Order-disorder effects

In absence of the Bloch theorem,155 the zero-order disorder effect—termed the minimum, or diagonal, disorder156 —enters the coulombic interaction hamiltonian in the following way ... 

While it is to some extent arbitrary, a classification of this kind provides a means of discussing some of the general features now emerging from studies of metallic oxides. We have stressed the evidence that a nonstoichiometric phase is disordered, but may be related to chemically similar phases of fixed composition where an anomaly of structure is ordered and identifiable by x-ray diffraction methods. Where such ordered phases are found, it is possible that features of them are retained as blocks or domains with short range order in the related berthollide. Efforts should be directed towards order-disorder effects, with a view to reconsidering the status of the nonstoichiometric compound with a very wide composition range. 

The theory is based on a method developed originally by Bethe for treating order-disorder effects in binary alloys. We suppose that every molecule is surrounded by z neighbours (z > 3) and that no two of the z neighbours are nearest neighbours of each other. (This implies that in writing down the interactions between the central molecule and its z... 

Beister. H.J., StrOssner, K. Syassen, K. (1990). Rhomboedral to simple-cubic phase transition in arsenic under pressure. Phys. Rev. B, 41,5535-5543 Chapuis, G. Zufiiga, F. (1988). The High temperature Phase of (CH3)3NHCdCl3 or How to Minimize Order-Disorder Effects in Phase Transitions. Acta Cryst. B44,243-249. International Tables for X-ray Crystallography (1983). Dordrecht Reidel. 

Such quantities depend on partial derivatives of the excess free energy with respect to molar fractions (cf. 1.8.2) which are much altered by the order-disorder effects. Especially the problem of the nature of the singularity at the critical temperature requires an exact solution of the combinatorial problem. These problems which are still awaiting a satisfactory general solution, will not be studied in this book. 

We shall use the approximation of random mixing, having previously shown that the influence of the order-disorder effects (Ch. Ill 3) is small (see also 5). 

It is easy to take into account the order-disorder effects (Prigogine and Lafleur [1954]). 

We could easily introduce order-disorder effects into this model. From what Ave have seen in Ch. Ill we may, however, infer that the "order-disorder correction will be of the second order in 0. In the case of dispersion forces (8,5.7) this would be at most an effect of the 4th order in d and hence completely negligible. In other cases (cf. 8.5.14) it may be of the second order but then the leading terms are of first order in d. In no case will there be any appreciable diange in the conclusions we have reached. For this reason we shall not go into the details of the calculations (it will be sufficient to follow the method of Ch. Ill, 4) which may be found in the original publications (Sarolea [1953], Salsburg and Kirkwood [1952], Prigogine [1953]). 

Once such a model has been introduced, the statistical method follows the lattice model outlined in Ch. III. Because of the big differences in the energies of the different contacts, one has to take account of order-disorder effects w hich are introduced by one of the existing approximation methods (cf. Ch. Ill 4). Generally the Guggenheim quasichemical treatment is used. By choosing appropriate values for the different parameters, it is possible to describe quantitatively the wide variety of excess functions which has been observed in such systems (cf. Barker, Brown and Smith [1953]). 

---