含铁后钙钛矿(Fe_xMg_(1-x))SiO_3的自旋、结构以及地震波特性的第一性原理研究
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摘要
运用基于密度泛函的第一性原理方法,对含Fe2+后钙钛矿相MgSiO3在高压下的性质进行了计算。计算结果表明,在0~160GPa的压强范围内Fe2+始终保持高自旋状态,但在高压下有转向中间自旋或低自旋的趋势。对于含有多个Fe2+的结构,通过比较可能结构的能量以及结合力学稳定性判据,发现Fe2+倾向于以最紧密方式替位占据Mg2+的位置。还计算了120GPa(D〃层压强)下的弹性波速,表明无论压缩波(P波)还是剪切波(S波),随着Fe2+浓度的增加,地震波速明显减小,并且S波的横向各向异性明显增强。
By using the first principles method based on density functional theory,the physical properties of ferrous-bearing post-perovskite MgSiO3 at high pressure were calculated.The results show that the high-spin state is conserved for ferrous irons from 0to 160 GPa.The transition tendency from high-spin state to intermediate-spin or low-spin state at higher pressure was also presented.For those structures containing several Fe2+,from the comparison of total enthalpies and the mechanical stability criterion we can conclude that the ferrous irons tend to take the closest positions of Mg2+.Moreover,the seismic velocities at120GPa(pressure in D〃layer)were calculated.The calculations show that both the compressional waves(P-waves)and the shear waves(S-waves)decrease obviously with the increasing concentration of Fe2+.Remarkably,the transverse anisotropy of shear wave increases significantly.
By using the first principles method based on density functional theory,the physical properties of ferrous-bearing post-perovskite MgSiO3 at high pressure were calculated.The results show that the high-spin state is conserved for ferrous irons from 0to 160 GPa.The transition tendency from high-spin state to intermediate-spin or low-spin state at higher pressure was also presented.For those structures containing several Fe2+,from the comparison of total enthalpies and the mechanical stability criterion we can conclude that the ferrous irons tend to take the closest positions of Mg2+.Moreover,the seismic velocities at120GPa(pressure in D〃layer)were calculated.The calculations show that both the compressional waves(P-waves)and the shear waves(S-waves)decrease obviously with the increasing concentration of Fe2+.Remarkably,the transverse anisotropy of shear wave increases significantly.
引文
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[3]Stackhouse S,Brodholt J P,Price G D.Elastic anisotropy of FeSiO3end-members of the perovskite and post-perovskite phases[J].Geophys Res Lett,2006,33(1):L01304.
[4]Iitaka T,Hirose K,Kawamura K,et al.The elasticity of the MgSiO3post-perovskite phase in the Earths lowermost mantle[J].Nature,2004,430(6998):442-445.
[5]Hsu H,Blaha P,Cococcioni M,et al.Spin-state crossover and hyperfine interactions of ferric iron in MgSiO3perovskite[J].Phys Rev Lett,2011,106(11):118501.
[6]Catalli K,Shim S H,Prakapenka V B,et al.Spin state of ferric iron in MgSiO3perovskite and its effect on elastic properties[J].Earth Planet Sc Lett,2010,289(1):68-75.
[7]Hsu H,Yu Y G,Wentzcovitch R M.Spin crossover of iron in aluminous MgSiO3 perovskite and post-perovskite[J].Earth Planet Sc Lett,2012,359/360:34-39.
[8]Jackson J M,Sturhahn W,Tschauner O,et al.Behavior of iron in(Mg,Fe)SiO3 post-perovskite assemblages at Mbar pressures[J].Geophys Res Lett,2009,36(10):L10301.
[9]Yamanaka T,Mao,W L,Mao H K,et al.New structure and spin state of iron-rich(Mg,Fe)SiO3 post-perovskite[J].J Phys:Conf Ser,2010,215(1):012100.
[10]Caracas R,Cohen R E.Ferrous iron in post-perovskite from first-principles calculations[J].Phys Earth Planet In,2008,168(3):147-152.
[11]Lin J F,Watson H,VankóG,et al.Intermediate-spin ferrous iron in lowermost mantle post-perovskite and perovskite[J].Nat Geosci,2008,1(10):688-691.
[12]Stackhouse S,Stixrude L,Karki B B.Thermal conductivity of periclase(MgO)from first principles[J].Phys Rev Lett,2010,104(20):208501.
[13]Suchiya J,Tsuchiya T,Wentzcovitch R M.Vibrational and thermodynamic properties of MgSiO3 post-perovskite[J].J Geophys Res:Solid Earth,2005,110(B2):B02204.
[14]Stackhouse S,Brodholt J P,Dobson D P,et al.Electronic spin transitions and the seismic properties of ferrous iron-bearing MgSiO3post-perovskite[J].Geophys Res Lett,2006,33(12):L12S03.
[15]Auzende A L,Badro J,Ryerson F J,et al.Element partitioning between magnesium silicate perovskite and ferropericlase:New insights into bulk lower-mantle geochemistry[J].Earth Planet Sc Lett,2008,269(1):164-174.
[16]Caracas R,Cohen R E.Effect of chemistry on the stability and elasticity of the perovskite and post-perovskite phases in the MgSiO3-FeSiO3-Al2O3system and implications for the lowermost mantle[J].Geophys Res Lett,2005,32(16):L16310.
[17]Hohenberg P,Kohn W.Inhomogeneous electron gas[J].Phys Rev,1964,136(3B):B864.
[18]Perdew J P,Burke K,Ernzerhof M.Generalized gradient approximation made simple[J].Phys Rev Lett,1996,77(18):3865-3868.
[19]Karki B B,Stixrude L,Wentzcovitch R M.High-pressure elastic properties of major materials of Earths mantle from first principles[J].Rev Geophys,2001,39(4):507-534.
[20]Hsu H,Umemoto K,Blaha P,et al.Spin states and hyperfine interactions of iron in(Mg,Fe)SiO3perovskite under pressure[J].Earth Planet Sc Lett,2010,294(1):19-26.
[21]Tsuchiya T,Tsuchiya J,Umemoto K,et al.Elasticity of post-perovskite MgSiO3[J].Geophys Res Lett,2004,31(14):L14603.
[22]Ni S D.Review on studies of ultra low velocity zone[J].Journal of University of Science and Technology of China,2007,37(8):820-829.(in Chinese)倪四道.超低速区研究进展与展望[J].中国科学技术大学学报,2007,37(8):820-829.
[23]Musgrave M J P.Crystal Acoustics:Introduction to the Study of Elastic Waves and Vibrations in Crystals[M].San Francisco,CA:Holden-Day,1970.