Structural similarities between dry diopside melt and superhydrous albite melt (X w >0.5) — both lack three-dimensional silicate units — suggest that thermodynamic relations may be similar. A model based on that assumption successfully predicts diopside melting relations and H2O solubilities. For the model, the three partial differential equations describing solution of H2O in albite melt for X w >0.5 have been integrated for diopside melt from X w =0 to X w at least as large as 0.76, with two exceptions: an alternative partial differential equation for Henrian solution of H2O in dilute melts was applied for X w <0.20, and an alternative differential equation for the pressure dependence of a w at pressures below 2 kbar was developed. The latter alternative equation yields relatively small ¯Vw's at low pressures rather than the large ¯Vw's calculated from the equation from the albite system. Available experimental solubility data are not precise enough to offer a choice between the small-¯Vw and large-¯Vw equations. Integration of all the partial differential equations was constrained solely by the P and T of a single experimentally-determined point on the H2O-saturated solidus.
Solubilities calculated by a Henrian-analogue solution model (a di=X di 2 ) from the experimental H2O saturated solidus lie outside experimental solubility constraints for dilute melts. On the other hand, a Henrian model (a di=Xdi) successfully predicts solubilities in dilute melts. The formulation of the Henrian model and magnitudes of model molar entropies of solution are consistent with the hypothesis that H2O dissolves in diopside melt as an essentially undissociated species with little ordering on melt structural sites. That species could in turn be consistently, if not uniquely, interpreted to be molecular H2O or a hydroxylation (OH−) complex formed from nonbridging oxygens.
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Eggler, D.H., Burnham, C.W. Solution of H2O in diopside melts: a thermodynamic model. Contr. Mineral. and Petrol. 85, 58–66 (1984). https://doi.org/10.1007/BF00380221
- Partial Differential Equation
- Thermodynamic Model
- Pressure Dependence