Configurational Geometry Bridges Equilibrium Structure Information from a Single to Multiple Compositions

TL;DR

This paper introduces a new theoretical approach that uses special microscopic states at a single composition to predict equilibrium structures across multiple compositions in binary systems, simplifying complex thermodynamic analysis.

Contribution

The study extends previous work by developing a formulation that characterizes equilibrium structures over all compositions from states at a single composition, validated through comparison with thermodynamic simulations.

Findings

Special microscopic states can predict equilibrium structures across compositions.

The approach reduces the need for extensive thermodynamic simulations.

Results confirm the concentration of composition- and temperature-dependent information into specific states.

Abstract

For classical discrete systems under constant composition, a set of microscopic state dominantly contributing to thermodynamically equilibrium structure should depend on temperature and energy through Boltzmann factor, exp(-bE). Despite this fact, our recent study find a set of special microscopic state that can characterize equilibrium properties, where these structures can be know a priori without any thermodynamic information. Here, for binary system, we extend the theoretical approach to develop a new formulation, where the special microscopic states at a given, single composition can characterize equilibrium structure over whole composition. We demonstrate the validity of the proposed formulation by comparing with results by conventional thermodynamic simulaton. The results strongly indicate that most information about composition- and temperature- dependence of thermodynamically equilibrium structure for disordered state on multiple compositions can be concentrated to a set of special microscopic state on any single composition.