The Mg2SiO4 polymorphs (olivine, modified spinel and spinel)–thermodynamic properties from oxide melt solution calorimetry, phase relations, and models of lattice vibrations

High temperature solution calorimetry of the α-, β-, and γ-Mg₂SiO₄ polymorphs gives $ΔH1000∘(α−β)=7610±680 cal mol−1$ and $ΔH1000∘(β→γ)=1630±900 cal mol−1$⁠. Based on the phase equilibrium data of Suito (1977) and appropriate thermal expansivity, compressibility, and heat capacity data, $ΔS1000∘=−2.5±0.5$ and −1.5±0.9 cal mol⁻¹K⁻¹ for the α→β and β→γ transitions, respectively. Infrared and Raman spectra have been obtained for the three phases, and the lattice vibrational thermodynamic properties of the Mg₂SiO₄ polymorphs have been calculated using the model approach developed by Kieffer (1979c). A range of models consistent with the infrared and Raman data and compressional and shear wave velocities give entropies and heat capacities consistent with reported heat capacities (available only at 350–700 K for β- and γ-Mg₂SiO₄) and with the entropies of transition calculated above. From the vibrational calculations $ΔS1000∘(α→β)=−2.8±0.6 cal mol−1K−1$ and $ΔS1000∘(β→γ)=−1.3±0.9 cal mol−1K−1$⁠. These two approaches to calculating ΔS° (calorimetry plus phase equilibria compared to vibrational calculations) offer means of constraining the P–T slopes of phase transitions at very high pressure, where experimental determinations suffer from serious uncertainties. The thermochemical data for α, β, and γ-Mg₂SiO₄ are used to construct the P,T diagram for these phases. The slopes of the α–β, β–γ, and α–γ boundaries are calculated to be positive and a triple point is predicted to be near 500 (±150) K and 120 (±10) kbar.