Statistical Mechanics of Solids

This chapter is devoted to an analysis of point defect equilibria in binary alloys for which the concentration of one of the constituents is much smaller than of the other. In such alloys, the minority constituent can itself be regarded as a defect or an impurity.
Our attention will be restricted to one-center and two-center defects, that is, to alterations in the local composition from that of the pure perfect crystal that involve either one atom or an adjacent pair of atoms. The perfect crystal is taken to be one in which all lattice sites are occupied by atoms of the type of the major constituent and all interstitial sites are empty. It will be assumed that all lattice atomic sites are equivalent and that all interstitial sites are equivalent. The results can be easily generalized to crystals in which atoms or interstitial sites are arranged on two or more nonequivalent sublattices, and to crystals containing more than one type of impurity.
The normal lattice on which the atoms in the perfect crystal are distributed will be called the L lattice and contains L sites, while the interstitial lattice is called the L ? lattice and contains L ? sites. The possible one- and two-center defects will be denoted as follows:
| V | a vacant lattice site (the monovacancy) |
| V 2 | two adjacent vacant L sites (the divacancy) |
| B | an impurity atom on an L site (the substitutional impurity) |
| B 2 | two... |