Thermal Expansion Behavior of AL and TA Using a Finite-Temperature Extension of the Quasicontinuum Method

Abstract

Numerical methods that bridge the atomistic andcontinuum scales concurrently have been applied successfully to anumber of materials science problems involving both nonlinear andlong-range deformation fields. However, extension of thesemethods to finite temperature, nonequilibrium dynamics isdifficult due to the intrinsic incoherency between moleculardynamics and continuum thermodynamics, which possess differentcrystal vibrational spectra and therefore result in unphysicalwave reflections across domain boundaries. Here we review ourrecent finite temperature extension of the three-dimensional,non-local quasicontinuum (QC) method based on Langevin dynamicsand carry out an analysis of the systematic errors associated withthe entropic depletion that results from the QC reduction. Weapply the method to Al and Ta structured meshes ranging fromatomistic resolution to minimum-node representations using thethermal expansion coefficient as the standard metric. We findthat, while Al errors scale linearly with the number of meshnodes, Ta displays a very erratic behavior that degrades rapidlywith mesh coarsening.

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