Temperature dependence of monovacancy formation parameters for simple metals. II. Extension of the Kanzaki lattice statics method to finite temperatures

For pt.I see ibid., vol.7, p.1651 (1977). The temperature dependence of monovacancy formation parameters such as the formation free energy, energy, entropy and fractional formation volume has been studied for simple metals using pseudopotential theory and the Gibbs-Bogoliubov inequality on the Helmholtz free energy. Application is made to Na and Al. Work presented in a previous paper is extended so that the relaxation in mean position and the shift in vibrational frequency in response to the vacancy are calculated variationally for every ion. This amounts to an extension to finite temperatures of the Kanzaki lattice statics method. The additional flexibility in the model leads to a doubling of the calculated formation entropy for Na over the previous result. Furthermore, the results support the earlier conclusion that, at least for Na and Al, the vacancy formation parameters at high temperatures are insensitive to temperature. This is also found to be the case for the lattice relaxations.