Calculation of point-defect entropy in metals

We investigate previously used methods and propose a new method for atomistic calculations of point-defect entropies in metals within the harmonic approximation to lattice vibrations. The key problem is to predict accurately the defect formation entropy in a macroscopic crystal from atomistic calculations performed on a small system containing relatively few atoms. The results of atomistic calculations may depend significantly on the system size, geometry and boundary conditions. Two previously used methods, which we call the supercell and embedded-cluster methods, are analysed in two ways: firstly, within a linear elasticity model of a point defect and, secondly, by atomistic calculations for a vacancy and an interstitial in copper using an embedded-atom potential. The results of atomistic calculations confirm the linear elasticity analysis and show that the supercell method is much more accurate than the embedded-cluster method. However, the latter is useful for computing the defect core entropy, which turns out to be a well-defined physical quantity. We propose a new method of defect entropy calculations that combines the embedded-cluster method with a quasicontinuum approximation outside the cluster. This method, which we call an elastically corrected embedded-cluster method, has an accuracy comparable with that of the supercell method and extends defect entropy calculations towards larger system sizes.