Accuracy of computation of crystalline defects at finite temperature

TL;DR

This paper develops a theoretical framework for accurately computing crystalline defects at finite temperature, introducing Gibbs distributions and asymptotic expansions, and compares computational methods' accuracy.

Contribution

It introduces a rigorous asymptotic expansion for Gibbs distributions of defects and compares different computational approaches in a one-dimensional setting.

Findings

Asymptotic expansion accurately describes defect distributions at finite temperature.

Comparison shows differences in accuracy between boundary condition methods and atomistic-to-continuum coupling.

Framework enables improved computational modeling of crystalline defects.

Abstract

The present paper aims at developing a theory of computation of crystalline defects at finite temperature. In a one-dimensional setting we introduce Gibbs distributions corresponding to such defects and rigorously establish their asymptotic expansion. We then give an example of using such asymptotic expansion to compare the accuracy of computations using the free boundary conditions and using an atomistic-to-continuum coupling method.