洋中脊玄武岩含铝矿物弹性和热力学性质计算
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摘要
越来越多的地震学、矿物物理学、地球化学、地球动力学模拟等研究显示在下地幔深度的地球深部存在俯冲板块的证据,这说明俯冲板块可以穿透过渡带到达下地幔,甚至到达核幔边界,最终参与到全球尺度的地幔物质循环中去。洋中脊玄武岩(MORB)代表了俯冲海洋板块中地壳的成分。对MORB的高温高压实验研究发现,与地幔岩(pyrolite)模型中铝元素主要以杂质形式赋存于钙钛矿结构的(Mg,Fe)SiO3中不同的是,MORB在下地幔的温度压力条件下形成的矿物集合体中含有一种独立的含铝矿物,铝元素主要富集在这些独立的含铝的高压相矿物中。钙铁结构和钙钛结构的MgAl2O4(以下简称钙铁相和钙钛相)很可能是组成该富铝相矿物的重要端元组分。因此,对钙铁相和钙钛相的弹性常数、状态方程和热力学性质等的认识,是建立地幔矿物模型和研究俯冲板块在下地幔中的命运所不可或缺的基础数据。本研究采用了在平面波赝势框架下的,基于密度泛函理论的第一性原理的方法。首先用应变能密度方法对钙铁相和钙钛相的弹性常数进行了计算,给出了压力范围从0到80 GPa的弹性常数。着重考察了钙铁相和钙钛相相变压力40 GPa附近的弹性波波速变化和各向异性。计算发现了在40 GPa时钙铁相和钙钛相的剪切波波速增加达到最大值,约为1.6%。由此造成的俯冲洋壳与周围地幔的波速差约为0.4%,比地震估计所需的数值小0.6%,这说明钙铁相和钙钛相相变不足以引起中部地幔1000公里附近发现的地震波不连续。同时发现钙铁相和钙钛相都具有强烈的地震波各向异性,在40 GPa时其剪切波分裂最大值约为25%。如果下地幔上部地幔流体的运动能够使洋壳物质定向排列,则其剪切波分裂的特征很可能被地震观测发现。接下来,对钙铁相的热力学性质进行了计算。因为密度泛函理论中两种主要的交换相关泛函,即局域密度近似(LDA)和广义梯度近似(GGA)对零温度下体系状态方程都有一定的偏差影响,本文中引入了压力校正的方法,利用常温常压体积的实验值作为唯一的经验参数,对两种泛函得出的状态方程进行了校正,结果表明GGA泛函通过校正和实验吻合得更好。本研究进一步采用了密度泛函微扰理论进行声子频谱的计算,从而得到原子振动部分对于体系总能量的贡献。将体系的状态方程拓展到了有限温度的条件下,可以得出体系在任意温度下的状态方程。文中给出了钙铁相在温度分别为300、800、1200、1600、2000和2400K时的状态方程,将这些状态方程与高温高压实验的结果进行对比,两者基本吻合,将计算得到的钙铁相的状态方程和通过实验得到的其它MORB集合体中的矿物的状态方程相结合,计算了温度为2000 K时MORB矿物集合体的密度随压力的变化关系,结果发现在35-60 GPa的压力范围内,MORB的密度比PREM地震模型的地幔平均密度大2%,这个结果支持了俯冲板块可能越过过渡带进入下地幔的假说。在已知Helmholtz自由能与体积、温度的关系的情况下,根据热力学量的函数关系可以推导出在任意压力温度下的各种热力学性质的参数。本文首先用上述方法计算了刚玉的热力学性质,得到的结果与实验值吻合得非常好,验证了该计算方法的准确性。本文以列表的形式给出了压力为0-40 GPa,温度为0-2000 K条件下,包括摩尔体积、等温体模量、绝热体模量、热膨胀系数、等容热容、等压热容、Gruneisen参数、熵和焓差等在内的各种热力学量的数值。最后,本文给出的计算高温高压矿物热力学参数的方法有望推广到计算其他地幔矿物中去,具有广泛的地质应用。
More and more evidences from seismic tomography, mineral physics, geochem-istry and geodynamics modeling methods support that the presence of subducted slabs in the Earth's lower mantle. It is likely that the subducted slabs could penetrate the transition zone and reach the lower mantle, even the core-mantle boundary (CMB) and eventually be evolved in the global mantle convection. The mid-ocean ridge basalts (MORB) represent the crustal part of subducted oceanic plate. Many high pres-sure experiments have been conducted on pyrolite (a representative mantle rock) and MORB composition to lower mantle conditions. In contrast with pyrolite composi-tion, in which the aluminum mainly resides in MgSiO3 perovskite, an independent aluminous phase was discovered by high-pressure and high-temperature experiments in the basaltic composition. Two polymorphs of MgAl2O4 with calcium-ferrite (CF) and calcium-titanate (CT) structures are likely major end-members of the aluminous phase. Therefore, the elasticity, equation of state (EOS) and thermodynamic proper-ties of the CF phase and CT phase are indispensable knowledge for building a mantle mineralogical model and interpreting the fate of subducted slabs in the lower mantle. In this thesis, the main study methods are first principles computational techniques based on density functional theory (DFT) in the framework of pseudo-potentials and plane waves. First, the elastic constants of CF phase and CT phase were determined using strain energy density method from 0 to 80 GPa. Special investigation was per-formed around 40 GPa, which is the possible transition pressure from CF to CT, on the change of elastic velocities and seismic anisotropy. At 40 GPa, shear velocity contrast between the two phases reached its maximum with a value of 1.6%, corresponding a 0.4% jump of velocity between MORB and surrounding mantle. However, this is about 0.6% lower than one requires from seismic estimation. Thus, the mid-mantle discon-tinuity around 1000km seems unlikely caused by this phase transition. On the other hand, the CF phase and CT phase show great seismic anisotropy, e.g. the max value of shear wave splitting was 25% at 40 GPa. If the oceanic crustal materials could be aligned in a preferred direction by mantle flow, the big shear wave splitting characteris-tic may be detected by seismic observations. Next, the thermodynamic properties of CF phase were calculated. Both of the two main exchange-correlation functional in DFT method, the local density approximation (LDA) and generalized gradient approxima-tion (GGA), produce some deviations of athermal EOS from experiment. GGA gives better performance than LDA after introducing a pressure correction for the athermal EOS. Furthermore, the lattice vibrational frequencies, i.e. phonons, were obtained us-ing density functional perturbation theory. The vibrational energy can be calculated from phonon frequencies. The athermal EOS was extended to finite temperature under quasi-harmonic approximation. It was shown that the high pressure equation of states calculated from 300 to 2400 K agree very well with experiments. The calculated den-sity profile along 2000 K from 35 to 60 GPa for the subducted slabs are 2% higher than typical seismological model (PREM), conforming the hypothesis that subducted slabs can sink in the lower mantle. One can derive all thermodynamic potentials from Leg-endre transformations if the Helmholtz free energy, volume and temperature relations F(V,T) are known. In this thesis, the following thermodynamic properties, the molar volume, isothermal and adiabatic bulk modulus, thermal expansivity, constant volume and pressure heat capacities, Gruneisen parameter, entropy and enthalpy difference, are listed as tables in a pressure range of 0 to 40 GPa and a temperature range of 0 to 2000 K. The accuracy of the thermodynamic properties are validated by comparing calculated results with experiments for a simpler system, corundum, and showed ex-cellent agreement. Finally, the calculation method used in this study is also promising for other mantle minerals and will have great impact on other geological applications.
More and more evidences from seismic tomography, mineral physics, geochem-istry and geodynamics modeling methods support that the presence of subducted slabs in the Earth's lower mantle. It is likely that the subducted slabs could penetrate the transition zone and reach the lower mantle, even the core-mantle boundary (CMB) and eventually be evolved in the global mantle convection. The mid-ocean ridge basalts (MORB) represent the crustal part of subducted oceanic plate. Many high pres-sure experiments have been conducted on pyrolite (a representative mantle rock) and MORB composition to lower mantle conditions. In contrast with pyrolite composi-tion, in which the aluminum mainly resides in MgSiO3 perovskite, an independent aluminous phase was discovered by high-pressure and high-temperature experiments in the basaltic composition. Two polymorphs of MgAl2O4 with calcium-ferrite (CF) and calcium-titanate (CT) structures are likely major end-members of the aluminous phase. Therefore, the elasticity, equation of state (EOS) and thermodynamic proper-ties of the CF phase and CT phase are indispensable knowledge for building a mantle mineralogical model and interpreting the fate of subducted slabs in the lower mantle. In this thesis, the main study methods are first principles computational techniques based on density functional theory (DFT) in the framework of pseudo-potentials and plane waves. First, the elastic constants of CF phase and CT phase were determined using strain energy density method from 0 to 80 GPa. Special investigation was per-formed around 40 GPa, which is the possible transition pressure from CF to CT, on the change of elastic velocities and seismic anisotropy. At 40 GPa, shear velocity contrast between the two phases reached its maximum with a value of 1.6%, corresponding a 0.4% jump of velocity between MORB and surrounding mantle. However, this is about 0.6% lower than one requires from seismic estimation. Thus, the mid-mantle discon-tinuity around 1000km seems unlikely caused by this phase transition. On the other hand, the CF phase and CT phase show great seismic anisotropy, e.g. the max value of shear wave splitting was 25% at 40 GPa. If the oceanic crustal materials could be aligned in a preferred direction by mantle flow, the big shear wave splitting characteris-tic may be detected by seismic observations. Next, the thermodynamic properties of CF phase were calculated. Both of the two main exchange-correlation functional in DFT method, the local density approximation (LDA) and generalized gradient approxima-tion (GGA), produce some deviations of athermal EOS from experiment. GGA gives better performance than LDA after introducing a pressure correction for the athermal EOS. Furthermore, the lattice vibrational frequencies, i.e. phonons, were obtained us-ing density functional perturbation theory. The vibrational energy can be calculated from phonon frequencies. The athermal EOS was extended to finite temperature under quasi-harmonic approximation. It was shown that the high pressure equation of states calculated from 300 to 2400 K agree very well with experiments. The calculated den-sity profile along 2000 K from 35 to 60 GPa for the subducted slabs are 2% higher than typical seismological model (PREM), conforming the hypothesis that subducted slabs can sink in the lower mantle. One can derive all thermodynamic potentials from Leg-endre transformations if the Helmholtz free energy, volume and temperature relations F(V,T) are known. In this thesis, the following thermodynamic properties, the molar volume, isothermal and adiabatic bulk modulus, thermal expansivity, constant volume and pressure heat capacities, Gruneisen parameter, entropy and enthalpy difference, are listed as tables in a pressure range of 0 to 40 GPa and a temperature range of 0 to 2000 K. The accuracy of the thermodynamic properties are validated by comparing calculated results with experiments for a simpler system, corundum, and showed ex-cellent agreement. Finally, the calculation method used in this study is also promising for other mantle minerals and will have great impact on other geological applications.
引文
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