Algorithmic detection of crystal structures from computer simulation data

Abstract

Detection of crystal structures from particle positions of crystalline assemblies formed in computer simulations is an unsolved problem. The standard protocol, formulated in the reciprocal space, for structure determination from experimental diffraction data is not suitable for analysis of computer simulation data, after converting them to the Fourier space. There is a long history of attempts to tackle this problem by analyzing the system in the real space by using ideas of local neighbors and broken symmetries of the crystalline state. In this paper, we propose a heuristic solution to this problem by detecting all possible unit cells directly from particle coordinates obtained in a typical computer simulation. The method is based on well known facts about crystal structures, some of which are underutilized in the context of the current problem. These include, the symmetry of the coordination polyhedron and its empirical relationship with directions of lattice vectors for a simple Bravais lattice, and the fact that any complex crystal can be systematically decomposed into multiple Bravais lattices. By using these ideas, along with standard computational techniques like search, clustering and convex hull construction, we were able to handle complex basis and construct all crystallographically viable unit cells from the coordinates. The method is capable of handling statistical noise by employing certain cutoffs and deals with multicomponent systems in a transparent manner. We validated it on real Monte Carlo simulation data and variety of test systems, including crystals with tens of particles in the basis. Our heuristic algorithm, which requires minimal human intervention and computational resources, provides a solution to the long standing problem and would be beneficial to the wider communities of condensed matter physics and computational materials science.