Elpasolite is the predominant quaternary crystal structure (${\mathrm{AlNaK}}_2{\mathrm{F}}_6$ prototype) reported in the Inorganic Crystal Structure Database. We develop a machine learning model to calculate density functional theory quality formation energies of all $\sim 2\times {10}^6$ pristine $AB{C}_2{D}_6$ 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 $0.1\mathrm{eV}/\mathrm{atom}$ for a training set consisting of $10\times {10}^3$ 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 $2\times {10}^6$ crystals, 90 unique structures are predicted to be on the convex hull—among which is ${\mathrm{NFAl}}_2{\mathrm{Ca}}_6$, with a peculiar stoichiometry and a negative atomic oxidation state for Al.

• Received 24 August 2015

DOI:https://doi.org/10.1103/PhysRevLett.117.135502

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society