Extension of Configurational Polyhedra to Finite Temperature Property

TL;DR

This paper extends the concept of configurational polyhedra to finite-temperature properties, demonstrating how temperature-dependent internal energy in alloys can be understood through the density of states in configuration space.

Contribution

It introduces a method to interpret finite-temperature internal energy in alloys using an extended configurational polyhedra framework.

Findings

Finite-temperature internal energy can be analyzed via density of states in configuration space.

The method applies to alloys and captures temperature dependence of thermodynamic properties.

Extension of CP provides new insights into thermodynamic behavior at finite temperatures.

Abstract

Configurational polyhedora (CP) is a hyperpolyhedra on multidimensional configuration space, whose vertex (and edges) corresponds to upper or lower limit value of correlation functions for all possible atomic configuration on given lattice. In classical systems where physical property including internal energy and elastic modulus can be a linear map for structures considered, it is known that atomic configuration having highest (or lowerst) physical quantity should always locate on one of the vertices at absolute zero temperature. The present study extend the idea of CP to finite-temperature property (especially, focusing on internal energy), and successfully provides demonstration of how temperature dependence of internal energy in equilibrium state for alloys is interpreted in terms of the density of states for non-interacting system along specially selected direction on cofiguration space.