Thermodynamics of multicomponent pyroxenes: I. Formulation of a general model

A model is proposed for the thermodynamic properties of multicomponent pyroxenes in the composition space defined by the end-member component CaMgSi₂O₆ and the exchange components Fe(Mg)_-1, TiAl₂(MgSi₂)_-1, Fe³⁺(Al)_-1, Fe³⁺Al(MgSi)_-1, and Mg(Ca)_-1. It is formulated for the simplifying assumptions that: (1) a molecular mixing type approximation describes changes in the molar configurational entropy associated with the coupled exchange substitutions TiAl₂MgSi₂, Fe³⁺AlMgSi, and Al₂MgSi (and their ferroan equivalents), and (2) Fe²⁺ and Mg²⁺, and Al³⁺ and Fe³⁺ display long-range non-convergent ordering between M2 and octahedral M1 sites, and octahedral M1 and tetrahedral sites, respectively. The molar vibrational Gibbs energy is described by a Taylor expansion of second degree in seven linearly independent composition and ordering variables, which is extended to third degree to account for asymmetry in the mixing of Ca and Mg, and Ca and Fe on the M2 site, and is further modified for the assumption that the standard state properties of Ca end-member components of clinopyroxenes are linearly dependent on the coordination number of Ca²⁺ on the M2 site. The model is shown to be consistent with miscibility gap feaures of pyroxenes in the system CaMgSi₂O₆–CaTiAl₂O₆–CaAl₂SiO₆. In subsequent papers, the model is calibrated for the simplifying assumptions that: (1) all regular-solution-type parameters are constants independent of temperature, (2) Pbca and C2/c end-members have identical heat capacities and coefficients of thermal expansion and compressibility, and (3) the heat capacities and coefficients of thermal expansion and compressibility are zero for all reciprocal reactions relating Pbca and pigeonite or high-calcium pyroxene C2/c endmember components.