Thermodynamic parameters of CaMgSi₂O₆-Mg₂Si₂O₆ pyroxenes based on regular solution and cooperative disordering models

Thermodynamic parameters for the reaction: {Mathematical expression} in the system CaO-MgO-SiO₂ have been deduced from phase equilibrium and enthalpy of solution data. From the regular solution theory, the seventeen currently available reversed experimental compositions of coexisting enstatite and clinopyroxene, presumed to be ordered diopside, lead, by a statistical regression, to the following best fit parameters: ΔH^o=6.80 kJ ΔS^o=2.75 J/K W_H^Cpx=24.47 kJ (regular solution enthalpy parameter) W_V^Cpx=0.105 J/bar (regular solution volume parameter). The derived parameters are not significantly affected by the (necessary) choice of W^Opx in the range 20-50 kJ. The above values are in very good agreement with deductions from the solution calorimetry on synthetic CaMgSi₂O₆-Mg₂Si₂O₆ clinopyroxenes of Newton et al. (1979), which also places bounds on possible departures from the optimal values of these parameters. The calorimetric data may also be interpreted in terms of a Bragg-Williams cooperative-disordering model (Navrotsky and Loucks, 1977), in which diopside-structure clinopyroxene and a 'relaxed' low-Ca clinopyroxene ('Fe-free pigeonite') approach each other in composition, structural state, and stability with increasing temperature. The ΔH^o parameter deduced from the regular solution theory is reinterpreted as the enthalpy change of enstatite to Mg₂Si₂O₆ pigeonite; the ΔH^o of the transformation of enstatite to the diopside structure would, in this case, be considerably larger than 6.8 kJ. The curvature of the enthalpy of solution data, explained by the regular solution theory in terms of M2-site energetics (involving W_H^cpx), is reinterpreted as due to disordering and 'relaxation' in the Navrotsky-Loucks model. Although the regular solution theory with the best-fit parameters accounts for all of the reversed enstatite and diopside compositions to within 18 ° C, and is a convenient representation of the phase equilibria for purposes of geothermometry, the disordering model is, at the present level of knowledge, equally valid and allows for a region of stability of two coexisting clinopyroxenes.