Evaluation of harmonic methods for calculating the free energy of defects in solids

The free energy of defects in solids is computed with Monte Carlo simulation techniques and by various approximate techniques. The results are compared in order to determine the accuracy and range of applicability of the various approximate methods. The systems studied are a bulk crystal, a vacancy, a (100) free surface, and a Σ5(310)/[001] symmetric tilt boundary in Cu described by embedded-atom method potentials. The Monte Carlo simulations employ both the Frenkel-Ladd method and thermodynamic integration. The approximate techniques include quasiharmonic calculations and the recently proposed local harmonic method. The results indicate that the harmonic methods significantly underestimate the temperature variation of the defect-free energies for this potential. The discrepancies become large for temperatures above about half of the melting point.