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Ab initio investigation into the elasticity of ultrahigh-pressure phases of SiO2

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Abstract

In this study, we report the elastic properties of three ultrahigh-pressure phases of SiO2: pyrite, cotunnite and Fe2P types between 300 and 1,500 GPa calculated by means of the density functional ab initio method. It is generally thought that materials tend to be more compact and isotropic with increasing pressure. These three ultrahigh-pressure phases of silica are mechanically stable in the investigated pressure range according to the Born criteria, while the cotunnite and Fe2P types are unstable at lower pressure. The elastic azimuthal anisotropy of these ultrahigh-pressure phases of silica shows that all the structures counterintuitively have considerable anisotropies even at multimegabar pressures. Among the three investigated structures, the cotunnite type of SiO2 is the most elastically anisotropic phase due to a soft compression along the b axis combined with a large distortion of the polyhedrons that make the structure. This might also be related to its thermodynamic unfavorability compared to the Fe2P type under extreme pressure condition. The bond property analyses clearly show that the Si–O bond remains an ionic-covalent mixed bond even at multimegabar pressures with an invariable ionicity with pressure. This argument can explain the monotonously pressure dependence of the elastic anisotropy in the case of pyrite, while the changes in the velocity distribution patterns out of the thermodynamic instability range largely contribute to those of the cotunnite and Fe2P types.

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References

  • Akins JA, Ahrens TJ (2002) Dynamic compression of SiO2: a new interpretation. Geophys Res Lett 29:101394. doi:10.1029/2002GL014806

    Article  Google Scholar 

  • Al-Khatatbeh Y, Lee KKM, Kiefer B (2009) High-pressure behavior of TiO2 as determined by experiment and theory. Phys Rev B 79:134114. doi:10.1103/PhysRevB.79.134114

    Article  Google Scholar 

  • Al-Khatatbeh Y, Lee KKM, Kiefer B (2010a) Phase relations and hardness trends of ZrO2 phases at high pressure. Phys Rev B 81:214102. doi:10.1103/PhysRevB.81.214102

    Article  Google Scholar 

  • Al-Khatatbeh Y, Lee KKM, Kiefer B (2010b) Phase diagram up to 105 GPa and mechanical strength of HfO2. Phys Rev B 82:144106. doi:10.1103/PhysRevB.82.144106

    Article  Google Scholar 

  • Bader RFW (1990) Atoms in molecules. Oxford Science Publications, Oxford

    Google Scholar 

  • Beaulieu JP et al (2006) Discovery of a cool planet of 5.5 Earth masses through gravitational microlensing. Nature 439:437–440. doi:10.1038/nature04441

    Google Scholar 

  • Born M, Huang K (1954) Dynamical theory of crystal lattices. Oxford at the Clarendon Press, Oxford

    Google Scholar 

  • Ceperley D, Alder B (1980) Ground state of the electron gas by a stochastic method. Phys Rev Lett 45(7):566–569

    Article  Google Scholar 

  • Charbonneau D et al (2008) A super-Earth transiting a nearby low-mass star. Nature 462:891–894

    Article  Google Scholar 

  • Cohen RE (1991) Bonding and elasticity of stishovite SiO2 at high pressure: linearized augmented plane wave calculations. Am Min 76:733–742

    Google Scholar 

  • Dekura H, Tsuchiya T, Tsuchiya J (2011a) First principles prediction of new post-pyrite phase transition in germanium dioxide. Phys Rev B 83:134114. doi:10.1103/PhysRevB.83.134114

    Article  Google Scholar 

  • Dekura H, Tsuchiya T, Kuwayama Y, Tsuchiya J (2011b) Theoretical and experimental evidence for a new post-cotunnite phase of titanium dioxide with significant optical absorption. Phys Rev Lett 107:045701. doi:10.1103/PhysRevLett.107.045701

    Article  Google Scholar 

  • Desgreniers S, Lagarec K (1999) High density ZrO2 and HfO2: crystalline structures and equations of state. Phys Rev B 59(13):8467–8472

    Article  Google Scholar 

  • Dubrovinsky LS, Dubrovinskaia NA, Swamy V, Muscat J, Harrison NM, Ahuja R, Holm B, Johansson B (2001) The hardest known oxide. Nature 410:653–654

    Article  Google Scholar 

  • Elsasser WM (1951) Quantum theoretical densities of solids at extreme compression. Science 113:105–107

    Article  Google Scholar 

  • Giannozzi P, Baroni S, Bonini N et al (2009) Quantum espresso: a modular and open-source software project for quantum simulations of materials. J Phys Cond Matt 21:395502

    Article  Google Scholar 

  • Guillot T (1999) Interiors of giant planets inside and outside the solar system. Science 286:72–77

    Article  Google Scholar 

  • Hemley RJ, Prewitt CT, King KJ (1994) High-pressure behavior of silica. In: Heaney PJ, Prewitt CT, Gibbs GV (eds) Silica. Mineral Society of America, Washington, pp 41–82

    Google Scholar 

  • Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136(3B):864–871

    Google Scholar 

  • Karki BB, Warren MC, Stixrude L, Ackland GJ, Crain J (1997a) Ab initio studies of high-pressure structural transformations in silica. Phys Rev B 55(6):3465–3471

    Article  Google Scholar 

  • Karki BB, Stixrude L, Crain J (1997b) Ab initio elasticity of three high-pressure polymorphs of silica. Geophys Res Lett 24(24):3269–3272

    Article  Google Scholar 

  • Karki BB, Stixrude L, Clark SJ, Warren MC, Ackland GJ, Crain J (1997c) Elastic properties of orthorhombic MgSiO3 perovskite at lower mantle pressures. Am Min 82:635–638

    Google Scholar 

  • Karki BB, Stixrude L, Wentzcovitch RM (2001) High-pressure elastic properties of major materials of Earth’s mantle from first principles. Rev Geophys 39(4):507–534

    Article  Google Scholar 

  • Kohn W, Sham L (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140(4A):1133–1138

    Google Scholar 

  • Kuwayama Y, Hirose K, Sata N, Ohishi Y (2005) The pyrite-type high-pressure form of silica. Science 309:923–925. doi:10.1126/science.1114879

    Article  Google Scholar 

  • Kuwayama Y, Hirose K, Sata N, Ohishi Y (2008) Phase relations of iron and iron-nickel alloys up to 300 GPa: implications for composition and structure of the Earth’s inner core. Earth Planet Sci Lett 273:379–385. doi:10.1016/j.epsl.2008.07.001

    Article  Google Scholar 

  • Landa A, Klepeis J, Söderlind P, Naumov I, Velikokhatnyi O, Vitos L, Ruban A (2006) Ab initio calculations of elastic constants of the bcc V-Nb system at high pressure. J Phys Chem Sol 67:2056–2064. doi:10.1016/j.jpcs.2006.05.027

    Article  Google Scholar 

  • Léger JM, Haines J, Atouf A (1996) The high pressure behaviour of the cotunnite and post-cotunnite phases of PbCl2 and SnCl2. J Phys Chem Solids 57:7–16

    Article  Google Scholar 

  • LePage Y, Rodgers JR (2005) Ab initio elasticity of FeS2 pyrite from 0 to 135 GPa. Phys Chem Min 32:564–567. doi:10.1007/s00269-005-0030-5

    Article  Google Scholar 

  • Louail L, Maouche D, Roumili A, Hachemi A (2005) Pressure effect on elastic constants of some transition metals. Mat Chem Phys 91:17–20. doi:10.1016/j.matchemphys.2004.10.040

    Article  Google Scholar 

  • Mainprice D (1990) An efficient FORTRAN program to calculate seismic anisotropy from the lattice preferred orientation of minerals. Comp Geo 16:385–393

    Article  Google Scholar 

  • Mainprice D, Barruol G, Ben Ismaïl W (2000) The seismic anisotropy of the Earth’s mantle: from single crystal to polycrystal. In: Karato SI, Forte AM, Liebermann RC, Masters G, Stixrude L (eds) Earth’s deep interior: mineral physics and tomography from the atomic to the global scale. American Geophysical Union, Washington, pp 237–264

    Chapter  Google Scholar 

  • Mattesini M, Magnuson M, Tasnádi F, Höglund C, Abrikosov IA, Hultman L (2009) Elastic properties and electrostrucutral correlations in ternary scandium-based cubic inverse perovskites: a first-principles study. Phys Rev B 79:125122. doi:10.1103/PhysRevB.79.125122

    Article  Google Scholar 

  • Monkhorst H, Pack J (1976) Special points for Brillouin-zone integrations. Phys Rev B 13(12):5188–5192

    Article  Google Scholar 

  • Nishio-Hamane D, Shimizu A, Nakahira R, Niwa K, Sano-Furukawa A, Okada T, Yagi T, Kikegawa T (2010) The stability and equation of state for the cotunnite phase of TiO2 up to 70 GPa. Phys Chem Min 37:129–136. doi:10.1007/s00269-009-0316-0

    Article  Google Scholar 

  • Oganov AR, Gillan MJ, Price GD (2005) Structural stability of silica at high pressures and temperatures. Phys Rev B 71:064104. doi:10.1103/PhysRevB.71.064104

    Article  Google Scholar 

  • Ohtaka O, Fukui H, Kunisada T, Fujisawa T, Funakoshi K, Utsumi W, Irifune T, Kuroda K, Kikegawa T (2001) Phase relations and volume changes of hafnia under high pressure and high temperature. J Am Ceram Soc 84(6):1369–1373

    Article  Google Scholar 

  • Ohtaka O, Andrault D, Bouvier P, Schultz E, Mezouar M (2005) Phase relations and equation of state of ZrO2 to 100 GPa. J Appl Crystallogr 38(5):727–733

    Article  Google Scholar 

  • Prewitt CT, Downs RT (1998) High-pressure crystal chemistry. In: Hemley RJ (ed) Ultrahigh-pressure mineralogy: physics and chemistry of the Earth’s deep interior. Mineral Society of America, Washington, pp 283–318

    Google Scholar 

  • Rivera EJ, Lissauer JJ, Butler RP, Marcy GW, Vogt SS, Fischer DA, Brown TM, Laughlin G, Henry GW (2005) A 7.5 M ⊕ planet orbiting the nearby star GJ 876. Astrophys J 634(1):625–640. doi:10.1086/491669

    Article  Google Scholar 

  • Schaefer L, Fegley B Jr (2009) Chemistry of silicate atmospheres of evaporating super-Earths. Astrophys J 703:L113–L117. doi:10.1088/0004-637X/703/2/L113

    Article  Google Scholar 

  • Söderlind P, Moriarty JA (1998) First-principles theory of Ta up to 10 Mbar pressure: structural and mechanical properties. Phys Rev B 57(17):10340–10350

    Article  Google Scholar 

  • Söderlind P, Moriarty JA, Wills JM (1998) First-principles theory of iron up to earth-core pressures: structural, vibrational, and elastic properties. Phys Rev B 53(21):14063–14072

    Article  Google Scholar 

  • Stacey FD, Davis PM (2004) High pressure equations of state with applications to the lower mantle and core. Phys Earth Planet Int 142:137–184. doi:10.1016/j.pepi.2004.02.003

    Article  Google Scholar 

  • Steinle-Neumann G, Stixrude L, Cohen RE (1999) First-principles elastic constants for the hcp transition metals Fe, Co, and Re at high pressure. Phys Rev B 60:791–799

    Article  Google Scholar 

  • Tateno S, Hirose K, Ohishi Y, Tatsumi Y (2010) The structure of iron in Earth’inner core. Science 330:359–361. doi:10.1126/science.1194662

    Article  Google Scholar 

  • Tsuchiya T, Tsuchiya J (2011) Prediction of a hexagonal SiO2 phase affecting stabilities of MgSiO3 and CaSiO3 at multimegabar pressures. Proc Nat Acad Sci 108(4):1252–1255. doi:10.1073/pnas.1013594108

  • Tsuchiya T, Caracas R, Tsuchiya J (2004a) First principles determination of the phase boundaries of high-pressure polymorphs of silica. Geophys Res Lett 31:L11610. doi:10.1029/2004GL019649

    Article  Google Scholar 

  • Tsuchiya T, Tsuchiya J, Umemoto K, Wentzcovitch RM (2004b) Elasticity of post-perovskite MgSiO3. Geophys Res Lett 31:L14603

    Article  Google Scholar 

  • Tvergaard V, Hutchinson JW (1988) Microcracking in ceramics induced by thermal expansion or elastic anisotropy. J Am Chem Soc 71:157

    Google Scholar 

  • Udry S, Bonfils X, Delfosse X, Forveille T, Mayor M, Perrier C, Bouchy F, Lovis C, Pepe F, Queloz D, Bertaux JL (2007) The HARPS search for southern extra-solar planets. XI. Super-Earths (5 and 8 M) in a 3-planet system. Astron Astrophys 469:L 43-L47. doi:10.1051/0004-6361:20077612

  • Umemoto K, Wentzcovitch RM, Allen PB (2006) Dissociation of MgSiO3 in the cores of gas giants and terrestrial exoplanets. Science 311:983–986. doi:10.1126/science.1120865

    Article  Google Scholar 

  • Valencia D, O’ Connell RJ, Sasselov D (2006) Internal structure of massive terrestrial planets. Icarus 181:545–554. doi:10.1016/j.icarus.2005.11.021

    Article  Google Scholar 

  • Valencia D, Ikoma M, Guillot T, Nettelmann N (2010) Composition and fate of short-period super-Earths. The case of CoRoT-7b. Astrono Astrophys 516(2):12839

    Google Scholar 

  • Vanderbilt D (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B 4(11):7892–7895

    Article  Google Scholar 

  • Wang J, Yip S, Phillpot SR, Wolf D (1993) Crystal instabilities at finite strain. Phys Rev Lett 71(25):4182–4185

    Article  Google Scholar 

  • Wang J, Li J, Yip S, Phillpot SR, Wolf D (1995) Mechanical instabilities of homogeneous crystals. Phys Rev B 52(17):12627–12635

    Article  Google Scholar 

  • Weidner D, Bass JD (1982) The single-crystal elastic moduli of stishovite. J Geophys Res 87(B6):4740–4746

    Google Scholar 

  • Wu S, Umemoto K, Ji M, Wang CZ, Ho KM, Wentzcovitch RM (2011) Identification of post-pyrite phase transitions in SiO2 by a genetic algorithm. Phys Rev B 83:184102. doi:10.1103/PhysRevB.83.184102

    Article  Google Scholar 

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Acknowledgments

This research was supported by the Ehime University Global Center Of Excellence program “Deep Earth Mineralogy” and KAKENHI 23540560. The authors acknowledge Masanori Matsui for helpful comments to improve the manuscript.

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Correspondence to Arnaud Metsue.

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Metsue, A., Tsuchiya, T. Ab initio investigation into the elasticity of ultrahigh-pressure phases of SiO2 . Phys Chem Minerals 39, 177–187 (2012). https://doi.org/10.1007/s00269-011-0473-9

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