Thermodynamics of order-disorder in minerals; II, Symmetric formalism applied to solid solutions

Abstract

The thermodynamics of order-disorder in mineral solid solutions are handled with symmetric formalism, whereby the mineral is treated as a solid solution between an independent set of end-members with which the range of composition and states of ordering of the phase can be represented. An n-component mineral, requiring s independent order parameters to represent the state of order in the mineral, involves an independent set of n + s end-members. Symmetric formalism involves ideal mixing-on-sites with regular-solution activity coefficients. It is applied to omphacite, orthopyroxene, ferromagnesian clinoamphibole, and alkali feldspar. The model for omphacite, with a single order parameter, successfully produces the topology of paired miscibility gaps with tricritical points at their apices and with a critical curve connecting them. Ferromagnesian orthopyroxene is shown to behave effectively as an ideal solution at all geologically relevant temperatures. Cummingtonite-grunerite solid solutions are slightly positively nonideal in either a two-site or a three-site model. Na-K alkali feldspars with order-parameter coupling involving tetrahedral site occupancies can show the essential topologic relationships in this system, with only one independent binary interaction energy. The power of symmetric formalism comes from the simplicity of its representation of the thermodynamics of minerals and its flexibility with few adjustable parameters.