On assessing the accuracy of defect free energy computations

Matthew Dobson; Manh Hong Duong; Christoph Ortner

doi:10.1051/m2an/2017052

On assessing the accuracy of defect free energy computations

Matthew Dobson, Manh Hong Duong, Christoph Ortner

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We develop a rigorous error analysis for coarse-graining of defect-formation
free energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the rate of convergence. We then construct a sequence of coarse-grained energies with the samerate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.

Original language	English
Journal	Mathematical Modelling and Numerical Analysis
DOIs	https://doi.org/10.1051/m2an/2017052
Publication status	Published - 5 Oct 2017

Keywords

Defect formation free energy
Finite temperature
Material defects
Cauchy-Born rule

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Cite this

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title = "On assessing the accuracy of defect free energy computations",

abstract = "We develop a rigorous error analysis for coarse-graining of defect-formationfree energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the rate of convergence. We then construct a sequence of coarse-grained energies with the samerate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.",

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AU - Dobson, Matthew

AU - Duong, Manh Hong

AU - Ortner, Christoph

PY - 2017/10/5

Y1 - 2017/10/5

N2 - We develop a rigorous error analysis for coarse-graining of defect-formationfree energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the rate of convergence. We then construct a sequence of coarse-grained energies with the samerate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.

AB - We develop a rigorous error analysis for coarse-graining of defect-formationfree energy. For a one-dimensional constrained atomistic system, we establish the thermodynamic limit of the defect-formation free energy and obtain explicitly the rate of convergence. We then construct a sequence of coarse-grained energies with the samerate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.

KW - Defect formation free energy

KW - Finite temperature

KW - Material defects

KW - Cauchy-Born rule

UR - https://spiral.imperial.ac.uk/handle/10044/1/61001

U2 - 10.1051/m2an/2017052

DO - 10.1051/m2an/2017052

M3 - Article

SN - 0764-583X

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

ER -

On assessing the accuracy of defect free energy computations

Abstract

Keywords

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