CALCULATION OF FORMATION VOLUME OF VACANCIES IN SOLIDS

By considering the creation of a vacancy as an isothermal and isobaric process the Gibbs formation energy gf can be expressed as gf=CBΩ, where B is the isothermal bulk modulus and Ω the mean volume per atom. In former publications a method was proposed in which C was assumed constant. It led to explicit expressions for the formation entropy sf and enthalpy hf as functions of T. Extending this method to the formation volume vf and to the parameters βf=(1vf)(vfT)P and κf=-(1vf)(vfP)T explicit relations with the pressure and temperature derivatives of the bulk properties B and β (the volume thermal-expansion coefficient) are derived. The main results can be summarized as follows. (i) The parameters vf, βf, and κf are found to depend on P and T but in a different way than the bulk properties Ω, β, and κ. (ii) The volume vf consists of two terms vhf=(hfP)T and vsf=-T(sfP)T. At high temperatures the term vsf is never negligible in comparison to vhf. (iii) The thermal-expansion coefficient of vhf is approximately equal to -β whereas that of vsf is positive and one order of magnitude larger. In order to check the reliability of the proposed method numerical values of vf were calculated by using elastic data. In all types of solids investigated close agreement with experiment was found. The calculated values of κf and βf, for alkali halides, agree with the corresponding values that can be extracted from the curvature of the plots of conductivity and diffusion versus pressure at various temperature. The same holds true for tracer experiments on Na and Cd. © 1978 The American Physical Society.