Finite-temperature defect properties from free-energy minimization

We present two simple, but accurate, techniques for calculating the finite-temperature atomic structure and free energy of any solid defect (point or extended). The finite-temperature equilibrium atomic structure and thermodynamic properties of defects in solids are obtained self-consistently by minimizing the rree energy of the solid with respect to the coordinates of the atoms. Application of the two methods to a perfect crystal and one with a vacancy show that both methods yield excellent agreement with Monte Carlo calculations for temperatures up to at least 75% of the melting point.