静水压力和单轴压力对后钙钛矿MgSiO_3中地震波速的影响
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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.
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.
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.
引文
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Caracas,R.,Mainprice D.,Thomas C.,2010.Is the SpinTransition in Fe2+-Bearing Perovskite Visible in Seis-mology?Geophys.Res.Lett.,37(3):L133091-L133096.doi:10.1029/2010GL043320
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Garnero,E.J.,Maupin,V.,Lay,T.,et al.,2004.VariableAzimuthal 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 theFate of Subducted Slabs.Phil.Trans.R.Soc.Lond.A,360(1800):2475-491.doi:10.1098/rsta.2002.1077
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Kárason,H.,van der Hilst,R.D.,2001.Tomographic Ima-ging of the Lowermost Mantle with Differential Timesof 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.Electron-ic Spin State of Ferric Iron in Al-Bearing Perovskite inthe 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 Propertiesof 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 forBrillouin-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 Con-straints on the South African Superplume;Could Be theOldest 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 ExperimentalEvidence for A Post-Perovskite Phase of MgSiO3inEarth's D''layer.Nature,430(6998):445-448.doi:10.1038/nature02701
Perdew,J.P.,Zunger,A.,1981.Self-interaction Correctionto Density-Functional Approximations for Many-Elec-tron Systems.Phys.Rev.B,23(10):5048-5079.doi:10.1103/PhysRevB.23.5048
Rost,S.,Garnero,E.J.,Stefan W.,2010.Thin and Intermit-tent 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.Stabilityand Crystal Structure of MgSiO3Perovskite to theCore-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 Propertiesof Ferrous Iron-Bearing MgSiO3Post-perovskite.Geo-phys.Res.Lett.,33(12):L12S031-L12S034.doi:10.1029/2005GL025589
Tang,Q.S.,Li,L.H.,2006.The Earth's Lowermost Mantleand Its Seismological Research Progress.Earth ScienceFrontiers,13(2):213-223(in Chinese with Englishabstract).
Tsuchiya,T.,Tsuchiya,J.,Umemoto,K.,et al.,2004.Elas-ticity of Post-Perovskite MgSiO3.Geophys.Res.Lett.,31(14):L146031-L146034.doi:10.1029/2004GL020278
Vanderbilt,D.,1990.Soft Self-Consistent Pseudopotentialsin 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 PartialMelt at the Core-Mantle Boundary North of Tonga fromthe Strong Scattering of Seismic Waves.Nature,391:682-684.doi:10.1038/35601
Wen,L.,Helmberger,D.V.,1998.Ultra-low Velocity ZonesNear the Core-Mantle Boundary from Broadband PKPPrecursors.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 Explanationfor 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 VelocityAnisotropy of the Lowermost Mantle Beneath the Si-beria.Acta Seismological Sinica,30(2):209-213(inChinese with English abstract).
Zhang,F.W.,Oganov,A.R.,2006.Valence State and Spin Transitions of Iron in Earth’s Mantle Silicates.EarthPlanet.Sci.Lett.,249(3-4):436-443.doi:10.1016/j.epsl.2006.07.023
Zhang,Y.,Shu,L.S.,2010.On Research Achievements inEarth's D''Layer in Core-Mantle Boundary:An Impor-tant Breakthrough in21st Experimental Petrology.Journal of Geology,34(2):113-116(in Chinese withEnglish abstract).
Zhang,Z.J.,2002.A Review of the Seismic Anisotropy andIts Applications.Progress in Geophysics,17(2):281-293(in Chinese with English abstract).
Zhao,D.P.,2001.Seismic Structure and Origin of Hotspotsand 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-MantleBoundary Region and Its Grodynamics.Advances inEarth Sciences,15(2):139-142(in Chinese with Eng-lish abstract).
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.
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.
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.
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.
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.
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.
Caracas,R.,Mainprice D.,Thomas C.,2010.Is the SpinTransition in Fe2+-Bearing Perovskite Visible in Seis-mology?Geophys.Res.Lett.,37(3):L133091-L133096.doi:10.1029/2010GL043320
Garnero,E.J.,Helmberger,D.V.,1995.A Very Slow BasalLayer Underlying Large-Scale Low-Velocity Anomaliesin the Lower Mantle Beneath the Pacific:Evidence fromCore 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.VariableAzimuthal 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 theFate 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.Modelsof the Mantle Shear Velocity and Discontinuities in thePattern of Lateral Heterogeneities.J.Geophys.Res.,106(B6):11169-11199.doi:10.1029/2001JB000340
Hou,W.,Xie,H.S.,Zhou,W.G.,2005.Lowermost MantleLayer and Its Significance in the Earth's Material Evo-lution.Earth-Science Frontiers,12(1):37-41(in Chi-nese with English abstract).
Hsu,H.,Umemoto,K.,Blaha,P.,et al.,2010.Spin Statesand Hyperfine Interactions of Iron in(Mg,Fe)SiO3Perovskite 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.TheElasticity of the MgSiO3Post-Perovskitep Phase in theEarth's Lowermost Mantle.Nature,430(6998):442-445.doi:10.1038/nature02702
Kárason,H.,van der Hilst,R.D.,2001.Tomographic Ima-ging of the Lowermost Mantle with Differential Timesof 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.Electron-ic Spin State of Ferric Iron in Al-Bearing Perovskite inthe 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 Propertiesof 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 forBrillouin-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 Con-straints on the South African Superplume;Could Be theOldest 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 ExperimentalEvidence for A Post-Perovskite Phase of MgSiO3inEarth's D''layer.Nature,430(6998):445-448.doi:10.1038/nature02701
Perdew,J.P.,Zunger,A.,1981.Self-interaction Correctionto Density-Functional Approximations for Many-Elec-tron Systems.Phys.Rev.B,23(10):5048-5079.doi:10.1103/PhysRevB.23.5048
Rost,S.,Garnero,E.J.,Stefan W.,2010.Thin and Intermit-tent 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.Stabilityand Crystal Structure of MgSiO3Perovskite to theCore-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 Propertiesof Ferrous Iron-Bearing MgSiO3Post-perovskite.Geo-phys.Res.Lett.,33(12):L12S031-L12S034.doi:10.1029/2005GL025589
Tang,Q.S.,Li,L.H.,2006.The Earth's Lowermost Mantleand Its Seismological Research Progress.Earth ScienceFrontiers,13(2):213-223(in Chinese with Englishabstract).
Tsuchiya,T.,Tsuchiya,J.,Umemoto,K.,et al.,2004.Elas-ticity of Post-Perovskite MgSiO3.Geophys.Res.Lett.,31(14):L146031-L146034.doi:10.1029/2004GL020278
Vanderbilt,D.,1990.Soft Self-Consistent Pseudopotentialsin 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 PartialMelt at the Core-Mantle Boundary North of Tonga fromthe Strong Scattering of Seismic Waves.Nature,391:682-684.doi:10.1038/35601
Wen,L.,Helmberger,D.V.,1998.Ultra-low Velocity ZonesNear the Core-Mantle Boundary from Broadband PKPPrecursors.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 Explanationfor 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 VelocityAnisotropy of the Lowermost Mantle Beneath the Si-beria.Acta Seismological Sinica,30(2):209-213(inChinese with English abstract).
Zhang,F.W.,Oganov,A.R.,2006.Valence State and Spin Transitions of Iron in Earth’s Mantle Silicates.EarthPlanet.Sci.Lett.,249(3-4):436-443.doi:10.1016/j.epsl.2006.07.023
Zhang,Y.,Shu,L.S.,2010.On Research Achievements inEarth's D''Layer in Core-Mantle Boundary:An Impor-tant Breakthrough in21st Experimental Petrology.Journal of Geology,34(2):113-116(in Chinese withEnglish abstract).
Zhang,Z.J.,2002.A Review of the Seismic Anisotropy andIts Applications.Progress in Geophysics,17(2):281-293(in Chinese with English abstract).
Zhao,D.P.,2001.Seismic Structure and Origin of Hotspotsand 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-MantleBoundary Region and Its Grodynamics.Advances inEarth Sciences,15(2):139-142(in Chinese with Eng-lish abstract).
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.
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.
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.
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.
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.
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.
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