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
计量
- 文章访问数: 4837
- HTML全文浏览量: 632
- PDF下载量: 1188
- 被引次数: 0
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

HTML全文

图 1 PPv-MgSiO₃结构

Fig. 1. Structure of PPv-MgSiO₃

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 全尺寸图片幻灯片

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

下载: 导出CSV

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%

下载: 导出CSV

参考文献(39)

Bengtson, A., Persson, K., Morgan, D., 2008. Ab Initio Study of the Composition Dependence of the Pressure-induced Spin Crossover in Perovskite (Mg_1-x, Fe_x)SiO₃. Earth Planet. Sci. Lett. , 265(3-4): 535-545. doi: 10.1016/j.epsl.2007.10.049
Caracas, R., Mainprice D., Thomas C., 2010. Is the Spin Transition in Fe²⁺-Bearing Perovskite Visible in Seismology? Geophys. Res. Lett. , 37(3): L133091- L133096. doi: 10.1029/2010GL043320
Garnero, E.J., Helmberger, D.V., 1995. A Very Slow Basal Layer Underlying Large-Scale Low-Velocity Anomalies in the Lower Mantle Beneath the Pacific: Evidence from Core Phases. Phys. Earth Planet. Int. , 91(1-3): 161-176. doi: 10.1016/0031-9201(95)03039-Y
Garnero, E.J., Maupin, V., Lay, T., et al., 2004. Variable Azimuthal Anisotropy in Earth's Lowermost Mantle. Science, 306(5694): 259-261. doi: 10.1126/science.1103411
Grand, S.P., 2002. Mantle Shear-wave Tomography and the Fate of Subducted Slabs. Phil. Trans. R. Soc. Lond. A, 360(1800): 2475-491. doi: 10.1098/rsta.2002.1077
Gu, Y.J., Dziewonski, A.M., Su W.J., et al., 2001. Models of the Mantle Shear Velocity and Discontinuities in the Pattern of Lateral Heterogeneities. J. Geophys. Res. , 106(B6): 11169-11199. doi: 10.1029/2001JB000340
Hou, W., Xie, H.S., Zhou, W.G., 2005. Lowermost Mantle Layer and Its Significance in the Earth's Material Evolution. Earth-Science Frontiers, 12(1): 37-41 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTotal-DXQY200501004.htm
Hsu, H., Umemoto, K., Blaha, P., et al., 2010. Spin States and Hyperfine Interactions of Iron in (Mg, Fe)SiO₃ Perovskite under Pressure. Earth Planet. Sci. Lett. , 294(1-2): 19-26. doi: 10.1016/j.epsl.2010.02.031
Iitaka, T., Hirose, K., Kawamura, K., et al., 2004. The Elasticity of the MgSiO₃ Post-Perovskitep Phase in the Earth's Lowermost Mantle. Nature, 430(6998): 442-445. doi: 10.1038/nature02702
Kárason, H., van der Hilst, R.D., 2001. Tomographic Imaging of the Lowermost Mantle with Differential Times of Refracted and Diffracted Core Phases (PKP, Pdiff). J. Geophys. Res. , 106(B4): 6569-6587. doi: 10.1029/2000JB900380
Li, L., Brodholt, J.P., Stackhouse, S., et al., 2005. Electronic Spin State of Ferric Iron in Al-Bearing Perovskite in the Lower Mantle. Geophys. Res. Lett. , 32(17): L173071-L173074. doi: 10.1029/2005GL023045
Liu, L., Du, J.G., Zhao, J.J., et al., 2009. Elastic Properties of Hydrous Forsterites under High Pressure: First-principle Calculations. Phys. Earth Planet. Int. , 176(1-2): 89-97. doi: 10.1016/j.pepi.2009.04.004
Mao, W.L., Shen, G.Y., Prakapenka, V.B., et al., 2004. Ferromagnesian Post-Perovskite Silicates in the D" Layer of the Earth. Proc. Nat. Acad. Sci. , 101(45): 15867-15869. doi: 10.1073/pnas.0407135101
Monkhorst, H.J., Pack, J.D., 1976. Special Points for Brillouin-zone Integrations. Phys. Rev. B, 13(12): 5188-5192. doi: 10.1103/PhysRevB.13.5188
Murakami, M., Hirose, K., Kawamura, K., et al., 2004. Post-Perovskite Phase Transition in MgSiO₃. Science, 304(5672): 855-858. doi: 10.1126/science.1095932
Ni, S.D., Helmberger, D.V., 2003. Seismological Constraints on the South African Superplume; Could Be the Oldest Distinct Structure on Earth. Earth Planet. Sci. Lett. , 206(1-2): 119-131. doi: 10.1016/S0012-821X(02)01072-5
Oganov, A.R., Ono, S., 2004. Theoretical and Experimental Evidence for A Post-Perovskite Phase of MgSiO₃ in Earth's D" layer. Nature, 430(6998): 445-448. doi: 10.1038/nature02701
Perdew, J.P., Zunger, A., 1981. Self-interaction Correction to Density-Functional Approximations for Many-Electron Systems. Phys. Rev. B, 23(10): 5048-5079. doi: 10.1103/PhysRevB.23.5048
Rost, S., Garnero, E.J., Stefan W., 2010. Thin and Intermittent Ultralow-Velocity Zones. J. Geophys. Res. , 115(B6): B0631201-B0631212. doi: 10.1029/2009JB006981
Shim, S.H., Duffy, T.S., Jeanloz, R., et al., 2004. Stability and Crystal Structure of MgSiO₃ Perovskite to the Core-mantle Boundary. Geophys. Res. Lett. , 31(10): L106031-L106035. doi: 10.1029/2004GL019639
Stackhouse, S., Brodolt, J.P., Dobson, D.P., et al., 2006. Electronic Spin Transitions and the Seismic Properties of Ferrous Iron-Bearing MgSiO₃ Post-perovskite. Geophys. Res. Lett. , 33(12): L12S031- L12S034. doi: 10.1029/2005GL025589
Tang, Q.S., Li, L.H., 2006. The Earth's Lowermost Mantle and Its Seismological Research Progress. Earth Science Frontiers, 13(2): 213-223 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DXQY200602024.htm
Tsuchiya, T., Tsuchiya, J., Umemoto, K., et al., 2004. Elasticity of Post-Perovskite MgSiO₃. Geophys. Res. Lett. , 31(14): L146031-L146034. doi: 10.1029/2004GL020278
Vanderbilt, D., 1990. Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism. Phys. Rev. B, 41(11): 7892-7895. doi: 10.1103/PhysRevB.41.7892
Vidale, J.E., Hedlin, M.A.H., 1998. Evidence for Partial Melt at the Core-Mantle Boundary North of Tonga from the Strong Scattering of Seismic Waves. Nature, 391: 682-684. doi: 10.1038/35601
Wen, L., Helmberger, D.V., 1998. Ultra-low Velocity Zones Near the Core-Mantle Boundary from Broadband PKP Precursors. Science, 279(5357): 1701-1703. doi: 10.1126/science.279.5357.1701
Wookey, J., Stackhouse, S., Kendall, J.M., et al., 2005. Efficacy of the Post-Perovskite Phase as an Explanation for Lowermost-mantle Seismic Properties. Nature, 438(7070): 1004-1007. doi: 10.1038/nature04345
Yang, F.Q., Liu, B., Ni, S.D., et al., 2008. Shear Velocity Anisotropy of the Lowermost Mantle Beneath the Siberia. Acta Seismological Sinica, 30(2): 209-213 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DZXB200802011.htm
Zhang, F.W., Oganov, A.R., 2006. Valence State and Spin Transitions of Iron in Earth's Mantle Silicates. Earth Planet. Sci. Lett. , 249(3-4): 436-443. doi: 10.1016/j.epsl.2006.07.023
Zhang, Y., Shu, L.S., 2010. On Research Achievements in Earth's D" Layer in Core-Mantle Boundary: An Important Breakthrough in 21st Experimental Petrology. Journal of Geology, 34(2): 113-116 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTotal-JSDZ201002004.htm
Zhang, Z.J., 2002. A Review of the Seismic Anisotropy and Its Applications. Progress in Geophysics, 17(2): 281-293 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQWJ200202013.htm
Zhao, D.P., 2001. Seismic Structure and Origin of Hotspots and Mantle Plumes. Earth Planet. Sci. Lett. , 192(3): 251-265. doi: 10.1016/S0012-821X(01)00465-4
Zhu, J.S., 2000. Structure of Lower Mantle and Core-Mantle Boundary Region and Its Grodynamics. Advances in Earth Sciences, 15(2): 139-142 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DXJZ200002002.htm
侯渭, 谢鸿森, 周文戈, 2005. 地幔底层及其在全球物质演化中的意义. 地学前缘, 12(1): 37-41. doi: 10.3321/j.issn:1005-2321.2005.01.006
唐群署, 李丽红, 2006. 核幔边界D"区的地震学研究进展. 地学前缘, 13(2): 213-223. doi: 10.3321/j.issn:1005-2321.2006.02.019
杨凤琴, 刘斌, 倪四道, 等, 2008. 西伯利亚下地幔底部的剪切波各向异性. 地震学报, 30(2): 209-213. doi: 10.3321/j.issn:0253-3782.2008.02.010
张苑, 舒良树, 2010.21世纪实验岩石学的重大突破——核幔边界D"层研究. 地质学刊, 34(2): 113-116. doi: 10.3969/j.issn.1674-3636.2010.02.113
张中杰, 2002. 地震各向异性研究进展, 地球物理学进展. 17(2): 281-293. doi: 10.3969/j.issn.1004-2903.2002.02.014
朱介寿, 2000. 下地幔及核幔边界结构及地球动力学. 地球科学进展, 15(2): 139-142. doi: 10.3321/j.issn:1001-8166.2000.02.003