A self-consistent method which was based upon conjugate gradients was used to calculate the atomic structures and thermodynamic properties of microstructural defects in solids at finite temperatures. The lattice free energy, in the local harmonic approximation, consisted of 2 contributions: static and vibrational. The former depended upon the atomic coordinates, which changed during thermal expansion, while the latter depended explicitly upon the temperature and the frequencies of the normal modes. The frequencies, obtained in an Einstein-type approximation, were implicit functions of the atomic coordinates. Therefore, they could also change during thermal expansion. The free energy of formation of self-interstitials and vacancy-type defects was calculated for Cu at temperatures ranging from 0 to 1200K. A marked decrease in the free energy of formation was observed with increasing temperature. The decrease was close to 20% for vacancy-type defects and close to 35% for self-interstitials over the entire temperature range.

A.M.Monti: Physica Status Solidi B, 1994, 184[1], 81-91