The configurational entropies of Ca2MgSi2O7-Ca2SiAl2O7 melilites and related minerals

Equations for the configurational entropy and homogeneous equilibria in Ca₂MgSi₂O₇-Ca₂SiAl₂O₇ melilites are derived for a site constraint that does not permit Mg on the smaller T₂ tetrahedral sites. This constraint leads to one ordering parameter and one composition parameter. The maximum configurational entropy for perfectly ordered crystalline solutions is 3.795 cal K^–1 mol^–1, corresponding to the structural formula Ca₂(Mg_0.33Al_0.67) (Si_0.67Al_0.33)₂O₇ and not the equimolar composition Ca₂(Mg_0.5Al_0.5)(Si_0.75Al_0.25)₂O₇. Similarly, the configuration Ca₂(Si_0.33Al_0.67)(Si_0.33Al_0.67)₂O₇ has the maximum entropy for the gehlenite end-member composition. The tabulated entropy of end-member gehlenite at 298.15 K must be corrected by at least 2Rln2, which corresponds to a substantial correction to its Gibbs energy at high temperature. The same corrections are applicable to other minerals having two crystallographically distinct sites in a 21 ratio and where the same configurational entropy equation applies: MgFe₂O₄ (magnesioferrite), NiFe₂O₄ (trevorite), TiFe₂O₄ (ulvospinel), TiMg₂O₄, TiZn₂O₄, CuFe₂O₄, and TiFe₂O₅ (pseudobrookite) inasmuch as these substances prefer the same inverse ordered state as gehlenite at low temperatures. The effects of the ideal enthalpy and entropy on temperatures of homogeneous equilibria in gehlenite and MgTi₂O₅ are evaluated. Geological-thermometer phase diagrams of the long-range ordering parameter plotted against temperature have a sigmoidal shape for these minerals owing to the fact that this type of disordering is non-convergent.