EVALUATION OF THE ACCURACY OF THE FREE-ENERGY-MINIMIZATION METHOD

We have made a detailed comparison between three competing methods for determining the free energies of solids and their defects: the thermo dynamic integration of Monte Carlo (TLMC) data, the quasiharmonic (QH) model, and the free-energy-minimization (FEM) method. The accuracy of these methods decreases from the TIMC to QH to FEM method, while the computational efficiency improves in that order. All three methods yie ld perfect crystal lattice parameters and free energies at finite temp eratures which are in good agreement for three different Cu interatomi c potentials [embedded atom method (EAM), Morse and Lennard-Jones]. Th e FEM error (relative to the TIMC) in the (001) surface free energy an d in the vacancy formation energy were found to be much larger for the EAM potential than for the other two potentials. Part of the errors i n the FEM determination of the free energies are associated with anhar monicities in the interatomic potentials, with the remainder attribute d to decoupling of the atomic vibrations. The anharmonicity of the EAM potential was found to be unphysically large compared with experiment al vacancy formation entropy determinations. Based upon these results, we show that the FEM method provides a reasonable compromise between accuracy and computational demands. However, the accuracy of this appr oach is sensitive to the choice of interatomic potential and the natur e of the defect to which it is being applied. The accuracy of the FEM is best in high-symmetry environments (perfect crystal, high-symmetry defects, etc.) and when used to describe materials where the anharmoni city is not too large.