Properties of Oxygen Vacancy and Hydrogen Interstitial Defects in Strontium Titanate: DFT + Ud,p CalculationsClick to copy article linkArticle link copied!
- Szymon Winczewski*Szymon Winczewski*Email: [email protected]Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, Gdańsk80-233, PolandMore by Szymon Winczewski
- Jacek DziedzicJacek DziedzicFaculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, Gdańsk80-233, PolandSchool of Chemistry, University of Southampton, Highfield, SouthamptonSO17 1BJ, U.K.More by Jacek Dziedzic
- Tadeusz MiruszewskiTadeusz MiruszewskiFaculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, Gdańsk80-233, PolandMore by Tadeusz Miruszewski
- Jarosław RybickiJarosław RybickiFaculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, Gdańsk80-233, PolandTASK Computer Centre, Gdansk University of Technology, Narutowicza 11/12, Gdańsk80-233, PolandMore by Jarosław Rybicki
- Maria GazdaMaria GazdaFaculty of Applied Physics and Mathematics, Gdansk University of Technology, Narutowicza 11/12, Gdańsk80-233, PolandMore by Maria Gazda
Abstract
This work presents extensive theoretical studies focused on the mixed ion-electron transport in cubic strontium titanate (STO). A new approach to the description of this difficult system was developed within the framework of linear-scaling Kohn–Sham density functional theory, as realized in the ONETEP program. The description we present is free of any empirical parameters and relies on the Hubbard U and Hund’s J corrections applied to both Ti and O atoms. The proposed methodology was validated by considering perfect STO. Its calculated properties were found to be in close agreement with experiments and calculations at higher levels of theory. The validated approach was subsequently employed to study the oxygen vacancy (VO) and the hydrogen interstitial (IH), using very large supercells (625 ± 1 atoms). The relaxed configurations of defects were obtained through fastidious energy minimization and later analyzed from a number of perspectives. The calculated defect formation energies and charge transition levels (CTLs) were found to be in close agreement with the experiment. With the exception of the charge-neutral VO, all considered defects were found to introduce shallow states, located down to 0.2 eV below the conduction band. Our calculations revealed a large 1 eV difference in the thermodynamic and optical CTLs of the neutral VO, explaining the inconsistencies observed─till now─between conduction and spectroscopic measurements. The influence of defects on the bonding characteristics and the crystalline structure of STO was quantified, revealing that both VO and IH defects lead to a significant polarization and strong tilting of the TiO6 octahedra.
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You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:
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1. Introduction
1.1. Strontium Titanate
1.2. Difficulties in Theoretical Description
1.3. Difficulties in Modeling of Defects
1.4. Aims and Outline of the Work
2. Methodology
2.1. ONETEP Approach
2.2. Theoretical Description
2.3. Calculations Performed
2.4. Formation Energies
2.5. Charge Transition Levels
3. Methodology Validation─Perfect STO
3.1. Validation Outline
3.2. Equation of State
property | |||||
---|---|---|---|---|---|
method | a (Å) | B0 (GPa) | B0′ | EgI(eV) | EgD(eV) |
this work | |||||
DFT (PBE) | 3.966 | 161.9 (0.2) | 4.37 (0.02) | 1.66 | 1.96 |
DFT + Ud | 3.986 | 154.2 (0.3) | 4.35 (0.02) | 1.95 | 2.32 |
DFT + Ud,p | 3.957 | 172.1 (0.2) | 4.25 (0.02) | 2.92 | 3.20 |
other computational studies | |||||
(a) DFT (all with PBE) | |||||
GTO | 3.93a, 3.96b | 171a,b | 1.8b, 1.99a | 2.1b, 2.35a | |
LAPW | 3.94c,d, 3.95e | 167e, 169c, 175d | 4.61c | 1.63d, 1.97c | |
PW | 3.94b,f,g, 3.95h | 168f,r, 169b, 171h | 1.8bf, 1.85h | 2.1b, 2.2f,r | |
hybrid | 3.94i | 172i | 1.74i | ||
(b) DFT + Ud (all with PBE and PW) | |||||
Ueff = 4 eV | 3.97j | 164j | 4.35j | ≈2.0j | |
U = 5 eV, J = 0.64 eV | 3.90g, 3.93k, 3.98l | 2.39l, 2.68k | |||
(c) hybrid DFT | |||||
B3LYP, GTO | 3.94a, 3.95m | 179m, 180a | 3.57a, 4.38m | 3.89a | |
B3PW, GTO | 3.89n, 3.90o,p, 3.92b, 3.93q | 190b | 3.4b, 3.6n, 3.63o, 3.64p | 3.7b, 3.96p | |
HSE06, PW | 3.90f,r | 192f,r | 3.01r, 3.07f,r | 3.47f,r | |
PBE0, GTO | 3.90b | 201b | 3.8b | 4.2b | |
PBE0, PW | 3.90b | 193b | 4.0b | 4.4b | |
(d) various GW approaches (all based on LDA) | |||||
QSGW | 3.32s | ||||
G0W0 | 3.40t | 3.76t | |||
QSGW80 + SO | 3.56u | ||||
QSGW + LP + 0.8Σ | 3.2v | 3.7v | |||
experimental data | 3.905w,x | 178.8 (4.6)y | 4.31 (0.1)y | 3.25z | 3.75z |
Values given in brackets denote errors, which for the calculated lattice constants were lower than 10–3 Å.
3.3. Electronic Structure
Ti 3s | Ti 3p | Sr 4s | O 2s | Sr 4p | O 2p | |
---|---|---|---|---|---|---|
DFT + Ud,p | –23.1 | 0 | 3.0 | 18.8 | 19.4 | 30.0 |
G0W0 | 0 | 0 | 16.0 | 18.1 | 29.8 | |
XPS | –24.8 | 0 | 15.7 | 18.3 | ≈31.7 |
4. Results─Defective Systems
4.1. Structural Relaxation
defect state | distances (Å) | |||||
---|---|---|---|---|---|---|
/init. | config. | total energy (eV) | defect level position (eV) | integral of |ρ↑ – ρ↓| (e) | ΔdTi–Ti | ΔdSr–Sr |
VO2+ | d | +404.640 | n/a | 0 | +0.221 | +0.144, +0.155 |
p | +0.039 | n/a | 0 | +0.240 | +0.132, +0.170 | |
VO1+ | p | +415.791 | –0.099 | 1.88 | +0.209 | +0.145, +0.155 |
d | +0.155 | –0.098 | 1.88 | +0.212 | +0.143, +0.160 | |
VO0,S=0 | p | +427.045 | –0.716, −0.716 | 2.39 | +0.046 | +0.134, +0.208 |
d | +0.046 | –0.719, −0.718 | 2.45 | +0.045 | +0.167, +0.186 | |
VO0,S=2 | d | +427.044 | –0.724, −0.721 | 2.47 | +0.046 | +0.165, +0.186 |
p | +0.015 | –0.719, −0.714 | 2.45 | +0.046 | +0.134, +0.208 |
Data for various charge/spin states (given in the first column) of the VO defect is presented. The second column indicates if the relaxation started from perfect (p) or distorted (d) positions. The total energies of the identified lowest energy minima (first rows) are measured relative to the perfect system (ED,q – EP is given). For other─higher-lying─minima, the energy difference to the corresponding lowest energy minimum is given. Positions of the defect levels are given as ϵdKS–ϵCBM, that is, they are measured with respect to the CBM of the perfect system. The fifth column gives the integral of |ρ↑(r) – ρ↓(r)| (spin up and spin down densities) over the entire supercell. The last two columns give the changes in the Ti–Ti and Sr–Sr distances for Ti and Sr atoms closest to the defect. For ΔdSr–Sr, the minimum and maximum is given.
defect state | distances (Å) | angles (degrees) | |||||||
---|---|---|---|---|---|---|---|---|---|
/init. | config. | total energy (eV) | defect level position (eV) | integral of |ρ↑ – ρ↓| (e) | ΔdTi–Ti | ΔdSr–Sr | dO–H | θTi–O–H | θSr–O–H |
IH1+ | d | –27.737 | n/a | 0 | +0.283 | +0.323 | 0.956 | 86.5 | 44.4 |
d | +0.071 | n/a | 0 | +0.298 | +0.308 | 0.957 | 85.1 | 43.9 | |
p | +0.123 | n/a | 0 | +0.300 | +0.306 | 0.957 | 85.5 | 43.8 | |
d | +0.148 | n/a | 0 | +0.301 | +0.303 | 0.957 | 85.4 | 43.8 | |
IH0 | d | –16.468 | –0.092 | 1.88 | +0.283 | +0.317 | 0.956 | 86.3 | 44.3 |
p | +0.119 | –0.089 | 1.88 | +0.295 | +0.301 | 0.957 | 85.5 | 43.8 | |
d | +0.129 | –0.092 | 1.88 | +0.290 | +0.308 | 0.956 | 85.8 | 44.0 | |
d | +0.148 | –0.090 | 1.88 | +0.296 | +0.300 | 0.957 | 85.4 | 43.7 | |
IH1-,S=0 | d | –5.288 | –0.115, −0.115 | 3.67 | +0.282 | +0.334 | 0.963 | 77.6 | 46.3 |
d | +0.014 | –0.108, −0.104 | 3.66 | +0.279 | +0.325 | 0.962 | 77.9 | 46.2 | |
d | +0.092 | –0.115, −0.115 | 3.66 | +0.288 | +0.326 | 0.957 | 86.2 | 44.3 | |
p | +0.105 | –0.107, −0.105 | 3.65 | +0.280 | +0.323 | 0.956 | 86.5 | 44.4 | |
IH1-,S=2 | d | –5.298 | –0.116, −0.110 | 3.75 | +0.282 | +0.334 | 0.963 | 77.5 | 46.2 |
p | +0.009 | –0.107, −0.099 | 3.75 | +0.280 | +0.324 | 0.961 | 78.5 | 45.9 | |
d | +0.021 | –0.106, −0.099 | 3.75 | +0.279 | +0.326 | 0.962 | 78.0 | 46.2 | |
d | +0.045 | –0.096, −0.089 | 3.73 | +0.282 | +0.331 | 0.962 | 78.1 | 46.0 |
Data for the IH defect. Columns 1–6 have the same meaning as in Table 3. Column 7 presents the change in the distance between two Sr atoms closest to the H atom. The last three columns describe the position of the H atom.
4.2. Formation Energies
formation energy | corrections | ||
---|---|---|---|
defect state | ΔH (eV) | EIIC (eV) | EPA (eV) |
VO2+ | +1.45 (0.12) | [0, 0.009] | [−0.062, +0.139] |
VO1+ | +4.36 (0.11) | [0, 0.002] | [−0.058, +0.017] |
VO0,S=0 | +7.32 (0.02) | 0 | 0 |
VO0,S=2 | +7.31 (0.01) | 0 | 0 |
IH1+ | –3.56 (0.13) | [0, 0.002] | [−0.050, +0.063] |
IH0 | –0.54 (0.07) | 0 | 0 |
IH1–,S=0 | +2.40 (0.11) | [0, 0.002] | [−0.093, +0.068] |
IH1–,S=2 | +2.34 (0.07) | [0, 0.002] | [−0.085, +0.058] |
Here, we do not distinguish different minima of the same defect. Instead, the results obtained for the various minima were used to determine the presented uncertainties. These uncertainties also account for the uncertainties of the EIIC and EPA corrections, for which bounds are given. Note that both corrections are zero by definition for the neutral defects.
4.3. Charge Transition Levels
charge transition level (eV) | |||
---|---|---|---|
transition type | thermodynamic | absorption | emission |
(q/q′) | ϵth(q/q′) | ϵop(q′/q) | ϵop(q/q′) |
oxygen vacancy | |||
(2+/1+) | –0.11 (0.20) | –0.08 (0.08) | –0.09 (0.10) |
(1+/0, S = 0) | –0.11 (0.13) | –0.98 (0.06) | –0.02 (0.04) |
(1+/0, S = 2) | –0.12 (0.12) | –0.98 (0.06) | –0.02 (0.04) |
(2+/0, S = 0) | –0.11 (0.05) | –1.09 (0.09) | –0.07 (0.09) |
(2+/0, S = 2) | –0.12 (0.05) | –1.09 (0.09) | –0.08 (0.08) |
hydrogen interstitial | |||
(1+/0) | –0.04 (0.20) | –0.11 (0.06) | –0.04 (0.06) |
(0/1 −, S = 0) | –0.12 (0.18) | –0.07 (0.08) | –0.02 (0.07) |
(0/1–, S = 2) | –0.18 (0.14) | –0.08 (0.07) | –0.03 (0.06) |
(1+/1–, S = 0) | –0.08 (0.12) | –0.08 (0.07) | –0.03 (0.06) |
(1+/1–, S = 2) | –0.11 (0.10) | –0.07 (0.07) | –0.04 (0.06) |
Locations of all levels are measured with respect to CBM. A negative value informs that the level is located below CB. The value given in brackets is the uncertainty. Note that the OTL presented in column 3 corresponds to the opposite transition q′ → q.
4.4. Defect Levels and Electronic Structure
4.5. Atomic Charges
acquired charge ΔqiNPA | ||||
---|---|---|---|---|
defect state | Ti1 | Ti2 | O (10 atoms) | Sr (4 atoms) |
VO2+ | +0.089 | +0.243 | –0.069 (0.024) | –0.010 (0.002) |
+0.092 | +0.253 | –0.067 (0.032) | –0.003 (0.002) | |
VO1+ | +0.163 | +0.288 | –0.088 (0.029) | –0.005 (0.004) |
+0.012 | +0.132 | –0.034 (0.023) | –0.021 (0.002) | |
VO0,S=0 | –0.077 | +0.001 | –0.145 (0.012) | +0.012 (0.001) |
–0.187 | –0.065 | –0.099 (0.026) | –0.008 (0.002) | |
VO0,S=2 | –0.125 | –0.056 | –0.115 (0.022) | –0.015 (0.002) |
–0.130 | –0.023 | –0.127 (0.018) | –0.008 (0.002) |
For the O and Sr atoms, the mean value (averaged over the specified number of atoms) and its standard deviation (in brackets) are given. They specify the charge acquired by a single Sr or O atom. The ordering of the minima is the same as in Table 3.
acquired charge ΔqiNPA | atomic charge qiNPA | |||||
---|---|---|---|---|---|---|
defect state | Ti1 | Ti2 | O (10 atoms) | Sr (4 atoms) | O | H |
IH1+ | +0.197 | +0.202 | –0.059 (0.018) | +0.013 (0.011) | –1.152 | +0.340 |
+0.142 | +0.141 | –0.044 (0.014) | +0.006 (0.012) | –1.207 | +0.403 | |
+0.061 | +0.056 | –0.008 (0.015) | +0.006 (0.012) | –1.209 | +0.427 | |
+0.175 | +0.181 | –0.050 (0.016) | +0.019 (0.009) | –1.218 | +0.408 | |
IH0 | +0.071 | +0.066 | –0.008 (0.016) | +0.002 (0.006) | –1.197 | +0.419 |
+0.057 | +0.075 | –0.014 (0.017) | +0.004 (0.008) | –1.230 | +0.437 | |
+0.037 | +0.036 | –0.010 (0.019) | +0.002 (0.005) | –1.207 | +0.429 | |
+0.053 | +0.058 | –0.009 (0.017) | –0.001 (0.013) | –1.199 | +0.416 | |
IH1–,S=0 | +0.076 | +0.126 | –0.020 (0.011) | –0.005 (0.010) | –1.132 | +0.343 |
+0.083 | +0.053 | –0.014 (0.009) | –0.008 (0.011) | –1.140 | +0.362 | |
+0.015 | +0.015 | +0.001 (0.019) | –0.004 (0.009) | –1.197 | +0.417 | |
+0.012 | +0.027 | –0.002 (0.015) | –0.006 (0.009) | –1.217 | +0.437 | |
IH1–,S=2 | +0.016 | +0.029 | –0.002 (0.017) | –0.007 (0.010) | –1.132 | +0.366 |
+0.048 | +0.084 | –0.016 (0.013) | –0.005 (0.010) | –1.192 | +0.393 | |
+0.003 | +0.008 | +0.001 (0.017) | –0.006 (0.009) | –1.188 | +0.409 | |
+0.070 | +0.104 | –0.020 (0.013) | –0.006 (0.010) | –1.155 | +0.375 |
4.6. Crystalline Structure
5. Conclusions
5.1. Summary
5.2. Discussion and Future Work
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.2c04681.
Detailed information related to the choice of U and J parameters, choice of the reference chemical potentials, calculation of the electrostatic corrections, and determination of the optical transition levels (PDF)
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Acknowledgments
This work was supported by the National Science Centre in Poland (grant number UMO-2016/23/B/ST5/02137). The authors gratefully acknowledge the PSNC Poznan Supercomputing and Networking Center (Poznan, Poland) and the TASK Academic Computer Centre (Gdansk, Poland) for providing computer time and facilities. This research was supported by the PL-Grid Infrastructure. S.W. gratefully acknowledges the help of and valuable discussions with D. D. O’Regan.
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- 5Wyckoff, R. W. G. Crystal Structures─Volume 2: Inorganic Compounds RXn, RnMX2, RnMX3; John Wiley & Sons: New York, London, Sydney, 1964.Google ScholarThere is no corresponding record for this reference.
- 6Unoki, H.; Sakudo, T. Electron spin resonance of Fe3+ in SrTiO3 with special reference to the 110 °K phase transition. J. Phys. Soc. Jpn. 1967, 23, 546– 552, DOI: 10.1143/jpsj.23.546Google Scholar6https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaF2sXltFaltbg%253D&md5=08f22f3ffe44d1e8a0ccf1e0c28cfef1Electron spin resonance of Fe3+ in strontium titanate with special reference to the 110°K. phase transitionUnoki, Hiromi; Sakudo, TunetaroJournal of the Physical Society of Japan (1967), 23 (3), 546-52CODEN: JUPSAU; ISSN:0031-9015.The E.S.R. of Fe3+ in single crystals of SrTiO3 has been studied in the low-temp. phase below 110°K. The resonance lines exhibited small splitting in addn. to the usual tetragonal splitting. The orientation dependence of the splitting was measured at 77°K. and at 4.2°K. The whole spectrum is attributed to the rotation of O octahedron in the (100) plane, the angle of rotation being 1.4° at 77°K.and 2.1° at 4.2°K. Corresponding splitting was also observed for the case of the "strong axial field" spectrum due to Fe3+ accompanied by the nearest neighbor oxygen vacancy. The observed angles of rotation are about 30% smaller than those of the former case. The crystal structure deduced from the at. positions of O ions will be D164h in the low-temp. phase. Correlation with the resonance data of Gd3+ in SrTiO3 is discussed. 18 references.
- 7Abramov, Y. A.; Tsirelson, V. G.; Zavodnik, V. E.; Ivanov, S. A.; Brown, I. D. The chemical bond and atomic displacements in SrTiO3 from X-ray diffraction analysis. Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. 1995, 51, 942– 951, DOI: 10.1107/s0108768195003752Google Scholar7https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XkvFWruw%253D%253D&md5=aef14babd22b7b86058ea7d47814257cThe chemical bond and atomic displacements in SrTiO3 from x-ray diffraction analysisAbramov, Yu. A.; Tsirelson, V. G.; Zavodnik, V. E.; Ivanov, S. A.; Brown, I. D.Acta Crystallographica, Section B: Structural Science (1995), B51 (6), 942-51CODEN: ASBSDK; ISSN:0108-7681. (Munksgaard)The deformation electron-d. (dynamic Fourier) maps and the anharmonicity of at. displacements in Sr titanate, SrTiO3 (Gram-Charlier model), were studied by high-precision single-crystal x-ray diffraction anal. at 145(1) and 296(2) K. SrTiO3 is cubic, space group Pm3m, Z = 1, T = 145(1) K, a 3.8996(5) Å, dc = 5.138(2), R = 0.0063, Rw = 0.0040, 131 unique reflections and T = 296(2) K, a 3.901(1) Å, dc = 5.133(4), R = 0.0071, Rw = 0.0050, 109 unique reflections. At. coordinates are given. Strong anharmonicity of the at. displacements was obsd. for all atoms at 145 K and for Ti and O atoms at 296 K. These are explained by a model in which electronic instability in the TiO6 octahedron leads to a displacement of the Ti atom from the center of the octahedron, and the lattice instability resulting from the consequent stretching of the Sr-O bonds leads to a rotation of the octahedra. Both distortions show only short-range order at the temps. studied, but show indications of freezing out as the temp. is lowered towards the rotational phase transition at 106 K. The exptl. dynamic Fourier deformation electron-d. maps and the Hirshfeld at. charges were calcd.
- 8Cao, L.; Sozontov, E.; Zegenhagen, J. Cubic to tetragonal phase transition of SrTiO3 under epitaxial stress: An X-ray backscattering study. Phys. Status Solidi A 2000, 181, 387– 404, DOI: 10.1002/1521-396x(200010)181:2<387::aid-pssa387>3.0.co;2-5Google Scholar8https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXotVKjsro%253D&md5=404a92ce5eedfe4c55fca01fef233c48Cubic to tetragonal phase transition of SrTiO3 under epitaxial stress: an x-ray backscattering studyCao, Lixin; Sozontov, E.; Zegenhagen, J.Physica Status Solidi A: Applied Research (2000), 181 (2), 387-404CODEN: PSSABA; ISSN:0031-8965. (Wiley-VCH Verlag Berlin GmbH)Employing synchrotron radiation in backscattering geometry the 105 K cubic to tetragonal (CT) phase transition of SrTiO3 was studied by x-ray diffraction using the (006) reflection of three (001) oriented samples. Two of the crystals were covered with ultrathin films of YBa2Cu3O7-δ (14 nm) and GdBa2Cu3O7-δ (28 nm), resp. The stress induced by the epitaxial layers influences the behavior of the CT transition in two ways. The crit. temp. increases by 1.2 K as a result of the homogeneous epitaxial stress (13.5 MPa) introduced into the substrate by the pseudomorphic GdBa2Cu3O7-δ film. Strain affects the crit. exponent of the temp. dependence of the order parameter. Also, the microstructure of the tetragonal domains and its temp. dependence are markedly different for the three samples.
- 9Schmidbauer, M.; Kwasniewski, A.; Schwarzkopf, J. High-precision absolute lattice parameter determination of SrTiO3, DyScO3 and NdGaO3 single crystals. Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. 2012, 68, 8– 14, DOI: 10.1107/s0108768111046738Google Scholar9https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtVGns7o%253D&md5=c0e8fcce5686a526aa593b4365d7a3d4High-precision absolute lattice parameter determination of SrTiO3, DyScO3 and NdGaO3 single crystalsSchmidbauer, Martin; Kwasniewski, Albert; Schwarzkopf, JuttaActa Crystallographica, Section B: Structural Science (2012), 68 (1), 8-14CODEN: ASBSDK; ISSN:0108-7681. (International Union of Crystallography)The lattice parameters of SrTiO3 and DyScO3, and NdGaO3 single crystals were measured with high precision at room temp. with a relative accuracy of the order of 10-5. The lattice parameters of three perovskite-related oxides were measured with high precision at room temp. An accuracy of the order of 10-5 was achieved by applying a sophisticated high-resoln. x-ray diffraction technique which is based on the modified Bond method. The results on cubic SrTiO3 [a = 3.905268(98) Å], orthorhombic DyScO3 [a 5.442417(54), b 5.719357(52) and c 7.904326(98) Å], and orthorhombic NdGaO3 [a 5.428410(54), b 5.498407(55) and c 7.708878(95) Å] are discussed in view of possible systematic errors as well as nonstoichiometry in the crystals.
- 10Edwards, L. R.; Lynch, R. W. The high pressure compressibility and Grüneisen parameter of strontium titanate. J. Phys. Chem. Solids 1970, 31, 573– 574, DOI: 10.1016/0022-3697(70)90098-3Google Scholar10https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE3cXhtFGjsb4%253D&md5=ac069e3ed86ac8911268c60aff23c5ebHigh pressure compressibility and Grueneisen parameter of strontium titanateEdwards, Leon Roger; Lynch, R. W.Journal of Physics and Chemistry of Solids (1970), 31 (3), 573-4CODEN: JPCSAW; ISSN:0022-3697.The compressibility of SrTiO3 (≥99.99% purity) was measured at 298°K and 0-200 kilobars. The data were fitted to the Murnaghan equation of state (1944). The Grueneisen parameter, calcd. from the zero pressure values of the compressibility, thermal expansion, heat capacity at const. vol., and molar vol., is γ = 1.89; and γ = (B10 - 1)/2 = 1.7, where B10 is the pressure deriv. of the bulk modulus at const. temp. detd. from the Murnaghan equation.
- 11Beattie, A. G.; Samara, G. A. Pressure dependence of the elastic constants of SrTiO3. J. Appl. Phys. 1971, 42, 2376– 2381, DOI: 10.1063/1.1660551Google Scholar11https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE3MXktFWntb8%253D&md5=20316529c57116cd51c9e238f1a069d6Pressure dependence of the elastic constants of strontium titanateBeattie, A. G.; Samara, G. A.Journal of Applied Physics (1971), 42 (6), 2376-81CODEN: JAPIAU; ISSN:0021-8979.The effects of hydrostatic pressure at 0-22 kbar on the elastic const. of SrTiO3 were measured at 295°K. All const. increased linearly with pressure in this range. The pressure derivs. of the adiabatic const. dCij/dP are: 10.21, 3.51, and 1.24 for C11, C12, and C44, resp. These pressure derivatives in conjunction with the recent, 2nd-harmonic generation results of Mackey and Arnold, allow the detn. of the complete set of 3rd-order elastic const. The results, in units of 1012 dyne/cm2, are: C111 = -49.6, C112 = -7.7, C123 = +0.2, C144 = -8.1, C166 = -3.0, and C456 = 0.9. Combined with the temp. derivs. of the (2nd-order) elastic const. at const. pressure, the pressure results allow a detn. of the explicit vol. and temp. dependences of these const. In addn., the present results calcn. of the acoustic mode Grueneisen parameters, an approx. value of the limiting Grueneisen const., γ0 = 1.52, and the coeffs. of the polynominal and logarithmic (Murnaghan) forms of the high pressure equation of state of SrTiO3.
- 12Fischer, G. J.; Wang, Z.; Karato, S. Elasticity of CaTiO3, SrTiO3 and BaTiO3 perovskites up to 3.0 GPa: The effect of crystallographic structure. Phys. Chem. Miner. 1993, 20, 97– 103, DOI: 10.1007/bf00207202Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2cXht1Wisrg%253D&md5=11acca4a2b3b4f9e1cecfd89907dbad7Elasticity of calcium titanate, strontium titanate, and barium titanate perovskites up to 3.0 GPa: the effect of crystallographic structureFischer, George J.; Wang, Zichao; Karato, ShunichiroPhysics and Chemistry of Minerals (1993), 20 (2), 97-103CODEN: PCMIDU; ISSN:0342-1791.Elasticity of CaTiO3, SrTiO3 and BaTiO3 perovskites was exptl. investigated as a function of pressure up to 3.0 GPa in a liq.-medium piston cylinder app. using a high precision ultrasonic interferometric technique. Specimens used are hot-pressed fine-grained (3-10 μm) polycryst. aggregates with low porosity (<1.5%). Compressional and shear wave velocities and their pressure derivs. were measured. The results are compared with previous studies on other perovskites and the role of structural transitions is examd. The role of TiO6 polyhedral tilting (such as obsd. in CaTiO3) is small in the sense that a single well-defined general trend exists in perovskites with a wide range of tilting angles, although there is suggestion that cubic perovskites have slightly higher bulk modulus than orthorhombic perovskites. In contrast, cation-anion displacement that changes crystal symmetry from cubic to tetragonal in BaTiO3 has very large effects on elasticity. This distortion significantly reduces the bulk modulus (but not much the shear modulus) and results in an unusually large pressure deriv. of bulk modulus (dK/dP ∼ 10). A large change in elasticity in BaTiO3 assocd. with the structural transition (without a significant vol. change) is a clear example of the breakdown of the Birch's law between densities and elastic wave velocities.
- 13Capizzi, M.; Frova, A. Optical gap of strontium titanate (deviation from Urbach tail behavior). Phys. Rev. Lett. 1970, 25, 1298– 1302, DOI: 10.1103/physrevlett.25.1298Google Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE3cXltlGls7k%253D&md5=ec9e3cd32ae6eeec58ca1f695f8ca687Optical gap of strontium titanate (deviation from Urbach tail behavior)Capizzi, M.; Frova, A.Physical Review Letters (1970), 25 (18), 1298-302CODEN: PRLTAO; ISSN:0031-9007.The absorption of SrTiO3 below the fundamental edge shows, near liq.-N temp., an oscillatory behavior, for which an explanation is proposed in terms of indirect transitions Γ15 → X3, centered around 3.27 eV and involving a 51-meV longitudinal optical phonon. There is no evidence of excitonic effects. The 1st direct transition is probably X5' → X3 and is located at ∼3.46 eV. Broadening effects mask the indirect structure at higher temps. where the absorption curves gradually evolve into normal Urbach tailing.
- 14Henrich, V. E.; Dresselhaus, G.; Zeiger, H. J. Surface defects and the electronic structure of SrTiO3 surfaces. Phys. Rev. B: Solid State 1978, 17, 4908– 4921, DOI: 10.1103/physrevb.17.4908Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE1cXlsFeit70%253D&md5=57d8b392f02b574fd784877b3d00e899Surface defects and the electronic structure of strontium titanate(IV) surfacesHenrich, Victor E.; Dresselhaus, G.; Zeiger, H. J.Physical Review B: Solid State (1978), 17 (12), 4908-21CODEN: PLRBAQ; ISSN:0556-2805.The electronic properties of various types of SrTiO3 surfaces were studied by UV-photoemission and electron-energy-loss spectroscopy, low-energy electron diffraction, and Auger spectroscopy. Vacuum-fractured surfaces exhibit weak photoemission in the region of the bulk band gap, probably due to residual surface defects. When surface defects are produced by Ar-ion bombardment, a stronger band of surface states appears in the band-gap region. These states arise from the creation of Ti3+-O-vacancy complexes and are predominantly of d-electron character. Two surface defect phases are seen, 1 due to surface disorder and the other to changes in surface compn. The latter phase is stable under annealing to ≥1100 K. Exposure to O, however, depopulates the band-gap surface states on both vacuum-fractured and ion-bombarded surfaces. Models for the structure of the defect surface states are discussed.
- 15Courths, R. Ultraviolet photoelectron spectroscopy (UPS) and LEED studies of BaTiO3 (001) and SrTiO3 (100) surfaces. Phys. Status Solidi B 1980, 100, 135– 148, DOI: 10.1002/pssb.2221000114Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL3cXkvVCmurw%253D&md5=9a4d6521b51ca66eedcc01b88103a4faUltraviolet photoelectron spectroscopy (UPS) and LEED studies of barium titanate(IV) (001) and strontium titanate(IV) (100) surfacesCourths, R.Physica Status Solidi B: Basic Research (1980), 100 (1), 135-48CODEN: PSSBBD; ISSN:0370-1972.UPS studies (21.2 and 40.8 eV) were performed on BaTiO3 (001) and SrTiO3 (100) surfaces. In both the compds. there is an enhanced emission at the top of the valence band for hν = 21.2 eV, which cannot be explained with the existing theor. bulk densities of states. From the results of angle-dependent UPS measurements it is concluded that the top of the valence band emission is due to an O surface state. This interpretation is supported by band structure calcns. for thin films of BaTiO3. A band gap state at 0.9 eV (BaTiO3) and 1.2 eV (SrTiO3) below the bottom of the conduction band can be detected on O deficient surfaces and is interpreted as arising from Ti3+ species. In UHV annealed surfaces are 1 × 1 ordered. They show a 2 × 2 or 2 mutually perpendicular 2 × 1 LEED patterns in case of a higher concn. of Ti3+-O-vacancy defects due to defect ordering.
- 16Kan, D.; Terashima, T.; Kanda, R.; Masuno, A.; Tanaka, K.; Chu, S.; Kan, H.; Ishizumi, A.; Kanemitsu, Y.; Shimakawa, Y. Blue-light emission at room temperature from Ar+-irradiated SrTiO3. Nat. Mater. 2005, 4, 816– 819, DOI: 10.1038/nmat1498Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXht1ShsbjI&md5=dbdc7e3663bac7e1280c542bc256d56dBlue-light emission at room temperature from Ar+-irradiated SrTiO3Kan, Daisuke; Terashima, Takahito; Kanda, Ryoko; Masuno, Atsunobu; Tanaka, Kazunori; Chu, Shucheng; Kan, Hirofumi; Ishizumi, Atsushi; Kanemitsu, Yoshihiko; Shimakawa, Yuichi; Takano, MikioNature Materials (2005), 4 (11), 816-819CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)Oxide-based electronic devices are expected to have fascinating properties, unlike those made from conventional semiconductors. SrTiO3 (STO) is a key material for this new field of electronics. Here the authors report on blue-light emission at room temp. from Ar+-irradiated, metallic STO. The irradn. introduces O deficiencies to a depth of ∼20 nm from the crystal surface. These deficiencies generate conduction carriers and stabilize a hole level in a self-trapped state. The authors propose a model by which the doped conduction electrons and the in-gap state produce a radiative process that results in blue-light emission. The emitting region can be patterned into any size and shape with conventional microscopic fabrication techniques.
- 17Dejneka, A.; Tyunina, M.; Narkilahti, J.; Levoska, J.; Chvostova, D.; Jastrabik, L.; Trepakov, V. A. Tensile strain induced changes in the optical spectra of SrTiO3 epitaxial thin films. Phys. Solid State 2010, 52, 2082– 2089, DOI: 10.1134/s1063783410100124Google Scholar17https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXht12ksbzF&md5=75963817efac6496c8a14fb8e3500776Tensile strain induced changes in the optical spectra of SrTiO3 epitaxial thin filmsDejneka, A.; Tyunina, M.; Narkilahti, J.; Levoska, J.; Chvostova, D.; Jastrabik, L.; Trepakov, V. A.Physics of the Solid State (2010), 52 (10), 2082-2089CODEN: PSOSED; ISSN:1063-7834. (Pleiades Publishing, Ltd.)Effect of biaxial tensile strains on optical function and band edge transitions of ultra thin epitaxial films was studied using as an example a 13 nm thick SrTiO3 films deposited on KTaO3 (100) single-crystal substrates. Optical functions in the 200-1200 nm spectral range were detd. by spectroscopic ellipsometry technique. It was found that tensile strains result in a shift of the low energy band gap optical transitions to higher energies and decrease the refractive index in the visible region. Comparison of the optical spectra for strained SrTiO3 films and for homoepitaxial strain-free SrTiO3: Cr (0.01 at %) films deposited on SrTiO3 (100) single cryst. substrates showed that this "blue" shift of the band gap could not be related to technol. imperfections or to reduced thickness. The obsd. effect is connected with changes in the lowest conduction and in the top valence bands that are due to increase of the in-plane lattice const. and/or onset of the polar phase in the tensile strain-induced ultra-thin epitaxial SrTiO3 films.
- 18Ravichandran, J.; Siemons, W.; Scullin, M. L.; Mukerjee, S.; Huijben, M.; Moore, J. E.; Majumdar, A.; Ramesh, R. Tuning the electronic effective mass in double-doped SrTiO3. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 035101, DOI: 10.1103/physrevb.83.035101Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhsFelu7k%253D&md5=bca36862990bd1ac039be942435c10fcTuning the electronic effective mass in double-doped SrTiO3Ravichandran, J.; Siemons, W.; Scullin, M. L.; Mukerjee, S.; Huijben, M.; Moore, J. E.; Majumdar, A.; Ramesh, R.Physical Review B: Condensed Matter and Materials Physics (2011), 83 (3), 035101/1-035101/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We elucidate the relationship between effective mass and carrier concn. in an oxide semiconductor controlled by a double-doping mechanism. In this model oxide system, Sr1-xLaxTiO3-δ, we can tune the effective mass ranging from 6 to 20me as a function of filling (carrier concn.) and the scattering mechanism, which are dependent on the chosen lanthanum- and oxygen-vacancy concns. The effective mass values were calcd. from the Boltzmann transport equation using the measured transport properties of thin films of Sr1-xLaxTiO3-δ. We show that the effective mass decreases with carrier concn. in this large-band-gap, low-mobility oxide, and this behavior is contrary to the traditional high-mobility, small-effective-mass semiconductors.
- 19Tarun, M. C.; McCluskey, M. D. Infrared absorption of hydrogen-related defects in strontium titanate. J. Appl. Phys. 2011, 109, 063706, DOI: 10.1063/1.3561867Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXjsFemur4%253D&md5=aef77bb186d313ab04ae17715c252d49Infrared absorption of hydrogen-related defects in strontium titanateTarun, M. C.; McCluskey, M. D.Journal of Applied Physics (2011), 109 (6), 063706/1-063706/4CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)H has a significant impact on the structural and electronic properties of metals, insulators, and semiconductors. Despite the prevalence of H, little is known about its behavior in oxides such as Sr titanate (SrTiO3). H-related defects in SrTiO3 were studied using IR absorption spectroscopy. Two local vibrational modes (LVMs) are obsd. at 3355 and 3384 cm-1 after hydrogenation at 800°. Isotope substitution expts. revealed that the defect consists of 2 H atoms bound to host O atoms. From the temp. dependence of the LVMs, the authors ascribe the complex to a Sr vacancy passivated by 2 H atoms. The thermal stability of the defect was detd. through isochronal annealing expts. on the hydrogenated SrTiO3 sample. These measurements provided evidence of hidden H, possibly H2 mols., in the crystal. (c) 2011 American Institute of Physics.
- 20Rice, W. D.; Ambwani, P.; Bombeck, M.; Thompson, J. D.; Haugstad, G.; Leighton, C.; Crooker, S. A. Persistent optically induced magnetism in oxygen-deficient strontium titanate. Nat. Mater. 2014, 13, 481– 487, DOI: 10.1038/nmat3914Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXks1Knu78%253D&md5=be9c7a8272f8059f6268854a49437794Persistent optically induced magnetism in oxygen-deficient strontium titanateRice, W. D.; Ambwani, P.; Bombeck, M.; Thompson, J. D.; Haugstad, G.; Leighton, C.; Crooker, S. A.Nature Materials (2014), 13 (5), 481-487CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)SrTiO3 is a foundational material in the emerging field of complex oxide electronics. Although its bulk electronic and optical properties are rich and were studied for decades, SrTiO3 has recently become a renewed focus of materials research catalyzed in part by the discovery of supercond. and magnetism at interfaces between SrTiO3 and other non-magnetic oxides. Here we illustrate a new aspect to the phenomenol. of magnetism in SrTiO3 by reporting the observation of an optically induced and persistent magnetization in slightly O-deficient bulk SrTiO3-δ crystals using magnetic CD (MCD) spectroscopy and SQUID magnetometry. This zero-field magnetization appears below ∼18 K, persists for hours below 10 K, and is tunable by the polarization and wavelength of sub-bandgap (400-500 nm) light. These effects occur only in crystals contg. O vacancies, revealing a detailed interplay between magnetism, lattice defects, and light in an archetypal complex oxide material.
- 21Li, Y.; Lei, Y.; Shen, B. G.; Sun, J. R. Visible-light-accelerated oxygen vacancy migration in strontium titanate. Sci. Rep. 2015, 5, 14576, DOI: 10.1038/srep14576Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhsFOrsb%252FE&md5=30b8428477dfcfe33e428923a8bc8d18Visible-light-accelerated oxygen vacancy migration in strontium titanateLi, Y.; Lei, Y.; Shen, B. G.; Sun, J. R.Scientific Reports (2015), 5 (), 14576CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)Strontium titanate is a model transition metal oxide that exhibits versatile properties of special interest for both fundamental and applied researches. There is evidence that most of the attractive properties of SrTiO3 are closely assocd. with oxygen vacancies. Tuning the kinetics of oxygen vacancies is then highly desired. Here we reported on a dramatic tuning of the electro-migration of oxygen vacancies by visible light illumination. It is found that, through depressing activation energy for vacancy diffusion, light illumination remarkably accelerates oxygen vacancies even at room temp. This effect provides a feasible approach towards the modulation of the anionic processes. The principle proved here can be extended to other perovskite oxides, finding a wide application in oxide electronics.
- 22Crespillo, M. L.; Graham, J. T.; Agulló-López, F.; Zhang, Y.; Weber, W. J. Isolated oxygen vacancies in strontium titanate shine red: Optical identification of Ti3+ polarons. Appl. Mater. Today 2018, 12, 131– 137, DOI: 10.1016/j.apmt.2018.04.006Google ScholarThere is no corresponding record for this reference.
- 23Crespillo, M. L.; Graham, J. T.; Agulló-López, F.; Zhang, Y.; Weber, W. J. Recent advances on carrier and exciton self-trapping in strontium titanate: Understanding the luminescence emissions. Crystals 2019, 9, 95, DOI: 10.3390/cryst9020095Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXos1aju7g%253D&md5=e9584da198c4cb2d65cec6359288c83cRecent advances on carrier and exciton self-trapping in strontium titanate: understanding the luminescence emissionsCrespillo, Miguel L.; Graham, Joseph T.; Agullo-Lopez, Fernando; Zhang, Yanwen; Weber, William J.Crystals (2019), 9 (2), 95CODEN: CRYSBC; ISSN:2073-4352. (MDPI AG)An up-to-date review on recent results for self-trapping of free electrons and holes, as well as excitons, in strontium titanate (STO), which gives rise to small polarons and self-trapped excitons (STEs) is presented. Special attention is paid to the role of carrier and exciton self-trapping on the luminescence emissions under a variety of excitation sources with special emphasis on expts. with laser pulses and energetic ion-beams. In spite of the extensive research effort, a definitive identification of such localized states, as well as a suitable understanding of their operative light emission mechanisms, has remained lacking or controversial. However, promising advances have been recently achieved and are the objective of the present review. In particular, significant theor. advances in the understanding of electron and hole self-trapping are discussed. Also, relevant exptl. advances in the kinetics of light emission assocd. with electron-hole recombination have been obtained through time-resolved expts. using picosecond (ps) laser pulses. The luminescence emission mechanisms and the light decay processes from the self-trapped excitons are also reviewed. Recent results suggest that the blue emission at 2.8 eV, often assocd. with oxygen vacancies, is related to a transition from unbound conduction levels to the ground singlet state of the STE. The stabilization of small electron polarons by oxygen vacancies and its connection with luminescence emission are discussed in detail. Through ion-beam irradn. expts., it has recently been established that the electrons assocd. with the vacancy constitute electron polaron states (Ti3+) trapped in the close vicinity of the empty oxygen sites. These exptl. results have allowed for the optical identification of the oxygen vacancy center through a red luminescence emission centered at 2.0 eV. Ab-initio calcns. have provided strong support for those exptl. findings. Finally, the use of Cr-doped STO has offered a way to monitor the interplay between the chromium centers and oxygen vacancies as trapping sites for the electron and hole partners resulting from the electronic excitation.
- 24Siebenhofer, M.; Viernstein, A.; Morgenbesser, M.; Fleig, J.; Kubicek, M. Photoinduced electronic and ionic effects in strontium titanate. Mater. Adv. 2021, 2, 7583– 7619, DOI: 10.1039/d1ma00906kGoogle Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitlWmt7zP&md5=00e368c16ccf370f81bc5818401efa72Photoinduced electronic and ionic effects in strontium titanateSiebenhofer, Matthaeus; Viernstein, Alexander; Morgenbesser, Maximilian; Fleig, Juergen; Kubicek, MarkusMaterials Advances (2021), 2 (23), 7583-7619CODEN: MAADC9; ISSN:2633-5409. (Royal Society of Chemistry)A review. The interaction of light with solids has been of ever-growing interest for centuries, even more so since the quest for sustainable utilization and storage of solar energy became a major task for industry and research. With SrTiO3 being a model material for an extensive exploration of the defect chem. of mixed conducting perovskite oxides, it has also been a vanguard in advancing the understanding of the interaction between light and the electronic and ionic structure of solids. In the course of these efforts, many phenomena occurring during or subsequent to the illumination of SrTiO3 have been investigated. Here, we give an overview of the numerous photoinduced effects in SrTiO3 and their inherent connection to electronic structure and defect chem. In more detail, advances in the fields of photocond., photoluminescence, photovoltages, photochromism and photocatalysis are summarized and their underlying elemental processes are discussed. In light of recent research, this review also emphasizes the fundamental differences between illuminating SrTiO3 either at low temps. (<RT) or at high temps. (>200°C), where in addn. to electronic processes, also photoionic interactions become relevant. A survey of the multitude of different processes shows that a profound and comprehensive understanding of the defect chem. and its alteration under illumination is both vital to optimizing devices and to pushing the boundaries of research and advancing the fundamental understanding of solids.
- 25Tufte, O. N.; Chapman, P. W. Electron mobility in semiconducting strontium titanate. Phys. Rev. 1967, 155, 796– 802, DOI: 10.1103/physrev.155.796Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaF2sXhtF2qs7c%253D&md5=2f0d180ae2f3c52368b6943baae2cf37Electron mobility in semiconducting strontium titanateTufte, Obert N.; Chapman, Paul W.Physical Review (1967), 155 (3), 796-802CODEN: PHRVAO; ISSN:0031-899X.The electron Hall mobility has been measured in semiconducting SrTiO3 at 1.6-550°K. Electron concns. of 1 × 1017-2.5 × 1019/cm.3 were obtained by redn. or by doping with Nb. The Nb donor centers remain fully ionized down to the lowest temps. investigated. The low-temp. mobility in Nb-doped SrTiO3 is approx. 4 times that in reduced SrTiO3 over the concn. range investigated, and mobility values ≤2.2 × 104 cm.2/v.-sec. were measured in Nb-doped samples having electron concns. of approx. 2 × 1017/cm.3 The mobility results are compared with the behavior expected for scattering by ionized defects and polar optical lattice modes at low and high temps., resp.
- 26Lee, C.; Yahia, J.; Brebner, J. L. Electronic conduction in slightly reduced strontium titanate at low temperatures. Phys. Rev. B: Solid State 1971, 3, 2525– 2533, DOI: 10.1103/physrevb.3.2525Google ScholarThere is no corresponding record for this reference.
- 27Neville, R. C.; Hoeneisen, B.; Mead, C. A. Permittivity of strontium titanate. J. Appl. Phys. 1972, 43, 2124– 2131, DOI: 10.1063/1.1661463Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE38XktFSqsLo%253D&md5=638d6a3809cd919601b7a5ba33b98fecPermittivity of strontium titanateNeville, R. C.; Hoeneisen, B.; Mead, C. A.Journal of Applied Physics (1972), 43 (5), 2124-31CODEN: JAPIAU; ISSN:0021-8979.The permittivity of single-crystal single-domain SrTiO3 was measured in detail in the [001], [011] and [111] directions, as a function of temp. (at 4.2-300°K), elec. field (from -23,000 to +23,000 V/cm), and frequency (from 1 kHz to 50 MHz). The free energy of the crystal was detd as a function of polarization with temp. as a parameter. The Curie-Weiss law is satisfied at 60-300°K, giving a Curie temp. of 30 ± 2°K for the 3 crystal orientations. The Lyddane-Sachs-Teller (LST) relation is satisfied at 30-300°K and for elec. fields of 0-12,000 V/cm. A generalized LST relation is used to calc. the permittivity of SrTiO3 from zero to optic frequencies. Two active optic modes are important. The lower-frequency mode is attributed mainly to motion of the Sr ions with respect to the rest of the lattice, while the higher-frequency active mode is attributed to motion of the Ti ions with respect to the O lattice. The restoring forces that act on the Ti ions begin to "harden" when these ions are displaced approx. 0.002 Å from their equil. positions.
- 28Maier, J.; Schwitzgebel, G.; Hagemann, H.-J. Electrochemical investigations of conductivity and chemical diffusion in pure and doped cubic SrTiO3 and BaTiO3. J. Solid State Chem. 1985, 58, 1– 13, DOI: 10.1016/0022-4596(85)90264-6Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL2MXksVKnur4%253D&md5=e8ffdc1c6abe788171a19fe0ab9d283aElectrochemical investigations of conductivity and chemical diffusion in pure and doped cubic strontium titanate (SrTiO3) and barium titanate (BaTiO3)Maier, J.; Schwitzgebel, G.; Hagemann, H. J.Journal of Solid State Chemistry (1985), 58 (1), 1-13CODEN: JSSCBI; ISSN:0022-4596.Pure Ba and Sr titanate as well as donor (La)- and acceptor (Mn, Fe, Cr)-doped materials were investigated as both ceramics and single crystals. The electronic and ionic conductivities, the dielec. const., and the phase boundary parameters were measured as functions of temp. (700°) and of O partial pressure (101-105 Pa). An ionic contribution via internal surfaces was found in BaTiO3 samples. The effective diffusion coeffs. of ceramic (10-8 cm2s-1 at 600-650°) and single-cryst. (10-9 cm2s-1 at 630-660°) BaTiO3 were detd. The formulas presented allow the evaluation of the expts. even for the case of defects with variable charges.
- 29Moos, R.; Hardtl, K. H. Defect chemistry of donor-doped and undoped strontium titanate ceramics between 1000° and 1400 °C. J. Am. Ceram. Soc. 1997, 80, 2549– 2562, DOI: 10.1111/j.1151-2916.1997.tb03157.xGoogle Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2sXmslejtrg%253D&md5=623f271a84dbed82a07d0729ce06a05eDefect chemistry of donor-doped and undoped strontium titanate ceramics between 1000°C and 1400°CMoos, Ralf; Hardtl, Karl HeinzJournal of the American Ceramic Society (1997), 80 (10), 2549-2562CODEN: JACTAW; ISSN:0002-7820. (American Ceramic Society)The elec. cond., σ, of donor-doped and undoped strontium titanate (SrTiO3) ceramics and, in some cases, single crystals, Sr1-xLaxTiO3 (0 ≤ x ≤ 0.1), was investigated in the temp. range of 1000-1400° under oxygen partial pressures, PO2, of 10-20-1 bar. In conjunction with Hall data and thermopower data from related papers, a set of consts. for a defect-chem. model was detd., precisely describing point-defect concns. and transport properties of these materials. In contrast to former works, temp.-dependent transport parameters and their non-negligible influence on the detn. of the consts. was considered, as well as the equil. restoration phenomena of the cation sublattice, which can be studied only at such high temps. It was shown that defects in the cation sublattice completely govern the elec. behavior of donor-doped and undoped SrTiO3. In the latter case, frozen-in strontium vacancies act as intrinsic acceptors, detg. the σ(PO2) curves at lower temps. This intrinsic acceptor concn. also can be calcd. with this model.
- 30Raevski, I. P.; Maksimov, S. M.; Fisenko, A. V.; Prosandeyev, S. A.; Osipenko, I. A.; Tarasenko, P. F. Study of intrinsic point defects in oxides of the perovskite family: II. Experiment. J. Phys.: Condens. Matter 1998, 10, 8015– 8032, DOI: 10.1088/0953-8984/10/36/012Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXmsVGhtrY%253D&md5=dd114ee3a9cb7efe8bb65ba6b3e59c37Study of intrinsic point defects in oxides of the perovskite family: II. ExperimentRaevski, I. P.; Maksimov, S. M.; Fisenko, A. V.; Prosandeyev, S. A.; Osipenko, I. A.; Tarasenko, P. F.Journal of Physics: Condensed Matter (1998), 10 (36), 8015-8032CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)The elec. cond. of ATiO3 and A1+B5+O3 perovskite-type oxides converted by vacuum annealing into states with weak and strong compensation between donors and acceptors was measured. The reduced samples had both shallow and comparatively deep levels which were attributed to the neutral and singly-charged O vacancy, resp. The exptl. detd. activation energies are consistent with the results of the theor. computation reported in Part I.
- 31van Benthem, K.; Elsässer, C.; French, R. H. Bulk electronic structure of SrTiO3: Experiment and theory. J. Appl. Phys. 2001, 90, 6156– 6164, DOI: 10.1063/1.1415766Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXoslKnurc%253D&md5=66a61cecc6d2e6ba9af5d5884c70a12fBulk electronic structure of SrTiO3: Experiment and theoryvan Benthem, K.; Elsasser, C.; French, R. H.Journal of Applied Physics (2001), 90 (12), 6156-6164CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)Valence EELS (VEELS) in a dedicated scanning transmission electron microscope, vacuum UV spectroscopy and spectroscopic ellipsometry, and ab initio band structure calcns. in the local d. approxn. were used to det. the optical properties and the electronic structure of SrTiO3. Assignments of the interband transitions in the electronic structure of bulk SrTiO3 were detd. quant. by comparison of VEELS spectra with vacuum UV spectra and with the ab initio calcd. densities of states. The exptl. detd. indirect band gap energy is 3.25 eV, while the direct band gap energy is 3.75 eV. The conduction bands in SrTiO3 correspond to the bands composed of mainly Ti 3d t2g and eg states, followed at higher energies by the bands of Sr 4d t2g and eg states, and free electron like states dominating at energies >15 eV. The upper valence band (UVB) contains 18 electrons in dominantly O 2p states, hybridized with Ti and Sr states, and has a bandwidth of 5 eV. The interband transitions from the UVB to the Ti 3d bands and to the Sr 4d bands give rise to the transitions spanning from the indirect band gap energy of 3.25 eV up to 15 eV. The lower valence band contains 12 electrons in Sr 4p and O 2s states which are sepd. by 2 eV, while having a bandwidth of 5 eV. The interband transitions from the Sr 4p to the Ti 3d and Sr 4d bands give rise to transition energies spanning from 15 to 24 eV. Interband transitions from the O 2s band to the conduction bands appear at 26 eV. A very narrow band at -33 eV below the top of the valence band is composed of Sr 4s and Ti 3p states and contains eight electrons.
- 32Wideroe, M.; Waser, R.; Norby, T. Transport of hydrogen species in a single crystal SrTiO3. Solid State Ionics 2006, 177, 1469– 1476, DOI: 10.1016/j.ssi.2006.07.029Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XpvFart7c%253D&md5=7c737a1978f808303f8fffa93a14f599Transport of hydrogen species in a single crystal SrTiO3Wideroe, Marius; Waser, Rainer; Norby, TrulsSolid State Ionics (2006), 177 (17-18), 1469-1476CODEN: SSIOD3; ISSN:0167-2738. (Elsevier B.V.)The total cond. and the partial H ion cond. of a single crystal of SrTiO3 were investigated by transport no. measurements using a H activity concn. cell/EMF method in wet atmospheres as a function of pO2 (10-20-1 atm) at 1000° and as a function of temp. (350-1050°) in wet H2. The single crystal exhibits a small but readily measurable proton cond. contribution in wet oxidizing atmospheres. Earlier indications of apparent, but unlikely, transport by neg. charged H ions under reducing conditions and high temps. in polycryst. SrTiO3 were reproduced for the single crystal, thus eliminating grain boundaries and porosity as a cause of such findings. The paper proposes transport of neutral H species through the oxide as an alternative cause. This results in polarization of the H activity at the interface between the electrodes and the electrolyte, in turn giving rise to an unintended gradient in O activity and an EMF resulting from the relatively high O ion transport no. of the material.
- 33Kreuer, K. D. Aspects of the formation and mobility of protonic charge carriers and the stability of perovskite-type oxides. Solid State Ionics 1999, 125, 285– 302, DOI: 10.1016/s0167-2738(99)00188-5Google Scholar33https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXntlOgtrg%253D&md5=ebd2714034de4fcd099424f8754f6502Aspects of the formation and mobility of protonic charge carriers and the stability of perovskite-type oxidesKreuer, K. D.Solid State Ionics (1999), 125 (1-4), 285-302CODEN: SSIOD3; ISSN:0167-2738. (Elsevier Science B.V.)Proton conducting acceptor-doped perovskite-type alk. earth cerates, zirconates, niobates and titanates have been investigated exptl. and by numerical simulations. For all cubic perovskites the concn. of protonic defects almost reaches the acceptor dopant concn. under appropriate conditions, and the mobility of protonic defects fall into a narrow range. Any symmetry redn., however, leads to a redn. of the concn. and mobility of protonic defects. For all oxides, dynamical hydrogen bonding is suggested to lead to a local lattice softening, which provides an advantageous environment for high proton-mobility. This effect may explain the very high proton cond. in covalent acceptor-doped BaZrO3, which has been found exptl. for the first time. Since this oxide also shows good thermodn. phase stability, it is an interesting candidate as separator material in high-drain electrochem. applications such as fuel cells.
- 34Steinsvik, S.; Larring, Y.; Norby, T. Hydrogen ion conduction in iron-substituted strontium titanate, SrTi1–xFexO3–x/2 (0 ≤ x ≤ 0.8). Solid State Ionics 2001, 143, 103– 116, DOI: 10.1016/s0167-2738(01)00838-4Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXktlWgtLg%253D&md5=8d71afa87874d0558b1f9a670e113ea2Hydrogen ion conduction in iron-substituted strontium titanate, SrTi1-xFexO3-x/2 (0≤x≤0.8)Steinsvik, S.; Larring, Y.; Norby, T.Solid State Ionics (2001), 143 (1), 103-116CODEN: SSIOD3; ISSN:0167-2738. (Elsevier Science B.V.)Conduction of hydrogen species in selected compns. of SrTi1-xFexO3-x/2 (0≤x≤0.8) has been investigated by a.c. cond. and concn. cell emf. transport no. measurements, as a function of pO2, pH2O and temp. (500-1100°C). The main contributions to the total cond. are n-type electronic, dominating at low pO2, ionic (oxygen vacancies) at intermediate pO2, and p-type electronic at high pO2. Hydrogen ion conduction is measurable, but the hydrogen contg. species are minority defects in this system at the temps. investigated, both in terms of concn. and cond. When the conditions are not too reducing, hydrogen ions are pos., assumed to be protons, H+. At lower pO2, however, there is a change in the sign of the emf. of the water vapor concn. cell, and thus apparently of the charge of the hydrogen-contg. charge carrying species. This can be rationalized by the presence and migration of substitutionally dissolved hydride ions, H-, but it is questioned whether these can be stable under the conditions used.
- 35Merkle, R.; Maier, J. How is oxygen incorporated into oxides? A comprehensive kinetic study of a simple solid-state reaction with SrTiO3 as a model material. Angew. Chem., Int. Ed. 2008, 47, 3874– 3894, DOI: 10.1002/anie.200700987Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXmsVertbg%253D&md5=51ca06b9c2c74529b94a146ec6bbe9a6How is oxygen incorporated into oxides? A comprehensive kinetic study of a simple solid-state reaction with SrTiO3 as a model materialMerkle, Rotraut; Maier, JoachimAngewandte Chemie, International Edition (2008), 47 (21), 3874-3894CODEN: ACIEF5; ISSN:1433-7851. (Wiley-VCH Verlag GmbH & Co. KGaA)A review; the kinetics of stoichiometry change of an oxide - a prototype of a simple solid-state reaction and a process of substantial technol. relevance - is studied and analyzed in great detail. Oxygen incorporation into strontium titanate was chosen as a model process. The complete reaction can be phenomenol. and mechanistically understood beginning with the surface reaction and ending with the transport in the perovskite. Key elements are a detailed knowledge of the defect chem. of the perovskite as well as the application of a variety of exptl. and theor. tools, many of them evolving from this study. The importance of the reaction and transport steps for (electro)chem. applications is emphasized.
- 36Phoon, B. L.; Lai, C. W.; Juan, J. C.; Show, P.-L.; Chen, W.-H. A review of synthesis and morphology of SrTiO3 for energy and other applications. Int. J. Energy Res. 2019, 43, 5151– 5174, DOI: 10.1002/er.4505Google Scholar36https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhsVarsbjN&md5=8df693a22591ca7cecd2d6928e7b107fA review of synthesis and morphology of SrTiO3 for energy and other applicationsPhoon, Bao Lee; Lai, Chin Wei; Juan, Joon Ching; Show, Pau-Loke; Chen, Wei-HsinInternational Journal of Energy Research (2019), 43 (10), 5151-5174CODEN: IJERDN; ISSN:0363-907X. (John Wiley & Sons Ltd.)A review. Summary : With the increasing demand and depleting trend of com. energies, it has forced the researchers all over the world to accelerate research and development in the area of renewable energy. Currently, unique and interesting features of binary compds. have gained more attention by researchers, and it became a favorite research topic among various groups of researchers around this world. It was noticed that strontium titanate (SrTiO3) consists of several extraordinary properties that can apply for misc. applications esp. for energy storage, fuel cells, as well as to generate hydrogen fuel via photocatalysis process. Besides that, it was noticed that SrTiO3 can be synthesized in different pathways. The method of prepn. and amt. of precursors can affect the surface properties of SrTiO3. Thus, this article presents a crit. review on how SrTiO3 synthesis methods affect its surface morphol. and the applications of SrTiO3 in various fields.
- 37Miruszewski, T.; Dzierzgowski, K.; Winiarz, P.; Wachowski, S.; Mielewczyk-Gryń, A.; Gazda, M. Structural properties and water uptake of SrTi1–xFexO3–x/2−δ. Materials 2020, 13, 965, DOI: 10.3390/ma13040965Google Scholar37https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXht1KqsLjN&md5=e582f4b77c2f35367aa930ba513d4456Structural properties and water uptake of SrTi1 - xFexO3 - x/2 - γMiruszewski, Tadeusz; Dzierzgowski, Kacper; Winiarz, Piotr; Wachowski, Sebastian; Mielewczyk-Gryn, Aleksandra; Gazda, MariaMaterials (2020), 13 (4), 965CODEN: MATEG9; ISSN:1996-1944. (MDPI AG)In this work, Fe-doped strontium titanate SrTi1 - xFexO3 - x/2 - γ, for x = 0-1 (STFx), has been fabricated and studied. The structure and microstructure anal. showed that the Fe amt. in SrTi1 - xFexO3 - x/2 - γ has a great influence on the lattice parameter and microstructure, including the porosity and grain size. Oxygen nonstoichiometry studies performed by thermogravimetry at different atmospheres showed that the Fe-rich compns. (x > 0.3) exhibit higher oxygen vacancies concn. of the order of magnitude 1022-1023 cm-3. The proton uptake investigations have been done using thermogravimetry in wet conditions, and the results showed that the compns. with x < 0.5 exhibit hydrogenation redox reactions. Proton concn. at 400 °C depends on the Fe content and was estd. to be 1.0 x 10-2 mol/mol for SrTi0.9Fe0.1O2.95 and 1.8 x 10-5 mol/mol for SrTi0.5Fe0.5O2.75. Above 20 mol% of iron content, a significant drop of proton molar concns. at 400 °C was obsd. This is related to the stronger overlapping of Fe and O orbitals after reaching the percolation level of approx. 30 mol% of the iron in SrTi1 - xFexO3 - x/2 - γ. The relation between the proton concn. and Fe dopant content has been discussed in relation to the B-site av. electronegativity, oxygen nonstoichiometry, and electronic structure.
- 38Miruszewski, T.; Dzierzgowski, K.; Winiarz, P.; Jaworski, D.; Wiciak-Pawłowska, K.; Skubida, W.; Wachowski, S.; Mielewczyk-Gryń, A.; Gazda, M. Structure and transport properties of triple-conducting BaxSr1–xTi1–yFeyO3−δ oxides. RSC Adv. 2021, 11, 19570– 19578, DOI: 10.1039/d0ra10048jGoogle Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhtF2qs7rE&md5=7877bb5eb5a71e1e0a7bd8532cd9e0e4Structure and transport properties of triple-conducting BaxSr1-xTi1-yFeyO3-δ oxidesMiruszewski, T.; Dzierzgowski, K.; Winiarz, P.; Jaworski, D.; Wiciak-Pawlowska, K.; Skubida, W.; Wachowski, S.; Mielewczyk-Gryn, A.; Gazda, M.RSC Advances (2021), 11 (32), 19570-19578CODEN: RSCACL; ISSN:2046-2069. (Royal Society of Chemistry)In this work, BaxSr1-xTi1-yFeyO3-δ perovskite-based mixed conducting ceramics (for x = 0, 0.2, 0.5 and y = 0.1, 0.8) were synthesized and studied. The structural anal. based on the X-ray diffraction results showed significant changes in the unit cell vol. and Fe(Ti)-O distance as a function of Ba content. The morphol. of the synthesized samples studied by means of SEM has shown different microstructures for different contents of barium and iron. Electrochem. impedance spectroscopy studies of transport properties in a wide temp. range in the dry- and wet air confirmed the influence of barium cations on charge transport in the studied samples. The total cond. values were in the range of 10-3 to 100 S cm-1 at 600 °C. Depending on the barium and iron content, the obsd. change of cond. either increases or decreases in humidified air. Thermogravimetric measurements have shown the existence of proton defects in some of the analyzed materials. The highest obsd. molar proton concn., equal to 5.0 x 10-2 mol mol-1 at 300 °C, was obtained for Ba0.2Sr0.8Ti0.9Fe0.1O2.95. The relations between the structure, morphol. and elec. cond. were discussed.
- 39Papac, M.; Stevanović, V.; Zakutayev, A.; O’Hayre, R. Triple ionic–electronic conducting oxides for next-generation electrochemical devices. Nat. Mater. 2021, 20, 301– 313, DOI: 10.1038/s41563-020-00854-8Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXis1Olu7rE&md5=261c33f2553860b7f2e111efa307cbe6Triple ionic-electronic conducting oxides for next-generation electrochemical devicesPapac, Meagan; Stevanovic, Vladan; Zakutayev, Andriy; O'Hayre, RyanNature Materials (2021), 20 (3), 301-313CODEN: NMAACR; ISSN:1476-1122. (Nature Research)A review. Triple ionic-electronic conductors (TIECs) are materials that can simultaneously transport electronic species alongside two ionic species. The recent emergence of TIECs provides intriguing opportunities to maximize performance in a variety of electrochem. devices, including fuel cells, membrane reactors and electrolysis cells. However, the potential application of these nascent materials is limited by lack of fundamental knowledge of their transport properties and electrocatalytic activity. The goal of this Review is to summarize and analyze the current understanding of TIEC transport and electrochem. in single-phase materials, including defect formation and conduction mechanisms. We particularly focus on the discovery criteria (for example, crystal structure and ion electronegativity), design principles (for example, cation and anion substitution chem.) and operating conditions (for example, atm.) of materials that enable deliberate tuning of the cond. of each charge carrier. Lastly, we identify important areas for further advances, including higher chem. stability, lower operating temps. and discovery of n-type TIEC materials.
- 40Samat, A. A.; Darus, M.; Osman, N.; Baharuddin, N. A.; Anwar, M. A short review on triple conducting oxide cathode materials for proton conducting solid oxide fuel cell. AIP Conf. Proc. 2021, 2339, 020233, DOI: 10.1063/5.0044224Google Scholar40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvV2ltbfO&md5=7318430ed6c0a6f0df7f45505beb2b69A short review on triple conducting oxide cathode materials for proton conducting solid oxide fuel cellSamat, Abdullah Abdul; Darus, Murizam; Osman, Nafisah; Baharuddin, Nurul Akidah; Anwar, MustafaAIP Conference Proceedings (2021), 2339 (1, Proceedings of Green Design and Manufacture 2020), 020233CODEN: APCPCS; ISSN:0094-243X. (American Institute of Physics)The performance of solid oxide fuel cells (SOFCs) is significantly affected by the properties of its components which are electrolyte, electrodes (cathode and anode) and interconnect. Among the components, cathode is considered as the most crit. component as high cathode polarization resistance (Rp) contributes to a major loss in SOFC performance. Thus, developing of good materials as cathode has been attempted to cater the problem. The development of cathode materials for SOFCs started with pure electronic conductor. This type of cathode materials provides limited electrochem. reaction sites, resulting in high Rp. Next, mixed ionic-electronic conductor (MIEC) cathode materials have been developed and followed by composite cathode materials. Both types of cathode materials are better than pure electronic conductor as they provide larger electrochem. reaction sites. However, some of them still resulting in high Rp esp. at operating temps. ranging from 400 °C to 800 °C. Then, the current researches are devoted to develop triple-conducting (H+/O2-/e-) oxide (TCO) cathode materials. This type of cathode materials is particularly useful for proton-conducting SOFC application. Therefore, this paper aims to provide a short review on the properties and performance of the TCO cathode materials along with the factors influencing its properties and performance. (c) 2021 American Institute of Physics.
- 41Rothschild, A.; Menesklou, W.; Tuller, H. L.; Ivers-Tiffée, E. Electronic structure, defect chemistry, and transport properties of SrTi1–xFexO3–y solid solutions. Chem. Mater. 2006, 18, 3651– 3659, DOI: 10.1021/cm052803xGoogle Scholar41https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xmsl2ksLc%253D&md5=f935c04262c260edab5ef9ce7ce32331Electronic Structure, Defect Chemistry, and Transport Properties of SrTi1-xFexO3-y Solid SolutionsRothschild, Avner; Menesklou, Wolfgang; Tuller, Harry L.; Ivers-Tiffee, EllenChemistry of Materials (2006), 18 (16), 3651-3659CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)The electronic structure, defect chem., and transport properties of members of the mixed ionic electronic conducting SrTi1-xFexO3-y (STF) solid-soln. system are revisited, and an improved defect chem. model is proposed in which Fe is considered to be one of the main constituents that shape the energy-band structure of STF, rather than an impurity dopant with acceptor-like character. As a consequence of the high inherent deficiency in the oxygen sublattice, introduced by the mixed-valence states of the B-site cations Ti4+ and Fe3+, oxygen vacancies and interstitials generated by the anion Frenkel reaction dominate the defect equil., leading to predominant ionic cond. at intermediate partial pressures of oxygen. Increasing Fe content results in both a systematic decrease in band-gap energy, Eg0 = 3.2-1.9x + 0.5x2 eV, and redn. enthalpy, ΔHred = 5.8-3.4x + 1.7x2 eV. The decrease in band gap is explained from the systematic broadening of the Fe-derived 3d band lying above the O-derived 2p valence band. The Fe-induced changes in band structure were exptl. confirmed by both optical and photoelectron (XPS) spectroscopies.
- 42Jung, W.; Tuller, H. L. Impedance study of SrTi1–xFexO3−δ (x=0.05 to 0.80) mixed ionic-electronic conducting model cathode. Solid State Ionics 2009, 180, 843– 847, DOI: 10.1016/j.ssi.2009.02.008Google Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXmvVOrsLc%253D&md5=b4653092a599dd7c9f12377f197069c2Impedance study of SrTi1-xFexO3-δ (x=0.05 to 0.80) mixed ionic-electronic conducting model cathodeJung, Woo-Chul; Tuller, Harry L.Solid State Ionics (2009), 180 (11-13), 843-847CODEN: SSIOD3; ISSN:0167-2738. (Elsevier B.V.)SrTi1-xFexO3-δ (STF) model cathodes, with compns. of x = 0.05 to 0.80 were deposited onto single crystal yttria stabilized zirconia by pulsed layer deposition as dense films with well defined area and thickness and studied by electrochem. impedance spectroscopy as a function of electrode geometry, temp. and pO2. The STF cathode was obsd. to exhibit typical mixed ionic-electronic behavior with the electrode reaction occurring over the full electrode surface area rather than being limited to the triple phase boundary. The electrode impedance was obsd. to be independent of electrode thickness and to the introduction of CGO interlayers and inversely proportional to the square of the electrode diam., pointing to surface exchange limited kinetics. Values for the surface exchange coeff., k, were calcd. and found to be comparable in magnitude to those exhibited by other popular mixed ionic-electronic conductors such as (La,Sr)(Co,Fe)O3, thereby, confirming the suitability of STF as a model mixed conducting cathode material. The surface exchange coeff., k, was also found to be insensitive to orders of magnitude change in both bulk electronic and ionic conductivities.
- 43Mroziński, A.; Molin, S.; Jasiński, P. Effect of sintering temperature on electrochemical performance of porous SrTi1–xFexO3−δ (x = 0.35, 0.5, 0.7) oxygen electrodes for solid oxide cells. J. Solid State Electrochem. 2020, 24, 873– 882, DOI: 10.1007/s10008-020-04534-0Google Scholar43https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXks1ektrs%253D&md5=185ce3b05a185f49be40878353e4b3b5Effect of sintering temperature on electrochemical performance of porous SrTi1-xFexO3-δ (x = 0.35, 0.5, 0.7) oxygen electrodes for solid oxide cellsMrozinski, A.; Molin, S.; Jasinski, P.Journal of Solid State Electrochemistry (2020), 24 (4), 873-882CODEN: JSSEFS; ISSN:1432-8488. (Springer)This work evaluates the effects of the sintering temp. (800°C, 900°C, 1000°C) of SrTi1-xFexO3-δ (x = 0.35, 0.5, 0.7) porous electrodes on their electrochem. performance as potential oxygen electrode materials of solid oxide cells. The materials were prepd. by a solid-state reaction method and revealed the expected cubic perovskite structure. After milling, the powders were characterized by a sub-micrometer particle size with high sinter-activity. It was shown that the lowest area specific resistance was achieved after sintering SrTi0.65Fe0.35O3 electrodes at 1000°C, and SrTi0.5Fe0.5O3 and SrTi0.30Fe0.70O3 electrodes at 800°C, which can be considered to be a relatively low temp. In general, EIS measurements showed that increasing the Fe content results in lowered electrode polarization and a decrease of the series resistance. Even though the studied materials have much lower total conductivities than state-of-the-art electrode materials (e.g. (La,Sr)(Co,Fe)O3), the polarization resistances obtained in this work can be considered low.
- 44Winiarz, P.; Mielewczyk-Gryń, A.; Wachowski, S.; Jasiński, P.; Witkowska, A.; Gazda, M. Structural and electrical properties of titanium-doped yttrium niobate. J. Alloys Compd. 2018, 767, 1186– 1195, DOI: 10.1016/j.jallcom.2018.07.134Google Scholar44https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtl2ls7jO&md5=33da7bd9a44d64c2a4fee7b3ed6ff7cfStructural and electrical properties of titanium-doped yttrium niobateWiniarz, P.; Mielewczyk-Gryn, A.; Wachowski, S.; Jasinski, P.; Witkowska, A.; Gazda, M.Journal of Alloys and Compounds (2018), 767 (), 1186-1195CODEN: JALCEU; ISSN:0925-8388. (Elsevier B.V.)In this work, the influence of the substitution of niobium by titanium in Y3Nb1-xTixO7-δ (x=0,0.01,0.02,0.03,0.04,0.05,0.06,0.08,0.1,0.15,0.18,0.2) on the structural and elec. properties is reported. Several exptl. techniques, i.e. X-Ray Diffraction (XRD), SEM (SEM), XPS and Electrochem. Impedance Spectroscopy (EIS), were applied to investigate the system Y3Nb1-xTixO7-δ. Titanium in Y3Nb1-xTixO7-δ is an acceptor-type dopant which charge is mainly compensated by oxygen vacancies, moreover, it may adopt different valence states, therefore, oxygen ion-, proton- and electronic-type cond. are expected. Very interesting, non-monotonic changes in elec. and structural properties as a function of titanium content were obsd. The competition between the increasing charge carrier concn. and structural phenomena such as short-range pyrochlore ordering and/or vacancy clustering was proposed as responsible for this non-monotonicity.
- 45Freysoldt, 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.86.253Google ScholarThere is no corresponding record for this reference.
- 46Piskunov, S.; Heifets, E.; Eglitis, R. I.; Borstel, G. Bulk properties and electronic structure of SrTiO3, BaTiO3, PbTiO3 perovskites: An ab initio HF/DFT study. Comput. Mater. Sci. 2004, 29, 165– 178, DOI: 10.1016/j.commatsci.2003.08.036Google Scholar46https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3sXhtVShsLnF&md5=135c92e552a07a089a752d6d95ba4e75Bulk properties and electronic structure of SrTiO3, BaTiO3, PbTiO3 perovskites: an ab initio HF/DFT studyPiskunov, S.; Heifets, E.; Eglitis, R. I.; Borstel, G.Computational Materials Science (2004), 29 (2), 165-178CODEN: CMMSEM; ISSN:0927-0256. (Elsevier Science B.V.)The results of detailed calcns. for bulk properties and the electronic structure of the cubic phase of SrTiO3 (STO), BaTiO3 (BTO), and PbTiO3 (PTO) perovskite crystals with detailed optimization of basis set (BS) are discussed. These are obtained using ab initio Hartree-Fock (HF) and d. functional theory (DFT) with Hay-Wadt pseudopotentials based on localized, Gaussian-type BS. A no. of different exchange-correlation functionals including hybrid (B3PW and B3LYP) exchange techniques are used. Results, obtained for seven methods, are compared with previous quantum mech. (QM) calcns. and available exptl. data. Esp. good agreement with the exptl. data has been achieved for hybrid functionals. With the polarization orbitals added to the BS of oxygen atom, the calcd. optical band gaps are 3.57, 3.42 and 2.87 eV for STO, BTO and PTO resp., in very good agreement with exptl. data.
- 47Wahl, R.; Vogtenhuber, D.; Kresse, G. SrTiO3 and BaTiO3 revisited using the projector augmented wave method: Performance of hybrid and semilocal functionals. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 104116, DOI: 10.1103/physrevb.78.104116Google Scholar47https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXht1Wms7bO&md5=8499c0db8e05cd1cd0521cfde3c8aa10SrTiO3 and BaTiO3 revisited using the projector augmented wave method: Performance of hybrid and semilocal functionalsWahl, Roman; Vogtenhuber, Doris; Kresse, GeorgPhysical Review B: Condensed Matter and Materials Physics (2008), 78 (10), 104116/1-104116/11CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The structural, electronic, and phonon properties of the cubic and tetragonal phase of SrTiO3 and BaTiO3 are studied from ab initio. The calcns. are performed in the projector augmented wave d.-functional theory framework using the local d. approxn., gradient cor. functionals, and hybrid functional as implemented in the Vienna ab initio simulation package. Due to the large variation of theor. predictions for the frequency of the Γ15 (TO1) zone-center phonon mode (94i-64 cm-1) special attention is accorded to this particular mode and its vol. dependence.
- 48Kinaci, A.; Sevik, C.; Çağin, T. Electronic transport properties of SrTiO3 and its alloys: Sr1–xLaxTiO3 and SrTi1–xMxO3 (M = Nb, Ta). Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 155114, DOI: 10.1103/PhysRevB.82.155114Google Scholar48https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhtlKltrrM&md5=f348063849765fa30937f9840b79b3a9Electronic transport properties of SrTiO3 and its alloys: Sr1-xLaxTiO3 and SrTi1-xMxO3 (M=Nb,Ta)Kinaci, A.; Sevik, C.; Cagin, T.Physical Review B: Condensed Matter and Materials Physics (2010), 82 (15), 155114/1-155114/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Wide band-gap oxide strontium titanate (SrTiO3) is highly recognized as potential thermoelec. material for its large Seebeck coeff. Recently, several exptl. studies emerged on how to improve the thermoelec. transport properties of SrTiO3 by doping with La and Nb. To aid this effort, a better understanding of the effect of doping on electronic structure and transport properties is essential. The electronic transport properties of SrTiO3, Sr1-xLaxTiO3, and SrTi1-xMxO3 (M = Nb,Ta) are detd. by detailed 1st-principles electronic band structure and Boltzmann transport calcns. Also, the effect of uniaxial and simple shear deformations on the transport properties of pure strontium titanate is also studied. For the treatment of the substitutional alloys, on-site Coulomb interaction added versions of electronic exchange and correlation functionals are preferred to obtain an accurate electronic band structure. Calcd. Seebeck coeff. and its variation as a function of temp. for the alloy systems are compared with available exptl. results; an excellent agreement is obsd. Addnl., the electronic relaxation time and electronic contribution to thermal cond. are predicted by fitting the calcd. elec. cond. to the exptl. elec. cond. A significant increase in electronic thermal cond. is obsd. for high carrier concns. Overall, the necessity of excessive carrier concns. that can only be achieved by highly doped structures is verified.
- 49Evarestov, R. A.; Blokhin, E.; Gryaznov, D.; Kotomin, E. A.; Maier, J. Phonon calculations in cubic and tetragonal phases of SrTiO3: A comparative LCAO and plane-wave study. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 134108, DOI: 10.1103/physrevb.83.134108Google Scholar49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXlsV2ltrc%253D&md5=20f29aac9a1457086e8b27375fccfc8aPhonon calculations in cubic and tetragonal phases of SrTiO3: A comparative LCAO and plane-wave studyEvarestov, Robert A.; Blokhin, Evgeny; Gryaznov, Denis; Kotomin, Eugene A.; Maier, JoachimPhysical Review B: Condensed Matter and Materials Physics (2011), 83 (13), 134108/1-134108/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The at., electronic structure and phonon frequencies have been calcd. in cubic and low-temp. tetragonal SrTiO3 phases at the ab initio level. We demonstrate that the use of the hybrid exchange-correlation PBE0 functional gives the best agreement with exptl. data. The results for the std. generalized gradient approxn. (PBE) and hybrid PBE0 functionals are compared for the two types of approaches: a LCAO (CRYSTAL09 computer code) and plane waves (VASP5.2 code). The relation between cubic and tetragonal phases and the relevant antiferrodistortive phase transition is discussed in terms of group theory and is illustrated with anal. of calcd. soft-mode frequencies at the Γ and R points in the Brillouin zone. Based on phonon calcns., the temp. dependence of the heat capacity is in good agreement with expt.
- 50Sakhya, A. P.; Maibam, J.; Saha, S.; Chanda, S.; Dutta, A.; Sharma, B. I.; Thapa, R.; Sinha, T. P. Electronic structure and elastic properties of ATiO3 (A = Ba, Sr, Ca) perovskites: A first principles study. Indian J. Pure Appl. Phys. 2015, 53, 102– 109Google ScholarThere is no corresponding record for this reference.
- 51Mubarak, A. A. The first-principle study of the electronic, optical and thermoelectric properties of XTiO3 (X = Ca, Sr and Ba) compounds. Int. J. Mod. Phys. B 2016, 30, 1650141, DOI: 10.1142/s0217979216501411Google Scholar51https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xhtleru7zF&md5=06da6d8545db44bac567674197cebb31The first-principle study of the electronic, optical and thermoelectric properties of XTiO3 (X = Ca, Sr and Ba) compoundsMubarak, A. A.International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Atomic, Molecular and Optical Physics (2016), 30 (20), 1650141CODEN: IJPBEV; ISSN:0217-9792. (World Scientific Publishing Co. Pte. Ltd.)The FP-LAPW method is utilized to investigate the elastic, optoelectronic and thermoelec. properties of XTiO3 (X = Ca, Sr and Ba) within the GGA. The calcd. lattice consts. and bulk modulus are found in agreement with previous studies. The present oxide-perovskite compds. are characterized as elastically stable and anisotropic. CaTiO3 and SrTiO3 are categorized as ductile compds., whereas the BaTiO3 compd. is in the crit. region between ductile and brittle. The DOS and the band structure calcns. reveal indirect (M-Γ) energy bandgap for the present compds. The hydrostatic pressure increases the energy bandgap and the width of the valence band. The character of the band structure does not change due to this pressure. The optical parameters are calcd. in different radiation regions. Beneficial optics applications are predicted as revealed from the optical spectra. The transport properties are applied as a function of the variable temps. or carrier concn. It is found that the compds. under study are classified as a p-type semiconductor. The majority charge carriers responsible for conduction in these calcd. compds. are holes rather than electrons.
- 52Holmström, E.; Spijker, P.; Foster, A. S. The interface of SrTiO3 and H2O from density functional theory molecular dynamics. Proc. R. Soc. A 2016, 472, 20160293, DOI: 10.1098/rspa.2016.0293Google ScholarThere is no corresponding record for this reference.
- 53Ricci, 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.68.224105Google Scholar53https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXkvFWhtg%253D%253D&md5=1a4e25a841514754fe1be8fb25973ce6Electronic structure of a neutral oxygen vacancy in SrTiO3Ricci, Davide; Bano, Giuseppe; Pacchioni, Gianfranco; Illas, FrancescPhysical 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.
- 54Eglitis, R. I.; Piskunov, S.; Heifets, E.; Kotomin, E. A.; Borstel, G. Ab initio study of the SrTiO3, BaTiO3 and PbTiO3 (001) surfaces. Ceram. Int. 2004, 30, 1989– 1992, DOI: 10.1016/j.ceramint.2003.12.176Google Scholar54https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXmvVGmtb8%253D&md5=753976dc9e85db69e75a8ce239deaa92Ab initio study of the SrTiO3, BaTiO3 and PbTiO3 (0 0 1) surfacesEglitis, R. I.; Piskunov, S.; Heifets, E.; Kotomin, E. A.; Borstel, G.Ceramics International (2004), 30 (7), 1989-1992CODEN: CINNDH; ISSN:0272-8842. (Elsevier B.V.)The results of first-principles calcns. of the two possible terminations of (001) surfaces of SrTiO3 (STO), BaTiO3 (BTO) and PbTiO3 (PTO) perovskites are presented. Surface at. structures and their electronic configurations have been calcd. using ab initio d. functional theory (DFT) combined with hybrid (B3PW) exchange-correlation technique. Our results are compared with previous quantum mech. calcns. and available exptl. data. Surface relaxations and the electronic states near valence band gap are discussed in details for all 3 perovskites.
- 55Heifets, E.; Piskunov, S.; Kotomin, E. A.; Zhukovskii, Y. F.; Ellis, D. E. Electronic structure and thermodynamic stability of double-layered SrTiO3(001) surfaces: Ab initio simulations. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 115417, DOI: 10.1103/physrevb.75.115417Google Scholar55https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXjvF2nsbY%253D&md5=b45cc77ae1d3ab2eec5cc1c927ab574fElectronic structure and thermodynamic stability of double-layered SrTiO3(001) surfaces: Ab initio simulationsHeifets, Eugene; Piskunov, Sergei; Kotomin, Eugene A.; Zhukovskii, Yuri F.; Ellis, Donald E.Physical Review B: Condensed Matter and Materials Physics (2007), 75 (11), 115417/1-115417/13CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Using the B3PW hybrid exchange-correlation functional within d.-functional theory and employing Gaussian-type basis sets, we calcd. the at. and electronic structures and thermodn. stability of three double-layered (DL) SrTiO3(001) surfaces: (i) SrO-terminated, (ii) TiO2-terminated, and (iii) (2×1) reconstruction of TiO2-terminated SrTiO3(001) recently suggested by Erdman et al. [Nature (London) 419, 55 (2002)]. A thermodn. stability diagram obtained from first-principles calcns. shows that regular TiO2- and SrO-terminated surfaces are the most stable. The stability regions of (2×1) DL TiO2- and DL SrO-terminated surfaces lie beyond the pptn. lines of SrO and TiO2 compds. and thus are less stable with respect to regular SrTiO3(001) surfaces. Anal. of the stability diagram suggests that Sr pptn. on SrTiO3 surface never occurs. Our simulations show a substantial increase of Ti-O covalency on the DL surfaces as compared to the regular surfaces, which are themselves more covalent than the cryst. bulk. The implications of our calcd. results for recent exptl. observations are discussed.
- 56Alexandrov, V. E.; Kotomin, E. A.; Maier, J.; Evarestov, R. A. First-principles study of bulk and surface oxygen vacancies in SrTiO3 crystal. Eur. Phys. J. B 2009, 72, 53– 57, DOI: 10.1140/epjb/e2009-00339-4Google Scholar56https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhsVyrsLfO&md5=319c1266807847704c2dd7785ae9afa3First-principles study of bulk and surface oxygen vacancies in SrTiO3 crystalAlexandrov, V. E.; Kotomin, E. A.; Maier, J.; Evarestov, R. A.European Physical Journal B: Condensed Matter and Complex Systems (2009), 72 (1), 53-57CODEN: EPJBFY; ISSN:1434-6028. (EDP Sciences)The structural and electronic properties of the neutral and pos. charged O vacancies (F and F+ centers) in the bulk and on the (001) surfaces of SrTiO3 crystal are examd. within the hybrid Hartree-Fock and d. functional theory (HF-DFT) method based upon the linear combination of AO (LCAO) approach. A comparison of the formation energy for surface and bulk defects indicates a perceptible propensity for the segregation of neutral and charged vacancies to both SrO and TiO2 surface terminations with a preference in the latter case which is important for interpretation of space charge effects at ceramic interfaces. The vacancies reveal more shallow energy levels in the band gap on surfaces rather than in the bulk, in particular, on the TiO2 surface. The charged F+ center has significantly deeper energy levels both in bulk and on the surfaces, as compared with the neutral F center.
- 57Mitra, 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.86.155105Google Scholar57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhslGltr7J&md5=a023c8f2827a92db127631878e59ef75Electronic structure of oxygen vacancies in SrTiO3 and LaAlO3Mitra, 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.
- 58Hamann, D. R.; Vanderbilt, D. Maximally localized Wannier functions for GW quasiparticles. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 045109, DOI: 10.1103/physrevb.79.045109Google Scholar58https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhtlGitbk%253D&md5=01b4feaf6c43192ead058abd2817b213Maximally localized Wannier functions for GW quasiparticlesHamann, D. R.; Vanderbilt, DavidPhysical Review B: Condensed Matter and Materials Physics (2009), 79 (4), 045109/1-045109/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We review the formalisms of the self-consistent GW approxn. to many-body perturbation theory and of the generation of optimally localized Wannier functions from groups of energy bands. We show that the quasiparticle Bloch wave functions from such GW calcns. can be used within this Wannier framework. These Wannier functions can be used to interpolate the many-body band structure from the coarse mesh of Brillouin-zone points on which it is known from the initial calcn. to the usual symmetry lines, and we demonstrate that this procedure is accurate and efficient for the self-consistent GW band structure. The resemblance of these Wannier functions to the bond orbitals discussed in the chem. community led us to expect differences between d.-functional and many-body functions that could be qual. interpreted. However, the differences proved to be minimal in the cases studied. Detailed results are presented for SrTiO3 and solid argon.
- 59Sponza, L.; Véniard, V.; Sottile, F.; Giorgetti, C.; Reining, L. Role of localized electrons in electron-hole interaction: The case of SrTiO3. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 235102, DOI: 10.1103/physrevb.87.235102Google Scholar59https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXht1Cls7zN&md5=750cd472453b2fbbd47448b36d33bcdfRole of localized electrons in electron-hole interaction: the case of SrTiO3Sponza, Lorenzo; Veniard, Valerie; Sottile, Francesco; Giorgetti, Christine; Reining, LuciaPhysical Review B: Condensed Matter and Materials Physics (2013), 87 (23), 235102/1-235102/11CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Strontium titanate SrTiO3 is an extensively studied material. Of particular interest are its electronic properties. Here we present a theor. study of its optical spectrum on the basis of state-of-the-art calcns. including many-body effects. The latter are evaluated by solving the Bethe-Salpeter equation within the GW approxn. for the self-energy. Excitonic effects are strong at the onset and at higher energies up to 10 eV. Agreement between theory and expt. is excellent at the onset, but only qual. at higher energies, where excitonic effects are stronger in theory than in expt. The origin of structures in the spectrum, as well as the remaining discrepancy between theory and expt., are discussed. We also present benchmark results for calcns. using more approx. ways to det. the spectra, including simplified time-dependent d.-functional theory.
- 60Deguchi, D.; Sato, K.; Kino, H.; Kotani, T. Accurate energy bands calculated by the hybrid quasiparticle self-consistent GW method implemented in the ecalj package. Jpn. J. Appl. Phys. 2016, 55, 051201, DOI: 10.7567/jjap.55.051201Google Scholar60https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhslCqtbzK&md5=e20d0fd29b9f6058ce35f212590e3580Accurate energy bands calculated by the hybrid quasiparticle self-consistent GW method implemented in the ecalj packageDeguchi, Daiki; Sato, Kazunori; Kino, Hiori; Kotani, TakaoJapanese Journal of Applied Physics (2016), 55 (5), 051201/1-051201/8CODEN: JJAPB6; ISSN:1347-4065. (IOP Publishing Ltd.)We have recently implemented a new version of the quasiparticle self-consistent GW (QSGW) method in the ecalj package released at http://github.com/tkotani/ecalj. Since the new version of the ecalj package is numerically stable and more accurate than the previous versions, we can perform calcns. easily without being bothered with tuning input parameters. Here we examine its ability to describe energy band properties, e.g., band-gap energy, eigenvalues at special points, and effective mass, for a variety of semiconductors and insulators. We treat C, Si, Ge, Sn, SiC (in 2H, 3C, and 4H structures), (Al, Ga, In) × (N, P, As, Sb), (Zn, Cd, Mg) × (O, S, Se, Te), SiO2, HfO2, ZrO2, SrTiO3, PbS, PbTe, MnO, NiO, and HgO. We propose that a hybrid QSGW method, where we mix 80% of QSGWand 20% of LDA, gives universally good agreement with expts. for these materials.
- 61Bhandari, C.; van Schilfgaarde, M.; Kotani, T.; Lambrecht, W. R. L. All-electron quasiparticle self-consistent GW band structures for SrTiO3 including lattice polarization corrections in different phases. Phys. Rev. Mater. 2018, 2, 013807, DOI: 10.1103/physrevmaterials.2.013807Google Scholar61https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltVKnsb4%253D&md5=c4b94a823837fcd3d6a9bae71acc91f2All-electron quasiparticle self-consistent GW band structures for SrTiO3 including lattice polarization corrections in different phasesBhandari, Churna; van Schilgaarde, Mark; Kotani, Takao; Lambrecht, Walter R. L.Physical Review Materials (2018), 2 (1), 013807CODEN: PRMHBS; ISSN:2475-9953. (American Physical Society)A review. The electronic band structure of SrTiO3 is investigated in the all-electron quasiparticle self-consistent GW (QSGW) approxn. Unlike previous pseudopotential-based QSGW or single-shot G0W0 calcns., the gap is found to be significantly overestimated compared to expt. After putting in a correction for the underestimate of the screening by the RPA in terms of a 0.8Σ approach, the gap is still overestimated. The 0.8Σ approach is discussed and justified in terms of various recent literature results including electron-hole corrections. Adding a lattice polarization correction (LPC) in the q→0 limit for the screening of W, agreement with expt. is recovered. The LPC is alternatively estd. using a polaron model. We apply our approach to the cubic and tetragonal phases as well as a hypothetical layered postperovskite structure and find that the local d. approxn. (LDA) to GW gap correction is almost independent of structure.
- 62Triggiani, L.; Muñoz-García, A. B.; Agostiano, A.; Pavone, M. Promoting oxygen vacancy formation and p-type conductivity in SrTiO3 via alkali metal doping: A first principles study. Phys. Chem. Chem. Phys. 2016, 18, 28951– 28959, DOI: 10.1039/c6cp05089aGoogle Scholar62https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsFGnu7nP&md5=a8d913f9fbf670ff51db2f843153d44bPromoting oxygen vacancy formation and p-type conductivity in SrTiO3 via alkali metal doping: a first principles studyTriggiani, Leonardo; Munoz-Garcia, Ana B.; Agostiano, Angela; Pavone, MichelePhysical Chemistry Chemical Physics (2016), 18 (41), 28951-28959CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)Strontium titanate (SrTiO3, STO) is a prototypical perovskite oxide, widely exploited in many technol. applications, from catalysis to energy conversion devices. In the context of solid-oxide fuel cells, STO has been recently applied as an epitaxial substrate for nano-sized layers of mixed ion-electron conductive catalysts with enhanced electrochem. performances. To extend the applications of such heterogeneous nano-cathodes in real devices, also the STO support should be active for both electron transport and oxide diffusion. To this end, we explored using first-principles calcns. the strategy of doping of STO at the Sr site with sodium and potassium. These two ions fit in the perovskite structure and induce holes in the STO valence band, so as to obtain the desired p-type electronic conduction. At the same time, the doping with alkali ions also promotes the formation of oxygen vacancies in STO, a prerequisite for effective oxide diffusion. Anal. of electron d. rearrangements upon defect formation allows relating the favorable vacancy formation energies to an improved electronic delocalization over the oxide sub-lattice, as obsd. in closely related materials (e.g. Sr2Fe1.5Mo0.5O6). Overall, our results suggest the alkali-doped STO as a new potential substrate material in nanoscale heterogeneous electrodes for solid oxide electrochem. cells.
- 63Himmetoglu, B.; Floris, A.; de Gironcoli, S.; Cococcioni, M. Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems. Int. J. Quantum Chem. 2014, 114, 14– 49, DOI: 10.1002/qua.24521Google Scholar63https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhtFKnu7jE&md5=eaee357312e5a88a6d0d6c0226f20398Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systemsHimmetoglu, Burak; Floris, Andrea; Gironcoli, Stefano; Cococcioni, MatteoInternational Journal of Quantum Chemistry (2014), 114 (1), 14-49CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)The aim of this review article is to assess the descriptive capabilities of the Hubbard-rooted LDA+U method and to clarify the conditions under which it can be expected to be most predictive. The article illustrates the theor. foundation of LDA+U and prototypical applications to the study of correlated materials, discusses the most relevant approxns. used in its formulation, and makes a comparison with other approaches also developed for similar purposes. Open "issues" of the method are also discussed, including the calcn. of the electronic couplings (the Hubbard U), the precise expression of the corrective functional and the possibility to use LDA+U for other classes of materials. The second part of the article presents recent extensions to the method and illustrates the significant improvements they have obtained in the description of several classes of different systems. The conclusive section finally discusses possible future developments of LDA+U to further enlarge its predictive power and its range of applicability. © 2013 Wiley Periodicals, Inc.
- 64Tolba, S. A.; Gameel, K. M.; Ali, B. A.; Almossalami, H. A.; Allam, N. K. Density Functional Calculations; Yang, G., Ed.; IntechOpen: London, 2018; Chapter 1.Google ScholarThere is no corresponding record for this reference.
- 65Harun, K.; Salleh, N. A.; Deghfel, B.; Yaakob, M. K.; Mohamad, A. A. DFT + U calculations for electronic, structural, and optical properties of ZnO wurtzite structure: A review. Results Phys. 2020, 16, 102829, DOI: 10.1016/j.rinp.2019.102829Google ScholarThere is no corresponding record for this reference.
- 66Capdevila-Cortada, M.; Łodziana, Z.; López, N. Performance of DFT+U approaches in the study of catalytic materials. ACS Catal. 2016, 6, 8370– 8379, DOI: 10.1021/acscatal.6b01907Google Scholar66https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xhsl2isr3K&md5=6978cd90109afcff6f7bf5aa194bbcedPerformance of DFT+U Approaches in the Study of Catalytic MaterialsCapdevila-Cortada, Marcal; Lodziana, Zbigniew; Lopez, NuriaACS Catalysis (2016), 6 (12), 8370-8379CODEN: ACCACS; ISSN:2155-5435. (American Chemical Society)A review. Catalysis development relies on the predictive abilities of the rational approaches provided by the study of complex reaction networks through d. functional theory, DFT. DFT constitutes a robust framework to study reaction networks on metal surfaces with the required accuracy. However, the problem of accuracy remains a challenge for materials where self-interaction severely affects the proper description of their electronic structures. Among practical approaches to address the problem, the Hubbard U cor. DFT has emerged as the most attractive tool in terms of resources balance that can allow the investigation of intricate reaction networks. Even if applying the DFT + U approaches in catalysis has reached some consensus, extensive benchmarks have not been performed. We have precisely done this benchmark against available expts. and hybrid (more accurate) functionals and seen that the dependence of thermodn. and kinetics for redox steps with the U parameter is different, thus being impossible to fit both with the same value of U (hence preventing the universality of the functional). The origin of this dependence can be traced back to the different electron localization between the initial, transition, and final states and points to the need of obtaining reaction profiles with geometry dependent U to reach adequate accuracy required for understanding and engineering.
- 67Cococcioni, M.; de Gironcoli, S. Linear response approach to the calculation of the effective interaction parameters in the LDA + U method. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 71, 035105, DOI: 10.1103/physrevb.71.035105Google Scholar67https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtVyqsLg%253D&md5=195d044afa4845213903f6928324efd2Linear response approach to the calculation of the effective interaction parameters in the LDA+U methodCococcioni, Matteo; de Gironcoli, StefanoPhysical Review B: Condensed Matter and Materials Physics (2005), 71 (3), 035105/1-035105/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We reexamine the LDA + U method of Anisimov and co-workers in the framework of a plane-wave pseudopotential approach. A simplified rotational-invariant formulation is adopted. The calcn. of the Hubbard U entering the expression of the functional is discussed and a linear response approach is proposed that is internally consistent with the chosen definition for the occupation matrix of the relevant localized orbitals. In this way we obtain a scheme whose functionality should not depend strongly on the particular implementation of the model in ab initio calcns. We demonstrate the accuracy of the method, computing structural and electronic properties of a few systems including transition and rare-earth correlated metals, transition metal monoxides, and iron silicate.
- 68Timrov, I.; Marzari, N.; Cococcioni, M. Hubbard parameters from density-functional perturbation theory. Phys. Rev. B 2018, 98, 085127, DOI: 10.1103/physrevb.98.085127Google Scholar68https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXlslWjsrg%253D&md5=c840267b4fac2a8b90b796723356779aHubbard parameters from density-functional perturbation theoryTimrov, Iurii; Marzari, Nicola; Cococcioni, MatteoPhysical Review B (2018), 98 (8), 085127/1-085127/15CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)We present a transparent and computationally efficient approach for the first-principles calcn. of Hubbard parameters from linear-response theory. This approach is based on d.-functional perturbation theory and the use of monochromatic perturbations. In addn. to delivering much improved efficiency, the present approach makes it straightforward to calc. automatically these Hubbard parameters for any given system, with tight numerical control on convergence and precision. The effectiveness of the method is showcased in three case studies-Cu2O, NiO, and LiCoO2-and by the direct comparison with finite differences in supercell calcns.
- 69Linscott, E. B.; Cole, D. J.; Payne, M. C.; O’Regan, D. D. Role of spin in the calculation of Hubbard U and Hund’s J parameters from first principles. Phys. Rev. B 2018, 98, 235157, DOI: 10.1103/physrevb.98.235157Google Scholar69https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltVOht7o%253D&md5=2d35d9f8eb2e8850968c8c9cccb4c349Role of spin in the calculation of Hubbard U and Hund's J parameters from first principlesLinscott, Edward B.; Cole, Daniel J.; Payne, Michael C.; O'Regan, David D.Physical Review B (2018), 98 (23), 235157CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)The d. functional theory (DFT)+U method is a pragmatic and effective approach for calcg. the ground-state properties of strongly correlated systems, and linear-response calcns. are widely used to det. the requisite Hubbard parameters from first principles. We provide a detailed treatment of spin within the linear-response framework, demonstrating that the conventional Hubbard U formula, unlike the conventional DFT+U corrective functional, incorporates interactions that are off-diagonal in the spin indexes and places greater wt. on one spin channel over the other. We construct alternative definitions for Hubbard and Hund's parameters that are consistent with the contemporary DFT+U functional, expanding upon the min.-tracking linear-response method. This approach allows Hund's J and spin-dependent U parameters to be calcd. with the same ease as for the std. Hubbard U. Our methods accurately reproduce the exptl. band gap, local magnetic moments, and the valence band edge character of manganese oxide, a canonical strongly correlated system. We also apply our approach to a complete series of transition-metal complexes [M(H2O)6]n+ (for M=Ti to Zn), showing that Hubbard corrections on oxygen atoms are necessary for preserving bond lengths, and demonstrating that our methods are numerically well behaved even for near-filled subspaces such as in zinc. However, spectroscopic properties appear to be beyond the reach of std. DFT+U. Collectively, these results shed new light on the role of spin in the calcn. of the corrective parameters U and J, and point the way toward avenues for further development of DFT+U and related methods.
- 70Aryasetiawan, F.; Imada, M.; Georges, A.; Kotliar, G.; Biermann, S.; Lichtenstein, A. I. Frequency-dependent local interactions and low-energy effective models from electronic structure calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 195104, DOI: 10.1103/physrevb.70.195104Google Scholar70https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXhtVGhu7rJ&md5=5f9d4d7fa01c2234cc7661b2c15778c9Frequency-dependent local interactions and low-energy effective models from electronic structure calculationsAryasetiawan, F.; Imada, M.; Georges, A.; Kotliar, G.; Biermann, S.; Lichtenstein, A. I.Physical Review B: Condensed Matter and Materials Physics (2004), 70 (19), 195104/1-195104/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We propose a systematic procedure for constructing effective models of strongly correlated materials. The parameters, in particular the on-site screened Coulomb interaction U, are calcd. from first principles, using the RPA. We derive an expression for the frequency-dependent U(ω) and show, for the case of nickel, that its high-frequency part has significant influence on the spectral functions. We propose a scheme for taking into account the energy dependence of U(ω), so that a model with an energy-independent local interaction can still be used for low-energy properties.
- 71Aryasetiawan, F.; Karlsson, K.; Jepsen, O.; Schönberger, U. Calculations of Hubbard U from first-principles. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 74, 125106, DOI: 10.1103/physrevb.74.125106Google Scholar71https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XhtVyksr%252FL&md5=58c04385bd2e41425b3c5a2264e2d581Calculations of Hubbard U from first-principlesAryasetiawan, F.; Karlsson, K.; Jepsen, O.; Schonberger, U.Physical Review B: Condensed Matter and Materials Physics (2006), 74 (12), 125106/1-125106/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The Hubbard U of the 3d transition metal series as well as SrVO3, YTiO3, Ce, and Gd has been estd. using a recently proposed scheme based on the RPA. The values obtained are generally in good accord with the values often used in model calcns. but for some cases the estd. values are somewhat smaller than those used in the literature. We have also calcd. the frequency-dependent U for some of the materials. The strong frequency dependence of U in some of the cases considered in this paper suggests that the static value of U may not be the most appropriate one to use in model calcns. We have also made comparison with the constrained local d. approxn. (LDA) method and found some discrepancies in a no. of cases. We emphasize that our scheme and the constrained local d. approxn. LDA method theor. ought to give similar results and the discrepancies may be attributed to tech. difficulties in performing calcns. based on currently implemented constrained LDA schemes.
- 72Bork, N.; Bonanos, N.; Rossmeisl, J.; Vegge, T. Ab initio charge analysis of pure and hydrogenated perovskites. J. Appl. Phys. 2011, 109, 033702, DOI: 10.1063/1.3536484Google Scholar72https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhtleks7g%253D&md5=3d9017d5ca02e3469393e956a113ffbaAb initio charge analysis of pure and hydrogenated perovskitesBork, N.; Bonanos, N.; Rossmeisl, J.; Vegge, T.Journal of Applied Physics (2011), 109 (3), 033702/1-033702/4CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)We present a d. functional theory based Bader anal. of the charge distribution in pure and hydrogenated SrTiO3. We find that the hydrogen defect carries a +0.56e charge and the OH defect carries a +0.50e charge compared to the host oxygen. Calcns. on BaNbO3, CaTiO3, and SrZrO3 support these findings. The distribution of the remaining electronic d. decays exponentially with distance to the hydrogen defect. Diffusional paths are calcd. wherein the hydrogenic species retain a charge between +0.57 and +0.54e showing that hydrogen permeation should not be viewed as consisting of virtually independent protonic and electronic transport processes. (c) 2011 American Institute of Physics.
- 73Bork, N.; Bonanos, N.; Rossmeisl, J.; Vegge, T. Thermodynamic and kinetic properties of hydrogen defect pairs in SrTiO3 from density functional theory. Phys. Chem. Chem. Phys. 2011, 13, 15256– 15263, DOI: 10.1039/c1cp20406hGoogle Scholar73https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhtVSrtbvP&md5=1b1d5f7d776e66953936136d30525177Thermodynamic and kinetic properties of hydrogen defect pairs in SrTiO3 from density functional theoryBork, Nicolai; Bonanos, Nikolaos; Rossmeisl, Jan; Vegge, TejsPhysical Chemistry Chemical Physics (2011), 13 (33), 15256-15263CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)A d. functional theory investigation of the thermodn. and kinetic properties of hydrogen-hydrogen defect interactions in the cubic SrTiO3 perovskite is presented. We find a net attraction between two hydrogen atoms with an optimal sepn. of ∼2.3 Å. The energy gain is ca. 0.33 eV compared to two non-interacting H defects. The main cause of the net attractive potential is elastic defect interactions through lattice deformation. Two possible diffusion paths for the hydrogen defect pair are investigated and are both detd. to be faster than the corresponding diffusion path for single hydrogen atoms. Finally, we set up a simple model to det. the contribution from the double hydrogen defect to the total hydrogen flux, and find the double defect to be the main diffusing species at temps. below ca. 400 °C. Post submission IR absorption expts. show excellent agreement with the proposed properties of the double hydrogen defect.
- 74Lee, J.; Demkov, A. A. Charge origin and localization at the n-type SrTiO3/LaAlO3 interface. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 193104, DOI: 10.1103/physrevb.78.193104Google Scholar74https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXhsVCksrbJ&md5=8f4ee6bd631d795fb29dc684ccaa4d2eCharge origin and localization at the n-type SrTiO3/LaAlO3 interfaceLee, Jaekwang; Demkov, Alexander A.Physical Review B: Condensed Matter and Materials Physics (2008), 78 (19), 193104/1-193104/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We report a first-principles study of (LaAlO3)m/(SrTiO3)n heterostructures using d.-functional theory at the LDA+U level. Our results support the original explanation of Ohtomo and Hwang that the charge at the n-type interface may be due to electrostatic doping. The internal elec. field in the LaAlO3 layer is calcd. to be 0.24 V/A. Though it is not sufficient to cause the dielec. breakdown in a wide band-gap La aluminate, it causes charge transfer into the adjacent narrower gap SrTiO3 layer. The quasi-two-dimensional nature of the charge distribution is caused by a combination of the crystal-field effect, pseudo-Jahn-Teller distortion, and interface chem. Our theor. est. suggests that the interfacial carrier d. of about 2 × 1013 cm-2 can be easily achieved.
- 75Kim, M. S.; Park, C. H. GW calculation of the electronic structure of cubic perovskite SrTiO3. J. Korean Phys. Soc. 2010, 56, 490– 493, DOI: 10.3938/jkps.56.362Google Scholar75https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXitFymsr4%253D&md5=4a9c06e667b3f2899218741ea6eb07c4GW calculation of the electronic structure of cubic perovskite SrTiO3Kim, M. S.; Park, C. H.Journal of the Korean Physical Society (2010), 56 (1, Pt. 2), 490-493CODEN: JKPSDV; ISSN:0374-4884. (Korean Physical Society)The electronic structure of SrTiO3 is calcd. by using the first-principles GW calcns., which is compared to the results calcd. using the local d. approxn. (LDA) and the LDA+U methods. The electronic energy levels of the conduction band (CB) states are found to be significantly upward shifted by the GW calcns. while the energy levels at the valence bands (VB) are only slightly lowered. These lead to a band gap widening; however, the calcd. band gap by GW calcn. is found to be larger than the exptl. value. An interesting result is that the GW correction is almost const. for energies around the CB and also around the VB, which means that the electronic structure calcd. by using the conventional LDA method can be nicely cor. by using a scissor operator while that calcd. by using the LDA+U method is significantly different from that calcd. by using GW calcns.
- 76Sikam, P.; Moontragoon, P.; Sararat, C.; Karaphun, A.; Swatsitang, E.; Pinitsoontorn, S.; Thongbai, P. DFT calculation and experimental study on structural, optical and magnetic properties of Co-doped SrTiO3. Appl. Surf. Sci. 2018, 446, 92– 113, DOI: 10.1016/j.apsusc.2018.02.161Google Scholar76https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXjsFWnsLs%253D&md5=a15cf13380a585b831a3ce1ae031eb6aDFT calculation and experimental study on structural, optical and magnetic properties of Co-doped SrTiO3Sikam, Pornsawan; Moontragoon, Pairot; Sararat, Chayanin; Karaphun, Attaphol; Swatsitang, Ekaphan; Pinitsoontorn, Supree; Thongbai, PrasitApplied Surface Science (2018), 446 (), 92-113CODEN: ASUSEE; ISSN:0169-4332. (Elsevier B.V.)SrTiO3 (STO) is an attractive material that offers a wide range of technol. applications, e.g., ferroelectricity, solar cell and photocatalysis. An application that the STO might be utilized is dild. magnetic semiconductors. Here, we would like to improve magnetic property of the STO by Ti site substitution using Co atoms. In this work, we present the structural, optical and magnetic properties of perfect and oxygen defect structures of STO and Co-doped SrTiO3 via exptl. and theor. aspects. In first-principles calcn., the structural properties, electronic band structure and magnetic properties of undoped STO and Co-doped STO supercells have been investigated by d. functional theory using GGA with Hubbard model scheme (GGA+U) on Vienna Ab initio Simulation Package (VASP). In calcn. detail, pure phase of STO with nanometer scale size of undoped STO and Co-doped STO have been synthesized using hydrothermal technique. The findings obtained from DFT computation reveal that the new states in gap between the valence band and conduction band of the STO were induced after Co atom was doped into the host structure. These impurity states narrow the band gap corresponding to exptl. results. In addn., band splitting was obsd. on O defect and dopant systems, indicating that missing O and doping Co on STO could induce magnetization on none-magnetic material of STO. In case of synthesized powder, ferromagnetic behaviors are detd. in the dopant system annealed in Ar. Addnl., another appreciated point of Co doping is that surface area of the STO is improved. Thus, it is expected that the surface activity, such as photocatalytic performance, of the STO will be enhanced. From all referred results, they introduce that the Co-doped STO might be a potential candidate to be a photocatalyst for the high photocatalytic performance under visible light radiation and the dild. magnetic semiconductor in spintronic devices.
- 77Brown, J. J.; Ke, Z.; Geng, W.; Page, A. J. Oxygen vacancy defect migration in titanate perovskite surfaces: Effect of the A-site cations. J. Phys. Chem. C 2018, 122, 14590– 14597, DOI: 10.1021/acs.jpcc.8b03322Google Scholar77https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtVWntL%252FP&md5=1326e291d26ad7b07c8507fb1a7a3244Oxygen Vacancy Defect Migration in Titanate Perovskite Surfaces: Effect of the A-Site CationsBrown, Joshua J.; Ke, Zhuofeng; Geng, Wei; Page, Alister J.Journal of Physical Chemistry C (2018), 122 (26), 14590-14597CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)Oxygen vacancy formation energies and migration barriers in (001) surfaces of CaTiO3, SrTiO3, and BaTiO3 were studied using 1st principles d. functional theory. The degree of distortion within the TiO2 sublattice in the presence of defects and consequently the defect formation energies in these titanate surfaces are detd. by the size of the A-site cation (Ca2+ < Sr2+ < Ba2+). This is notably the case for CaTiO3, in which the presence of a vacancy defect leads to a heavily distorted local orthorhombic structure within the (001) slab depending on the defect position, despite the overall cubic symmetry of the material modeled. This effectively leads to the TiO2 sublattice acting as a thermodn. trap for oxygen vacancy defects in CaTiO3. By contrast, calcd. vacancy diffusion pathways in SrTiO3 and BaTiO3 indicate that vacancy diffusion with these larger A-site cations is kinetically and not thermodynamically controlled.
- 78Pavarini, E.; Biermann, S.; Poteryaev, A.; Lichtenstein, A. I.; Georges, A.; Andersen, O. K. Mott transition and suppression of orbital fluctuations in orthorhombic 3d1 perovskites. Phys. Rev. Lett. 2004, 92, 176403, DOI: 10.1103/physrevlett.92.176403Google Scholar78https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXjs1Wjs7k%253D&md5=61831618268d10af744d2afd7bd9e9f3Mott Transition and Suppression of Orbital Fluctuations in Orthorhombic 3d PerovskitesPavarini, E.; Biermann, S.; Poteryaev, A.; Lichtenstein, A. I.; Georges, A.; Andersen, O. K.Physical Review Letters (2004), 92 (17), 176403/1-176403/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Using t2g Wannier functions, a low-energy Hamiltonian is derived for orthorhombic 3d1 transition-metal oxides. Electronic correlations are treated with a new implementation of dynamical mean-field theory for noncubic systems. Good agreement with photoemission data is obtained. The interplay of correlation effects and cation covalency (GdFeO3-type distortions) is found to suppress orbital fluctuations in LaTiO3 and even more in YTiO3, and to favor the transition to the insulating state.
- 79Okamoto, S.; Millis, A. J.; Spaldin, N. A. Lattice relaxation in oxide heterostructures: LaTiO3/SrTiO3 superlattices. Phys. Rev. Lett. 2006, 97, 056802, DOI: 10.1103/physrevlett.97.056802Google Scholar79https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XnvVWltL0%253D&md5=acb550a258fc28f8b32af314604cc87dLattice relaxation in oxide heterostructures. LaTiO3/SrTiO3 superlatticesOkamoto, Satoshi; Millis, Andrew J.; Spaldin, Nicola A.Physical Review Letters (2006), 97 (5), 056802/1-056802/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Local d. approxn. + Hubbard U and many-body effective Hamiltonian calcns. are used to det. the effects of lattice relaxation in LaTiO3/SrTiO3 superlattices. Large ferroelec.-like distortions of the TiO6 octahedra are found, which substantially affect the Ti d-electron d., bringing the calcd. results into good agreement with exptl. data. The relaxations also change the many-body physics, leading to a novel symmetry-breaking-induced ordering of the xy orbitals, which does not occur in bulk LaTiO3, or in the hypothetical unrelaxed structure.
- 80Cuong, D. D.; Lee, B.; Choi, K. M.; Ahn, H.-S.; Han, S.; Lee, J. Oxygen vacancy clustering and electron localization in oxygen-deficient SrTiO3: LDA + U study. Phys. Rev. Lett. 2007, 98, 115503, DOI: 10.1103/physrevlett.98.115503Google Scholar80https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXjtF2qu78%253D&md5=22d4928e0ed342001eb9827b4c2abba7Oxygen vacancy clustering and electron localization in oxygen-deficient SrTiO3. LDA+U studyCuong, Do Duc; Lee, Bora; Choi, Kyeong Mi; Ahn, Hyo-Shin; Han, Seungwu; Lee, JaichanPhysical Review Letters (2007), 98 (11), 115503/1-115503/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Using a local d. approxn. +Hubbard U method, that O vacancies tend to cluster in a linear way in SrTiO3, a prototypical perovskite oxide, accompanied by strong electron localization at the 3d state of the nearby Ti transition metal ion. The vacancy clustering and the assocd. electron localization lead to a profound impact on materials properties, e.g., the redn. in free-carrier densities, the appearance of characteristic optical spectra, and the decrease in vacancy mobility. The high stability against the vacancy migration also suggests the phys. reality of the vacancy cluster.
- 81Hou, Z.; Terakura, K. Defect states induced by oxygen vacancies in cubic SrTiO3: First-principles calculations. J. Phys. Soc. Jpn. 2010, 79, 114704, DOI: 10.1143/jpsj.79.114704Google Scholar81https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhsFCnsb7F&md5=68f0fb7e4af6c92a53e14bee64564eebDefect States induced by oxygen vacancies in cubic SrTiO3: first-principles calculationsHou, Zhufeng; Terakura, KiyoyukiJournal of the Physical Society of Japan (2010), 79 (11), 114704/1-114704/6CODEN: JUPSAU; ISSN:0031-9015. (Physical Society of Japan)Using the first-principles calcns. with the correction of on-site Coulomb interaction, we found that single O vacancy (VO) in cubic SrTiO3 takes a magnetic ground state in which VO induces a singly-occupied localized state in the band gap and a delocalized state in the conduction band. Our calcns. showed that VO energetically prefers the singly-ionized state VO+ rather than forming a pair of neutral VO0 and doubly ionized VO2+ states from 2VO+. Furthermore, we found that two O vacancies of a vacancy pair complex tend to align in a magnetically anti-parallel shoulder-to-shoulder configuration in the xy plane, rather than in a non-magnetic head-to-head configuration along the z direction as predicted in an available theor. work. For O divacancies in the al five configurations considered here, localized states were found in the band gap. Our results not only clarify the puzzling findings reported in literature, but also can provide a better understanding of the role of O vacancies in the low temp. cond. and the optical excitation of oxygen-deficient SrTiO3.
- 82Choi, M.; Oba, F.; Kumagai, Y.; Tanaka, I. Anti-ferrodistortive-like oxygen-octahedron rotation induced by the oxygen vacancy in cubic SrTiO3. Adv. Mater. 2013, 25, 86– 90, DOI: 10.1002/adma.201203580Google Scholar82https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsFGjtLbL&md5=43eb7b56c894776c48c86d4ed3b58ae6Anti-ferrodistortive-Like Oxygen-Octahedron Rotation Induced by the Oxygen Vacancy in Cubic SrTiO3Choi, Minseok; Oba, Fumiyasu; Kumagai, Yu; Tanaka, IsaoAdvanced Materials (Weinheim, Germany) (2013), 25 (1), 86-90CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)The authors used the DFT-PBE+U method to study oxygen vacancies Vo in cubic SrTiO3 showing atomistic structure and electronic properties different from earlier understanding. The oxygen-octahedron rotation, similar to the at. configurations in the low-temp. antiferrodistortive tetragonal phase, occurs locally around Vo even in the cubic phase, leading to localized electronic states in the band gap, strongly correlated with the exptl. obsd. elec. and optical properties of SrTiO3.
- 83Liu, B.; Cooper, V. R.; Xu, H.; Xiao, H.; Zhang, Y.; Weber, W. J. Composition dependent intrinsic defect structures in SrTiO3. Phys. Chem. Chem. Phys. 2014, 16, 15590– 15596, DOI: 10.1039/c4cp01510jGoogle Scholar83https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtVamsrjL&md5=5a3790c0fe991dad1c05581de2a4229bComposition dependent intrinsic defect structures in SrTiO3Liu, Bin; Cooper, Valentino R.; Xu, Haixuan; Xiao, Haiyan; Zhang, Yanwen; Weber, William J.Physical Chemistry Chemical Physics (2014), 16 (29), 15590-15596CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)Intrinsic point defect complexes in SrTiO3 under different chem. conditions are studied using d. functional theory. The Schottky defect complex consisting of nominally charged Sr, Ti and O vacancies is predicted to be the most stable defect structure in stoichiometric SrTiO3, with a relatively low formation energy of 1.64 eV per defect. In addn., the mechanisms of defect complex formation in nonstoichiometric SrTiO3 are investigated. Excess SrO leads to the formation of oxygen vacancies and a strontium-titanium antisite defect, while a strontium vacancy together with an oxygen vacancy and a titanium-strontium antisite defect are produced in an excess TiO2 environment. Since point defects, such as oxygen vacancies and cation antisite defects, are intimately related to the functionality of SrTiO3, these results provide guidelines for controlling the formation of intrinsic point defects and optimizing the functionality of SrTiO3 by controlling nonstoichiometric chem. compns. of SrO and TiO2 in expts.
- 84Gogoi, P. K.; Trevisanutto, P. E.; Yang, M.; Santoso, I.; Asmara, T. C.; Terentjevs, A.; Della Sala, F.; Breese, M. B. H.; Venkatesan, T.; Feng, Y. P. Optical conductivity renormalization of graphene on SrTiO3 due to resonant excitonic effects mediated by Ti 3d orbitals. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91, 035424, DOI: 10.1103/physrevb.91.035424Google Scholar84https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXmt12qsL4%253D&md5=4b03baf4ede0bf2a9b4bc2687ce407a7Optical conductivity renormalization of graphene on SrTiO3 due to resonant excitonic effects mediated by Ti 3d orbitalsGogoi, Pranjal Kumar; Trevisanutto, Paolo E.; Yang, Ming; Santoso, Iman; Asmara, Teguh Citra; Terentjevs, Aleksandrs; Della Sala, Fabio; Breese, Mark B. H.; Venkatesan, T.; Feng, Yuan Ping; Loh, Kian Ping; Castro Neto, Antonio H.; Rusydi, AndrivoPhysical Review B: Condensed Matter and Materials Physics (2015), 91 (3), 035424/1-035424/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We present evidence of a drastic renormalization of the optical cond. of graphene on SrTiO3 resulting in almost full transparency in the UV region. These findings are attributed to resonant excitonic effects further supported by ab initio Bethe-Salpeter equation and d. functional theory calcns. The (π,π*) orbitals of graphene and Ti-3dt2g orbitals of SrTiO3 are strongly hybridized and the interactions of electron-hole states residing in those orbitals play dominant role in the graphene optical cond. These interactions are present much below the optical band gap of bulk SrTiO3. These results open a possibility of manipulating interaction strengths in graphene via d orbitals, which could be crucial for optical applications.
- 85Jeschke, H. O.; Shen, J.; Valentí, R. Localized versus itinerant states created by multiple oxygen vacancies in SrTiO3. New J. Phys. 2015, 17, 023034, DOI: 10.1088/1367-2630/17/2/023034Google Scholar85https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXlsVaqsLY%253D&md5=708a5d6fb81c0c6d2288a3d2693f875dLocalized versus itinerant states created by multiple oxygen vacancies in SrTiO3Jeschke, Harald O.; Shen, Juan; Valenti, RoserNew Journal of Physics (2015), 17 (Feb.), 023034/1-023034/8CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)Oxygen vacancies in strontium titanate surfaces (SrTiO3) have been linked to the presence of a two-dimensional electron gas with unique behavior. We perform a detailed d. functional theory study of the lattice and electronic structure of SrTiO3 slabs with multiple oxygen vacancies, with a main focus on two vacancies near a titanium dioxide terminated SrTiO3 surface. We conclude based on total energies that the two vacancies preferably inhabit the first two layers, i.e. they cluster vertically, while in the direction parallel to the surface, the vacancies show a weak tendency towards equal spacing. Anal. of the nonmagnetic electronic structure indicates that oxygen defects in the surface TiO2 layer lead to population of Ti t2g states and thus itinerancy of the electrons donated by the oxygen vacancy. In contrast, electrons from subsurface oxygen vacancies populate Ti eg states and remain localized on the two Ti ions neighboring the vacancy. We find that both the formation of a bound oxygen-vacancy state composed of hybridized Ti 3eg and 4p states neighboring the oxygen vacancy as well as the elastic deformation after extg. oxygen contribute to the stabilization of the in-gap state.
- 86Zhang, L.; Liu, B.; Zhuang, H.; Kent, P. R. C.; Cooper, V. R.; Ganesh, P.; Xu, H. Oxygen vacancy diffusion in bulk SrTiO3 from density functional theory calculations. Comput. Mater. Sci. 2016, 118, 309– 315, DOI: 10.1016/j.commatsci.2016.02.041Google Scholar86https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XksVKku70%253D&md5=3aea50a7ed317e9478091aa8b741a085Oxygen vacancy diffusion in bulk SrTiO3 from density functional theory calculationsZhang, Lipeng; Liu, Bin; Zhuang, Houlong; Kent, P. R. C.; Cooper, Valentino R.; Ganesh, P.; Xu, HaixuanComputational Materials Science (2016), 118 (), 309-315CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)A review. Point defects and their diffusion contribute significantly to the properties of perovskite materials. However, even for the prototypical case of oxygen vacancies in SrTiO3 (STO), the predictions of oxygen vacancy activity vary widely. Here we present a comprehensive and systematic study of the diffusion barriers in bulk STO. Using d. functional theory (DFT), we assess the role of different supercell sizes, d. functionals, and charge states. Our results show that vacancy-induced octahedral rotations, which are limited by the boundary conditions of the supercell, can significantly affect the computed oxygen vacancy diffusion energy barrier. In addn., we find that the diffusion energy barrier of a charged oxygen vacancy is lower than that of a neutral one. This difference is magnified in small supercells. We demonstrate that with increasing supercell size, the effects of the oxygen vacancy charge state and the type of DFT exchange and correlation functional diminish, and all DFT predicted migration energy barriers asymptote to a range of 0.39-0.49 eV, which is smaller than the reported exptl. values. This work provides important insights and guidance that should be considered for investigations of point defect diffusion in perovskite materials and in oxide superlattices.
- 87Brovko, O. O.; Tosatti, E. Controlling the magnetism of oxygen surface vacancies in SrTiO3 through charging. Phys. Rev. Mater. 2017, 1, 044405, DOI: 10.1103/physrevmaterials.1.044405Google Scholar87https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhs1ehtbvL&md5=2922ce9541605d186378dbe1cdfe7945Controlling the magnetism of oxygen surface vacancies in SrTiO3 through chargingBrovko, Oleg O.; Tosatti, ErioPhysical Review Materials (2017), 1 (4), 044405/1-044405/8CODEN: PRMHBS; ISSN:2475-9953. (American Physical Society)A review. We discuss, based on first-principles calcns., the possibility of tuning the magnetism of oxygen vacancies at the (001) surface of strontium titanate (SrTiO3). The magnetic moment of single and clustered vacancies stemming from Ti-O broken bonds can be both quenched and stabilized controllably by chem. potential adjustment assocd. with doping the system with electrons or holes. We discuss to what extent this route to magnetization state control is robust against other external influences such as chem. doping, mech. action, and elec. field. Such control of the vacancy state and magnetization can conceivably be achieved exptl. by using local probe tips.
- 88Solovyev, I.; Hamada, N.; Terakura, K. t2g versus all 3d localization in LaMO3 perovskites (M=Ti–Cu): First-principles study. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 53, 7158– 7170, DOI: 10.1103/physrevb.53.7158Google ScholarThere is no corresponding record for this reference.
- 89Xie, Y.; Cao, H.-Y.; Zhou, Y.; Chen, S.; Xiang, H.; Gong, X.-G. Oxygen vacancy induced flat phonon mode at FeSe/SrTiO3 interface. Sci. Rep. 2015, 5, 10011, DOI: 10.1038/srep10011Google Scholar89https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhtFyiurrJ&md5=a80d691b6ffca6ce3414b0e63b821834Oxygen Vacancy Induced Flat Phonon Mode at FeSe /SrTiO3 interfaceXie, Yun; Cao, Hai-Yuan; Zhou, Yang; Chen, Shiyou; Xiang, Hongjun; Gong, Xin-GaoScientific Reports (2015), 5 (), 10011CODEN: SRCEC3; ISSN:2045-2322. (Nature Publishing Group)A high-frequency optical phonon mode of SrTiO3 (STO) was found to assist the high-temp. supercond. obsd. recently at the interface between monolayer FeSe and STO substrate. However, the origin of this mode is not clear. Through first-principles calcns., we find that there is a novel polar phonon mode on the surface layers of the STO substrate, which does not exist in the STO crystals. The oxygen vacancies near the FeSe/STO interface drives the dispersion of this phonon mode to be flat and lowers its energy, whereas the charge transfer between STO substrate and FeSe monolayer further reduces its energy to 81 meV. This energy is in good agreement with the exptl. value fitted by Lee et al. for the phonon mode responsible for the obsd. replica band sepns. and the increased superconducting gap. The oxygen-vacancy-induced flat and polar phonon mode provides clues for understanding the origin of high Tc supercond. at the FeSe/STO interface.
- 90Kim, Y. S.; Kim, J.; Moon, S. J.; Choi, W. S.; Chang, Y. J.; Yoon, J.-G.; Yu, J.; Chung, J.-S.; Noh, T. W. Localized electronic states induced by defects and possible origin of ferroelectricity in strontium titanate thin films. Appl. Phys. Lett. 2009, 94, 202906, DOI: 10.1063/1.3139767Google Scholar90https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXmsVGnsLk%253D&md5=57ea9b604014481651500b6010625875Localized electronic states induced by defects and possible origin of ferroelectricity in strontium titanate thin filmsKim, Y. S.; Kim, J.; Moon, S. J.; Choi, W. S.; Chang, Y. J.; Yoon, J.-G.; Yu, J.; Chung, J.-S.; Noh, T. W.Applied Physics Letters (2009), 94 (20), 202906/1-202906/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)Several defect configurations including oxygen vacancies have been investigated as possible origins of the reported room-temp. ferroelectricity of strontium titanate (STO) thin films. First-principles calcns. revealed that the Sr-O-O vacancy complexes create deep localized states in the band gap of SrTiO3 without affecting its insulating property. These results are consistent with electronic structural changes detd. from optical transmission and x-ray absorption measurements. Our work suggests importance of oxygen vacancies and their complexes in understanding of electronic properties of perovskite oxide thin films, including STO. (c) 2009 American Institute of Physics.
- 91Carlotto, S.; Natile, M. M.; Glisenti, A.; Vittadini, A. Electronic structure of SrTi1–xMxO3−δ (M=Co, Ni, Cu) perovskite-type doped-titanate crystals by DFT and DFT+U calculations. Chem. Phys. Lett. 2013, 588, 102– 108, DOI: 10.1016/j.cplett.2013.10.020Google Scholar91https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhs1yqsLnI&md5=73016eb70f2fd44c7c372f60d6e9a068Electronic structure of SrTi1-xMxO3-δ (M = Co, Ni, Cu) perovskite-type doped-titanate crystals by DFT and DFT + U calculationsCarlotto, Silvia; Natile, Marta Maria; Glisenti, Antonella; Vittadini, AndreaChemical Physics Letters (2013), 588 (), 102-108CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)We study the electronic structure of Co, Ni, and Cu impurities and of their vacancy-assocd. complexes in SrTiO3 crystals by d. functional theory (DFT) and DFT + U calcns. Simple substitutionals prefer low-spin states, as expected from ligand field theory. On the other hand, the formation energy of vacancies (which tend to stay close to the impurity) is rather low for all the doped systems, and decreases with Z. This reflects the low stability of the +IV oxidn. state for the impurities. Contrary to simple impurities, high-spin states are predicted to be stable when impurities are assocd. to vacancies.
- 92Maldonado, F.; Maza, L.; Stashans, A. Electronic properties of Cr-, B-doped and codoped SrTiO3. J. Phys. Chem. Solids 2017, 100, 1– 8, DOI: 10.1016/j.jpcs.2016.09.003Google Scholar92https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsFWgs7vE&md5=777b794f61f6312d707949bab3f77972Electronic properties of Cr-, B-doped and codoped SrTiO3Maldonado, Frank; Maza, Luz; Stashans, ArvidsJournal of Physics and Chemistry of Solids (2017), 100 (), 1-8CODEN: JPCSAW; ISSN:0022-3697. (Elsevier Ltd.)Spin-polarized d. functional theory (DFT) computations have been carried out to investigate Cr-, B-doping as well as codoping in the SrTiO3 crystal. Impact of the oxygen vacancy as an intrinsic point defect has been also taken into consideration. In order to describe more precisely 3d electrons of the Ti and Cr atoms, Hubbard-like U term in the DFT has been introduced. Outcomes of the calcns. reveal occupied states within the forbidden energy region arguing that these in-gap states might be responsible for visible light photocatalysis in the SrTiO3. Structural and magnetic features of the doped and codoped material are discussed as well.
- 93Ricca, 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.2.023313Google Scholar93https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsFCnurrO&md5=b7b6116eb4e8fb8f56fd608abd0e8a60Self-consistent DFT+U+V study of oxygen vacancies in SrTiO3Ricca, Chiara; Timrov, Iurii; Cococcioni, Matteo; Marzari, Nicola; Aschauer, UlrichPhysical 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.
- 94Campo, V. L., Jr.; Cococcioni, M. Extended DFT + U + V method with on-site and inter-site electronic interactions. J. Phys.: Condens. Matter 2010, 22, 055602Google Scholar94https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXjtVWqsLY%253D&md5=52060c83388535541f19adfec453968fExtended DFT + U + V method with on-site and inter-site electronic interactionsCampo, Vivaldo Leiria, Jr.; Cococcioni, MatteoJournal of Physics: Condensed Matter (2010), 22 (5), 055602/1-055602/12CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)In this paper we introduce a generalization of the popular DFT + U method based on the extended Hubbard model that includes on-site and inter-site electronic interactions. The novel corrective Hamiltonian is designed to study systems for which electrons are not completely localized on at. states (according to the general scheme of Mott localization) and hybridization between orbitals from different sites plays an important role. The application of the extended functional to archetypal Mott-charge-transfer (NiO) and covalently bonded insulators (Si and GaAs) demonstrates its accuracy and versatility and the possibility to obtain a unifying and equally accurate description for a broad range of very diverse systems.
- 95Orhan, O. K.; O’Regan, D. D. First-principles Hubbard U and Hund’s J corrected approximate density functional theory predicts an accurate fundamental gap in rutile and anatase TiO2. Phys. Rev. B 2020, 101, 245137, DOI: 10.1103/physrevb.101.245137Google Scholar95https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsFCgsr3M&md5=c2b3534319c2e1b3e36e30d48164f230First-principles Hubbard U and Hund's J corrected approximate density functional theory predicts an accurate fundamental gap in rutile and anatase TiO2Orhan, Okan K.; O'Regan, David D.Physical Review B (2020), 101 (24), 245137CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)Titanium dioxide (TiO2) presents a long-standing challenge for approx. Kohn-Sham d. functional theory (KS-DFT), as well as to its Hubbard-cor. extension, DFT+U. We find that a previously proposed extension of first-principles DFT+U to incorporate a Hund's J correction, termed DFT+U+J, in combination with parameters calcd. using a recently proposed linear-response theory, predicts fundamental band gaps that are accurate to well within the exptl. uncertainty in rutile and anatase TiO2. Our approach builds upon established findings that Hubbard correction of both the titanium 3d and oxygen 2p subspaces in TiO2, symbolically giving DFT+Ud,p, is necessary to achieve acceptable band gaps using DFT+U. This requirement remains when the first-principles Hund's J is included. We also find that the calcd. gap depends on the correlated subspace definition even when using subspace-specific first-principles U and J parameters. Using the simplest reasonable correlated subspace definition and underlying functional, the local d. approxn., we show that high accuracy results from using a relatively uncomplicated form of the DFT+U+J functional. For closed-shell systems such as TiO2, we describe how various DFT+U+J functionals reduce to DFT+U with suitably modified parameters, so that reliable band gaps can be calcd. for rutile and anatase with no modifications to a conventional DFT+U code.
- 96Prentice, J. C. A.; Aarons, J.; Womack, J. C.; Allen, A. E. A.; Andrinopoulos, L.; Anton, L.; Bell, R. A.; Bhandari, A.; Bramley, G. A.; Charlton, R. J. The ONETEP linear-scaling density functional theory program. J. Chem. Phys. 2020, 152, 174111, DOI: 10.1063/5.0004445Google Scholar96https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXovFKntrs%253D&md5=4fd582310ed3af1f09fe2b6fcca9e1acThe ONETEP linear-scaling density functional theory programPrentice, Joseph C. A.; Aarons, Jolyon; Womack, James C.; Allen, Alice E. A.; Andrinopoulos, Lampros; Anton, Lucian; Bell, Robert A.; Bhandari, Arihant; Bramley, Gabriel A.; Charlton, Robert J.; Clements, Rebecca J.; Cole, Daniel J.; Constantinescu, Gabriel; Corsetti, Fabiano; Dubois, Simon M.-M.; Duff, Kevin K. B.; Escartin, Jose Maria; Greco, Andrea; Hill, Quintin; Lee, Louis P.; Linscott, Edward; O'Regan, David D.; Phipps, Maximillian J. S.; Ratcliff, Laura E.; Serrano, Alvaro Ruiz; Tait, Edward W.; Teobaldi, Gilberto; Vitale, Valerio; Yeung, Nelson; Zuehlsdorff, Tim J.; Dziedzic, Jacek; Haynes, Peter D.; Hine, Nicholas D. M.; Mostofi, Arash A.; Payne, Mike C.; Skylaris, Chris-KritonJournal of Chemical Physics (2020), 152 (17), 174111CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present an overview of the ONETEP program for linear-scaling d. functional theory (DFT) calcns. with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the d. matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calcn., both the d. matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, ONETEP is able to perform calcns. including thousands of atoms with computational effort, which scales linearly with the no. or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temp. methods for metallic systems, methods for strongly correlated systems, mol. dynamics, vibrational calcns., time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mech. (QM)/mol. mech. and QM-in-QM embedding, d. of states calcns., distributed multipole anal., and methods for partitioning charges and interactions between fragments. Calcns. with ONETEP provide unique insights into large and complex systems that require an accurate at.-level description, ranging from biomol. to chem., to materials, and to phys. problems, as we show with a small selection of illustrative examples. ONETEP has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications. (c) 2020 American Institute of Physics.
- 97Skylaris, C.-K.; Haynes, P. D.; Mostofi, A. A.; Payne, M. C. Introducing ONETEP: Linear-scaling density functional simulations on parallel computers. J. Chem. Phys. 2005, 122, 084119, DOI: 10.1063/1.1839852Google Scholar97https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXitVGgtrk%253D&md5=507bea06e9c40dbe363d219d3a5242efIntroducing ONETEP: Linear-scaling density functional simulations on parallel computersSkylaris, Chris-Kriton; Haynes, Peter D.; Mostofi, Arash A.; Payne, Mike C.Journal of Chemical Physics (2005), 122 (8), 084119/1-084119/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present ONETEP (order-N electronic total energy package), a d. functional program for parallel computers whose computational cost scales linearly with the no. of atoms and the no. of processors. ONETEP is based on our reformulation of the plane wave pseudopotential method which exploits the electronic localization that is inherent in systems with a nonvanishing band gap. We summarize the theor. developments that enable the direct optimization of strictly localized quantities expressed in terms of a delocalized plane wave basis. These same localized quantities lead us to a phys. way of dividing the computational effort among many processors to allow calcns. to be performed efficiently on parallel supercomputers. We show with examples that ONETEP achieves excellent speedups with increasing nos. of processors and confirm that the time taken by ONETEP as a function of increasing no. of atoms for a given no. of processors is indeed linear. What distinguishes our approach is that the localization is achieved in a controlled and math. consistent manner so that ONETEP obtains the same accuracy as conventional cubic-scaling plane wave approaches and offers fast and stable convergence. We expect that calcns. with ONETEP have the potential to provide quant. theor. predictions for problems involving thousands of atoms such as those often encountered in nanoscience and biophysics.
- 98Lany, S.; Zunger, A. Light- and bias-induced metastabilities in Cu(In,Ga)Se2 based solar cells caused by the (VSe-VCu) vacancy complex. J. Appl. Phys. 2006, 100, 113725, DOI: 10.1063/1.2388256Google Scholar98https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXht1Kqtg%253D%253D&md5=f5bdef4a454e490c23fd8fba306d333cLight- and bias-induced metastabilities in Cu(In,Ga)Se2 based solar cells caused by the (VSe-VCu) vacancy complexLany, Stephan; Zunger, AlexJournal of Applied Physics (2006), 100 (11), 113725/1-113725/15CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)The light- and bias-induced metastabilities in Cu(In,Ga)Se2 (CIGS) based solar cells were studied, suggesting the Se-Cu di-vacancy complex (VSe-VCu) as the source of these phenomena. Due to its amphoteric nature, the VSe-VCu complex can convert by persistent carrier capture or emission from a shallow donor into a shallow acceptor configuration, and vice versa, thereby changing in a metastable fashion the local net acceptor d. inside the CIGS absorber of the solar cell, e.g., in a CdS/CIGS heterojunction. To understand the metastability caused by the VSe-VCu complex, defect formation energies were detd. from 1st-principle calcns. with numerical simulation of equil. defect thermodn. A model for the transition dynamics was developed after creation of a metastable nonequil. state. The VSe-VCu complex can account for the light-induced metastabilities, i.e., the red and blue illumination effects, as well as for the reverse-bias effect. Thus, the VSe-VCu model implies that the different metastabilities obsd. in CIGS share a common origin. A defect state in the band gap caused by VSe-VCu in the acceptor configuration creates a potentially detrimental recombination center and may contribute to the satn. of the open circuit voltage in larger-gap Cu(In,Ga)Se2 alloys with higher Ga content. Therefore, the presence of metastable defects impacts on solar cell performance.
- 99Lany, S.; Zunger, A. Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 235104, DOI: 10.1103/physrevb.78.235104Google Scholar99https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXit12jsA%253D%253D&md5=11bbb3f01ce352d0a7702d9eef7ba5aeAssessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAsLany, Stephan; Zunger, AlexPhysical Review B: Condensed Matter and Materials Physics (2008), 78 (23), 235104/1-235104/25CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Contemporary theories of defects and impurities in semiconductors rely to a large extent on supercell calcns. within d.-functional theory using the approx. local-d. approxn. (LDA) or generalized gradient approxn. (GGA) functionals. Such calcns. are, however, affected by considerable uncertainties assocd. with: (i) the "band-gap problem," which occurs not only in the Kohn-Sham single-particle energies but also in the quasiparticle gap (LDA or GGA) calcd. from total-energy differences, and (ii) supercell finite-size effects. In the case of the oxygen vacancy in ZnO, uncertainties (i) and (ii) have led to a large spread in the theor. predictions, with some calcns. suggesting negligible vacancy concns., even under Zn-rich conditions, and others predicting high concns. Here, we critically assess (i) the different methodologies to correct the band-gap problem. We discuss approaches based on the extrapolation of perturbations which open the band gap, and the self-consistent band-gap correction employing the LDA + U method for d and s states simultaneously. From the comparison of the results of different gap-correction, including also recent results from other literature, we conclude that to date there is no universal scheme for band gap correction in general defect systems. Therefore, we turn instead to classification of different types of defect behavior to provide guidelines on how the phys. correct situation in an LDA defect calcn. can be recovered. (ii) Supercell finite-size effects: We performed test calcns. in large supercells of up to 1728 atoms, resolving a long-standing debate pertaining to image charge corrections for charged defects. We show that once finite-size effects not related to electrostatic interactions are eliminated, the analytic form of the image charge correction as proposed by Makov and Payne leads to size-independent defect formation energies, thus allowing the calcn. of well-converged energies in fairly small supercells. We find that the delocalized contribution to the defect charge (i.e., the defect-induced change of the charge distribution) is dominated by the dielec. screening response of the host, which leads to an unexpected effective 1/L scaling of the image charge energy, despite the nominal 1/L3 scaling of the third-order term. Based on this anal., we suggest that a simple scaling of the first order term by a const. factor (approx. 2/3) yields a simple but accurate image-charge correction for common supercell geometries. Finally, we discuss the theor. controversy pertaining to the formation energy of the O vacancy in ZnO in light of the assessment of different methodologies in the present work, and we review the present exptl. situation on the topic.
- 100Gallino, F.; Pacchioni, G.; Di Valentin, C. Transition levels of defect centers in ZnO by hybrid functionals and localized basis set approach. J. Chem. Phys. 2010, 133, 144512, DOI: 10.1063/1.3491271Google Scholar100https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXht1yrsLvP&md5=afa201a4a8a382a4da533a6cf747247eTransition levels of defect centers in ZnO by hybrid functionals and localized basis set approachGallino, Federico; Pacchioni, Gianfranco; Di Valentin, CristianaJournal of Chemical Physics (2010), 133 (14), 144512/1-144512/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)A hybrid d. functional study based on a periodic approach with localized AO basis functions has been performed in order to compute the optical and thermodn. transition levels between different charge states of defect impurities in bulk ZnO. The theor. approach presented allows the accurate computation of transition levels starting from single particle Kohn-Sham eigenvalues. The results are compared to previous theor. findings and with available exptl. data for a variety of defects ranging from oxygen vacancies, zinc interstitials, and hydrogen and nitrogen impurities. We find that H and Zn impurities give rise to shallow levels; the oxygen vacancy is stable only in the neutral VO and doubly charged VO2 + variants, while N-dopants act as deep acceptor levels. (c) 2010 American Institute of Physics.
- 101Mattioli, G.; Alippi, P.; Filippone, F.; Caminiti, R.; Amore Bonapasta, A. Deep versus shallow behavior of intrinsic defects in rutile and anatase TiO2 polymorphs. J. Phys. Chem. C 2010, 114, 21694– 21704, DOI: 10.1021/jp1041316Google Scholar101https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhsVGktLbO&md5=cc0c3c393bd5f0415c7d45963f454308Deep versus Shallow Behavior of Intrinsic Defects in Rutile and Anatase TiO2 PolymorphsMattioli, Giuseppe; Alippi, Paola; Filippone, Francesco; Caminiti, Ruggero; Bonapasta, Aldo AmoreJournal of Physical Chemistry C (2010), 114 (49), 21694-21704CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)The structural and electronic properties of oxygen vacancies (VOx) and titanium interstitials (Ti(i)) in the bulk of the rutile and anatase forms of TiO2 have been investigated with LSD-GGA + U ab initio simulations. In particular, formation energies of the charged and neutral forms of the VOx and Ti(i) defects as well as the corresponding vertical and thermodn. transition levels have been estd. The achieved results can reconcile the apparent inconsistency of exptl. obsd. deep donor levels with the n-type cond. obsd. in reduced TiO2. They show indeed that both defects give rise to vertical transition levels about 1 eV below the conduction band (CB), in agreement with exptl. measures, and to thermodn. transition levels close to the CB. That is, these defects behave as deep donors, when looking at vertical transitions, and as shallow donors, when the effects of the structural relaxations are taken into account. A major part of the explanation of this behavior is played by the polaron-like character of the defect states, which was already noted, but not deepened, in literature. Finally, it is shown that the application of the U correction to both Ti and O species gives qual. similar results, but with a better agreement to exptl. findings, with respect to the application to Ti only. The former approach gives pretty similar results, for both rutile and anatase bulk properties, to those coming from HSE hybrid functional calcns.
- 102Chakrabarty, A.; Patterson, C. H. Transition levels of defects in ZnO: Total energy and Janak’s theorem methods. J. Chem. Phys. 2012, 137, 054709, DOI: 10.1063/1.4739316Google Scholar102https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtFClt7nO&md5=ff19a927f30b323ec96d0161bcb965beTransition levels of defects in ZnO: Total energy and Janak's theorem methodsChakrabarty, Aurab; Patterson, Charles H.Journal of Chemical Physics (2012), 137 (5), 054709/1-054709/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Transition levels of defects are commonly calcd. using either methods based on total energies of defects in relevant charge states or energy band single particle eigenvalues. The former method requires calcn. of total energies of charged, perfect bulk supercells, as well as charged defect supercells, to obtain defect formation energies for various charge states. The latter method depends on Janak's theorem to obtain differences in defect formation energies for various charge states. Transition levels of VZn, VO, and VZnO vacancy defects in ZnO are calcd. using both methods. The mean abs. deviation in transition level calcd. using either method is 0.3 eV. Relative computational costs and accuracies of the methods are discussed. (c) 2012 American Institute of Physics.
- 103Gerosa, M.; Bottani, C. E.; Caramella, L.; Onida, G.; Di Valentin, C.; Pacchioni, G. Defect calculations in semiconductors through a dielectric-dependent hybrid DFT functional: The case of oxygen vacancies in metal oxides. J. Chem. Phys. 2015, 143, 134702, DOI: 10.1063/1.4931805Google Scholar103https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhs1Sru7nI&md5=d15299e3adcbc6c2c56e16b716691e57Defect calculations in semiconductors through a dielectric-dependent hybrid DFT functional: The case of oxygen vacancies in metal oxidesGerosa, Matteo; Bottani, Carlo Enrico; Caramella, Lucia; Onida, Giovanni; Di Valentin, Cristiana; Pacchioni, GianfrancoJournal of Chemical Physics (2015), 143 (13), 134702/1-134702/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The authors study the behavior of oxygen vacancies in three different metal-oxide semiconductors (rutile and anatase TiO2, monoclinic WO3, and tetragonal ZrO2) using a recently proposed hybrid d.-functional method in which the fraction of exact exchange is material-dependent but obtained ab initio in a self-consistent scheme. In particular, the authors calc. charge-transition levels relative to the oxygen-vacancy defect and compare computed optical and thermal excitation/emission energies with the available exptl. results, shedding light on the underlying excitation mechanisms and related materials properties. This novel approach is able to reproduce not only ground-state properties and band structures of perfect bulk oxide materials but also provides results consistent with the optical and elec. behavior obsd. in the corresponding substoichiometric defective systems. (c) 2015 American Institute of Physics.
- 104Makov, G.; Payne, M. C. Periodic boundary conditions in ab initio calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 1995, 51, 4014– 4022, DOI: 10.1103/physrevb.51.4014Google Scholar104https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2MXjvVGksbk%253D&md5=e43f50b6b2ab0d05c4f834f98f531bbaPeriodic boundary conditions in ab initio calculationsMakov, G.; Payne, M. C.Physical Review B: Condensed Matter (1995), 51 (7), 4014-22CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The convergence of the electrostatic energy in calcns. using periodic boundary conditions is considered in the context of periodic solids and localized aperiodic systems in the gas and condensed phases. Conditions for the abs. convergence of the total energy in periodic boundary conditions are obtained, and their implications for calcns. of the properties of polarized solids under the zero-field assumption are discussed. For aperiodic systems the exact electrostatic energy functional in periodic boundary conditions is obtained. The convergence in such systems is considered in the limit of large supercells, where, in the gas phase, the computational effort is proportional to the vol. It is shown that for neutral localized aperiodic systems in either the gas or condensed phases, the energy can always be made to converge as O (L-5) where L is the linear dimension of the supercell. For charged systems, convergence at this rate can be achieved after adding correction terms to the energy to account for spurious interactions induced by the periodic boundary conditions. These terms are derived exactly for the gas phase and heuristically for the condensed phase.
- 105Freysoldt, C.; Neugebauer, J.; Van de Walle, C. G. Fully ab initio finite-size corrections for charged-defect supercell calculations. Phys. Rev. Lett. 2009, 102, 016402, DOI: 10.1103/PhysRevLett.102.016402Google Scholar105https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXkvVSgsQ%253D%253D&md5=98db09b342c3036fd7020a0bf24540c1Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell CalculationsFreysoldt, Christoph; Neugebauer, Jorg; Van de Walle, Chris G.Physical Review Letters (2009), 102 (1), 016402/1-016402/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)In ab initio theory, defects are routinely modeled by supercells with periodic boundary conditions. Unfortunately, the supercell approxn. introduces artificial interactions between charged defects. Despite numerous attempts, a general scheme to correct for these is not yet available. We propose a new and computationally efficient method that overcomes limitations of previous schemes and is based on a rigorous anal. of electrostatics in dielec. media. Its reliability and rapid convergence with respect to cell size is demonstrated for charged vacancies in diamond and GaAs.
- 106Hine, N. D. M.; Frensch, K.; Foulkes, W. M. C.; Finnis, M. W. Supercell size scaling of density functional theory formation energies of charged defects. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 024112, DOI: 10.1103/physrevb.79.024112Google Scholar106https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXhtlOisbw%253D&md5=e8556d1ce95b494537796cfd62c4d14aSupercell size scaling of density functional theory formation energies of charged defectsHine, N. D. M.; Frensch, K.; Foulkes, W. M. C.; Finnis, M. W.Physical Review B: Condensed Matter and Materials Physics (2009), 79 (2), 024112/1-024112/13CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We address the calcn. within d. functional theory (DFT) of defect formation energies in alumina, a ceramic oxide often considered an archetype for a wide variety of other similar oxides. We examine the conditions under which calcd. defect formation energies, esp. those of charged defects, are independent of the principal approxns. of the plane-wave DFT formalism, most significant of which is the finite-sized supercell in which the calcn. must be performed. We introduce a variation on existing methods of extrapolation to infinite system size to reduce dependence of the result on finite-size errors in the electrostatic and elastic energies of a periodic supercell contg. a defect. We also show how the results can be made relatively insensitive to the choice of exchange-correlation functional and pseudopotential by a suitable treatment of the chem. potentials of the at. species. Our results for formation energies of charged defects are less sensitive than traditional approaches to supercell size and choices of exchange-correlation functional and pseudopotential, and differ notably from previous results.
- 107Corsetti, F.; Mostofi, A. A. System-size convergence of point defect properties: The case of the silicon vacancy. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 035209, DOI: 10.1103/physrevb.84.035209Google Scholar107https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXpslKjtb4%253D&md5=849b1004100e84f959fb96f3566eeae1System-size convergence of point defect properties: The case of the silicon vacancyCorsetti, Fabiano; Mostofi, Arash A.Physical Review B: Condensed Matter and Materials Physics (2011), 84 (3), 035209/1-035209/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We present a comprehensive study of the vacancy in bulk silicon in all its charge states from 2+ to 2-, using a supercell approach within plane-wave d.-functional theory, and systematically quantify the various contributions to the well-known finite size errors assocd. with calcg. formation energies and stable charge state transition levels of isolated defects with periodic boundary conditions. Furthermore, we find that transition levels converge faster with respect to supercell size when only the Γ-point is sampled in the Brillouin zone, as opposed to a dense k-point sampling. This arises from the fact that defect level at the Γ-point quickly converges to a fixed value which correctly describes the bonding at the defect center. Our calcd. transition levels with 1000-atom supercells and Γ-point only sampling are in good agreement with available exptl. results. We also demonstrate two simple and accurate approaches for calcg. the valence band offsets that are required for computing formation energies of charged defects, one based on a potential averaging scheme and the other using maximally-localized Wannier functions (MLWFs). Finally, we show that MLWFs provide a clear description of the nature of the electronic bonding at the defect center that verifies the canonical Watkins model.
- 108Hine, N. D. M.; Dziedzic, J.; Haynes, P. D.; Skylaris, C.-K. Electrostatic interactions in finite systems treated with periodic boundary conditions: Application to linear-scaling density functional theory. J. Chem. Phys. 2011, 135, 204103, DOI: 10.1063/1.3662863Google Scholar108https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhsFeitLjP&md5=0236a335cb8add166315a7bd36b89f5eElectrostatic interactions in finite systems treated with periodic boundary conditions: Application to linear-scaling density functional theoryHine, Nicholas D. M.; Dziedzic, Jacek; Haynes, Peter D.; Skylaris, Chris-KritonJournal of Chemical Physics (2011), 135 (20), 204103/1-204103/17CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within d. functional theory (DFT), with particular emphasis on linear-scaling (LS) DFT. Often, PBCs are not phys. realistic but are an unavoidable consequence of the choice of basis set and the efficacy of using Fourier transforms to compute the Hartree potential. In such cases the effects of PBCs on the calcns. need to be avoided, so that the results obtained represent the open rather than the periodic boundary. The very large systems encountered in LS-DFT make the demands of the supercell approxn. for isolated systems more difficult to manage, and we show cases where the open boundary (infinite cell) result cannot be obtained from extrapolation of calcns. from periodic cells of increasing size. We discuss, implement, and test three very different approaches for overcoming or circumventing the effects of PBCs: truncation of the Coulomb interaction combined with padding of the simulation cell, approaches based on the min. image convention, and the explicit use of open boundary conditions (OBCs). We have implemented these approaches in the ONETEP LS-DFT program and applied them to a range of systems, including a polar nanorod and a protein. We compare their accuracy, complexity, and rate of convergence with simulation cell size. We demonstrate that corrective approaches within PBCs can achieve the OBC result more efficiently and accurately than pure OBC approaches. (c) 2011 American Institute of Physics.
- 109Taylor, S. E.; Bruneval, F. Understanding and correcting the spurious interactions in charged supercells. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 075155, DOI: 10.1103/physrevb.84.075155Google Scholar109https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXhtFagsr7M&md5=65ac0fecdb17c923b91fd790e8f63721Understanding and correcting the spurious interactions in charged supercellsTaylor, Samuel E.; Bruneval, FabienPhysical Review B: Condensed Matter and Materials Physics (2011), 84 (7, Pt. A), 075155/1-075155/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The supercell technique is widely spread for the simulation of charged point defects. Charged defects in a supercell are unfortunately subjected to spurious image interactions, which are usually handled by introducing two correcting terms: a Madelung-type correction that accounts for the electrostatic interactions of repeated charges in a compensating background and a potential alignment term that refers the charged supercell to the electron reservoir. We demonstrate that the Madelung correction already brings a large potential shift that slowly converges as 1/L with increasing supercell sizes. We hence define a potential alignment devoid of any double counting. We finally propose a simple evaluation for the nearest-neighbor interaction that removes the remaining spurious hybridization of the defect wave functions between images. The application of these three corrections together drastically speeds up the convergence with respect to supercell size for all defects that are not too shallow.
- 110Komsa, H.-P.; Rantala, T. T.; Pasquarello, A. Finite-size supercell correction schemes for charged defect calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 045112, DOI: 10.1103/physrevb.86.045112Google Scholar110https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtlSlt7jI&md5=dac99787b4bd15d284b1ff51d90837d9Finite-size supercell correction schemes for charged defect calculationsKomsa, Hannu-Pekka; Rantala, Tapio T.; Pasquarello, AlfredoPhysical Review B: Condensed Matter and Materials Physics (2012), 86 (4), 045112/1-045112/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Various schemes for correcting the finite-size supercell errors in the case of charged defect calcns. are analyzed and their performance for a series of defect systems is compared. We focus on the schemes proposed by Makov and Payne (MP), Freysoldt, Neugebauer, and Van de Walle (FNV), and Lany and Zunger (LZ). The role of the potential alignment is also assessed. We demonstrate a connection between the defect charge distribution and the potential alignment, which establishes a relation between the MP and FNV schemes. Calcns. are performed using supercells of various sizes and the cor. formation energies are compared to the values obtained by extrapolation to infinitely large supercells. For defects with localized charge distributions, we generally find that the FNV scheme improves upon the LZ one, while the MP scheme tends to overcorrect except for point-charge-like defects. We also encountered a class of defects, for which all the correction schemes fail to produce results consistent with the extrapolated values. This behavior is found to be caused by partial delocalization of the defect charge. We assoc. this effect to hybridization between the defect state and the bandedge states of the host. The occurrence of defect charge delocalization also reflects in the evolution of the defect Kohn-Sham levels with increasing supercell size. We discuss the phys. relevance of the latter class of defects.
- 111Chen, W.; Pasquarello, A. Correspondence of defect energy levels in hybrid density functional theory and many-body perturbation theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 115104, DOI: 10.1103/physrevb.88.115104Google Scholar111https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhslCjtL%252FN&md5=2485e6d9bf0c76325dc85248ae973548Correspondence of defect energy levels in hybrid density functional theory and many-body perturbation theoryChen, Wei; Pasquarello, AlfredoPhysical Review B: Condensed Matter and Materials Physics (2013), 88 (11), 115104/1-115104/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We demonstrate the correspondence between charge transition levels of localized point defects in hybrid d. functional theory and in G0W0 many-body perturbation theory. To achieve this correspondence, it is necessary to properly combine the treatments of the finite-size effect, the delocalization error, and the path dependency in the G0W0 scheme. In particular, we introduce a beyond-monopole finite-size electrostatic correction for the eigenvalue which is fully consistent with the analogous correction for the total energy. We illustrate how the comparison with expt. is affected by the calcd. band-edge positions, which unlike the defect levels are sensitive to the adopted electronic-structure method.
- 112Murphy, S. T.; Hine, N. D. M. Anisotropic charge screening and supercell size convergence of defect formation energies. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 094111, DOI: 10.1103/physrevb.87.094111Google Scholar112https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXmvFSmu7c%253D&md5=ff25d3790f21567c5b92f749d7c5842bAnisotropic charge screening and supercell size convergence of defect formation energiesMurphy, Samuel T.; Hine, Nicholas D. M.Physical Review B: Condensed Matter and Materials Physics (2013), 87 (9), 094111/1-094111/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)One of the main sources of error assocd. with the calcn. of defect formation energies using plane-wave d. functional theory (DFT) is finite size error resulting from the use of relatively small simulation cells and periodic boundary conditions. Most widely used methods for correcting this error, such as that of Makov and Payne, assume that the dielec. response of the material is isotropic and can be described using a scalar dielec. const. ε. However, this is strictly only valid for cubic crystals, and cannot work in highly anisotropic cases. Here we introduce a variation of the technique of extrapolation based on the Madelung potential that allows the calcn. of well-converged dil. limit defect formation energies in noncubic systems with highly anisotropic dielec. properties. As an example of the implementation of this technique we study a selection of defects in the ceramic oxide Li2TiO3 which is currently being considered as a lithium battery material and a breeder material for fusion reactors.
- 113Kumagai, Y.; Oba, F. Electrostatics-based finite-size corrections for first-principles point defect calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 195205, DOI: 10.1103/physrevb.89.195205Google Scholar113https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhsFentLbM&md5=d6770228bbb92ebf69b0f59ac048adedElectrostatics-based finite-size corrections for first-principles point defect calculationsKumagai, Yu; Oba, FumiyasuPhysical Review B: Condensed Matter and Materials Physics (2014), 89 (19), 195205/1-195205/15, 15 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Finite-size corrections for charged defect supercell calcns. typically consist of image-charge and potential alignment corrections. Regarding the image-charge correction, Freysoldt, Neugebauer, and Van de Walle (FNV) recently proposed a scheme that constructs the correction energy a posteriori through alignment of the defect-induced potential to a model charge potential. This, however, still has two shortcomings in practice. First, it uses a planar-averaged electrostatic potential for detg. the potential offset, which can not be readily applied to defects with large at. relaxation. Second, Coulomb interaction is screened by a macroscopic scalar dielec. const., which can bring forth large errors for defects in layered and low-dimensional structures. In this study, we use the at. site potential as a potential marker, and extend the FNV scheme by estg. long-range Coulomb interactions with a point charge model in an anisotropic medium. The authors also revisit the conventional potential alignment and show that it is unnecessary for correcting defect formation energies after the image-charge correction is properly applied. A systematic assessment of the accuracy of the extended FNV scheme is performed for defects and impurities in diverse materials: β-Li2TiO3, ZnO, MgO, Al2O3, HfO2, cubic and hexagonal BN, Si, GaAs, and diamond. Defect formation energies with -6 to +3 charges calcd. using supercells contg. around 100 atoms are successfully cor. even after at. relaxation within 0.2 eV compared to those in the dil. limit.
- 114Durrant, T. R.; Murphy, S. T.; Watkins, M. B.; Shluger, A. L. Relation between image charge and potential alignment corrections for charged defects in periodic boundary conditions. J. Chem. Phys. 2018, 149, 024103, DOI: 10.1063/1.5029818Google Scholar114https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhtlSksL7J&md5=5c4b8f93111de9eaf547e96d6a5f0839Relation between image charge and potential alignment corrections for charged defects in periodic boundary conditionsDurrant, T. R.; Murphy, S. T.; Watkins, M. B.; Shluger, A. L.Journal of Chemical Physics (2018), 149 (2), 024103/1-024103/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Charged defects are often studied within the periodic d. functional theory (DFT), but this introduces strong finite-size artifacts. In this work, we develop an electrostatic image interaction correction (IIC) method based on the direct soln. of the Poisson equation for charge models constructed directly from DFT calcns. These IICs are found to be detail-insensitive, depending almost entirely on bulk dielec. properties. As these IICs are not able to fully explain the obsd. finite-size scaling, we explore potential alignment in detail and introduce a novel decompn. to sep. out different contributions. We find that the two main sources of potential alignment are defect image interactions and changes in the no. of atoms present in the supercell. This first effect is accurately predicted by the periodic part of our IIC. The second contribution is unrelated to the IIC and justifies the common observation that the magnitude of finite-size dependence can strongly vary between vacancy and interstitial defects. It can be approx. predicted using at. radius, but is strongly sensitive to the pseudopotential employed. Combined, these developments provide a new justification for known finite-size scaling rules. Our results suggest that for cubic supercells, the Lany-Zunger IIC, combined with simplified potential alignment between neutral systems, can yield accurate corrections in spite of the simplicity of the approach. (c) 2018 American Institute of Physics.
- 115Naik, M. H.; Jain, M. CoFFEE: corrections for formation energy and eigenvalues for charged defect simulations. Comput. Phys. Commun. 2018, 226, 114– 126, DOI: 10.1016/j.cpc.2018.01.011Google Scholar115https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisVegs7w%253D&md5=4c54e6b727c7e465a400026d06f84155CoFFEE: Corrections For Formation Energy and Eigenvalues for charged defect simulations [Erratum to document cited in CA169:479110]Naik, Mit H.; Jain, ManishComputer Physics Communications (2018), 226 (), 114-126CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)Charged point defects in materials are widely studied using D. Functional Theory (DFT) packages with periodic boundary conditions. The formation energy and defect level computed from these simulations need to be cor. to remove the contributions from the spurious long-range interaction between the defect and its periodic images. To this effect, the CoFFEE code implements the Freysoldt-Neugebauer-Van de Walle (FNV) correction scheme. The corrections can be applied to charged defects in a complete range of material shapes and size: bulk, slab (or two-dimensional), wires and nanoribbons. The code is written in Python and features MPI parallelization and optimizations using the Cython package for slow steps.Program title: CoFFEEProgram Files doi:http://dx.doi.org/10.17632/s2x4d542dc.1Licensing provisions: BSD 3-clauseProgramming language: PythonExternal routines/libraries: numpy, scipy, mpi4py, matplotlibNature of problem: Most electronic structure codes based on D. Functional Theory use periodic boundary conditions. This leads to spurious electrostatic interactions during simulation of charged defects, which affects the computed defect formation energy and the defect eigenvalue.Soln. method: We implement the Freysoldt-Neugebauer-Van de Walle (FNV) correction scheme to correct the defect formation energy and eigenvalues. Our implementation can be applied to charged defects in 3D bulk materials as well as materials having 2D and 1D geometries.
- 116Tsunoda, N.; Kumagai, Y.; Takahashi, A.; Oba, F. Electrically benign defect behavior in zinc tin nitride revealed from first principles. Phys. Rev. Appl. 2018, 10, 011001, DOI: 10.1103/physrevapplied.10.011001Google Scholar116https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXisFOku74%253D&md5=96b9af43d6ea4ca6d72b3021959b5771Electrically Benign Defect Behavior in Zinc Tin Nitride Revealed from First PrinciplesTsunoda, Naoki; Kumagai, Yu; Takahashi, Akira; Oba, FumiyasuPhysical Review Applied (2018), 10 (1), 011001CODEN: PRAHB2; ISSN:2331-7019. (American Physical Society)Zinc tin nitride (ZnSnN2) is attracting growing interest as a nontoxic and earth-abundant photoabsorber for thin-film photovoltaics. Carrier transport in ZnSnN2 and consequently cell performance are strongly affected by point defects with deep levels acting as carrier recombination centers. In this study, the point defects in ZnSnN2 are revisited by careful first-principles modeling based on recent exptl. and theor. results. It is shown that ZnSnN2 does not have low-energy defects with deep levels, in contrast to previously reported results. Therefore, ZnSnN2 is more promising as a photoabsorber material than formerly considered.
- 117Chagas da Silva, M.; Lorke, M.; Aradi, B.; Farzalipour Tabriz, M.; Frauenheim, T.; Rubio, A.; Rocca, D.; Deák, P. Self-consistent potential correction for charged periodic systems. Phys. Rev. Lett. 2021, 126, 076401, DOI: 10.1103/PhysRevLett.126.076401Google Scholar117https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXls1Kjtbw%253D&md5=3c6d7af70c2e979859b60fcd54d640c6Self-Consistent Potential Correction for Charged Periodic SystemsChagas da Silva, Mauricio; Lorke, Michael; Aradi, Balint; Farzalipour Tabriz, Meisam; Frauenheim, Thomas; Rubio, Angel; Rocca, Dario; Deak, PeterPhysical Review Letters (2021), 126 (7), 076401CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)Supercell models are often used to calc. the electronic structure of local deviations from the ideal periodicity in the bulk or on the surface of a crystal or in wires. When the defect or adsorbent is charged, a jellium counter charge is applied to maintain overall neutrality, but the interaction of the artificially repeated charges has to be cor., both in the total energy and in the one-electron eigenvalues and eigenstates. This becomes paramount in slab or wire calcns., where the jellium counter charge may induce spurious states in the vacuum. We present here a self-consistent potential correction scheme and provide successful tests of it for bulk and slab calcns.
- 118Astala, R.; Bristowe, P. D. Ab initio study of the oxygen vacancy in SrTiO3. Modell. Simul. Mater. Sci. Eng. 2001, 9, 415– 422, DOI: 10.1088/0965-0393/9/5/306Google Scholar118https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXovVKjs7k%253D&md5=f2646d9656585f775f7f5481c6cb385cAb initio study of the oxygen vacancy in SrTiO3Astala, R.; Bristowe, P. D.Modelling and Simulation in Materials Science and Engineering (2001), 9 (5), 415-422CODEN: MSMEEU; ISSN:0965-0393. (Institute of Physics Publishing)The elec. properties of SrTiO3 are strongly dependent on the O vacancy concn. The authors have studied the at. and electronic properties of a single O vacancy using a local spin d. approxn.-plane-wave pseudopotential method. The total energies, relaxed geometries, valence charge and spin densities, and densities of electron states are calcd. for different charge states of the vacancy. The doubly pos. charged state is the most stable. With some charge states, a spin-polarized defect state is obsd. Also, the authors have evaluated the formation energy of the vacancy in the OO → VO + 0.5O2 process.
- 119Tanaka, T.; Matsunaga, K.; Ikuhara, Y.; Yamamoto, T. First-principles study on structures and energetics of intrinsic vacancies in SrTiO3. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 205213, DOI: 10.1103/physrevb.68.205213Google Scholar119https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3sXpvFyis7s%253D&md5=710ca725f7b6dd80114bef1b1f8990c7First-principles study on structures and energetics of intrinsic vacancies in SrTiO3Tanaka, Tomohito; Matsunaga, Katsuyuki; Ikuhara, Yuichi; Yamamoto, TakahisaPhysical Review B: Condensed Matter and Materials Physics (2003), 68 (20), 205213/1-205213/8CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The authors have performed first-principles plane-wave pseudopotential calcns. to study the electronic structures, structural optimization, and formation energies of intrinsic vacancies in bulk SrTiO3. The anion and cation vacancy-induced levels appeared near the valence- and conduction-band edges in the band gap. The formation energies of isolated vacancies with different charge states were obtained, and the defect reaction energies, such as Sr partial Schottky (VSr2- + VO2+), Ti partial Schottky (VTi4- + 2VO2+), and full Schottky (VSr2- + VTi4- + 3VO2+) were also evaluated. It was found that depending on the at. chem. potentials, the relative stability of the defect species or reactions is different. The overall trend of the stable defect structures can explain the elec. cond. of SrTiO3 for different chem. environments exptl. obsd.
- 120Buban, J. P.; Iddir, H.; Öğüt, S. Structural and electronic properties of oxygen vacancies in cubic and antiferrodistortive phases of SrTiO3. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 69, 180102, DOI: 10.1103/physrevb.69.180102Google Scholar120https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXltVeksrc%253D&md5=6bde7a0ba62131788f320ed6bee1620fStructural and electronic properties of oxygen vacancies in cubic and antiferrodistortive phases of SrTiO3Buban, James P.; Iddir, Hakim; Ogut, SerdarPhysical Review B: Condensed Matter and Materials Physics (2004), 69 (18), 180102/1-180102/4CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The structural and electronic properties of oxygen vacancy (VO) defects in cubic and antiferrodistortive (AFD) phases of bulk SrTiO3 are investigated using results from first principles pseudopotential calcns. By systematically increasing the supercell size from 40 to 320 atoms, the authors show that large supercells are necessary to investigate the structural energetics of this seemingly simple defect properly. With the increase in the supercell size, the formation energy of VO decreases by ∼1.3 eV due to long-ranged relaxations, and the character of the defect wave function changes from a deep to a shallow level. Calcns. indicate that the presence of VO decreases the relative stability of the AFD phase over the cubic phase, consistent with recent exptl. results, which find a lowering of the AFD-cubic transition temp. in samples with higher VO concns.
- 121Luo, W.; Duan, W.; Louie, S. G.; Cohen, M. L. Structural and electronic properties of n-doped and p-doped SrTiO3. Phys. Rev. B: Condens. Matter Mater. Phys. 2004, 70, 214109, DOI: 10.1103/physrevb.70.214109Google Scholar121https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXisleguw%253D%253D&md5=d0728c13de479d02f5d7060d15effb1eStructural and electronic properties of n-doped and p-doped SrTiO3Luo, Weidong; Duan, Wenhui; Louie, Steven G.; Cohen, Marvin L.Physical Review B: Condensed Matter and Materials Physics (2004), 70 (21), 214109/1-214109/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We study the effects of n-doping and p-doping on the structural and electronic properties of SrTiO3 using the ab initio pseudopotential d. functional theory. Two types of electron doping and one type of hole doping are considered: introducing O vacancies, substituting V for Ti, and substituting Sc for Ti. All dopings lead to small structural distortions. The effect of O vacancies on the structure is the largest. Electron doping leads to significant changes of the conduction band. For the O vacancy case, there is a Ti 3d-eg type defect state near the lower conduction band; while in the case of substitutional V, some parts of the lowest conduction bands become very flat. Hole doping yields a larger d. of states at the Fermi level than electron doping. The rigid band model with a Fermi level shift upwards or downwards is not applicable to describe the effects of oxygen vacancy induced electron doping on the electronic properties; however, this may be a reasonable approxn. for the case of hole doping. Finally, we est. the electron-phonon coupling parameters and discuss the implications of this study on supercond. in the SrTiO3 system.
- 122Carrasco, J.; Illas, F.; Lopez, N.; Kotomin, E. A.; Zhukovskii, Y. F.; Evarestov, R. A.; Mastrikov, Y. A.; Piskunov, S.; Maier, J. First-principles calculations of the atomic and electronic structure of F centers in the bulk and on the (001) surface of SrTiO3. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 064106, DOI: 10.1103/physrevb.73.064106Google Scholar122https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XisVaksrY%253D&md5=ab4982d9d7ac3f9620304429ffdd8694First-principles calculations of the atomic and electronic structure of F centers in the bulk and on the (001) surface of SrTiO3Carrasco, J.; Illas, F.; Lopez, N.; Kotomin, E. A.; Zhukovskii, Yu. F.; Evarestov, R. A.; Mastrikov, Yu. A.; Piskunov, S.; Maier, J.Physical Review B: Condensed Matter and Materials Physics (2006), 73 (6), 064106/1-064106/11CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)The at. and electronic structure, formation energy, and the energy barriers for migration were calcd. for the neutral O vacancy point defect (F center) in cubic SrTiO3 employing various implementations of d. functional theory (DFT). Both bulk and TiO2-terminated (001) surface F centers were considered. Supercells of different shapes contg. up to 320 atoms were employed. The limit of an isolated single O vacancy in the bulk corresponds to a 270-atom supercell, in contrast to commonly used supercells contg. ∼40-80 atoms. Calcns. carried out with the hybrid B3PW functional show that the F center level approaches the conduction band bottom to within ∼0.5 eV, as the supercell size increases up to 320 atoms. The anal. of the electronic d. maps indicates, however, that this remains a small-radius center with the two electrons left by the missing O ion being redistributed mainly between the vacancy and the 3d(z2) AOs of the two nearest Ti ions. As for the dynamical properties, the calcd. migration energy barrier in the low oxygen depletion regime is predicted to be 0.4 eV. In contrast, the surface F center exhibits a more delocalized character, which leads to significantly reduced ionization and migration energies. Results obtained are compared with available exptl. data.
- 123Evarestov, 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.20855Google Scholar123https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XmtVamtLs%253D&md5=6538d6f205d0182324c1500719a7becdDFT study of a single F center in cubic SrTiO3 perovskiteEvarestov, 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.
- 124Zhukovskii, Y. F.; Kotomin, E. A.; Evarestov, R. A.; Ellis, D. E. Periodic models in quantum chemical simulations of F centers in crystalline metal oxides. Int. J. Quantum Chem. 2007, 107, 2956– 2985, DOI: 10.1002/qua.21483Google Scholar124https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXht1WktrbO&md5=025fec48166ad3472c2a8eb7790f27fbPeriodic models in quantum chemical simulations of F centers in crystalline metal oxidesZhukovskii, Yuri F.; Kotomin, Eugene A.; Evarestov, Robert A.; Ellis, Donald E.International Journal of Quantum Chemistry (2007), 107 (14), 2956-2985CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)We present a survey of recent first principles simulations of the neutral oxygen vacancies (F centers) existing as native or radiation-induced point defects in various cryst. metal oxides in different forms (bulk, bare substrate surface, and on the interface with metal adsorbates). We mainly consider periodic models in calcns. of point defects using the metal oxide supercell or cyclic clusters. We compare different formalisms of first principles calcns., mostly the D. Functional Theory (DFT) as implemented in the framework of either localized basis set of AOs or delocalized basis sets of plane waves. We analyze in detail the structural and electronic properties of F centers in binary oxides of light metals (MgO and Al2O3), and ternary metal oxides (SrTiO3, BaTiO3, PbTiO3, KNbO3, and PbZrO3 perovskites). When available, we compare results of ab initio periodic defect calcns. with exptl. data, results of the first principles cluster calcns. (both embedded and mol.) as well as with semi-empirical calcns.
- 125Zhukovskii, Y. F.; Kotomin, E. A.; Piskunov, S.; Ellis, D. E. 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.2009.05.023Google Scholar125https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXosValur0%253D&md5=b208b24a4ea69ac5ec531add52e0f52aA comparative ab initio study of bulk and surface oxygen vacancies in PbTiO3, PbZrO3 and SrTiO3 perovskitesZhukovskii, 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.
- 126Zhukovskii, Y. F.; Kotomin, E. A.; Piskunov, S.; Mastrikov, Y. A.; Ellis, D. E. The effect of oxygen vacancies on the atomic and electronic structure of cubic ABO3 perovskite bulk and the (001) surface: Ab initio calculations. Ferroelectrics 2009, 379, 191– 198, DOI: 10.1080/00150190902852240Google Scholar126https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXmsFWksbY%253D&md5=2803fba4a2ae08b9aa99b0fcdcd150f3The effect of oxygen vacancies on the atomic and electronic structure of cubic ABO3 perovskite bulk and the (001) surface: ab initio calculationsZhukovskii, Y. F.; Kotomin, E. A.; Piskunov, S.; Mastrikov, Y. A.; Ellis, D. E.Ferroelectrics (2009), 379 (), 191-198CODEN: FEROA8; ISSN:0015-0193. (Taylor & Francis, Inc.)We employed the hybrid DFT-LCAO and GGA-PW approaches as implemented in the CRYSTAL and VASP codes, resp., for large supercell calcns. of neutral O vacancies with trapped electrons (known as 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 for three perovskites under study. We demonstrate how the difference in chem. compn. of host materials leads to quite different defect properties.
- 127Djermouni, M.; Zaoui, A.; Kacimi, S.; Bouhafs, B. Vacancy defects in strontium titanate: Ab initio calculation. Comput. Mater. Sci. 2010, 49, 904– 909, DOI: 10.1016/j.commatsci.2010.06.045Google Scholar127https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXpvFeit74%253D&md5=df3cc184e0977f96a32020527ec97812Vacancy defects in strontium titanate: Ab initio calculationDjermouni, M.; Zaoui, A.; Kacimi, S.; Bouhafs, B.Computational Materials Science (2010), 49 (4), 904-909CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)A full-potential linearized-augmented plane-wave calcn. was used to study structural and electronic properties of defected SrTiO3 with two concns. of oxygen vacancies. These properties were found to remarkably depend on the oxygen vacancy concn. The defect states assocd. with oxygen vacancies are identified within the energy gap. The ground state properties, equil. lattice consts., bulk moduli, the formation energy, densities of electron states, band structures and charge d. are detd. and discussed for this compd. It is found that an oxygen vacancy creates more localized in-gap states. With increasing oxygen deficiency, the electrons left behind by oxygen removal not only localize on Sr (Ti) 3d orbitals but also on the vacancy sites. Model structures of 2 × 2 × n (n = 1, 2, 3 and 4) supercells are used.
- 128Ertekin, E.; Srinivasan, V.; Ravichandran, J.; Rossen, P. B.; Siemons, W.; Majumdar, A.; Ramesh, R.; Grossman, J. C. Interplay between intrinsic defects, doping, and free carrier concentration in SrTiO3 thin films. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 195460, DOI: 10.1103/physrevb.85.195460Google Scholar128https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtVWju77N&md5=2f29fe543bf2470538af3a6f2fd76bd6Interplay between intrinsic defects, doping, and free carrier concentration in SrTiO3 thin filmsErtekin, Elif; Srinivasan, Varadharajan; Ravichandran, Jayakanth; Rossen, Pim B.; Siemons, Wolter; Majumdar, Arun; Ramesh, Ramamoorthy; Grossman, Jeffrey C.Physical Review B: Condensed Matter and Materials Physics (2012), 85 (19), 195460/1-195460/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Using both computational and exptl. anal., we demonstrate a rich point-defect phase diagram in doped strontium titanate as a function of thermodn. variables such as oxygen partial pressure and electronic chem. potential. Computational modeling of point-defect energetics demonstrates that a complex interplay exists between dopants, thermodn. parameters, and intrinsic defects in thin films of SrTiO3 (STO). We synthesize STO thin films via pulsed laser deposition and explore this interplay between intrinsic defects, doping, compensation, and carrier concn. Our point-defect anal. (i) demonstrates that careful control over growth conditions can result in the tunable presence of anion and cation vacancies, (ii) suggests that compensation mechanisms will pose intrinsic limits on the dopability of perovskites, and (iii) provides a guide for tailoring the properties of doped perovskite thin films.
- 129Evarestov, R.; Blokhin, E.; Gryaznov, D.; Kotomin, E. A.; Merkle, R.; Maier, J. Jahn-Teller effect in the phonon properties of defective SrTiO3 from first principles. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 174303, DOI: 10.1103/physrevb.85.174303Google Scholar129https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XpvVyqtbs%253D&md5=4037eb38ec4441d8848fc13e475ef9b8Jahn-Teller effect in the phonon properties of defective SrTiO3 from first principlesEvarestov, Robert; Blokhin, Evgeny; Gryaznov, Denis; Kotomin, Eugene A.; Merkle, Rotraut; Maier, JoachimPhysical Review B: Condensed Matter and Materials Physics (2012), 85 (17), 174303/1-174303/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Using a hybrid d. functional theory method combined with LCAO basis set and periodic supercell approach, the at., electronic structure, and phonon properties were calcd. for SrTiO3 contg. either Fe4+ substituting host Ti4+ ions or neutral oxygen vacancies Vo. For both defects, the Jahn-Teller effect occurs, thus reducing the cubic symmetry of a perfect crystal and leading to the appearance of both Raman- and IR-active vibrational modes. The calcd. phonon densities of states and group-theor. anal. of defect-induced phonon frequencies were used for the interpretation of the relevant exptl. data, once defect-induced local modes are identified. The temp. dependence of the Vo formation energy based on the calcd. Gibbs free energy was also compared with expts., and the phonon contribution therein estd.
- 130Lin, 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.86.161102Google Scholar130https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xhslyls7jE&md5=d37a3be9a826896daf6f0aeca4533b43Orbital ordering under reduced symmetry in transition metal perovskites: oxygen vacancy in SrTiO3Lin, 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.
- 131Al-Hamadany, R.; Goss, J. P.; Briddon, P. R.; Mojarad, S. A.; Al-Hadidi, M.; O’Neill, A. G.; Rayson, M. J. Oxygen vacancy migration in compressively strained SrTiO3. J. Appl. Phys. 2013, 113, 024108, DOI: 10.1063/1.4775397Google Scholar131https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXmvVOlsg%253D%253D&md5=ba0cd1ff770cad3defd6e23a1b8bfe1fOxygen vacancy migration in compressively strained SrTiO3Al-Hamadany, Raied; Goss, J. P.; Briddon, P. R.; Mojarad, Shahin A.; Al-Hadidi, Meaad; O'Neill, A. G.; Rayson, M. J.Journal of Applied Physics (Melville, NY, United States) (2013), 113 (2), 024108/1-024108/8CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)The intrinsic properties of SrTiO3 render it promising in applications such as gate dielecs. and capacitors. However, there is growing evidence that O vacancies significantly impact upon its use, with the diffusion and deep donor level of the O vacancy leading to elec. leakage. Where grown epitaxially on a lattice mismatched substrate, SrTiO3 undergoes bi-axial strain, altering its crystal structure and electronic properties. We present the results of first-principles simulations to evaluate the impact of strain in a (001) plane upon the migration of O vacancies. In the range of strains consistent with common substrate materials, diffusion energies in different directions are significantly affected, and for high values of strain may be altered by as much as a factor of 2. The resulting diffusion anisotropy is expected to impact upon the rate at which O vacancies are injected into the films under bias, a crit. factor in the leakage and resistive switching seen in this material. (c) 2013 American Institute of Physics.
- 132Souto-Casares, J.; Spaldin, N. A.; Ederer, C. Oxygen vacancies in strontium titanate: A DFT + DMFT study. Phys. Rev. Res. 2021, 3, 023027, DOI: 10.1103/physrevresearch.3.023027Google Scholar132https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhsFSgtLrF&md5=c4997b6bab87abe3beafc1107282acd7Oxygen vacancies in strontium titanate: A DFT+DMFT studySouto-Casares, Jaime; Spaldin, Nicola A.; Ederer, ClaudePhysical Review Research (2021), 3 (2), 023027CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)We address the long-standing question of the nature of oxygen vacancies in strontium titanate, using a combination of d. functional theory and dynamical mean-field theory (DFT+DMFT) to investigate in particular the effect of vacancy-site correlations on the electronic properties. Our approach uses a minimal low-energy electronic subspace including the Ti-t2g orbitals plus an addnl. vacancy-centered Wannier function, and it provides an intuitive and phys. transparent framework to study the effect of the local electron-electron interactions on the excess charge introduced by the oxygen vacancies. We est. the strength of the screened interaction parameters using the constrained RPA, and we find a sizable Hubbard U parameter for the vacancy orbital. Our main finding, which reconciles previous exptl. and computational results, is that the ground state is either a state with double occupation of the localized defect state or a state with a singly occupied vacancy and one electron transferred to the conduction band. The balance between these two competing states is detd. by the strength of the interaction both on the vacancy and the Ti sites, and on the Ti-Ti distance across the vacancy. Finally, we contrast the case of vacancy doping in SrTiO3 with doping via La substitution, and we show that the latter is well described by a simple rigid-band picture.
- 133Xiong, K.; Robertson, J.; Clark, S. J. Behavior of hydrogen in wide band gap oxides. J. Appl. Phys. 2007, 102, 083710, DOI: 10.1063/1.2798910Google Scholar133https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXht1Gkt7fO&md5=ca5814ec1b70f32591e4c0e5643a2e2dBehavior of hydrogen in wide band gap oxidesXiong, K.; Robertson, J.; Clark, S. J.Journal of Applied Physics (2007), 102 (8), 083710/1-083710/13CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)The energy levels of interstitial hydrogen in various wide band gap oxides are calcd. using a d. function based method that does not need a band gap correction. The pos. charge state has a large stabilization energy due to the formation of an O-H bond. The hydrogen level is shallow in CdO, ZrO2, HfO2, La2O3, LaAlO3, SnO2, TiO2, SrTiO3, PbTiO3, and SrBi2Ta2O9, but deep in MgO, Al2O3, SiO2, ZrSiO4, HfSiO4, and SrZrO3. It is borderline in SrO. The predictions agree well with the exptl. behavior of muonium in these oxides.
- 134Bork, N.; Bonanos, N.; Rossmeisl, J.; Vegge, T. Simple descriptors for proton-conducting perovskites from density functional theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 014103, DOI: 10.1103/physrevb.82.014103Google Scholar134https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXpsFymtrY%253D&md5=a31ae7b16f02386b8a446814390063d2Simple descriptors for proton-conducting perovskites from density functional theoryBork, N.; Bonanos, N.; Rossmeisl, J.; Vegge, T.Physical Review B: Condensed Matter and Materials Physics (2010), 82 (1), 014103/1-014103/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)A series of (pseudo)cubic perovskites, ABO3, were investigated using the DFT-PW91 method. The structures were optimized and thermodn. properties and activation energies for the relevant steps of the hydrogen/proton diffusion mechanism were calcd. using the nudged elastic band path technique. We found a strong correlation between the O-H binding energy for hydrogen/proton uptake in perovskites and the energy barriers involved in the obsd. Grotthuss-type diffusion process. We demonstrated the possibility of estg. diffusion rates based on O-H binding energy and temp. only, without detg. transition states and vibrational frequencies. We detd. the binding energy providing the optimal tradeoff between occupation and diffusion rate at a given temp., and finally we showed how these correlations can be used to suggest candidate materials with improved kinetic properties for potential application as hydrogen permeable membranes and proton-conducting electrolytes.
- 135Baker, J. N.; Bowes, P. C.; Irving, D. L. Hydrogen solubility in donor-doped SrTiO3 from first principles. Appl. Phys. Lett. 2018, 113, 132904, DOI: 10.1063/1.5047793Google Scholar135https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhvVSitL3E&md5=d5a52d5c5ee17799dfc41189e3ab5847Hydrogen solubility in donor-doped SrTiO3 from first principlesBaker, Jonathon N.; Bowes, Preston C.; Irving, Douglas L.Applied Physics Letters (2018), 113 (13), 132904/1-132904/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)Hydrogen contamination of strontium titanate (STO) during processing and usage is a known problem. However, it is relatively little-studied due to the difficulty in quantifying the amt. of hydrogen that dissolves in the lattice. Here, the authors use hybrid exchange-correlation d. functional theory calcns. as input to a grand canonical thermodn. framework to est. hydrogen soly. and site preferences in donor-doped STO. The results provide clear theor. evidence that hydrogen contamination in donor-doped STO occurs at a low enough level to essentially ignore. But, this simple conclusion belies hydrogen's rich behavior; unlike many dopants, it is able to easily change its incorporation site in response to changes in processing conditions. Overall, the findings are consistent with prevailing wisdom and suggest that the presented first principles approach could be used for systematic exploration of hydrogen's impact as a function of doping and processing in this and other wide band gap materials. (c) 2018 American Institute of Physics.
- 136T-Thienprasert, J.; Fongkaew, I.; Singh, D. J.; Du, M.-H.; Limpijumnong, S. Identification of hydrogen defects in SrTiO3 by first-principles local vibration mode calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 125205, DOI: 10.1103/physrevb.85.125205Google Scholar136https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xpt1yrtb8%253D&md5=d07a09ba464e8450f4f1c7fdf167c955Identification of hydrogen defects in SrTiO3 by first-principles local vibration mode calculationsT.-Thienprasert, Jiraroj; Fongkaew, Ittipon; Singh, D. J.; Du, M.-H.; Limpijumnong, SukitPhysical Review B: Condensed Matter and Materials Physics (2012), 85 (12), 125205/1-125205/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)For over three decades, the IR spectroscopy peaks of around 3500 cm-1 obsd. in hydrogen-doped SrTiO3 samples have been assigned to an interstitial hydrogen (Hi) attached to a lattice oxygen with two possible configuration models: the octahedral edge (OE) and the cubic face (CF) models. Based on our first-principles calcns. of Hi around O, both OE and CF configurations are not energetically stable. Starting from either configuration, the Hi would spontaneously relax into an off axis (OA) site; lowering the energy by 0.25 eV or more. The calcd. vibrational frequency of 2745 cm-1 for OA invalidates the assignment of Hi to the obsd. 3500 cm-1 peak. In addn., the calcd. diffusion barrier is low, suggesting that Hi can be easily annealed out. We propose that the obsd. peaks around 3500 cm-1 are assocd. with defect complexes. A Sr vacancy (VSr) can trap Hi and form a H-VSr complex which is both stable and has the frequency in agreement with the obsd. main peak. The complex can also trap another Hi and form 2H-VSr; consistent with the obsd. addnl. peaks at slightly higher frequencies (3510-3530 cm-1).
- 137Münch, W.; Kreuer, K.-D.; Seifertli, G.; Majer, J. A quantum molecular dynamics study of proton diffusion in SrTiO3 and CaTiO3. Solid State Ionics 1999, 125, 39– 45, DOI: 10.1016/s0167-2738(99)00156-3Google ScholarThere is no corresponding record for this reference.
- 138Münch, W.; Kreuer, K.-D.; Seifert, G.; Maier, J. Proton diffusion in perovskites: Comparison between BaCeO3, BaZrO3, SrTiO3, and CaTiO3 using quantum molecular dynamics. Solid State Ionics 2000, 136-137, 183– 189, DOI: 10.1016/s0167-2738(00)00304-0Google Scholar138https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXlslChtA%253D%253D&md5=ee27f863e08c3122ec0796a59501f2f6Proton diffusion in perovskites: comparison between BaCeO3, BaZrO3, SrTiO3, and CaTiO3 using quantum molecular dynamicsMunch, W.; Kreuer, K.-D.; Seifert, G.; Maier, J.Solid State Ionics (2000), 136-137 (), 183-189CODEN: SSIOD3; ISSN:0167-2738. (Elsevier Science B.V.)Quantum mol. dynamics simulations have been carried out to calc. the diffusion coeffs. and the activation energies of protonic defects in BaCeO3, BaZrO3, SrTiO3 and CaTiO3. The calcd. activation energies are in agreement with exptl. data within statistical uncertainty. The activation energy for proton transfer is found to be significantly affected by the repulsive interaction of the proton with the B-cation (B = Ce, Zr, Ti). A phys. interpretation for the measured infra-red spectra can also be obtained from the numerical results.
- 139Villamagua, L.; Barreto, R.; Prócel, L. M.; Stashans, A. Hydrogen impurity in SrTiO3: Structure, electronic properties and migration. Phys. Scr. 2007, 75, 374– 378, DOI: 10.1088/0031-8949/75/3/024Google Scholar139https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXjsFCnsb0%253D&md5=c7722f1c21a227304ff64a6b32db8a73Hydrogen impurity in SrTiO3: structure, electronic properties and migrationVillamagua, Luis; Barreto, Rafael; Procel, Luis Miguel; Stashans, ArvidsPhysica Scripta (2007), 75 (3), 374-378CODEN: PHSTBO; ISSN:0031-8949. (Institute of Physics Publishing)The present paper reports a computational investigation of the geometry and electronic structure as well as the migration of a hydrogen impurity in the cubic SrTiO3 crystal. The study is done using an approach based on the Hartree-Fock theory and developed for periodic systems. It is found that the H impurity forms the so-called OH group at the equil. Anal. of electron d. within the defective region implies the enhancement in covalent chem. bonding. A possible defect migration has been also investigated.
- 140Kohn, W. Density functional and density matrix method scaling linearly with the number of atoms. Phys. Rev. Lett. 1996, 76, 3168– 3171, DOI: 10.1103/physrevlett.76.3168Google Scholar140https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XisVKntb0%253D&md5=d06ca53bef9cd0c721b8f3bfc4f0abd4Density functional and density matrix method scaling linearly with the number of atomsKohn, W.Physical Review Letters (1996), 76 (17), 3168-71CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)A widely applicable "nearsightedness" principle is first discussed as the phys. basis for the existence of computational methods scaling linearly with the no. of atoms. This principle applies to the one particle d. matrix n(r,r') but not to individual eigenfunctions. A variational principle for n(r,r') is derived in which, by the use of a penalty functional P[n(r,r')], the (difficult) idempotency of n(r,r') need not be assured in advance but is automatically achieved. The method applies to both insulators and metals.
- 141Prodan, E.; Kohn, W. Nearsightedness of electronic matter. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 11635– 11638, DOI: 10.1073/pnas.0505436102Google Scholar141https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXpsFGgtr8%253D&md5=436e15a263cdc2def8182fdac61e3714Nearsightedness of electronic matterProdan, E.; Kohn, W.Proceedings of the National Academy of Sciences of the United States of America (2005), 102 (33), 11635-11638CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)In an earlier paper, W. Kohn had qual. introduced the concept of "nearsightedness" of electrons in many-atom systems. It can be viewed as underlying such important ideas as Pauling's "chem. bond," "transferability," and Yang's computational principle of "divide and conquer.". It describes the fact that, for fixed chem. potential, local electronic properties, such as the d. n(r), depend significantly on the effective external potential only at nearby points. Changes of that potential, no matter how large, beyond a distance R have limited effects on local electronic properties, which rapidly tend to zero as a function of R. In the present paper, the concept is first sharpened for representative models of uncharged fermions moving in external potentials, and then the effects of electron-electron interactions and of perturbing external charges are discussed.
- 142Skylaris, C.-K.; Mostofi, A. A.; Haynes, P. D.; Pickard, C. J.; Payne, M. C. Accurate kinetic energy evaluation in electronic structure calculations with localized functions on real space grids. Comput. Phys. Commun. 2001, 140, 315– 322, DOI: 10.1016/s0010-4655(01)00248-xGoogle Scholar142https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXnslOksbo%253D&md5=cd1e9a053aa7a7747803c182b17dd367Accurate kinetic energy evaluation in electronic structure calculations with localized functions on real space gridsSkylaris, Chris-Kriton; Mostofi, Arash A.; Haynes, Peter D.; Pickard, Chris J.; Payne, Mike C.Computer Physics Communications (2001), 140 (3), 315-322CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier Science B.V.)We present a method for calcg. the kinetic energy of localized functions represented on a regular real space grid. This method uses fast Fourier transforms applied to restricted regions commensurate with the simulation cell and is applicable to grids of any symmetry. In the limit of large systems it scales linearly with system size. Comparison with the finite difference approach shows that our method offers significant improvements in accuracy without loss of efficiency.
- 143O’Regan, D. D.; Hine, N. D. M.; Payne, M. C.; Mostofi, A. A. Linear-scaling DFT + U with full local orbital optimization. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 085107Google Scholar143https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XkslChu74%253D&md5=13902cf9811a2525569ea4b635047970Linear-scaling DFT + U with full local orbital optimizationO'Regan, David D.; Hine, Nicholas D. M.; Payne, Mike C.; Mostofi, Arash A.Physical Review B: Condensed Matter and Materials Physics (2012), 85 (8), 085107/1-085107/10CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We present an approach to the DFT + U method (d. functional theory + Hubbard model) within which the computational effort for calcn. of ground-state energies and forces scales linearly with system size. We employ a formulation of the Hubbard model using nonorthogonal projector functions to define the localized subspaces, and we apply it to a local orbital DFT method including in situ orbital optimization. The resulting approach thus combines linear-scaling and systematic variational convergence. We demonstrate the scaling of the method by applying it to nickel-oxide nanoclusters with sizes exceeding 7000 atoms.
- 144O’Regan, D. D.; Hine, N. D. M.; Payne, M. C.; Mostofi, A. A. Projector self-consistent DFT + U using nonorthogonal generalized Wannier functions. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 081102Google Scholar144https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXhtFWlurnF&md5=7a02fd62b1de15e15a034185f268e4faProjector self-consistent DFT+U using nonorthogonal generalized Wannier functionsO'Regan, David D.; Hine, Nicholas D. M.; Payne, Mike C.; Mostofi, Arash A.Physical Review B: Condensed Matter and Materials Physics (2010), 82 (8), 081102/1-081102/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We present a formulation of the d.-functional theory+Hubbard model (DFT+U) method that is self-consistent over the choice of Hubbard projectors used to define the correlated subspaces. In order to overcome the arbitrariness in this choice, we propose the use of nonorthogonal generalized Wannier functions (NGWFs) as projectors for the DFT+U correction. We iteratively refine these NGWF projectors and, hence, the DFT+U functional, such that the correlated subspaces are fully self-consistent with the DFT+U ground state. We discuss the convergence characteristics of this algorithm and compare ground-state properties thus computed with those calcd. using hydrogenic projectors. Our approach is implemented within, but not restricted to, a linear-scaling DFT framework, opening the path to DFT+U calcns. on systems of unprecedented size.
- 145O’Regan, D. D.; Payne, M. C.; Mostofi, A. A. Subspace representations in ab initio methods for strongly correlated systems. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 245124Google Scholar145https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXosVGhtbg%253D&md5=ebf3a22f634a84fb961b82ac3cf8c179Subspace representations in ab initio methods for strongly correlated systemsO'Regan, David D.; Payne, Mike C.; Mostofi, Arash A.Physical Review B: Condensed Matter and Materials Physics (2011), 83 (24), 245124/1-245124/14CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We present a generalized definition of subspace occupancy matrixes in ab initio methods for strongly correlated materials, such as DFT + U (d. functional theory + Hubbard U) and DFT + DMFT (dynamical mean-field theory), which is appropriate to the case of nonorthogonal projector functions. By enforcing the tensorial consistency of all matrix operations, we are led to a subspace-projection operator for which the occupancy matrix is tensorial and accumulates only contributions which are local to the correlated subspace at hand. For DFT + U, in particular, the resulting contributions to the potential and ionic forces are automatically Hermitian, without resort to symmetrization, and localized to their corresponding correlated subspace. The tensorial invariance of the occupancies, energies, and ionic forces is preserved. We illustrate the effect of this formalism in a DFT + U study using self-consistently detd. projectors.
- 146Hine, N. D. M.; Robinson, M.; Haynes, P. D.; Skylaris, C.-K.; Payne, M. C.; Mostofi, A. A. Accurate ionic forces and geometry optimization in linear-scaling density-functional theory with local orbitals. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 195102, DOI: 10.1103/physrevb.83.195102Google Scholar146https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXotVOmsL0%253D&md5=7ee40e861960dedb99ecc6a1f0c92111Accurate ionic forces and geometry optimization in linear-scaling density-functional theory with local orbitalsHine, Nicholas D. M.; Robinson, Mark; Haynes, Peter D.; Skylaris, Chris-Kriton; Payne, Mike C.; Mostofi, Arash A.Physical Review B: Condensed Matter and Materials Physics (2011), 83 (19), 195102/1-195102/10CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Linear scaling methods for d.-functional theory (DFT) simulations are formulated in terms of localized orbitals in real space, rather than the delocalized eigenstates of conventional approaches. In local-orbital methods, relative to conventional DFT, desirable properties can be lost to some extent, such as the translational invariance of the total energy of a system with respect to small displacements and the smoothness of the potential-energy surface. This has repercussions for calcg. accurate ionic forces and geometries. In this work we present results from ONETEP, our linear scaling method based on localized orbitals in real space. The use of psinc functions for the underlying basis set and on-the-fly optimization of the localized orbitals results in smooth potential-energy surfaces that are consistent with ionic forces calcd. using the Hellmann-Feynman theorem. This enables accurate geometry optimization to be performed. Results for surface reconstructions in silicon are presented, along with three example systems demonstrating the performance of a quasi-Newton geometry optimization algorithm: an org. zwitterion, a point defect in an ionic crystal, and a semiconductor nanostructure.
- 147Ruiz-Serrano, Á.; Hine, N. D. M.; Skylaris, C.-K. Pulay forces from localized orbitals optimized in situ using a psinc basis set. J. Chem. Phys. 2012, 136, 234101, DOI: 10.1063/1.4728026Google Scholar147https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xos12gs70%253D&md5=d96ba78c5c485fde2591f67d7bd6f93fPulay forces from localized orbitals optimized in situ using a psinc basis setRuiz-Serrano, Alvaro; Hine, Nicholas D. M.; Skylaris, Chris-KritonJournal of Chemical Physics (2012), 136 (23), 234101/1-234101/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)In situ optimization of a set of localized orbitals with respect to a systematically improvable basis set independent of the position of the atoms, such as psinc functions, would theor. eliminate the correction due to Pulay forces from the total ionic forces. We demonstrate that for strict localization constraints, esp. with small localization regions, there can be non-negligible Pulay forces that must be calcd. as a correction to the Hellmann-Feynman forces in the ground state. Geometry optimization calcns., which rely heavily upon accurate evaluation of the total ionic forces, show much better convergence when Pulay forces are included. The more conventional case, where the local orbitals remain fixed to pseudo-AO multiple-ζ basis sets, also benefits from this implementation. We have validated the method on several test cases, including a DNA fragment with 1045 atoms. (c) 2012 American Institute of Physics.
- 148Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865– 3868, DOI: 10.1103/physrevlett.77.3865Google Scholar148https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XmsVCgsbs%253D&md5=55943538406ee74f93aabdf882cd4630Generalized gradient approximation made simplePerdew, John P.; Burke, Kieron; Ernzerhof, MatthiasPhysical 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.
- 149Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 2008, 100, 136406, DOI: 10.1103/physrevlett.100.136406Google Scholar149https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXktlygt7c%253D&md5=bb5e35a295ab7af85d65ac410d6f898cRestoring the Density-Gradient Expansion for Exchange in Solids and SurfacesPerdew, John P.; Ruzsinszky, Adrienn; Csonka, Gabor I.; Vydrov, Oleg A.; Scuseria, Gustavo E.; Constantin, Lucian A.; Zhou, Xiaolan; Burke, KieronPhysical Review Letters (2008), 100 (13), 136406/1-136406/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Popular modern generalized gradient approxns. are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of d. gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approxn. that improves equil. properties of densely packed solids and their surfaces.
- 150The Rappe group. PBE GGA PSP database. https://www.sas.upenn.edu/rappegroup/research/pseudo-potential-gga.html (accessed Feb 3, 2022).Google ScholarThere is no corresponding record for this reference.
- 151Rappe, A. M.; Rabe, K. M.; Kaxiras, E.; Joannopoulos, J. D. Optimized pseudopotentials. Phys. Rev. B: Condens. Matter Mater. Phys. 1990, 41, 1227– 1230, DOI: 10.1103/physrevb.41.1227Google Scholar151https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC2sfltVGqug%253D%253D&md5=b962588f113d88f2270ca2209ecc796fOptimized pseudopotentialsRappe; Rabe; Kaxiras; JoannopoulosPhysical review. B, Condensed matter (1990), 41 (2), 1227-1230 ISSN:0163-1829.There is no expanded citation for this reference.
- 152Himmetoglu, B.; Wentzcovitch, R. M.; Cococcioni, M. First-principles study of electronic and structural properties of CuO. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 115108, DOI: 10.1103/physrevb.84.115108Google Scholar152https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXht1Kju7%252FJ&md5=15fceb412ca3ae11019bd8b7bc25ea60First-principles study of electronic and structural properties of CuOHimmetoglu, Burak; Wentzcovitch, Renata M.; Cococcioni, MatteoPhysical Review B: Condensed Matter and Materials Physics (2011), 84 (11), 115108/1-115108/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We investigate the electronic and structural properties of CuO, which shows significant deviations from the trends obeyed by other transition-metal monoxides. Using an extended Hubbard-based corrective functional, we uncover an orbitally ordered insulating ground state for the cubic phase of this material, which was expected but, to the best of our knowledge, was not found in the literature. This insulating state results from a fine balance between the tendency of Cu to complete its d-shell and Hund's rule magnetism. Starting from the ground state for the cubic phase, we also study tetragonal distortions of the unit cell (recently reported in expts.) and identify the equil. structure. Our calcns. reveal an unexpected richness of possible magnetic and orbital orders, relatively close in energy to the ground state, whose stability depends on the sign and nature of distortion.
- 153Plata, J. J.; Márquez, A. M.; Sanz, J. F. Communication: Improving the density functional theory+U description of CeO2 by including the contribution of the O 2p electrons. J. Chem. Phys. 2012, 136, 041101, DOI: 10.1063/1.3678309Google Scholar153https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtVOjtLg%253D&md5=8d5aa6a3461d037f0c51277203ebac7cCommunication: Improving the density functional theory + U description of CeO2 by including the contribution of the O 2p electronsPlata, Jose J.; Marquez, Antonio M.; Sanz, Javier Fdez.Journal of Chemical Physics (2012), 136 (4), 041101/1-041101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)D. functional theory (DFT) based approaches within the local-d. approxn. or generalized gradient approxn. frameworks fail to predict the correct electron localization in strongly correlated systems due to the lack of cancellation of the Coulomb self-interaction. This problem might be circumvented either by using hybrid functionals or by introducing a Hubbard-like term to account for the on site interactions. This latter DFT + U approach is less expensive and therefore more practical for extensive calcns. in solid-state computational simulations. By and large, the U term only affects the metal electrons, in our case the Ce 4f ones. In the present work, we report a systematic anal. of the effect of adding such a U term also to the oxygen 2p electrons. We find that using a set of Uf = 5 eV and Up = 5eV effective terms leads to improved description of the lattice parameters, band gaps, and formation and redn. energies of CeO2. (c) 2012 American Institute of Physics.
- 154Marzari, N.; Mostofi, A. A.; Yates, J. R.; Souza, I.; Vanderbilt, D. Maximally localized Wannier functions: Theory and applications. Rev. Mod. Phys. 2012, 84, 1419– 1475, DOI: 10.1103/revmodphys.84.1419Google Scholar154https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXit1SmtL4%253D&md5=e6c12b131e81c188931582e3d126b18dMaximally localized Wannier functions: theory and applicationsMarzari, Nicola; Mostofi, Arash A.; Yates, Jonathan R.; Souza, Ivo; Vanderbilt, DavidReviews of Modern Physics (2012), 84 (4), 1419-1475CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)A review. The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrixes, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calcn. into a unique set of maximally localized Wannier functions, accomplishing the solid-state equiv. of constructing localized MOs, or "Boys orbitals" as previously known from the chem. literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chem. bonding, or as a local probe of phenomena related to elec. polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.
- 155Sathe, P.; Harper, F.; Roy, R. Compactly supported Wannier functions and strictly local projectors. J. Phys. A: Math. Theor. 2021, 54, 335302, DOI: 10.1088/1751-8121/ac1167Google ScholarThere is no corresponding record for this reference.
- 156Stukowski, A. Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool. Modell. Simul. Mater. Sci. Eng. 2009, 18, 015012, DOI: 10.1088/0965-0393/18/1/015012Google ScholarThere is no corresponding record for this reference.
- 157Baker, J.; Kessi, A.; Delley, B. The generation and use of delocalized internal coordinates in geometry optimization. J. Chem. Phys. 1996, 105, 192– 212, DOI: 10.1063/1.471864Google Scholar157https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XjvVOnsLo%253D&md5=4bdf29f37f4a674f627ac5f47eb700e6The generation and use of delocalized internal coordinates in geometry optimizationBaker, Jon; Kessi, Alain; Delley, BernardJournal of Chemical Physics (1996), 105 (1), 192-212CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Following the earlier work of Pulay and Fogarasi [J. Chem. Phys. 96, 2856 (1992)], the authors present an alternative definition of natural internal coordinates. This set of delocalized internal coordinates can be generated for any mol. topol., no matter how complicated, and is fully nonredundant. Using an appropriate Schmidt-orthogonalization procedure, all std. bond length, bond angle, and dihedral angle constraints can be imposed within our internal coordinate scheme. Combinatorial constraints (in which sums or differences of stretches, bends, and torsions remain const.) can also be imposed. Optimization on some fairly large systems (50-100 atoms) show that delocalized internal coordinates are far superior to Cartesians even with reliable Hessian information available at the starting geometry.
- 158Andzelm, J.; King-Smith, R. D.; Fitzgerald, G. Geometry optimization of solids using delocalized internal coordinates. Chem. Phys. Lett. 2001, 335, 321– 326, DOI: 10.1016/s0009-2614(01)00030-6Google Scholar158https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXhsFSjsLs%253D&md5=c29d29c73ec4ad50ebd924b409d08613Geometry optimization of solids using delocalized internal coordinatesAndzelm, J.; King-Smith, R. D.; Fitzgerald, G.Chemical Physics Letters (2001), 335 (3,4), 321-326CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)A new algorithm is presented that uses delocalized internal coordinates to optimize structures of periodic systems. The algorithm employs translational symmetry to construct the B matrix. It requires generation of all unique primitive internals in the unit cell. B is subsequently used to generate a set of delocalized internals as described in the earlier work by Pulay, Baker and coworkers for mol. systems. A detailed anal. of the algorithm for bulk Si is given, and the performance of the method in applications to surface reactions and zeolites is briefly mentioned.
- 159Fletcher, R. Practical Methods of Optimization, 2nd ed.; John Wiley & Sons: New York, USA, 1987.Google ScholarThere is no corresponding record for this reference.
- 160Pfrommer, B. G.; Côté, M.; Louie, S. G.; Cohen, M. L. Relaxation of crystals with the quasi-Newton method. J. Comput. Phys. 1997, 131, 233– 240, DOI: 10.1006/jcph.1996.5612Google Scholar160https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2sXhvFWitro%253D&md5=c4a3a3cde9e647f7266331e123925fd7Relaxation of crystals with the quasi-Newton methodPfrommer, Bernd G.; Cote, Michel; Louie, Steven G.; Cohen, Marvin L.Journal of Computational Physics (1997), 131 (1), 233-240CODEN: JCTPAH; ISSN:0021-9991. (Academic)A quasi-Newton method was used to simultaneously relax the internal coordinates and lattice parameters of crystals under pressure. The symmetry of the crystal structure is preserved during the relaxation. From the inverse of the Hessian matrix, elastic properties, and some optical phonon frequencies at the Brillouin zone center can be estd. The efficiency of the method is demonstrated for Si test systems.
- 161Packwood, D.; Kermode, J.; Mones, L.; Bernstein, N.; Woolley, J.; Gould, N.; Ortner, C.; Csányi, G. A universal preconditioner for simulating condensed phase materials. J. Chem. Phys. 2016, 144, 164109, DOI: 10.1063/1.4947024Google Scholar161https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XntFGgsbo%253D&md5=70d75b8ab4527399c491b8af188efa9fA universal preconditioner for simulating condensed phase materialsPackwood, David; Kermode, James; Mones, Letif; Bernstein, Noam; Woolley, John; Gould, Nicholas; Ortner, Christoph; Csanyi, GaborJournal of Chemical Physics (2016), 144 (16), 164109/1-164109/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)We introduce a universal sparse preconditioner that accelerates geometry optimization and saddle point search tasks that are common in the at. scale simulation of materials. Our preconditioner is based on the neighborhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and mol. solids. The simple structure of the preconditioner means that the gains can be realized in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes. (c) 2016 American Institute of Physics.
- 162Zhang, S. B.; Northrup, J. E. Chemical potential dependence of defect formation energies in GaAs: Application to Ga self-diffusion. Phys. Rev. Lett. 1991, 67, 2339– 2342, DOI: 10.1103/physrevlett.67.2339Google Scholar162https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXms1Ohs7s%253D&md5=934ed2e750dc1e82f8f8e6bc9a819db5Chemical-potential dependence of defect formation energies in gallium arsenide: application to gallium self-diffusionZhang, S. B.; Northrup, John E.Physical Review Letters (1991), 67 (17), 2339-42CODEN: PRLTAO; ISSN:0031-9007.Abs. formation energies of native defects in GaAs were calcd. The formation energy and hence the equil. concn. of the defects depends strongly on the at. chem. potentials of As and Ga as well as the electron chem. potential. For example, the Ga vacancy concn. changes by >10 orders of magnitude as the chem. potentials of As and Ga vary over the thermodynamically allowed range. This result indicates that the rate of self-diffusion depends strongly on the surface-annealing conditions.
- 163Janak, J. F. Proof that ∂E∂ni=ϵ in density-functional theory. Phys. Rev. B: Condens. Matter Mater. Phys. 1978, 18, 7165– 7168, DOI: 10.1103/physrevb.18.7165Google Scholar163https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaE1MXhsFOhtLw%253D&md5=599785d5d7ae6be888e09d690eb8ac14Proof that .vdelta.E/.vdelta.ni = εi in density-functional theoryJanak, J. F.Physical Review B: Condensed Matter and Materials Physics (1978), 18 (12), 7165-8CODEN: PRBMDO; ISSN:0163-1829.The variation of the total energy, as constructed in d.-functional theory, with respect to an orbital occupation in equal to the eigenvalue of that orbital, independent of the detailed form of the exchange-correlation functional. This leads to a rigorous connection between the ground-state energies of N- and (N + 1)-particle systems, which is useful in the calcn. of certain excitation energies.
- 164Sanna, S.; Frauenheim, T.; Gerstmann, U. Validity of the Slater-Janak transition-state model within the LDA + U approach. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 085201, DOI: 10.1103/physrevb.78.085201Google Scholar164https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXhtVKitLvN&md5=3d5153134212637fc3e7870bd2e0714aValidity of the Slater-Janak transition-state model within the LDA+U approachSanna, Simone; Frauenheim, Th.; Gerstmann, U.Physical Review B: Condensed Matter and Materials Physics (2008), 78 (8), 085201/1-085201/7CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Known with the name of the Slater-Janak transition-state model, Janak's theorem allows a calcn. of charge transition levels by analyzing the Kohn-Sham eigenvalues of the d.-functional theory without the need of explicitly comparing differently charged systems. Unfortunately, the usual local-d. approxn. (LDA) and its gradient extensions fail in describing the Kohn-Sham eigenvalues sufficiently well. In this work we show that the Slater-Janak transition state becomes a powerful tool if applied self-consistently within an LDA + U approach. We first explain this fact anal. and then present a numerical validation, calcg. the Slater-Janak transition state for a selection of representative examples in GaN. The formalism is found to be valid for all the investigated examples, which are, besides oxygen donors (ON) and carbon acceptors (CN), also systems with neg.-U effect (nitrogen vacancies, VN) and strongly correlated electrons (europium substitutionals, EuGa).
- 165Skylaris, C.-K.; Haynes, P. D.; Mostofi, A. A.; Payne, M. C. Using ONETEP for accurate and efficient density functional calculations. J. Phys.: Condens. Matter 2005, 17, 5757– 5769, DOI: 10.1088/0953-8984/17/37/012Google Scholar165https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtFOrtbzI&md5=d9530da1af1b5db3495798a2bbf2e4a4Using ONETEP for accurate and efficient O(N) density functional calculationsSkylaris, Chris-Kriton; Haynes, Peter D.; Mostofi, Arash A.; Payne, Mike C.Journal of Physics: Condensed Matter (2005), 17 (37), 5757-5769CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)We present a detailed comparison between ONETEP, our linear-scaling d. functional method, and the conventional pseudopotential plane wave approach in order to demonstrate its high accuracy. Further comparison with all-electron calcns. shows that only the largest available Gaussian basis sets can match the accuracy of routine ONETEP calcns. Results indicate that our minimization procedure is not ill conditioned and that convergence to self-consistency is achieved efficiently. Finally, we present calcns. with ONETEP, on systems of about 1000 atoms, of electronic, structural and chem. properties of a wide variety of materials such as metallic and semiconducting carbon nanotubes, cryst. silicon and a protein complex.
- 166Skylaris, C.-K.; Haynes, P. D. Achieving plane wave accuracy in linear-scaling density functional theory applied to periodic systems: A case study on crystalline silicon. J. Chem. Phys. 2007, 127, 164712, DOI: 10.1063/1.2796168Google Scholar166https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXht12jsb%252FN&md5=015ba0284a7fce45c02f01c85ea2a188Achieving plane wave accuracy in linear-scaling density functional theory applied to periodic systems: A case study on crystalline siliconSkylaris, Chris-Kriton; Haynes, Peter D.Journal of Chemical Physics (2007), 127 (16), 164712/1-164712/5CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Linear-scaling methods for d. functional theory promise to revolutionize the scope and scale of first-principles quantum mech. calcns. Cryst. silicon has been the system of choice for exploratory tests of such methods in the literature, yet attempts at quant. comparisons under linear-scaling conditions with traditional methods or exptl. results have not been forthcoming. A detailed study using the ONETEP code is reported here, demonstrating for the first time that plane wave accuracy can be achieved in linear-scaling calcns. on periodic systems.
- 167Ruiz-Serrano, Á.; Skylaris, C.-K. A variational method for density functional theory calculations on metallic systems with thousands of atoms. J. Chem. Phys. 2013, 139, 054107, DOI: 10.1063/1.4817001Google Scholar167https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXht1Whtb3L&md5=ea379794a98bbb8738dee588144c2e95A variational method for density functional theory calculations on metallic systems with thousands of atomsRuiz-Serrano, Alvaro; Skylaris, Chris-KritonJournal of Chemical Physics (2013), 139 (5), 054107/1-054107/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)A new method for finite-temp. d. functional theory calcns. which significantly increases the no. of atoms that can be simulated in metallic systems is presented. A self-consistent, direct minimization technique is used to obtain the Helmholtz free energy of the electronic system, described in terms of a set of non-orthogonal, localized functions which are optimized in situ using a periodic-sinc basis set, equiv. to plane waves. Most parts of the calcn., including the demanding operation of building the Hamiltonian matrix, have a computational cost that scales linearly with the no. of atoms in the system. Also, this approach ensures that the Hamiltonian matrix has a minimal size, which reduces the computational overhead due to diagonalization, a cubic-scaling operation that is still required. Large basis set accuracy is retained via the optimization of the localized functions. This method allows accurate simulations of entire metallic nanostructures, demonstrated with calcns. on a supercell of bulk copper with 500 atoms and on gold nanoparticles with up to 2057 atoms. (c) 2013 American Institute of Physics.
- 168Tinte, S.; Stachiotti, M. G.; Rodriguez, C. O.; Novikov, D. L.; Christensen, N. E. Applications of the generalized gradient approximation to ferroelectric perovskites. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, 11959– 11963, DOI: 10.1103/physrevb.58.11959Google Scholar168https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXntVeitrk%253D&md5=0cc780f1c0905eb52154643fae490c1aApplications of the generalized gradient approximation to ferroelectric perovskitesTinte, S.; Stachiotti, M. G.; Rodriguez, C. O.; Novikov, D. L.; Christensen, N. E.Physical Review B: Condensed Matter and Materials Physics (1998), 58 (18), 11959-11963CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The Perdew-Burke-Ernzerhof generalized gradient approxn. to the d. functional theory is tested with respect to sensitivity to the choice of the value of the parameter κ, which is assocd. with the degree of localization of the exchange-correlation hole. A study of structural and dynamical properties of four selected ferroelec. perovskites is presented. The originally proposed value of κ=0.804 works well for some solids, whereas for the ABO3 perovskites it must be decreased in order to predict equil. lattice parameters in good agreement with expts. The effects on the structural instabilities and zone center phonon modes are examd. The need of varying κ from one system to another reflects the fact that the localization of the exchange-correlation hole is system dependent, and the sensitivity of the structural properties to its actual value illustrates the necessity of finding a universal function for κ.
- 169Nakamatsu, H.; Adachi, H.; Ikeda, S. Electronic structure of the valence band for perovskite-type titanium double oxides studied by XPS and DV-Xα cluster calculations. J. Electron Spectrosc. Relat. Phenom. 1981, 24, 149– 159, DOI: 10.1016/0368-2048(81)80002-3Google Scholar169https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL3MXmtFamt7w%253D&md5=fe2037864e46c215f2175f1eac3e863bElectronic structure of the valence band for perovskite-type titanium double oxides studied by XPS and DV-Xα cluster calculationsNakamatsu, Hirohide; Adachi, Hirohiko; Ikeda, ShigeroJournal of Electron Spectroscopy and Related Phenomena (1981), 24 (2), 149-59CODEN: JESRAW; ISSN:0368-2048.XPS spectra of the valence bands for the perovskite-type double oxides BaTiO3, SrTiO3 and CaTiO3 were measured and analyzed by means of DV-Xα calcns. for the TiO6 embedded cluster model. The theor. photoelectron spectra modulated by the photoionization cross-sections are in good agreement with expt. The XPS results show that the O 2p valence band is constructed of 2 peaks whose spacing becomes larger in the order BaTiO3 < SrTiO3 < CaTiO3. The DV-Xα results indicate that the greater part of the lower-energy peak is attributed to the levels which have O 2p orbitals pointing to Ti cations and are thus stabilized to the levels which have O 2p orbitals pointing to Ti cations and are thus stabilized by the electrostatic potential concomitant with a decreased Ti-O bond distance. The electrostatic potential also reduces the O 2p-Ti 3d mixing and, together with the repulsion of the electron cloud between the Ti and O ions, makes the Ti-O bond more ionic.