Volume 52, Number 4, July-August 2018
|Page(s)||1315 - 1352|
|Published online||28 September 2018|
On assessing the accuracy of defect free energy computations
Department of Mathematics and Statistics, UMass Amherst, 710 N Pleasant Street, Amherst, MA 01003, USA
2 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
* Corresponding author: firstname.lastname@example.org
Accepted: 28 September 2017
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.
Mathematics Subject Classification: 65G99 / 74E15 / 74S60
Key words: Defect formation free energy / finite temperature / material defects / Cauchy–Born rule
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.