Effects on Seismic Velocity of Post-Perovskite MgSiO3 under Hydrostatic and Uniaxial Pressure
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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.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.
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Key words:
- Post-Perovskite MgSiO3 /
- hydrostatic pressure /
- uniaxial pressure /
- D" layer /
- seismic velocity /
- mineral materials
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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 表 2 PPv-MgSiO3中在压力下的压缩波(Ap)和剪切波(As)的各向异性
Table 2. Anisotropies of seismic velocities of PPv-MgSiO3 under pressure
Ap As 静水压力 100 GPa 15.1% 17.6% 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% -
Bengtson, A., Persson, K., Morgan, D., 2008. Ab Initio Study of the Composition Dependence of the Pressure-induced Spin Crossover in Perovskite (Mg1-x, Fex)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