Coarse-graining description of solid systems at nonzero temperature

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 (τc) is compared with the “exact” τ computed by the usual atomistic MC procedure for several thermodynamic states. The observed linear dependence of the error in τc on the degree of coarse-graining is rationalized by an analytical treatment of the model within the local harmonic approximation.