Statistical thermodynamic models for ideal oxide and silicate solid solutions, with application to plagioclase

Abstract

Activity-composition relations are derived for ideal substitutional solid solutions through the Helmholtz free energy expressed in terms of the partition function. For solutions of the type (A, B) u Z w involving mixing on one type of atom site, ideal activities of end-member components are expressed by: a A u Z w = ( X A u Z w ) u , and a B u Z w = ( X B u Z w ) u . With multi-site mixing excluding charge balance restrictions, as in (A, B) α u (C, D) β v Z w , the ideal activity of an end-member component such as A u C v Z w is calculated as: a A u C v Z w = ( X α A ) u ( X β c ) v . These expressions support the ‘ionic solid solution model for the activities of components in ideal solid solutions. Ideal solution models for coupled substitutions involving charge balance are considered using plagioclase as an example. Ideal activity expressions for solid solution of albite and anorthite are derived with and without adherence to the Al avoidance principle. Mixing models involving local electrostatic balance are contrasted with those involving independent, random mixing of Na-Ca and Al-Si. Of several possible ideal solution models for plagioclase, only that specifying complete Al-Si ordering and local electrostatic neutrality yields activities conforming to Raoult's Law.