Finite Temperature Quasicontinuum Methods

In this paper we extend the quasi-continuum method to study equilibrium properties of defects at finite temperatures. We present a derivation of an effective energy function to perform Monte Carlo simulations in a mixed atomistic and continuum setting. It is shown that the free energy minimization technique can be easily incorporated into the quasi-continuum frame work, permitting a reduction of the full set of atomistic degrees of freedom even in the finite temperature setting. The validity of the proposed methods is demonstrated by computing the thermal expansion and the temperature dependence of the elastic moduli for Cu. We also employ the quasi-continuum free energy minimization method to study the finite temperarure structure of a dislocation core in Al.