Tetrahedron-tiling method for crystal structure prediction

Qi‐Jun Hong ,Joseph A Yasi

doi:10.1103/physrevmaterials.1.020801

Abstract

Reliable and robust methods of predicting the crystal structure of a compound, based only on its chemical composition, is crucial to the study of materials and their applications. Despite considerable ongoing research efforts, crystal structure prediction remains a challenging problem that demands large computational resources. Here we propose an efficient approach for first-principles crystal structure prediction. The new method explores and finds crystal structures by tiling together elementary tetrahedra that are energetically favorable and geometrically matching each other. This approach has three distinguishing features: a favorable building unit, an efficient calculation of local energy, and a stochastic Monte Carlo simulation of crystal growth. By applying the method to the crystal structure prediction of various materials, we demonstrate its validity and potential as a promising alternative to current methods.

Highlights

Crystal structure prediction (CSP) [1,2,3] has been a topic of great interest with both fundamental importance in physical science—an ambitious goal to predict the structure of a crystal from the knowledge of its chemical composition—and enormous potential in modern materials design and discovery ranging from petrochemical industry [4] and electrical energy storage [5] to the study of phase diagrams [6]
Starting from a small training set of common crystal structures, we first calculate the local energies of the tetrahedra from these structures, based on local energy density method (EDM) [18,19] in density functional theory (DFT) [20,21,22] and the Delaunay triangulation [23]
The simulations generate a series of stable crystal structures, which are further added to the training set to provide more data points on new tetrahedra, systematically improving the empirical tetrahedron energy landscape

Summary

RAPID COMMUNICATIONS

Qi-Jun Hong,1,* Joseph Yasi, and Axel van de Walle1 1School of Engineering, Brown University, Providence, Rhode Island 02912, USA. Structure prediction remains a challenging problem that demands large computational resources To address this issue, we propose an alternative CSP approach, by which new crystal structures are predicted by tiling from energetically favorable and geometrically matching elementary tetrahedra. Starting from a small training set of common crystal structures, we first calculate the local energies of the tetrahedra from these structures, based on local energy density method (EDM) [18,19] in density functional theory (DFT) [20,21,22] and the Delaunay triangulation [23] These data points of known tetrahedra enable us to interpolate, at a very low cost, an empirical energy landscape for any tetrahedron with general coordinates.

Delaunay Triangulation energy of tetrahedron interpolation

Number of tetrahedra Number of atoms