静水压力和单轴压力对后钙钛矿MgSiO<sub>3</sub>中地震波速的影响

何开华; 陈琦丽; 王清波; 王希成; 高本州; 姬广富

doi:10.3799/dqkx.2013.050

静水压力和单轴压力对后钙钛矿MgSiO₃中地震波速的影响

doi: 10.3799/dqkx.2013.050

1.
中国地质大学数学与物理学院, 湖北武汉 430074
2.
中国工程物理研究院流体物理研究所冲击波物理与爆轰物理国防科技重点实验室, 四川绵阳 621900

基金项目:

国家自然科学基金项目 41104054

详细信息

作者简介:
何开华(1978-), 男, 讲师, 主要从事纳米材料和矿物材料的计算模拟研究.E-mail: he23981006@126.com

中图分类号: P315.3;O482.1
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出版历程
- 收稿日期: 2012-08-25
- 刊出日期: 2013-05-15

Effects on Seismic Velocity of Post-Perovskite MgSiO₃ under Hydrostatic and Uniaxial Pressure

1.
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
2.
Institute of Shock Wave and Detonation Physics Research, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, China

摘要

摘要: 后钙钛矿MgSiO₃对于重新认识地球的基本结构和成分具有重大意义.采用基于密度泛函理论的第一性原理计算对后钙钛矿MgSiO₃在静水压力和单轴压力下的弹性性质和地震波速特征进行了研究.首先通过总能比较和力学稳定性判据验证了后钙钛矿MgSiO₃在高压下的稳定性, 并且计算得到的晶格常数与前人结果符合很好.计算表明在高压下(D"层), 后钙钛矿具有比钙钛矿大的体变模量、剪切模量及密度, 并且具有大的地震波速, 这与地震观测D"层中地震波速的不连续性一致.在静水压力作用下, 计算结果显示压缩波各向异性基本保持不变, 而剪切波各向异性增强.有单轴应力作用时, 后钙钛矿地震波各向异性差异非常明显, 当压力作用在a轴或c轴上时, 能够得到比对应静水压力下后钙钛矿更强的各向异性, 而恰好相反的是, 压缩b轴时, 各向异性有减小的趋势.本研究能为解释地幔底部地震波不连续性和横向差异提供一定的参考.
- 后钙钛MgSiO₃ /
- 静水压力 /
- 单轴压力 /
- D"层 /
- 地震波速 /
- 矿物材料
Abstract: The elastic property and seismic velocity of Post-Perovsikt (PPv) MgSiO₃ have been studied using first-principles calculations based on density of functional theory (DFT).Firstly, the stability of PPv-MgSiO₃ under high pressure is validated through total energy calculations and the criterion of mechanical stability.The obtained lattice constants are in accordance well with the previous calculated and experimental results.The calculations indicate that the bulk modulus, shear modulus, density and seismic velocity of PPv-MgSiO₃ are larger than those of Pv-MgSiO₃, which are in agreement with seismic observations.Under hydrostatic pressure, the anisotropy of compressed wave has little change, while that of shear wave is enhanced.For the uniaxial pressure, both compressed and shear anisotropies are increased with strain along the a or c axis, while are decreased with strain along the b axis with respect to that of hydrostatic pressure.This study is useful for explaining the seismic velocity discontinuity and lateral heterogeneity in the D" layer.
- Post-Perovskite MgSiO₃ /
- hydrostatic pressure /
- uniaxial pressure /
- D" layer /
- seismic velocity /
- mineral materials

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图 1 PPv-MgSiO₃结构

Fig. 1. Structure of PPv-MgSiO₃

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图 2 Pv-与PPv-MgSiO₃的焓差值(ΔH)与压力(P)的关系

Fig. 2. Difference of enthalpy between Pv- and PPv-MgSiO₃

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图 3 Pv-与PPv-MgSiO₃中晶格常数比值(b/a，c/a)与压力(P)的关系

Fig. 3. Pressure dependence of b/a and c/a of Pv- and PPv-MgSiO₃

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图 4 体变模量(B)，剪切模量(G)及密度(D)与静水压力(P)的关系

Fig. 4. Pressure dependence of bulk modulus, shear modulus and density

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图 5 Pv-与PPv-MgSiO₃中波速(V)与压力(P)关系

Fig. 5. Pressure dependence of seismic velocity of Pv- and PPv-MgSiO₃

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图 6 体变模量(B)和剪切模量(G)与单轴压力的关系

Fig. 6. Uniaxial pressure dependence of bulk modulus and shear modulus

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图 7 PPv-MgSiO₃中不同传播方向压缩波波速与压力(应变)的关系

Fig. 7. Hydrostatic and uniaxial pressures dependence of seismic velocities of different directions

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表 1 PPv-MgSiO₃在不同压力下(P)的弹性常数(单位：GPa)

Table 1. Elastic constants of PPv-MgSiO₃ under different pressure (in GPa)

P	C₁₁	C₂₂	C₃₃	C₄₄	C₅₅	C₆₆	C₁₂	C₁₃	C₂₃
0	624	435	516	100	134	96	49	84	119
120	1 290	962	1 290	300	286	415	418	325	487
160	1 475	1 103	1 496	352	331	504	521	402	593

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表 2 PPv-MgSiO₃中在压力下的压缩波(A_p)和剪切波(A_s)的各向异性

Table 2. Anisotropies of seismic velocities of PPv-MgSiO₃ under pressure

		A_p	A_s
静水压力	100 GPa	15.1%	17.6%
静水压力	180 GPa	15.1%	23.6%
单轴压力	a/a₀=0.907 6	15.65%	19.84%
	a/a₀=0.877 0	40.97%	28.73%
	b/b₀=0.876 0	14.62%	9.5%
	b/b₀=0.836 0	13.63%	17.77%
	c/c₀=0.910 4	27.11%	26.52%
	c/c₀=0.882 0	29.97%	31.93%

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