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Abstract

A convenient and widely used model for analysing the thermodynamic changes which accompany mixing and ordering processes in mineral solid solutions is based on pairwise interactions between atoms which occupy nearest neighbour structural sites. The simplest of such models reduces to a single parameter, the sum z[wAB – ½(wAA + wBB)], where z is the coordination number for A cations around Β cations (and vice versa) and wAB, wAA, wBB are interaction energies for A-B, A-A and B-B pairs. In the regular solution model, this sum is expressed as-WH and gives rise to an enthalpy of mixing, ΔHmix = WH XA XB, for a binary solid solution; XA and XB are the mole fractions of end-member components containing A and Β cations. This leads to the prediction of a symmetrical solvus with its crest at a temperature, Tc, given by Tc =WH/2nR; is the number of cation sites per formula unit on which mixing occurs and R is the gas constant. If A-B interactions are energetically favoured relative to A-A and B-B interactions, the sum of interaction energies, expressed as WBW in the Bragg-Williams model, favours ordering. A structure with AB stoichiometry would be expected to order below a critical temperature, Tc, given by Tc = WBW/2R.

During the 1970’s and 1980’s, the enthalpies of mixing of many important rockforming silicate solid solutions were measured by solution calorimetry (reviewed by Geiger, 2001). The regular solution model, modified to allow for asymmetry in the mixing, has continued to provide an effective phenomenological description of mixing properties.

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