Order and disorder in arrangements of small numbers of atoms

Abstract

Situations in binary lattices of composition AB are defined by two disorder parameters: u is an exchange parameter, η is an equal neighbour parameter. These parameters are connected to Bragg and Williams' degree of long distance order and to Bethe's degree of local order respectively, to Borelius' measure of disorder and to the configuration energy. For a couple of examples the frequencies W( u, η) of situations belonging to values of both these parameters are evaluated. It is pointed out that the critical behaviour of the specific heat depends on the sums A(η) of W( u,η) at constant η. In the thermodynamical distributions the most probable energy value and the mean energy value need not coincide. The critical behaviour of the long range order is shown to depend on the maximum of W( u,η) at constant η being shifted, for low values of η, to the extremities of u corresponding to higher order. The shift of the relative thermodynamical probabilities near the critical temperature is numerically shown in three tables containing, at three consecutive temperatures, the separate terms of the configuration partition function. For the case of a one-dimensional chain the numbers W( u,η) are given for any number of atoms.