下地幔主要矿物的熔化、弹性和热力学特性研究
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摘要
随着现代地球科学的发展，对地球物质科学的研究已经成为一个非常重要的领域。组成地球的物质在物理和化学性质上控制着地球各圈层的演化及其动力学过程，因此运用现代物理学和现代地球化学手段对地球物质进行全面研究具有非常重要的意义。MgSiO_3钙钛矿同质异构体(～75vol％)、MgO(～20vol％)和CaSiO_3钙钛矿(～5vol％)是地球下地幔最主要的成分，研究它们的高压行为对理解地球的结构、动力学、演化及起源至关重要。然而，在实验室很难达到下地幔对应的压强(24—136 GPa)，因而对地球深部矿物物理性质的认识仍十分有限。随着计算机模拟技术的发展，对其物性的认识逐渐成为可能。本工作采用先进的计算机模拟方法，较为深入系统地研究了它们的物理性质，内容主要包括：
1．利用经典分子动力学和Buckingham对势模型，确定了MgSiO_3钙钛矿和MgO的高压熔化曲线。在地球下地幔的高温高压条件下，理解下地幔的熔化行为对解释地球早期的历史和演化以及对确定地幔的局部熔化在核—幔边界是否是地震观测到超低速区域的原因极其重要。本工作首先在常温常压下对MgSiO_3钙钛矿和MgO的热力学特性进行了数值模拟，检验了相互作用势模型的可靠性。随后预测了温度上升到3000 K压强上升到120 GPa时它们的状态方程。由于熔化是凝聚态物理中很难理解的现象之一，因此对熔化温度的研究也就成了一个难点。本文提出的解决方案是计算热不稳定性温度(也叫过热温度)，然后估计过热度来确定熔化曲线。通过计算MgSiO_3钙钛矿和MgO在常压下对应的热不稳定性温度，发现它们的过热度分别为42％和30％，这个结果在Luo Shennian等对元素和化合物均匀形核的归一化能垒分类研究给出的过热范围(10～50％)内。根据不同压强下计算的热不稳定性温度和过热度，最后确定了压强上升到136 GPa(核—幔边界压强)时MgSiO_3钙钛矿和MgO的高压熔化曲线。研究表明：MgO的高压熔化曲线和最近Alfè等利用两相分子动力学模拟的结果吻合的相当好，MgSiO_3钙钛矿的熔化曲线在60 GPa以下相对陡一些，随着压强的增加逐渐变得平缓；在实验研究的范围内与实验结果基本一致；在下地幔压强范围内，与Belonoshko等模拟的熔化温度随压强变化的趋势完全相同，并与其通过现象学计算的结果完全一致。确定下地幔主要矿物的高压熔化线，不仅可为科学地球物理模型的建立奠定坚实的物理基础，而且可以为其它材料高压熔化曲线的理论研究提供方法，从而可以为建立科学的熔化规律提供有效的理论数据。
2．利用第一性原理平面波赝势方法，研究了MgSiO_3钙钛矿同质异构体、MgO和CaSiO_3钙钛矿的高压弹性行为。在极端条件(如高压，高温等)下，对MgSiO_3钙钛矿同质异构体、MgO和CaSiO_3钙钛矿弹性常数的测量仍面临着极大的挑战。第一性原理计算可为实验方法提供理想的补充，因为它们不需要输入实验参数，也就是说，在理论中没有自由参数。如此的计算具有真正预测的能力，并能提供包括实验很难测量的关键信息。高压弹性的研究表明：1)MgO的B1相(类NaCl结构)稳定上升到397 GPa，排除了在下地幔内B1-B2(类CsCl结构)的相变。压强上升到20 GPa时，MgO的弹性各向异性随着压强的增加逐渐减小。高压下，弹性各向异性符号变为负值，并随着压强的增加其数值逐渐增大，从而预测到MgO在下地幔底部有较大的弹性各向异性。另外，MgO和CaSiO_3钙钛矿强烈地违背了Cauchy条件，这反应了非中心多体力的重要性。2)CaSiO_3钙钛矿的体弹模量类似于MgSiO_3的体弹模量，然而在下地幔对应的压强范围内，它的剪切模量比MgSiO_3的高很多。这表明CaSiO_3钙钛矿不再被看作是地球下地幔主要组成模型的不可见成分，甚至这个矿物少量的成分可对地震性质产生明显的影响，尤其是对剪切波速。此外，CaSiO_3钙钛矿在过渡区和下地幔顶部对应的压强范围内表现出强烈的各向异性。3)研究了压强上升到200 GPa，温度上升到4000 K时，MgSiO_3钙钛矿和后钙钛矿的状态方程，发现后钙钛矿相总是比钙钛矿致密。根据焓相等理论，得到了从钙钛矿相转变到后钙钛矿相的压强为108 GPa。在整个下地幔压强范围内，MgSiO_3钙钛矿和后钙钛矿均表现出强烈的各向异性，各向异性随着压强有明显变化。MgSiO_3钙钛矿相和后钙钛矿相的各向同性波速表明后钙钛矿相是下地幔D″区域(核—幔边界之上200～300 km的地方)最丰富的矿物，而钙钛矿相是下地幔其它区域最主要的矿物。由此可见，地球材料高压弹性的研究与球形地震X线断层摄影术、地理学和放射状局部区域的地震学研究、地幔的不连续、固有振荡模式的分析和研究的其它类型贡献一样详细地揭示了地幔的性质。
3．利用准谐近似Debye模型，系统地预测了CaSiO_3钙钛矿高温高压下的热力学特性。尽管CaSiO_3钙钛矿是下地幔最丰富的矿物之一，但是人们对其热力学特性的认识极其有限。本文利用该模型首次预测了CaSiO_3钙钛矿的体弹模量、热膨胀系数、热容和熵与温度和压强的关系。研究发现：1)体弹模量与压强成线性关系，随温度的增加而减小；随着压强的增加而增加。2)低温下热膨胀系数迅速增加，高温时变化的趋势变得非常平缓；随着压强的增加，热膨胀系数快速减小。3)高温高压时热容接近某一极限。4)与热膨胀系数和热容不同，熵几乎对压强不敏感。这个结果可为其它矿物和材料的热力学特性研究提供科学的指导意义。
The behavior of Earth materials at high pressure is central to our understanding of the structure, dynamics, and origin of the Earth. Over the range of conditions that exist within the Earth's mantle, the physical properties of condensed matter depend more strongly on pressure than on other factors such as temperature. The high pressure physical properties of Earth materials are difficult to obtain directly through laboratory experiments. However, computer simulations have been increasingly popular in exploring various properties of the Earth's materials at the geophysically relevant conditions. In this paper, the physical properties of the main composition (MgSiO_3 perovskite and post-perovskite, MgO and CaSiO_3 perovskite) of the Earth's lower mantle at high pressures have systemically study using state-of-the-art computer simulation techniques. The main work contains the following sections:
1. The melting curve of MgSiO_3 perovskite and MgO are simulated by using the constant temperature and pressure molecular dynamics method combined with effective pair potentials. Understanding the melting behavior of Earth materials at the pressure and temperature conditions of the Earth's lower mantle is crucial to deciphering the early history and differentiation of the Earth and to determining if partial melting of the mantle is responsible for the seismologically observed ultra-low velocity zone at the core-mantle boundary. In this work, Firstly, the reliability of the present potential model has been verified. Secondly, the pressure-volume equations of state of MgSiO_3 perovskite and MgO were predicted at higher temperatures and higher pressures. Melting is arguably one of the least well understood processes in condensed matter physics, so a rigorous study of the minerals melting is prohibited either by technical problems or by the present state of the theory. This makes the problem of finding melting temperature of the minerals really challenging. A possible solution is to calculate the temperature of overheating (thermal instability temperature) and then estimate the degree of overheating. It is found that the degree of superheating of MgSiO_3 perovskite and MgO are 42％and 30％, respectively. According to this value, the melting curve of MgSiO_3 perovskite and MgO were determined.
2. High-pressure elasticity of MgSiO_3 perovskite polymorph, MgO and CaSiO_3 perovskite. Experimental studies in understanding high-pressure behavior of elastic properties of relevant phases are still lacking. First-principles calculations provide the ideal complement to the laboratory approach because they require no input from experiment; that is, there are no free parameters in the theory. Such calculations have true predictive power and can supply critical information including that which is difficult to measure experimentally. High-pressure elasticity of the relevant minerals contains the following sections: 1) The observed B1 phase of MgO was found to be stable up to 397 GPa, precluding the B1-B2 phase transition within the lower mantle. MgO was found to be highly anisotropic in its elastic properties, with the magnitude of the anisotropy first decreasing between 0 and 20 GPa and then increasing from 20 to 150 GPa. We found the high pressure reversal of the sign of elastic anisotropy in MgO and the prediction that MgO has a large elastic anisotropy in the lowermost mantle. The Cauchy condition was found to be strongly violated in MgO and CaSiO_3 perovskite, reflecting the importance of noncentral many-body forces. 2) The bulk modulus of CaSiO_3 perovskite is similar to that of MgSiO_3 perovskite; however, its shear modulus is much higher at pressures corresponding to the lower mantle. This suggests that CaSiO_3 perovskite can no longer be considered as an invisible component in modelling the composition of the lower mantle, and even small amounts of the mineral may affect significantly the seismic properties, particularly shear wave velocity, of the generally accepted Mg-rich silicate perovskite dominated composition of this region. Moreover, CaSiO_3 perovskite exhibits strong anisotropy at pressures corresponding to the transition zone and the top of the lower mantle. 3)Comparison between the volumes of the MgSiO_3 perovskite phase to the post-perovskite phase at the same pressure-temperature conditions indicates that the post-perovskite phase is always denser than the perovskite. According to the usual condition of equal enthalpies, it is shown that the transition from the perovskite phase to the post-perovskite phase occurs at the pressure of 108 GPa. It is found that the MgSiO_3 post-perovskite phase has similar bulk modulus and larger shear modulus than perovskite at relevant pressures. This phase is remarkably anisotropic. Comparisons with seismological observation show that post-perovskite may be the most abundant mineral in the D" region.
3. The thermodynamic properties of CaSiO_3 perovskite are systemically predicted using the quasi-harmonic Debye model for the first time at high pressure and high temperature. It can be seen that the thermal expansion coefficient increases with T~3 at low temperatures and gradually approaches a linear increase at high temperatures, and then the increasing trend becomes gentler. The effects of the pressure on the thermal expansion coefficient are very small at low temperatures; the effects are increasingly obvious as the temperature increases. As pressure increases, the thermal expansion coefficient decreases rapidly and the effects of temperature become less and less pronounced, resulting in linear high temperature behaviour. The thermal expansion coefficient and heat capacity are shown to converge to a nearly constant value at high pressures and temperatures. Unlike the thermal expansion coefficient and heat capacity, the entropy is nearly insensitive to pressure.
1．利用经典分子动力学和Buckingham对势模型，确定了MgSiO_3钙钛矿和MgO的高压熔化曲线。在地球下地幔的高温高压条件下，理解下地幔的熔化行为对解释地球早期的历史和演化以及对确定地幔的局部熔化在核—幔边界是否是地震观测到超低速区域的原因极其重要。本工作首先在常温常压下对MgSiO_3钙钛矿和MgO的热力学特性进行了数值模拟，检验了相互作用势模型的可靠性。随后预测了温度上升到3000 K压强上升到120 GPa时它们的状态方程。由于熔化是凝聚态物理中很难理解的现象之一，因此对熔化温度的研究也就成了一个难点。本文提出的解决方案是计算热不稳定性温度(也叫过热温度)，然后估计过热度来确定熔化曲线。通过计算MgSiO_3钙钛矿和MgO在常压下对应的热不稳定性温度，发现它们的过热度分别为42％和30％，这个结果在Luo Shennian等对元素和化合物均匀形核的归一化能垒分类研究给出的过热范围(10～50％)内。根据不同压强下计算的热不稳定性温度和过热度，最后确定了压强上升到136 GPa(核—幔边界压强)时MgSiO_3钙钛矿和MgO的高压熔化曲线。研究表明：MgO的高压熔化曲线和最近Alfè等利用两相分子动力学模拟的结果吻合的相当好，MgSiO_3钙钛矿的熔化曲线在60 GPa以下相对陡一些，随着压强的增加逐渐变得平缓；在实验研究的范围内与实验结果基本一致；在下地幔压强范围内，与Belonoshko等模拟的熔化温度随压强变化的趋势完全相同，并与其通过现象学计算的结果完全一致。确定下地幔主要矿物的高压熔化线，不仅可为科学地球物理模型的建立奠定坚实的物理基础，而且可以为其它材料高压熔化曲线的理论研究提供方法，从而可以为建立科学的熔化规律提供有效的理论数据。
2．利用第一性原理平面波赝势方法，研究了MgSiO_3钙钛矿同质异构体、MgO和CaSiO_3钙钛矿的高压弹性行为。在极端条件(如高压，高温等)下，对MgSiO_3钙钛矿同质异构体、MgO和CaSiO_3钙钛矿弹性常数的测量仍面临着极大的挑战。第一性原理计算可为实验方法提供理想的补充，因为它们不需要输入实验参数，也就是说，在理论中没有自由参数。如此的计算具有真正预测的能力，并能提供包括实验很难测量的关键信息。高压弹性的研究表明：1)MgO的B1相(类NaCl结构)稳定上升到397 GPa，排除了在下地幔内B1-B2(类CsCl结构)的相变。压强上升到20 GPa时，MgO的弹性各向异性随着压强的增加逐渐减小。高压下，弹性各向异性符号变为负值，并随着压强的增加其数值逐渐增大，从而预测到MgO在下地幔底部有较大的弹性各向异性。另外，MgO和CaSiO_3钙钛矿强烈地违背了Cauchy条件，这反应了非中心多体力的重要性。2)CaSiO_3钙钛矿的体弹模量类似于MgSiO_3的体弹模量，然而在下地幔对应的压强范围内，它的剪切模量比MgSiO_3的高很多。这表明CaSiO_3钙钛矿不再被看作是地球下地幔主要组成模型的不可见成分，甚至这个矿物少量的成分可对地震性质产生明显的影响，尤其是对剪切波速。此外，CaSiO_3钙钛矿在过渡区和下地幔顶部对应的压强范围内表现出强烈的各向异性。3)研究了压强上升到200 GPa，温度上升到4000 K时，MgSiO_3钙钛矿和后钙钛矿的状态方程，发现后钙钛矿相总是比钙钛矿致密。根据焓相等理论，得到了从钙钛矿相转变到后钙钛矿相的压强为108 GPa。在整个下地幔压强范围内，MgSiO_3钙钛矿和后钙钛矿均表现出强烈的各向异性，各向异性随着压强有明显变化。MgSiO_3钙钛矿相和后钙钛矿相的各向同性波速表明后钙钛矿相是下地幔D″区域(核—幔边界之上200～300 km的地方)最丰富的矿物，而钙钛矿相是下地幔其它区域最主要的矿物。由此可见，地球材料高压弹性的研究与球形地震X线断层摄影术、地理学和放射状局部区域的地震学研究、地幔的不连续、固有振荡模式的分析和研究的其它类型贡献一样详细地揭示了地幔的性质。
3．利用准谐近似Debye模型，系统地预测了CaSiO_3钙钛矿高温高压下的热力学特性。尽管CaSiO_3钙钛矿是下地幔最丰富的矿物之一，但是人们对其热力学特性的认识极其有限。本文利用该模型首次预测了CaSiO_3钙钛矿的体弹模量、热膨胀系数、热容和熵与温度和压强的关系。研究发现：1)体弹模量与压强成线性关系，随温度的增加而减小；随着压强的增加而增加。2)低温下热膨胀系数迅速增加，高温时变化的趋势变得非常平缓；随着压强的增加，热膨胀系数快速减小。3)高温高压时热容接近某一极限。4)与热膨胀系数和热容不同，熵几乎对压强不敏感。这个结果可为其它矿物和材料的热力学特性研究提供科学的指导意义。
The behavior of Earth materials at high pressure is central to our understanding of the structure, dynamics, and origin of the Earth. Over the range of conditions that exist within the Earth's mantle, the physical properties of condensed matter depend more strongly on pressure than on other factors such as temperature. The high pressure physical properties of Earth materials are difficult to obtain directly through laboratory experiments. However, computer simulations have been increasingly popular in exploring various properties of the Earth's materials at the geophysically relevant conditions. In this paper, the physical properties of the main composition (MgSiO_3 perovskite and post-perovskite, MgO and CaSiO_3 perovskite) of the Earth's lower mantle at high pressures have systemically study using state-of-the-art computer simulation techniques. The main work contains the following sections:
1. The melting curve of MgSiO_3 perovskite and MgO are simulated by using the constant temperature and pressure molecular dynamics method combined with effective pair potentials. Understanding the melting behavior of Earth materials at the pressure and temperature conditions of the Earth's lower mantle is crucial to deciphering the early history and differentiation of the Earth and to determining if partial melting of the mantle is responsible for the seismologically observed ultra-low velocity zone at the core-mantle boundary. In this work, Firstly, the reliability of the present potential model has been verified. Secondly, the pressure-volume equations of state of MgSiO_3 perovskite and MgO were predicted at higher temperatures and higher pressures. Melting is arguably one of the least well understood processes in condensed matter physics, so a rigorous study of the minerals melting is prohibited either by technical problems or by the present state of the theory. This makes the problem of finding melting temperature of the minerals really challenging. A possible solution is to calculate the temperature of overheating (thermal instability temperature) and then estimate the degree of overheating. It is found that the degree of superheating of MgSiO_3 perovskite and MgO are 42％and 30％, respectively. According to this value, the melting curve of MgSiO_3 perovskite and MgO were determined.
2. High-pressure elasticity of MgSiO_3 perovskite polymorph, MgO and CaSiO_3 perovskite. Experimental studies in understanding high-pressure behavior of elastic properties of relevant phases are still lacking. First-principles calculations provide the ideal complement to the laboratory approach because they require no input from experiment; that is, there are no free parameters in the theory. Such calculations have true predictive power and can supply critical information including that which is difficult to measure experimentally. High-pressure elasticity of the relevant minerals contains the following sections: 1) The observed B1 phase of MgO was found to be stable up to 397 GPa, precluding the B1-B2 phase transition within the lower mantle. MgO was found to be highly anisotropic in its elastic properties, with the magnitude of the anisotropy first decreasing between 0 and 20 GPa and then increasing from 20 to 150 GPa. We found the high pressure reversal of the sign of elastic anisotropy in MgO and the prediction that MgO has a large elastic anisotropy in the lowermost mantle. The Cauchy condition was found to be strongly violated in MgO and CaSiO_3 perovskite, reflecting the importance of noncentral many-body forces. 2) The bulk modulus of CaSiO_3 perovskite is similar to that of MgSiO_3 perovskite; however, its shear modulus is much higher at pressures corresponding to the lower mantle. This suggests that CaSiO_3 perovskite can no longer be considered as an invisible component in modelling the composition of the lower mantle, and even small amounts of the mineral may affect significantly the seismic properties, particularly shear wave velocity, of the generally accepted Mg-rich silicate perovskite dominated composition of this region. Moreover, CaSiO_3 perovskite exhibits strong anisotropy at pressures corresponding to the transition zone and the top of the lower mantle. 3)Comparison between the volumes of the MgSiO_3 perovskite phase to the post-perovskite phase at the same pressure-temperature conditions indicates that the post-perovskite phase is always denser than the perovskite. According to the usual condition of equal enthalpies, it is shown that the transition from the perovskite phase to the post-perovskite phase occurs at the pressure of 108 GPa. It is found that the MgSiO_3 post-perovskite phase has similar bulk modulus and larger shear modulus than perovskite at relevant pressures. This phase is remarkably anisotropic. Comparisons with seismological observation show that post-perovskite may be the most abundant mineral in the D" region.
3. The thermodynamic properties of CaSiO_3 perovskite are systemically predicted using the quasi-harmonic Debye model for the first time at high pressure and high temperature. It can be seen that the thermal expansion coefficient increases with T~3 at low temperatures and gradually approaches a linear increase at high temperatures, and then the increasing trend becomes gentler. The effects of the pressure on the thermal expansion coefficient are very small at low temperatures; the effects are increasingly obvious as the temperature increases. As pressure increases, the thermal expansion coefficient decreases rapidly and the effects of temperature become less and less pronounced, resulting in linear high temperature behaviour. The thermal expansion coefficient and heat capacity are shown to converge to a nearly constant value at high pressures and temperatures. Unlike the thermal expansion coefficient and heat capacity, the entropy is nearly insensitive to pressure.
引文
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