 2013, 46, 1162– 1170, DOI: 10.1107/S0021889813017214
  44
  xrayutilities: a versatile tool for reciprocal space conversion of scattering data recorded with linear and area detectors
  Kriegner, Dominik; Wintersberger, Eugen; Stangl, Julian
  Journal of Applied Crystallography (2013), 46 (4), 1162-1170CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
  General algorithms to convert scattering data of linear and area detectors recorded in various scattering geometries to reciprocal space coordinates are presented. These algorithms work for any goniometer configuration including popular four-circle, six-circle and kappa goniometers. The use of commonly employed approxns. is avoided and therefore the algorithms work also for large detectors at small sample-detector distances. A recipe for detg. the necessary detector parameters including mostly ignored misalignments is given. The algorithms are implemented in a freely available open-source package.
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45. 45
  Ruiz Caridad, A.; Erni, R.; Vogel, A.; Rossell, M. D. Applications of a Novel Electron Energy Filter Combined With a Hybrid-Pixel Direct Electron Detector for the Analysis of Functional Oxides by STEM-EELS and Energy-Filtered Imaging. Micron 2022, 160, 103331, DOI: 10.1016/j.micron.2022.103331
  45
  Applications of a novel electron energy filter combined with a hybrid-pixel direct electron detector for the analysis of functional oxides by STEM/EELS and energy-filtered imaging
  Ruiz Caridad, Alicia; Erni, Rolf; Vogel, Alexander; Rossell, Marta D.
  Micron (2022), 160 (), 103331CODEN: MCONEN; ISSN:0968-4328. (Elsevier Ltd.)
  The performance and suitability of a new electron energy filter in combination with a hybrid pixel, direct electron detector for anal. (scanning) transmission electron microscopy are demonstrated using four examples. The STEM-EELS capabilities of the CEOS Energy Filtering and Imaging Device (CEFID) were tested with focus on weak signals and high spatio-temporal resoln. A multiferroic, multilayer structure of REMnO3 (RE = Yb, Er, Tb, Y), grown on yttria-stabilized zirconia (YSZ), is used to exemplify that this new instrumental setup produces valuable electron energy-loss spectroscopy (EELS) data at high energy losses even when using short acquisition times, providing detailed chem. information about the interfaces in this complex multilayer sample. Another functional oxide, namely a ferromagnetic La2NiMnO6 thin film grown on SrTiO3, demonstrates that atomically resolved spectrum images can be recorded, using short dwell times and moderate beam currents in order to warrant the integrity of the sample. In a third example, inhomogeneously Er-doped YSZ shows by EELS spectrum imaging that elements at low concns. can be detected semi-quant., uncovering the expected layered Er distribution but revealing substantial interdiffusion. In a final example, we simply demonstrate that the hybrid pixel detector in combination with the energy filter can also be used for energy-filtered imaging and thus for elemental mapping complementary to EELS in scanning transmission mode.
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46. 46
  Campanini, M.; Erni, R.; Yang, C.-H.; Ramesh, R.; Rossell, M. D. Periodic Giant Polarization Gradients in Doped BiFeO₃ Thin Films. Nano Lett. 2018, 18, 717– 724, DOI: 10.1021/acs.nanolett.7b03817
  46
  Periodic Giant Polarization Gradients in Doped BiFeO3 Thin Films
  Campanini, Marco; Erni, Rolf; Yang, Chan-Ho; Ramesh, Ramamoorthy; Rossell, Marta D.
  Nano Letters (2018), 18 (2), 717-724CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)
  The ultimate challenge for the development of new multiferroics with enhanced properties lies in achieving nanoscale control of the coupling between different ordering parameters. In oxide-based multiferroics, substitutional cation dopants offer the unparalleled possibility to modify both the elec. and magnetic properties at a local scale. Herein it is demonstrated the formation of a dopant-controlled polar pattern in BiFeO3 leading to the spontaneous instauration of periodic polarization waves. In particular, nonpolar Ca-doped rich regions act as spacers between consecutive dopant-depleted regions displaying coupled ferroelec. states. n. This alternation of layers with different ferroelec. state creates a novel vertical polar structure exhibiting giant polarization gradients as large as 70 μC cm-2 across 30 Å thick domains. The drastic change in the polar state of the film is visualized using high-resoln. differential phase-contrast imaging able to map changes in ferroelec. polarization at at. scale. Also, a periodic distortion in the Fe-O-Fe bonding angle suggests a local variation in the magnetic ordering. The findings provide a new insight into the role of doping and reveal hitherto unexplored means to tailor the functional properties of multiferroics by doping engineering.
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47. 47
  Muller, D. A.; Nakagawa, N.; Ohtomo, A.; Grazul, J. L.; Hwang, H. Y. Atomic-Scale Imaging of Nanoengineered Oxygen Vacancy Profiles in SrTiO₃. Nature 2004, 430, 657– 661, DOI: 10.1038/nature02756
  47
  Atomic-scale imaging of nanoengineered oxygen vacancy profiles in SrTiO3
  Muller, David A.; Nakagawa, Naoyuki; Ohtomo, Akira; Grazul, John L.; Hwang, Harold Y.
  Nature (London, United Kingdom) (2004), 430 (7000), 657-661CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
  At the heart of modern oxide chem. lies the recognition that beneficial (as well as deleterious) materials properties can be obtained by deliberate deviations of oxygen atom occupancy from the ideal stoichiometry. Conversely, the capability to control and confine oxygen vacancies will be important to realize the full potential of perovskite ferroelec. materials, varistors and field-effect devices. In transition metal oxides, oxygen vacancies are generally electron donors, and in strontium titanate (SrTiO3) thin films, oxygen vacancies (unlike impurity dopants) are particularly important because they tend to retain high carrier mobilities, even at high carrier densities. Here the authors report the successful fabrication, using a pulsed laser deposition technique, of SrTiO3 superlattice films with oxygen doping profiles that exhibit subnanometre abruptness. The authors profile the vacancy concns. on an at. scale using annular-dark-field electron microscopy and core-level spectroscopy, and demonstrate abs. detection sensitivities of one to four oxygen vacancies. The authors' findings open a pathway to the microscopic study of individual vacancies and their clustering, not only in oxides, but in cryst. materials more generally.
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48. 48
  Aschauer, U.; Vonrüti, N.; Spaldin, N. A. Effect of Epitaxial Strain on Cation and Anion Vacancy Formation in MnO. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 054103, DOI: 10.1103/PhysRevB.92.054103
  48
  Effect of epitaxial strain on cation and anion vacancy formation in MnO
  Aschauer, Ulrich; Vonruti, Nathalie; Spaldin, Nicola A.
  Physical Review B: Condensed Matter and Materials Physics (2015), 92 (5), 054103/1-054103/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  Biaxial strain in coherent epitaxial thin films can have a pronounced effect on the point-defect profile in the films' material. Detailed fundamental knowledge of the interaction of strain with point defects is crucial to understanding the stoichiometry and resulting properties of strained thin films. Here we investigate the effect of biaxial strain on the formation energy of cation and anion vacancies using MnO as a model system. Our d.-functional-theory calcns. show that, as expected from local vol. arguments, compressive strain favors the formation of cation vacancies. Interestingly, we find that small compressive and tensile strains lead to ordering of the resulting holes along the in-plane and normal direction, resp., which should manifest in different anisotropic properties in the two strain states.
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49. 49
  Abbate, M.; de Groot, F. M. F.; Fuggle, J. C.; Fujimori, A.; Tokura, Y.; Fujishima, Y.; Strebel, O.; Domke, M.; Kaindl, G.; van Elp, J.; Thole, B. T.; Sawatzky, G. A.; Sacchi, M.; Tsuda, N. Soft-X-Ray-Absorption Studies of the Location of Extra Charges Induced by Substitution in Controlled-Valence Materials. Phys. Rev. B: Condens. Matter Mater. Phys. 1991, 44, 5419– 5422, DOI: 10.1103/PhysRevB.44.5419
  49
  Soft-x-ray-absorption studies of the location of extra charges induced by substitution in controlled-valence materials
  Abbate, M.; De Groot, F. M. F.; Fuggle, J. C.; Fujimori, A.; Tokura, Y.; Fujishima, Y.; Strebel, O.; Domke, M.; Kaindl, G.; et al.
  Physical Review B: Condensed Matter and Materials Physics (1991), 44 (11), 5419-22CODEN: PRBMDO; ISSN:0163-1829.
  High-resoln. 2p x-ray-absorption spectra are presented from 3d transition metals M in three series of pseudobinary and pseudoternary oxides. The detailed shape of the multiplet within the spectra can be used to det. the valence of the M ions. The spectra of the early-transition-metal compds. show dramatic changes as a function of substitution due to changes in the M 3d occupancy, indicating that the extra holes or electrons are located predominantly at the 3d-metal sites. This contrasts strongly with the behavior of the spectra of late-transition-metal compds., for which the extra charges induced by substitution go to oxygen states.
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50. 50
  Ricca, C.; Timrov, I.; Cococcioni, M.; Marzari, N.; Aschauer, U. Self-Consistent DFT+U+V Study of Oxygen Vacancies in SrTiO₃. Phys. Rev. Res. 2020, 2, 023313, DOI: 10.1103/PhysRevResearch.2.023313
  50
  Self-consistent DFT+U+V study of oxygen vacancies in SrTiO3
  Ricca, Chiara; Timrov, Iurii; Cococcioni, Matteo; Marzari, Nicola; Aschauer, Ulrich
  Physical Review Research (2020), 2 (2), 023313CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)
  Contradictory theor. results for oxygen vacancies in SrTiO3 (STO) were often related to the peculiar properties of STO, which is a d0 transition metal oxide with mixed ionic-covalent bonding. Here, we apply, for the first time, d. functional theory (DFT) within the extended Hubbard DFT+U+V approach, including onsite as well as intersite electronic interactions, to study oxygen-deficient STO with Hubbard U and V parameters computed self-consistently via d.-functional perturbation theory. Our results demonstrate that the extended Hubbard functional is a promising approach to study defects in materials with electronic properties similar to STO. Indeed, DFT+U+V provides a better description of stoichiometric STO compared to std. DFT or DFT+U, the band gap and crystal field splitting being in good agreement with expts. In turn, also the description of the electronic properties of oxygen vacancies in STO is improved, with formation energies in excellent agreement with expts. as well as results obtained with the most frequently used hybrid functionals, however, at a fraction of the computational cost. While our results do not fully resolve the contradictory findings reported in literature, our systematic approach leads to a deeper understanding of their origin, which stems from different cell sizes, STO phases, the exchange-correlation functional, and the treatment of structural relaxations and spin-polarization.
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51. 51
  Ricci, D.; Bano, G.; Pacchioni, G.; Illas, F. Electronic Structure of a Neutral Oxygen Vacancy in SrTiO₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 224105, DOI: 10.1103/PhysRevB.68.224105
  51
  Electronic structure of a neutral oxygen vacancy in SrTiO3
  Ricci, Davide; Bano, Giuseppe; Pacchioni, Gianfranco; Illas, Francesc
  Physical Review B: Condensed Matter and Materials Physics (2003), 68 (22), 224105/1-224105/9CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The electronic structure of an isolated oxygen vacancy in SrTiO3 has been investigated with a variety of ab initio quantum mech. approaches. In particular we compared pure d. functional theory (DFT) approaches with the Hartree-Fock method, and with hybrid methods where the exchange term is treated in a mixed way. Both local cluster models and periodic calcns. with large supercells contg. up to 80 atoms have been performed. Both diamagnetic (singlet state) and paramagnetic (triplet state) solns. have been considered. We found that the formation of an O vacancy is accompanied by the transfer of two electrons to the 3d(z2) orbitals of the two Ti atoms along the Ti-Vac-Ti axis. The two electrons are spin coupled and the ground state is diamagnetic. New states assocd. with the defect center appear in the gap just below the conduction band edge. The formation energy computed with respect to an isolated oxygen atom in the triplet state is 9.4 eV.
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52. 52
  Evarestov, R. A.; Kotomin, E. A.; Zhukovskii, Y. F. DFT Study of a Single F Center in Cubic SrTiO₃ Perovskite. Int. J. Quantum Chem. 2006, 106, 2173– 2183, DOI: 10.1002/qua.20855
  52
  DFT study of a single F center in cubic SrTiO3 perovskite
  Evarestov, R. A.; Kotomin, E. A.; Zhukovskii, Yu. F.
  International Journal of Quantum Chemistry (2006), 106 (10), 2173-2183CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)
  Various properties of a cubic phase of SrTiO3 perovskite contg. single F centers (neutral oxygen vacancies), including energies of their formation and migration, were simulated using different formalisms of d. functional theory (DFT) as implemented into CRYSTAL-2003 and VASP computer codes. The lattice relaxation around the F center was found to be sensitive to both shape and size of supercells used. The larger the supercell, the closer the defect energy level in the bandgap lies to the conduction band bottom. It approaches the optical ionization energy of 0.49 eV for 270- and 320-atom supercells, where the distance between neighboring defects increases up to four lattice consts. The defect bandwidth decreases for these supercells down to 0.02 eV, i.e., the defect-defect interaction becomes negligible. Thus, the two different first-principles periodic approaches combined provide results that are converged with respect to the supercell size and correspond to a single defect limit.
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53. 53
  Zhukovskii, Y. F.; Kotomin, E. A.; Piskunov, S.; Ellis, D. A Comparative Ab Initio Study of Bulk and Surface Oxygen Vacancies in PbTiO₃, PbZrO₃ and SrTiO₃ Perovskites. Solid State Commun. 2009, 149, 1359– 1362, DOI: 10.1016/j.ssc.2009.05.023
  53
  A comparative ab initio study of bulk and surface oxygen vacancies in PbTiO3, PbZrO3 and SrTiO3 perovskites
  Zhukovskii, Yu. F.; Kotomin, E. A.; Piskunov, S.; Ellis, D. E.
  Solid State Communications (2009), 149 (33-34), 1359-1362CODEN: SSCOA4; ISSN:0038-1098. (Elsevier Ltd.)
  Using the DFT-HF hybrid LCAO approach as implemented in the CRYSTAL computer code, we have performed large supercell comparative calcns. of neutral O vacancies (F centers) in the bulk and on the (001) surface of three cubic perovskite crystals (SrTiO3, PbTiO3, and PbZrO3). The local lattice relaxation, charge redistribution, and positions of defect energy levels within the band gap are compared. The difference in the chem. compn. of host materials leads to quite different defect properties.
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54. 54
  Mitra, C.; Lin, C.; Robertson, J.; Demkov, A. A. Electronic Structure of Oxygen Vacancies in SrTiO₃ and LaAlO₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 155105, DOI: 10.1103/PhysRevB.86.155105
  54
  Electronic structure of oxygen vacancies in SrTiO3 and LaAlO3
  Mitra, C.; Lin, C.; Robertson, J.; Demkov, Alexander A.
  Physical Review B: Condensed Matter and Materials Physics (2012), 86 (15), 155105/1-155105/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  The electronic structure of oxygen vacancies in bulk perovskite oxides SrTiO3 and LaAlO3 is studied using the Heyd, Scuseria, Ernzerhof (HSE) hybrid d. functional. In SrTiO3 the oxygen vacancy defect introduces a localized state comprised of 3dz2 and 4pz orbitals of the adjacent Ti atoms. This results in a bound state 0.7 eV below the conduction band edge. For LaAlO3, the oxygen vacancy creates a deep state 2.19 eV below the conduction band edge. The defect state is a hybrid of the adjacent La 5d and the Al 3p states. We compute the formation energies of the neutral oxygen vacancy defect V0 in bulk SrTiO3 and LaAlO3 to be 6.0 and 8.3 eV, resp.
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55. 55
  Lin, C.; Mitra, C.; Demkov, A. A. Orbital Ordering Under Reduced Symmetry in Transition Metal Perovskites: Oxygen Vacancy in SrTiO₃. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 161102, DOI: 10.1103/physrevb.86.161102
  55
  Orbital ordering under reduced symmetry in transition metal perovskites: oxygen vacancy in SrTiO3
  Lin, Chungwei; Mitra, Chandrima; Demkov, Alexander A.
  Physical Review B: Condensed Matter and Materials Physics (2012), 86 (16), 161102/1-161102/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  By using a combination of d. function theory and model Hamiltonian anal., we explain the general electronic structure features induced by an oxygen vacancy (OV) in SrTiO3. We show that the most important effect caused by an oxygen vacancy is the direct on-site coupling between the 3d3z2-r2 and 4s,4p orbitals of Ti atoms adjacent to the vacancy caused by lifting of the local cubic symmetry. This would be the case for any transition metal perovskite under symmetry-reduced environments such as an interface, surface, or a defect. We find that the OV-induced localized state is highly one dimensional and is mainly composed of Ti 3d3z2-r2 orbitals along the Ti-OV-Ti axis (defined as the z axis) and Ti 4s,4p orbitals at the OV site. The oxygen vacancy does not lead to Ti t2g-based localized states.
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Combined Theoretical and Experimental Study of the Moiré Dislocation Network at the SrTiO3-(La,Sr)(Al,Ta)O3 InterfaceClick to copy article linkArticle link copied!

ACS Applied Materials & Interfaces

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1. Introduction

2. Methods

2.1. Computational Details

2.1.1. Dislocation Models

Figure 1

2.1.2. Molecular Dynamics

2.1.3. DFT Calculations

2.2. Experimental Methods

2.2.1. X-ray Diffraction

2.2.2. Scanning Transmission Electron Microscopy

3. Results and Discussion

3.1. Structure and Strain Field at the Dislocation Core

Figure 2

3.2. Defect Chemistry of the Dislocation Core

3.2.1. Oxygen Vacancies

Figure 3

Figure 4

Figure 5

3.2.2. Cation Vacancies

Figure 6

Figure 7

Figure 8

3.2.3. Substitutional Defects

Figure 9

Figure 10

Figure 11

4. Conclusions

Author Information

Acknowledgments

References

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Combined Theoretical and Experimental Study of the Moiré Dislocation Network at the SrTiO₃-(La,Sr)(Al,Ta)O₃ Interface
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