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- Faber, Felix A., et al.
(författare)
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Machine Learning Energies of 2 Million Elpasolite (AB2D6) Crystals
- 2016
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Ingår i: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 117:13
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Tidskriftsartikel (refereegranskat)abstract
- Elpasolite is the predominant quaternary crystal structure (AlNaK2F6 prototype) reported in the Inorganic Crystal Structure Database. We develop a machine learning model to calculate density functional theory quality formation energies of all ∼2×106 pristine ABC2D6 elpasolite crystals that can be made up from main-group elements (up to bismuth). Our model’s accuracy can be improved systematically, reaching a mean absolute error of 0.1 eV/atom for a training set consisting of 10×103 crystals. Important bonding trends are revealed: fluoride is best suited to fit the coordination of the D site, which lowers the formation energy whereas the opposite is found for carbon. The bonding contribution of the elements A and B is very small on average. Low formation energies result from A and B being late elements from group II, C being a late (group I) element, and D being fluoride. Out of 2×106 crystals, 90 unique structures are predicted to be on the convex hull—among which is NFAl2Ca6, with a peculiar stoichiometry and a negative atomic oxidation state for Al.
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| 2. |
- Faber, Felix, et al.
(författare)
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Crystal structure representations for machine learning models of formation energies
- 2015
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Ingår i: International Journal of Quantum Chemistry. - : Wiley. - 0020-7608 .- 1097-461X. ; 115:16, s. 1094-1101
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Tidskriftsartikel (refereegranskat)abstract
- We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a dataset of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37eV/atom for the respective representations.
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