Thermal equation of state of majoritic knorringite and its significance for continental upper mantle

The P-V-T equation of state (EoS) for majoritic knorringite Mg_3.19Cr_1.60Si_3.19O₁₂ at pressures to 17 GPa and temperatures to 1673 K was obtained from in situ X-ray diffraction experiments using a Kawai-type multi-anvil apparatus. Fitting of the room-temperature P-V data to a third-order Birch-Murnaghan EoS yielded an isothermal bulk modulus, K_0,300 = 154 (4) GPa, and a pressure derivative, K_0,300 = 5.4 (1.2). When fitting a high-temperature Birch-Murnaghan EoS using all of the P-V-T data at a fixed V₀ = 1549.08 ų, we find that K_0,300 = 157 (2) GPa, K_0,T = 4.5 (6), (∂K_0,T/∂T)_P = -0.019 (4) (GPa K^-1), a = 3.00 (14) × 10^-5 K^-1, and b = 0.65 (24) × 10^-8 K^-2, where α = a + bT is the volumetric thermal expansion coefficient. Fitting the Mie-Grüneisen-Debye EoS with the present data with a Debye temperature fixed at θ₀ = 731 K yielded a Grüneisen parameter, γ₀ = 1.34 at q = 1.0 (fixed). The thermoelastic parameters of pure knorringite were estimated and were compared with the previous data on other garnet compositions. The presence of Cr₂O₃ in pyrope garnets in the upper mantle decreases P- and S-velocities by 1.6% and the density increases by 1.7% (for 20 mol.% knorringite end member) compared to pure pyrope. The results show the importance of accounting knorringite end-member for accurate estimation of mantle garnet acoustic velocities.