Statistical Mechanics of Defect-Containing Solids. I. General Formalism

A formalism is set up for treating the contributions of point defects to the thermodynamic functions of crystalline solids by means of a cluster expansion of the partition function. Similar expansions for the defect distribution functions and potentials of average force are derived. The assumptions involved and the necessary differences between the formalism and the McMillan—Mayer theory of solutions are discussed. Problems arising in the explicit evaluation of the coefficients of the virial expansions are discussed and possible applications of the formalism suggested.