地幔对流是驱动热物质上涌和冷板片俯冲的主要过程。这些过程取决于密度,并受到地幔过渡带(MTZ)/下地幔(LM)中尖晶石后和石榴石后过渡的影响。这些转变的克拉佩龙斜率的知识可用于表达地幔块的动力学,并且对于了解地球深处是必要的。在这里,我们提供了镁铝榴石 Mg 3 Al 2 Si 3 O 12的 Kunc-Einstein 状态方程 (EoS)(Prp) 通过对实验测量的等压热容、体积模量、热膨胀、压力 (P)、晶胞体积 (V)、温度 (T) 数据的联合分析计算得出。根据我们的模型,体积模量及其压力导数为 K 0,T0 = 168.5 GPa、K′ 0、T = 4.77 和 V 0 = 1501.7 Å。优化参数包括两个爱因斯坦温度,即 θ 1 = 331 和 θ 2 = 1093 K,环境条件下的 Grüneisen 参数 γ 0 = 1.77,无限压缩 γ ∞ = 0,β = 1.12 以及固有非谐参数 a 0 = – 20. 计算出热膨胀系数值为 α = 2.33·10−5 K −1,热力学 Grüneisen 参数估计为 γ th = 1.42。获得的 Prp 的 EoS 和初步拟合的含铝秋本石 (Al-Aki) 的 EoS,结合桥锰石 (Bdm) 和刚玉 (Crn) 的文献数据,可以计算 75 mol 体系的相图LM 条件下% MgSiO 3 + 25 mol% Al 2 O 3 。从 Prp 到 Bdm + Crn 的转变是在 24 GPa 和 1570 K 下计算的,并表现出略为正的克拉佩龙斜率 (d P /d T = 2.1 MPa/K)。Al-Aki 的稳定场在T = 1250–1570 K 和P = 23–27 GPa 时检测到。在P值高于 24-27 GPa,Al-Aki 转变为具有高度负 Clapeyron 斜率的 Bdm + Crn 组合。研究阶段的声速计算表明,从 Prp 到 Bdm + Crn 的转变增加了V p和 V s分别高达 9% 和 20%。声速的如此大的跳跃表明,后石榴石转变是比后 Aki 转变更好的候选者,可以在 MTZ 底部产生双不连续性,并结合尖橄榄石转变为 Bdm + 铁方镁石组合。与 Al-Aki 的形成和溶解相关的声速增加不太可能对 MTZ 敏感。660-720公里深度附近的后石榴石期、后尖晶石期和后阿基期过渡的结合可能使上涌的热地幔和俯冲的冷板块都变得迟缓。MTZ 底部停滞的热 LM 物质使俯冲过程中堆积的方辉橄榄岩和榴辉岩层变暖。加热的 MTZ 可能参与了进一步的上升流。
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Equation of state for Mg3Al2Si3O12 pyrope: Implications for post-garnet transitions and mantle dynamics
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.