Does Stochastic Disorder Conform to Configurational Disorder?

TL;DR

This paper investigates whether the stochastically disordered state (SDS) in alloy thermodynamics accurately represents the configurationally disordered state (CDS), especially in finite systems, and identifies conditions for their equivalence.

Contribution

It provides a quantitative analysis of the differences between SDS and CDS in multisite correlation and clarifies when SDS can be considered equivalent to CDS in practical systems.

Findings

Differences in multisite correlation are within a few percent for systems below 100,000 atoms.

SQS can be reliably used for subsystems like surfaces and interfaces under certain conditions.

Careful application of SQS is necessary for high-temperature property investigations in finite systems.

Abstract

In alloy thermodynamics, stochastically disordered state (SDS), where each lattice point is stochastically occupied by constituents according to given composition, is typically referred to investigating physical properties for homogeneously substitutional state: The so-called special quasirandom structure (SQS) of a single microscopic structure, that mimics multisite correlation function for SDS, is amply, widely used for bulk, surface, interface and nano-cluster properties. Despite the widely-used concept for SDS, it has not been clear whether the SDS should conform to configurationally disordered state (CDS) for discrete system, i.e., average over all possible configuration. Here we quantitatively discuss the difference between SDS and CDS for multisite correlation, and show the condition where SDS conforms to CDS. The results show that when practical system size contains below around 100,000 atoms, differences in multisite correlation between SDS and CDS remains few percent depending on the geometry of lattice as well as of figure, indicating that SQS for subsystem of surface and interface, and for isolated clusters, should be carefully applied to investigate high-temperature properties as CDS.