1. Hohenberg P, Kohn W. Inhomogeneous Electron Gas. Phys Rev. 1964;136(3B):864-871. doi:10.1103/PhysRev.136.B864
2. Kohn W, Sham LJ. Self-Consistent Equations Including Exchange and Correlation Effects. Phys Rev. 1965;140(4A):1133-1138. doi:10.1103/PhysRev.140.A1133
3. Midgley SD, Hamad S, Butler KT, Grau-Crespo R. Bandgap Engineering in the Configurational Space of Solid Solutions via Machine Learning: (Mg,Zn)O Case Study. J Phys Chem Lett. 2021;12(21):5163-5168. doi:10.1021/acs.jpclett.1c01031
4. Hart GLW, Mueller T, Toher C, Curtarolo S. Machine learning for alloys. Nat Rev Mater. 2021;6(8):730-755. doi:10.1038/s41578-021-00340-w
5. Yaghoobi M, Alaei M. Machine learning for compositional disorder : A comparison between different descriptors and machine learning frameworks. Comput Mater Sci. 2022;207:111284. doi:10.1016/j.commatsci.2022.111284
6. Askanazi EM, Yadav S, Grinberg I. Prediction of the Curie temperatures of ferroelectric solid solutions using machine learning methods. Comput Mater Sci. 2021;199:110730. doi:10.1016/j.commatsci.2021.110730
7. Pentyala P, Singhania V, Duggineni VK, Deshpande PA. Machine learning-assisted DFT reveals key descriptors governing the vacancy formation energy in Pd-substituted multicomponent ceria. Mol Catal. 2022;522:112190. doi:10.1016/j.mcat.2022.112190
8. Pei Z, Yin J, Hawk JA, Alman DE, Gao MC. Machine-learning informed prediction of high-entropy solid solution formation : Beyond the Hume-Rothery rules. npj Comput Mater. 2020;6:50. doi:10.1038/s41524-020-0308-7
9. Chandran M, Lee SC, Shim J hyeok. Machine learning assisted first-principles calculation of multicomponent solid solutions : estimation of interface energy in Ni-based superalloys. Model Simul Mater Sci Eng. 2018;26:025010. doi:10.1088/1361-651X/aa9f37
10. Morita K, Davies DW, Butler KT, Walsh A. Modeling the dielectric constants of crystals using machine learning. J Chem Phys. 2020;153:024503. doi:10.1063/5.0013136
11. Butler KT, Le MD, Thiyagalingam J, Perring TG. Interpretable, calibrated neural networks for analysis and understanding of inelastic neutron scattering data. J Phys Condens Matter. 2021;33:194006. doi:10.1088/1361-648X/abea1c
12. Mo S Di, Ouyang L, Ching WY, Tanaka I, Koyama Y, Riedel R. Interesting physical properties of the new spinel phase of Si3N4 and C3N4. Phys Rev Lett. 1999;83(24):5046-5049. doi:10.1103/PhysRevLett.83.5046
13. Zerr A, Miehe G, Serghiou G, et al. Synthesis of cubic silicon nitride. Nature. 1999;400:340-342. doi:10.1038/22493
14. Zerr A, Riedel R, Sekine T, Lowther JE, Ching WY, Tanaka I. Recent advances in new hard high-pressure nitrides. Adv Mater. 2006;18(22):2933-2948. doi:10.1002/adma.200501872
15. Boyko TD, Moewes A. The hardness of group 14 spinel nitrides revisited. J Ceram Soc Japan. 2016;124(10):1063-1066. doi:10.2109/jcersj2.16097
16. Hu H, Peslherbe GH. Accurate Mechanical and Electronic Properties of Spinel Nitrides from Density Functional Theory. J Phys Chem C. 2021;125(17):8927-8937. doi:10.1021/acs.jpcc.0c09896
17. Boyko TD, Hunt A, Zerr A, Moewes A. Electronic structure of spinel-type nitride compounds Si3N4, Ge3N4, and Sn3N4 with tunable band gaps: Application to light emitting diodes. Phys Rev Lett. 2013;111(9):097402. doi:10.1103/PhysRevLett.111.097402
18. Caskey CM, Seabold JA, Stevanović V, et al. Semiconducting properties of spinel tin nitride and other IV3N4 polymorphs. J Mater Chem C. 2015;3(6):1389-1396. doi:10.1039/c4tc02528h
19. Qu F, Yuan Y, Yang M. Programmed Synthesis of Sn3N4 Nanoparticles via a Soft Chemistry Approach with Urea: Application for Ethanol Vapor Sensing. Chem Mater. 2017;29(3):969-974. doi:10.1021/acs.chemmater.6b03435
20. Li X, Hector AL, Owen JR, Shah SIU. Evaluation of nanocrystalline Sn3N4 derived from ammonolysis of Sn(NEt2)4 as a negative electrode material for Li-ion and Na-ion batteries. J Mater Chem A. 2016;4(14):5081-5087. doi:10.1039/c5ta08287k
21. Wang J, Chen H, Wei SH, Yin WJ. Materials Design of Solar Cell Absorbers Beyond Perovskites and Conventional Semiconductors via Combining Tetrahedral and Octahedral Coordination. Adv Mater. 2019;31(17):1806593. doi:10.1002/adma.201806593
22. Rosenbrock CW, Gubaev K, Shapeev A V., et al. Machine-learned interatomic potentials for alloys and alloy phase diagrams. npj Comput Mater. 2021;7:24. doi:10.1038/s41524-020-00477-2
23. Kostiuchenko T, Körmann F, Neugebauer J, Shapeev A. Impact of lattice relaxations on phase transitions in a high-entropy alloy studied by machine-learning potentials. npj Comput Mater. 2019;5:55. doi:10.1038/s41524-019-0195-y
24. Batchelor TAA, Pedersen JK, Winther SH, Castelli IE, Jacobsen KW, Rossmeisl J. High-Entropy Alloys as a Discovery Platform for Electrocatalysis. Joule. 2019;3(3):834-845. doi:10.1016/j.joule.2018.12.015
25. Sun S, Tiihonen A, Oviedo F, et al. A data fusion approach to optimize compositional stability of halide perovskites. Matter. 2021;4(4):1305-1322. doi:10.1016/j.matt.2021.01.008
26. Kusne AG, Yu H, Wu C, et al. On-the-fly closed-loop materials discovery via Bayesian active learning. Nat Commun. 2020;11(1):1-11. doi:10.1038/s41467-020-19597-w
27. Sánchez-Palencia P, García G, Conesa JC, Wahnón P, Palacios P. Spinel-Type nitride compounds with improved features as solar cell absorbers. Acta Mater. 2020;197:316-329. doi:10.1016/j.actamat.2020.07.034
28. Hart JN, Allan NL, Claeyssens F. Ternary silicon germanium nitrides: A class of tunable band gap materials. Phys Rev B - Condens Matter Mater Phys. 2011;84(24). doi:10.1103/PhysRevB.84.245209
29. Dudiy S V., Zunger A. Searching for alloy configurations with target physical properties: Impurity design via a genetic algorithm inverse band structure approach. Phys Rev Lett. 2006;97(4):1-4. doi:10.1103/PhysRevLett.97.046401
30. Seminovski Y, Palacios P, Wahnn P, Grau-Crespo R. Band gap control via tuning of inversion degree in CdIn2S4 spinel. Appl Phys Lett. 2012;100:102112. doi:10.1063/1.3692780
31. Roychowdhury S, Ghosh T, Arora R, et al. Enhanced atomic ordering leads to high thermoelectric performance in AgSbTe2. Science (80- ). 2021;371(6530):722-727. doi:10.1126/science.abb3517
32. Nechache R, Harnagea C, Li S, et al. Bandgap tuning of multiferroic oxide solar cells. Nat Photonics. 2014;9:61-67. doi:10.1038/nphoton.2014.255
33. Wang Y, Kavanagh SR, Burgués-Ceballos I, Walsh A, Scanlon DO, Konstantatos G. Cation disorder engineering yields AgBiS2 nanocrystals with enhanced optical absorption for efficient ultrathin solar cells. Nat Photonics. 2022;16:235-241. doi:10.1038/s41566-021-00950-4
34. Lundberg SM, Lee SI. A Unified Approach to Interpreting Model Predictions. In: von Luxburg U, Guyon I, Bengio S, Wallach H, Fergus R, eds. NIPS’17: Proceedings of the 31st International Conference on Neural Information Processing Systems. Curran Associates Inc.; 2017:4768–4777.
35. Kresse G, Furthmüller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci. 1996;6(1):15-50. doi:10.1016/0927-0256(96)00008-0
36. Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B. 1996;54(16):169-186. doi:10.1103/PhysRevB.54.11169
37. Blöchl PE. Projector augmented-wave method. Phys Rev B. 1994;50(24):17953-17979. doi:10.1103/PhysRevB.50.17953
38. Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett. 1996;77(18):3865-3868. doi:10.1103/PhysRevLett.77.3865
39. Hubbard J. Electron correlations in narrow energy bands. Proc R Soc London Ser A Math Phys Sci. 1963;276(1365):238-257. doi:10.1098/rspa.1963.0204
40. Dudarev S, Botton G. Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys Rev B. 1998;57(3):1505-1509. doi:10.1103/PhysRevB.57.1505
41. Heyd J, Scuseria GE, Ernzerhof M. Hybrid functionals based on a screened Coulomb potential. J Chem Phys. 2003;118(18):8207-8215. doi:10.1063/1.1564060
42. Feldbach E, Zerr A, Museur L, et al. Electronic Band Transitions in γ-Ge3N4. Electron Mater Lett. 2021;17(4):315-323. doi:10.1007/s13391-021-00291-y
43. Grau-Crespo R, Hamad S, Catlow CRA, De Leeuw NH. Symmetry-adapted configurational modelling of fractional site occupancy in solids. J Phys Condens Matter. 2007;19(25). doi:10.1088/0953-8984/19/25/256201
44. Schmidt J, Marques MRG, Botti S, Marques MAL. Recent advances and applications of machine learning in solid-state materials science. npj Comput Mater. 2019;5:83. doi:10.1038/s41524-019-0221-0
45. Faber F, Lindmaa A, Von Lilienfeld OA, Armiento R. Crystal structure representations for machine learning models of formation energies. Int J Quantum Chem. 2015;115(16):1094-1101. doi:10.1002/qua.24917
46. Rupp M, Tkatchenko A, Müller KR, Von Lilienfeld OA. Fast and accurate modeling of molecular atomization energies with machine learning. Phys Rev Lett. 2012;108:058301. doi:10.1103/PhysRevLett.108.058301
47. Huo H, Rupp M. Unified Representation of Molecules and Crystals for Machine Learning. Published online 2017. doi:10.48550/arXiv.1704.06439
48. Sanchez JM, Ducastelle F, Gratias D. Generalized cluster description of multicomponent systems. Phys A Stat Mech its Appl. 1984;128(1-2):334-350. doi:10.1016/0378-4371(84)90096-7
49. Troppenz M, Rigamonti S, Draxl C. Predicting Ground-State Configurations and Electronic Properties of the Thermoelectric Clathrates Ba8AlxSi46-x and Sr8AlxSi46-x. Chem Mater. 2017;29(6):2414-2424. doi:10.1021/acs.chemmater.6b05027
50. Tibshirani R. Regression Shrinkage and Selection Via the Lasso. J R Stat Soc Ser B. 1996;58(1):267-288. doi:10.1111/j.2517-6161.1996.tb02080.x
51. Friedman JH. Stochastic gradient boosting. Comput Stat Data Anal. 2002;38(4):367-378. doi:10.1016/S0167-9473(01)00065-2
52. Hornik K, Stinchcombe M, White H. Multilayer feedforward networks are universal approximators. Neural Networks. 1989;2(5):359-366. doi:10.1016/0893-6080(89)90020-8
53. Xu X, Jiang H. Cluster expansion based configurational averaging approach to bandgaps of semiconductor alloys. J Chem Phys. 2019;150(3). doi:10.1063/1.5078399
54. Liu J, Wang X, Borkiewicz OJ, et al. Unified View of the Local Cation-Ordered State in Inverse Spinel Oxides. Inorg Chem. 2019;58(21):14389-14402. doi:10.1021/acs.inorgchem.9b01685
55. Stevanović V, D’Avezac M, Zunger A. Simple point-ion electrostatic model explains the cation distribution in spinel oxides. Phys Rev Lett. 2010;105(7):11-14. doi:10.1103/PhysRevLett.105.075501
56. Seko A, Oba F, Tanaka I. Classification of spinel structures based on first-principles cluster expansion analysis. Phys Rev B. 2010;81:054114. doi:10.1103/PhysRevB.81.054114
57. Seko A, Yuge K, Oba F, Kuwabara A, Tanaka I. Prediction of ground-state structures and order-disorder phase transitions in II-III spinel oxides: A combined cluster-expansion method and first-principles study. Phys Rev B. 2006;73:184117. doi:10.1103/PhysRevB.73.184117
58. Wechsler BA, Navrotsky A. Thermodynamics and structural chemistry of compounds in the system MgOTiO2. J Solid State Chem. 1984;55(2):165-180. doi:10.1016/0022-4596(84)90262-7
59. Santos-Carballal D, Roldan A, Grau-Crespo R, De Leeuw NH. First-principles study of the inversion thermodynamics and electronic structure of FeM2X4 (thio)spinels (M=Cr, Mn, Co, Ni; X= O, S). Phys Rev B. 2015;91:195106. doi:10.1103/PhysRevB.91.195106
60. O’Neill HSC, Navrotsky A. Simple spinels: crystallographic parameters, cation radii, lattice energies, and cation distribution. Am Mineral. 1983;68:181-194.
61. Callen HB, Harrison SE, Kriessman CJ. Cation distributions in ferrospinels. Theoretical. Phys Rev. 1956;103(4):851-856. doi:10.1103/PhysRev.103.851
62. Grau-crespo R, Waghmare U V. Simulation of Crystals with Chemical Disorder at Lattice Sites. In: Rai B, ed. Molecular Modeling for the Design of Novel Performance Chemicals and Materials. CRC Press; 2012:319-342. doi:10.1201/b11590-12
63. Gautam A, Sadowski M, Prinz N, et al. Rapid Crystallization and Kinetic Freezing of Site-Disorder in the Lithium Superionic Argyrodite Li6PS5Br. Chem Mater. 2019;31(24):10178-10185. doi:10.1021/acs.chemmater.9b03852
64. Redfern SA, Harrison RJ, O’Neill HSC, Wood DR. Thermodynamics and kinetics of cation ordering in MgAl2O4 spinel up to 1600 C from in situ neutron diffraction. Am Mineral. 1999;84:299-310. doi:10.2138/am-1999-0313