Equation of state of spinel (MgAl₂O₄): constraints on self-consistent thermodynamic parameters and implications for elastic geobarometry of peridotites and chromitites

Spinel is potentially one of the best minerals for elastic geobarometry, but the large uncertainties in the published equation of state (EoS) of spinel prevent the application of elastic geobarometry using spinel. We have determined the EoS of MgAl₂O₄ from literature data on the volume, elasticity, and isobaric heat capacity by paying particular attention to the consistency of the thermoelastic data within the dataset and the influence of the inversion degree (i; (Mg_1-iAl_i)[Mg_iAl_2-i]O₄) on the physical properties. After appropriate data selection, normalization, and correction, the resulting dataset was fitted with various EoS. Thermal pressure EoS that combined the third-order Birch–Murnaghan EoS and the Mie–Grüneisen–Debye EoS explain the data most successfully. The analysis yielded the following six EoS parameters: V₀ = 39.78 cm³/mol (fixed), K_T0 = 196.43(12) GPa, K′_T0 = 4.37(4), θ_D0 = 898(10) K, γ₀ = 1.136(11), and q = 1.94(9). The EoS has the properties at room conditions of α_V = 1.6765(10) × 10^–5 K^–1 and K_S0 = 197.55(12) GPa. Combining our EoS with the published EoS, it was found that MgAl₂O₄ inclusions trapped in olivine and orthopyroxene derived from the spinel-lherzolite stability field should always have positive residual pressures (P_inc) at room conditions. This implies that elastic geobarometry using these host-inclusion systems can be expected to be new methods for estimating the depth provenance of spinel-bearing peridotites. In contrast olivine, orthopyroxene, and clinopyroxene inclusions in MgAl₂O₄ are expected to have P_inc > 0 only when trapped (or re-equilibrated) in geological environments with geotherms corresponding to surface heat flows below about 50, 60 and 70 mW/m², respectively.