Driver K P, Cohen R E, Wu Zhigang, Militzer B, Ríos P López, Towler M D, Needs R J, Wilkins J W
Department of Physics, Ohio State University, Columbus, OH 43210, USA.
Proc Natl Acad Sci U S A. 2010 May 25;107(21):9519-24. doi: 10.1073/pnas.0912130107. Epub 2010 May 10.
Silica (SiO(2)) is an abundant component of the Earth whose crystalline polymorphs play key roles in its structure and dynamics. First principle density functional theory (DFT) methods have often been used to accurately predict properties of silicates, but fundamental failures occur. Such failures occur even in silica, the simplest silicate, and understanding pure silica is a prerequisite to understanding the rocky part of the Earth. Here, we study silica with quantum Monte Carlo (QMC), which until now was not computationally possible for such complex materials, and find that QMC overcomes the failures of DFT. QMC is a benchmark method that does not rely on density functionals but rather explicitly treats the electrons and their interactions via a stochastic solution of Schrödinger's equation. Using ground-state QMC plus phonons within the quasiharmonic approximation of density functional perturbation theory, we obtain the thermal pressure and equations of state of silica phases up to Earth's core-mantle boundary. Our results provide the best constrained equations of state and phase boundaries available for silica. QMC indicates a transition to the dense alpha-PbO(2) structure above the core-insulating D" layer, but the absence of a seismic signature suggests the transition does not contribute significantly to global seismic discontinuities in the lower mantle. However, the transition could still provide seismic signals from deeply subducted oceanic crust. We also find an accurate shear elastic constant for stishovite and its geophysically important softening with pressure.
二氧化硅（SiO₂）是地球的一种丰富成分，其晶体多晶型物在地球的结构和动力学中起着关键作用。第一性原理密度泛函理论（DFT）方法经常被用于精确预测硅酸盐的性质，但却出现了根本性的失败。即使在最简单的硅酸盐二氧化硅中也会出现这种失败情况，而理解纯二氧化硅是理解地球岩石部分的先决条件。在这里，我们用量子蒙特卡罗（QMC）方法研究二氧化硅，到目前为止，对于这种复杂材料，QMC在计算上是不可能实现的，我们发现QMC克服了DFT的失败。QMC是一种基准方法，它不依赖于密度泛函，而是通过薛定谔方程的随机解来明确处理电子及其相互作用。在密度泛函微扰理论的准谐近似下，使用基态QMC加声子，我们获得了直至地球核幔边界的二氧化硅相的热压力和状态方程。我们的结果提供了目前最精确的二氧化硅状态方程和相边界。QMC表明在核幔边界层（D"层）上方会转变为致密的α-PbO₂结构，但缺乏地震信号表明这种转变对下地幔的全球地震不连续现象贡献不大。然而，这种转变仍可能提供来自深度俯冲洋壳的地震信号。我们还发现了斯石英准确的剪切弹性常数及其在地球物理上重要的随压力软化现象。
