Investigating phase transitions from local crystallographic analysis based on statistical learning of atomic environments in 2D MoS₂-ReS₂

The mechanisms of phase transitions have been previously explored at various theoretical and experimental levels. For a wide variety of compounds, the majority of studies are limited by observations at fixed temperature and composition, in which case, relevant information can be determined only from the behaviors at topological and structural defects. All analyses to date utilize macroscopic descriptors derived from structural information such as polarization or octahedral tilts extracted from the atomic positions, ignoring the multiple degrees of freedom observable from atomically resolved images. In this article, we provide a solution, by exploring the mechanisms of a phase transition between the trigonal prismatic and distorted octahedral phases of layered chalcogenides in the 2D MoS2-ReS2 system from the observations of local degrees of freedom, namely atomic positions by scanning transmission electron microscopy. We employ local crystallographic analysis based on statistical learning of atomic environments to build a picture of the transition from the atomic level up and determine local and global variables controlling the local symmetry breaking. We highlight how the dependence of the average symmetry-breaking distortion amplitude on global and local concentration can be used to separate local chemical as well as global electronic effects on the transition. This approach allows for the exploring of atomic mechanisms beyond the traditional macroscopic descriptions, utilizing the imaging of compositional fluctuations in solids to explore phase transitions over a range of observed local stoichiometries and atomic configurations.