Order-disorder model of cation exchange in silicates

Order-disorder theory has been used to treat ion-exchange equilibrium for ions of A and B on a uniform group of exchange sites more numerous than the number of monovalent cations required for electrical neutrality. The method allowed consideration of the effects of extra relaxation energy terms arising from one, two or three of the pairs AA, AB and BB on two nearest neighbour sites. These energies are additional to the energies of 2(OA), (OA + OB) and 2(OB) respectively where O denotes an empty site. Isotherms and thermodynamic equilibrium constants have been compared for different site co-ordination numbers, ion valences, and choices of the three extra energies and of the ratio, n, of the total number of sites to the number of cationic charges needed for electrical neutrality. Miscibility gaps in the isotherms occurred less readily the larger the value of n and the smaller the co-ordination number. Such gaps were also less in evidence when the two exchange ions carried different charges. The model has been considered in relation to the random interstratification of cation layers sometimes observed in clay minerals.