Investigating grain boundary segregation in latent space via dimensionality reduction and descriptor-based interfacial diagrams

We perform hybrid molecular dynamics/Monte Carlo simulations to investigate Ag segregation at representative Cu Σ5 grain boundaries (GBs) and compute smooth overlap of atomic positions (SOAP) vectors to characterize the local environment of each atom. The resulting high-dimensional SOAP vectors are subsequently transformed into a latent representation using both linear and non-linear dimensionality reduction methods. Among these approaches, principal component analysis demonstrates the most robust performance, as it not only effectively distinguishes the atoms in the GB regions from those in the bulk phases, but also captures the Ag segregation behavior at Cu GBs. In contrast, non-linear reduction methods work well only for pristine GBs and become less efficient for Ag-segregated boundaries. Furthermore, we show that the mean and variance of the SOAP vectors can serve as effective fingerprints for describing key structural features and local chemistry of GBs in three-dimensional (3D) space. By mapping these descriptors as a function of temperature and composition, we construct descriptor-based interfacial diagrams that correlate strongly with conventional GB diagrams, including those associated with segregation and disorder. This study not only demonstrates the critical roles of developing GB descriptors for GB structural analysis in latent representations, but also significantly enriches the family of interfacial diagrams.