2024/03/27 by Abhijit Chatterjee, Chatterjee, Abhijit
Computer Science · #FOS: Physical sciences #Matrix Theory and Algorithms #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2403.18380
openalex publication_date 2024/03/27 · openalex created_date 2024/03/29 · openalex updated_date 2026/08/01
In multicomponent lattice problems, e.g., in alloys, and at crystalline surfaces and interfaces, atomic arrangements exhibit spatial correlations that dictate the kinetic and thermodynamic phase behavior. These correlations emerge from interparticle interactions and are frequently reported in terms of the short-range order (SRO) parameter. Expressed usually in terms of pair distributions and other cluster probabilities, the SRO parameter gives the likelihood of finding atoms/molecules of a particular type in the vicinity of others atoms. This study focuses on fundamental constraints involving the SRO parameters that are imposed by the underlying lattice topology. Using a data-driven approach, we uncover the interrelationships between different SRO parameters (e.g., pairs, triplets, quadruplets, etc.) on a lattice. The main finding is that while some SRO parameters are independent, the remaining are collinear, i.e., the latter are dictated by the independent ones through linear relationships. A kinetic and thermodynamic modeling framework based on these constraints is introduced.