Crystal structure and melting in a cell model. I. Solvable lattices and isomorphisms

Abstract

The free energy and crystal structure of some particular cases of a cell model of melting are obtained. These include (i) a class of one-dimensional cases with interactions extending to many neighbouring cells, (ii) the plane hexagonal, bcc and triangular lattices with nearest-neighbour interactions, (iii) a case of the plane, square lattice with first- and second-neighbour (diagonal) interactions, and others. The solutions for the simple cubic lattices in all dimensions were obtained in a previous paper (abstr. A46569 of 1971). It is shown that some of the 2, 3, etc dimensional cases are closely related ('isomorphic') to one-dimensional cases.