Abstract
In activity-composition relationships for multisite phases, it often occurs that end-members possess individual sites that contain more than one element. For example, in hornblende, ☐Ca2Mg3[MgAl][AlSi3]Si4O22(OH)2, the M2 site contains one Mg and one Al, and the Tl site contains one Al and three Si. In such cases, normalization is required to ensure that the ideal mixing activity and the activity coefficient of each end-member are each unity for the pure end-member. Such normalization is well known for the former, but not for the latter. A new formulation of normalization for activity coefficients is presented. In the context of symmetric (regular and reciprocal) interactions, the formulation is used to show that the thermodynamics can always be written in terms of ½n(n − 1) interaction parameters, where n is the minimum number of components needed to represent the composition of the phase. These macroscopic interaction parameters are particular linear combinations of the constituent regular and reciprocal model microscopic interaction parameters. With this, a further generalization leads to a dramatic simplification in the writing of activity coefficients: for any end-member, a, of a complex phase, including all symmetric microscopic interactions:
in which pk is the proportion of end-member, k, in the phase, is the value of pk in pure a, and Wij is the macroscopic interaction parameter for the ij binary. The summations are over an independent set of end-members chosen to represent the composition of the phase.
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