The thermodynamic properties of reciprocal solid solutions

Bernard J. Wood*, J. Nicholls

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    111 Citations (Scopus)


    A multisite solid solution of the type (A, B) (X, Y) has the four possible components AX, AY, BX, BY. Taking the standard state to be the pure phase at the pressure and temperature of interest, the mixing of these components is shown not to be ideal unless the condition: {Mathematical expression} applies. Even for the case in which mixing on each of the individual sublattices is ideal, ΔG0 contributes terms of the following form to the activity coefficients of the constituent components: {Mathematical expression} (XJi refers to the atomic fraction of J on sublattice i). The above equation, which assumes complete disorder on (A, B) sites and on (X, Y) sites is extended to the general n-component case. Methods of combining the "cross-site" or reciprocal terms with non-ideal terms for each of the individual sites are also described. The reciprocal terms appear to be significant in many geologically important solid solutions, and clinopyroxene, garnet and spinel solid solutions are all used as examples. Finally, it is shown that the assumption of complete disorder only applies under the condition: {Mathematical expression} where z is the number of nearest-neighbour (X, Y) sites around A and n1 is the number of (A, B) sites in the formula unit. If ΔG0 is relatively large, then substantial short range oder must occur and the activity coefficient is given by (ignoring individual site terms): {Mathematical expression} where X′Y2 is the equilibrium atomic fraction of Y atoms surrounding A atoms in the structure. The ordered model may be developed for multicomponent solutions and individual site interactions added, but numerical methods are needed to solve the simultaneous equations involved.

    Original languageEnglish
    Pages (from-to)389-400
    Number of pages12
    JournalContributions to Mineralogy and Petrology
    Issue number4
    Publication statusPublished - Jun 1978


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