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 same rate but significantly reduced computational cost. We illustrate our analytical results through explicit computations for the case of harmonic potentials and through numerical simulations.
Accepté le :
DOI : 10.1051/m2an/2017052
Mots-clés : Defect formation free energy, finite temperature, material defects, Cauchy–Born rule
@article{M2AN_2018__52_4_1315_0,
author = {Dobson, Matthew and Duong, Manh Hong and Ortner, Christoph},
title = {On assessing the accuracy of defect free energy computations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1315--1352},
publisher = {EDP-Sciences},
volume = {52},
number = {4},
year = {2018},
doi = {10.1051/m2an/2017052},
mrnumber = {3875288},
zbl = {1455.74023},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2017052/}
}
TY - JOUR AU - Dobson, Matthew AU - Duong, Manh Hong AU - Ortner, Christoph TI - On assessing the accuracy of defect free energy computations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1315 EP - 1352 VL - 52 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017052/ DO - 10.1051/m2an/2017052 LA - en ID - M2AN_2018__52_4_1315_0 ER -
%0 Journal Article %A Dobson, Matthew %A Duong, Manh Hong %A Ortner, Christoph %T On assessing the accuracy of defect free energy computations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1315-1352 %V 52 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017052/ %R 10.1051/m2an/2017052 %G en %F M2AN_2018__52_4_1315_0
Dobson, Matthew; Duong, Manh Hong; Ortner, Christoph. On assessing the accuracy of defect free energy computations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 4, pp. 1315-1352. doi : 10.1051/m2an/2017052. http://www.numdam.org/articles/10.1051/m2an/2017052/
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