Abstract Quartz, one of most abundant mineral in the continental Crust, is conventionally used in exploration of the stress state of the Crust through analysis of its structural and mechanical properties. To better infer the state of stress in the Crust, we quantified such properties of quartz under non-hydrostatic stress environment through First-principles calculation. The reduction of the crystal lattice and shear modulus under non-hydrostatic stresses differ from their hydrostatic results. The differences of lattice constants under non-hydrostatic stress with their hydrostatic equivalent values nearly linear increase with increasing differential stress (σd). The bulk modulus of quartz, however, does not display any non-hydrostatic effect. Non-hydrostatic stress has no obvious effect on the Young's modulus-Yc (The Ya, Yb, and Yc used here to represent the Young's modulus in a, b, and c axis); however when the positive additional stress applied on a-axis, it would cause an increase in Ya and Yb; and when negative additional stress applied on a-axis, it would cause a decrease in Ya and Yb. The difference of Ya and Yb at different stress state indicates that σd has significant effect on the lattice strain of quartz that would influence the dynamic process in depth of the Earth. The quantified function of non-hydrostatic stress on lattice and elastic properties of quartz were listed and would be an important part in establishing the stress state in the Crust and would influence the understanding of the past and on-going dynamic process at the depth.

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非静水应力作用下石英力学性能的第一性原理计算

摘要 石英是大陆地壳中含量最丰富的矿物之一，通常通过对其结构和力学性质的分析来探索地壳应力状态。为了更好地推断地壳中的应力状态，我们通过第一性原理计算量化了石英在非静水应力环境下​​的这些特性。在非流体静力应力下晶格和剪切模量的减少与其流体静力结果不同。非静水应力下的晶格常数与其静水等效值的差异随着微分应力 (σd) 的增加而几乎线性增加。然而，石英的体积模量不显示任何非流体静力效应。非静水应力对杨氏模量-Yc (Ya, Yb, 和 Yc 在此用于表示 a、b 和 c 轴上的杨氏模量）；但是当a轴上施加正的附加应力时，会引起Ya和Yb的增加；当 a 轴上施加负的附加应力时，会导致 Ya 和 Yb 的减少。Ya和Yb在不同应力状态下的差异表明σd对石英晶格应变有显着影响，从而影响地球深处的动力过程。列出了非静水应力对石英晶格和弹性特性的量化函数，这将是建立地壳应力状态的重要组成部分，并将影响对过去和正在进行的深度动态过程的理解。但是当a轴上施加正的附加应力时，会引起Ya和Yb的增加；当 a 轴上施加负的附加应力时，会导致 Ya 和 Yb 的减少。Ya和Yb在不同应力状态下的差异表明σd对石英晶格应变有显着影响，从而影响地球深处的动力过程。列出了非静水应力对石英晶格和弹性特性的量化函数，这将是建立地壳应力状态的重要组成部分，并将影响对过去和正在进行的深度动态过程的理解。但是当a轴上施加正的附加应力时，会引起Ya和Yb的增加；当 a 轴上施加负的附加应力时，会导致 Ya 和 Yb 的减少。Ya和Yb在不同应力状态下的差异表明σd对石英晶格应变有显着影响，从而影响地球深处的动力过程。列出了非静水应力对石英晶格和弹性特性的量化函数，这将是建立地壳应力状态的重要组成部分，并将影响对过去和正在进行的深度动态过程的理解。Ya和Yb在不同应力状态下的差异表明σd对石英晶格应变有显着影响，从而影响地球深处的动力过程。列出了非静水应力对石英晶格和弹性特性的量化函数，这将是建立地壳应力状态的重要组成部分，并将影响对过去和正在进行的深度动态过程的理解。Ya和Yb在不同应力状态下的差异表明σd对石英晶格应变有显着影响，从而影响地球深处的动力过程。列出了非静水应力对石英晶格和弹性特性的量化函数，这将是建立地壳应力状态的重要组成部分，并将影响对过去和正在进行的深度动态过程的理解。