Equation of state for Mg3Al2Si3O12 pyrope: Implications for post-garnet transitions and mantle dynamics

Abstract

Mantle convection is the dominant process driving the upwelling of hot materials and subduction of cold slabs. These processes are density-dependent and influenced by post-spinel and post-garnet transitions in the mantle transition zone (MTZ)/ lower mantle (LM). Knowledge of the Clapeyron slope of these transformations is used to express the dynamics of mantle blocks and is necessary for understanding the deep Earth. Here, we provide the Kunc-Einstein equation of state (EoS) for the pyrope Mg3Al2Si3O12 (Prp) calculated from a joint analysis of the experimentally measured isobaric heat capacity, bulk moduli, thermal expansion, pressure (P), unit cell volume (V), temperature (T) data. Based on our model, the bulk modulus and its pressure derivatives were K0,T0 = 168.5 GPa, K′0,T = 4.77, and V0 = 1501.7 Å. The optimised parameters include two Einstein temperatures, i.e., θ1 = 331 and θ2 = 1093 K, Grüneisen parameter at ambient condition γ0 = 1.77, infinite compression γ∞ = 0 with β = 1.12 and an intrinsic anharmonicity parameter a0 = –20. The value for the thermal expansion coefficient was calculated to be α = 2.33·10−5 K−1, and the thermodynamic Grüneisen parameter was estimated as γth = 1.42. The obtained EoS for Prp and the preliminarily fitted EoS for Al-bearing akimotoite (Al-Aki), in combination with literature data on bridgmanite (Bdm) and corundum (Crn), allowed the calculation of the phase diagram of the system with 75 mol% MgSiO3 + 25 mol% Al2O3 under LM conditions. The transformation from Prp to Bdm + Crn was computed at 24 GPa and 1570 K and exhibited a slightly positive Clapeyron slope (dP/dT = 2.1 MPa/K). The stability field of Al-Aki was detected at T = 1250–1570 K and P = 23–27 GPa. At P values higher than 24–27 GPa, the Al-Aki transforms into a Bdm + Crn assemblage with a highly negative Clapeyron slope. Calculations of sound velocities for the studied phases showed that the transformation from Prp to Bdm + Crn increased Vp and Vs by up to 9 and 20%, respectively. Such a big jump in the sound velocities indicates that the post-garnet transition is a better candidate than the post-Aki transition for producing a double discontinuity at the base of the MTZ, in combination with the transformation of ringwoodite into the Bdm + ferropericlase assemblage. The increase in sound velocities associated with the formation and dissolution of Al-Aki is unlikely to be sensitive to the MTZ. The combination of post-garnet, post-spinel, and post-Aki transitions near 660–720 km depths may have sluggished both the upwelling hot mantle and the subducted cold plates. The stagnant, hot LM material at the base of MTZ warmed the harzburgite and eclogite layers stacked during subduction. The heated MTZ may have been involved in further upwelling.