Coarse-graining description of solid systems at nonzero temperature
Z. B. Wu, D. J. Diestler, R. Feng and X. C. Zeng
Journal of Chemical Physics, 119, 8013-8023 (2003).
ABSTRACT
The quasicontinuum (QC) technique, in which the atomic lattice of a solid is
coarse-grained by overlaying it with a finite-element mesh, has been employed
previously to treat the quasistatic evolution of defects in materials at zero
temperature. It is extended here to nonzero temperature. A coarse-grained
Hamiltonian is derived for the nodes of the mesh, which behave as
quasiparticles whose interactions are mediated by the underlying (non-nodal)
atoms constrained to move in unison with the nodes. Coarse-grained
thermophysical properties are computed by means of the Monte Carlo (MC)
method. This dynamically constrained QC MC procedure is applied to a simple
model: A pure single crystal of two-dimensional Lennard-Jonesium. The
coarse-grained isotropic stress (tau(c)) is compared with the "exact" tau
computed by the usual atomistic MC procedure for several thermodynamic
states. The observed linear dependence of the error in tau(c) on the degree
of coarse-graining is rationalized by an analytical treatment of the model
within the local harmonic approximation.