Atom’s Dynamics and Crystal Structure: An Ordinal Pattern Method

Abstract

The ubiquitous nature of thermal fluctuations poses a limitation on the identification of crystal structures. However, the trajectory of an atom carries a fingerprint of its surroundings. This rationalizes the search for a method that can determine the local atomic configuration via the analysis of the movement of an individual atom. Here, we report, while using molecular modeling, how a statistical analysis of a single-atom speed trajectory, represented by ordinal patterns, distinguishes between actual crystal structures. Using the Shannon entropy of ordinal patterns enabled discernment of the studied high-pressure silicon phases. Identification of the atoms occupying the 2(c) and 6(f) Wyckoff positions of the r8 crystal revealed an increase in the developed method’s accuracy with trajectory length. The proposed concept of studying the structure of crystals offers new opportunities in solid-solid phase transformation studies.