THERMODYNAMICS OF MULTICOMPONENT PYROXENES .1. 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 componen t 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 simplif ying assumptions that: (1) a molecular mixing type approximation descr ibes changes in the molar configurational entropy associated with the coupled exchange substitutions TiAl2 double-line arrow pointing left a nd right MgSi2, Fe3+Al double-line arrow pointing left and right MgSi, and Al2 double-line arrow pointing left and right MgSi (and their fer roan equivalents), and (2) Fe2+ and Mg2+, and Al3+ and Fe3+ display lo ng-range non-convergent ordering between M2 and octahedral M1 sites, a nd octahedral M1 and tetrahedral sites, respectively. The molar vibrat ional Gibbs energy is described by a Taylor expansion of second degree in seven linearly independent composition and ordering variables, whi ch 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 fo r the assumption that the standard state properties of Ca end-member c omponents of clinopyroxenes are linearly dependent on the coordination number of Ca2+ on the M2 site. The model is shown to be consistent wi th miscibility gap features of pyroxenes in the system CaMgSi2O6 - CaT iAl2O6 - CaAl2SiO6. In subsequent papers, the model is calibrated for the simplifying assumptions that: (1) all regular-solution-type parame ters are constants independent of temperature, (2) Pbca and C2/c end-m embers have identical heat capacities and coefficients of thermal expa nsion and compressibility, and (3) the heat capacities and coefficient s of thermal expansion and compressibility are zero for all reciprocal reactions relating Pbca and pigeonite or high-calcium pyroxene C2/c e nd-member components.