Dilution Effects in Regular Assemblies

A study is made of the thermal behaviour of solid mixtures, containing a component A with molecules having several orientation states whose co-operative interaction leads, in pure A, to a second-order transition with a discontinuity in the specific heat and a diluting component B with molecules of the same size. Regular models are used and it can be shown from previous work on ternary assemblies that if A has two equivalent orientation states and complete equilibrium is attained, then the curve of critical temperature against the mole fraction x A of A passes through the origin. It is shown here that if A-B diffusion is forbidden in the temperature range concerned so that the distribution of A and B is fixed, though A molecules can change their orientation, then the specific heat is continuous below a critical value of x A . This effect depends on short-range ordering and a first-order quasi-chemical approximation is used. Similar results are obtained when A has three available orientation states. A short investigation is also made of results when the interaction with B removes the equivalence between the two states of A. The effects here do not depend on short-range ordering, a random statistical approximation is used and it is found that even the smallest proportion of B renders the specific heat continuous with a maximum replacing the discontinuity. Finally, these various types of behaviour are briefly compared with some observed dilution effects.