Garnet EoS: a critical review and synthesis

Abstract

AbstractAll available volume and elasticity data for the garnet end-members grossular, pyrope, almandine and spessartine have been re-evaluated for both internal consistency and for consistency with experimentally measured heat capacities. The consistent data were then used to determine the parameters of third-order Birch–Murnaghan EoS to describe the isothermal compression at 298 K and a Mie–Grüneisen–Debye thermal-pressure EoS to describe the PVT behaviour. In a full Mie–Grüneisen–Debye EoS, the variation of the thermal Grüneisen parameter with volume is defined as $$\gamma = {\gamma }_{0}{\left(\frac{V}{{V}_{0}}\right)}^{q}$$ γ = γ 0 V V 0 q . For grossular and pyrope garnets, there is sufficient data to refine q which has a value of q = 0.8(2) for both garnets. For other garnets, the data do not constrain the value of q and we therefore refined a q-compromise version of the Mie–Grüneisen–Debye EoS in which both γ/V and the Debye temperature θ D are held constant at all P and T, leading to $$\left( {{\raise0.7ex\hbox{${\partial C_{{\text{V}}} }$} \!\mathord{\left/ {\vphantom {{\partial C_{{\text{V}}} } {\partial P}}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\partial P}$}}} \right)_{{\text{T}}} = 0$$ ∂ C V ∂ P T = 0 , parallel isochors and constant isothermal bulk modulus along an isochor. Final refined parameters for the q-compromise Mie–Grüneisen–Debye EoS are: Pyrope Almandine Spessartine Grossular V0 (cm3/mol)a 113.13 115.25 117.92 125.35 K0T (GPa) 169.3 (3) 174.6 (4) 177.57 (6) 167.0 (2) $$K^{\prime}_{{0{\text{T}}}}$$ K 0 T ′ 4.55 (5) 5.41 (13) 4.6 (3) 5.07 (8) θ D0 771 (28) 862 (22) 860 (35) 750 (13) γ0 1.185 (12) 1.16 (fixed) 1.18 (3) 1.156 (6) for pyrope and grossular, the two versions of the Mie–Grüneisen–Debye EoS predict indistinguishable properties over the metamorphic pressure and temperature range, and the same properties as the EoS based on experimental heat capacities. The biggest change from previously published EoS is for almandine for which the new EoS predicts geologically reasonable entrapment conditions for zircon inclusions in almandine-rich garnets.