Thermal Expansion Behavior of Al and Ta Using a Finite-temperature Extension of the Quasicontinuum Method

Numerical methods that bridge the atomistic and continuum scales concurrently have been applied successfully to a number of materials science problems involving both nonlinear and long-range deformation fields. However, extension of these methods to finite temperature, nonequilibrium dynamics is difficult due to the intrinsic incoherency between molecular dynamics and continuum thermodynamics, which possess different crystal vibrational spectra and therefore result in unphysical wave reflections across domain boundaries. Here we review our recent finite temperature extension of the three-dimensional, non-local quasicontinuum (QC) method based on Langevin dynamics and carry out an analysis of the systematic errors associated with the entropic depletion that results from the QC reduction. We apply the method to Al and Ta structured meshes ranging from atomistic resolution to minimum-node representations using the thermal expansion coefficient as the standard metric. We find that, while Al errors scale linearly with the number of mesh nodes, Ta displays a very erratic behavior that degrades rapidly with mesh coarsening.