Statistical thermodynamics of super-lattices

Abstract There is no need to define super-lattices, since they have been so freely discussed in recent years. An excellent summary of the subject, with complete references to the literature, has been given by Nix and Shockley (1938). The application of statistical mechanics to the theoretical development is due to Gorsky (1928) and to Bragg and Williams (1934). Improved approximations have since then been introduced by Bethe (1935), Peierls (1936) and Kirkwood (1938), all of which are fully reviewed by Nix and Shockley (1938). We shall therefore be able to confine ourselves to a comparison, at a later stage, of their formulae with those which we shall derive here. We introduce in this paper a new method of approach which we shall call the quasi-chemical method. The method was first devised and used by Guggenheim (1935) in a treatment of regular solutions. An error in this treatment was corrected by Rushbrooke (1938), who showed that the correct treatment by the quasi-chemical method is equivalent to the use of Bethe’s method in its first approximation. It has recently been shown (Guggenheim 1938) that the quasi-chemical method is equivalent to the method of Bethe, and in certain respects more convenient to use, not only for regular solutions but for a whole class of assemblies which may be called regular assemblies.