VII. Second neighbour interaction in regular binary assemblies

A study is made of regular assemblies of species A and B, whose configurational energy is given by the expression w 1 N AB(1) + w 2 N AB(2), N AB(1) and N AB(2) being the numbers of first and second neighbour A-B pairs respectively. Positive and negative values of w 1 and w 2 are treated and results apply to phase-separation, order-disorder and Ising ferromagnets and antiferromagnets at zero field. Generalized quasi-chemical approximations giving the correct ratio of total first and second neighbour pair numbers are used and the consistency is checked by the critical points in the limiting cases w 1=0 and w 2=0 and by the value of w 2/w 1 at which the critical temperature becomes zero. The simple cubic lattice is treated in detail and a critical temperature curve derived for the plane square lattice. Fluctuation effects are diminished for reinforcing first and second interactions and increased for opposing ones. The quadruplet approximation which has been used by certain authors is critically examined and it is pointed out that it would be consistent for the disordered state on the face-centred cubic lattice.