Accuracy of computation of crystalline defects at finite temperature

2014/09/19 by Alexander V. Shapeev, Shapeev, Alexander V., Mitchell Luskin +1
Materials Science · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Material Dynamics and Properties #Materials Science (cond-mat.mtrl-sci) #Microstructure and mechanical properties #Numerical Analysis (math.NA) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1409.5739

openalex publication_date 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
• On atomistic-to-continuum couplings without ghost forces in three\n dimensions
• An Optimization-Based Atomistic-to-Continuum Coupling Method

Related

• Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
• Structure of Defective Crystals at Finite Temperatures: A Quasi-Harmonic Lattice Dynamics Approach
• Imperfections are not 0 K: free energy of point defects in crystals
• On assessing the accuracy of defect free energy computations
• Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding