Advertisement

Physics and Chemistry of Minerals

, Volume 33, Issue 2, pp 126–137 | Cite as

Equations of state of CaSiO3 Perovskite: a molecular dynamics study

  • Yigang ZhangEmail author
  • Dapeng Zhao
  • Masanori Matsui
  • Guangjun Guo
Original Paper

Abstract

The molar volumes and bulk moduli of CaSiO3 perovskite are calculated in the temperature range from 300 to 2,800 K and the pressure range from 0 to 143 GPa using molecular dynamics simulations that employ the breathing shell model for oxygen and the quantum correction in addition to the conventional pairwise interatomic potential models. The performance of five equations of state, i.e., the Keane, the generalized-Rydberg, the Holzapfel, the Stacey–Rydberg, and the third-order Birch–Murnaghan equations of state are examined using these data. The third-order Birch–Murnaghan equation of state is found to have a clear tendency to overestimate the bulk modulus at very high pressures. The Stacey–Rydberg equation of state degrades slightly at very high pressures along the low-temperature isotherms. In comparison, the Keane and the Holzapfel equations of state remain accurate in the whole temperature and pressure range considered in the present study. K 0′ derived from the Holzapfel equation of state also agrees best with that calculated independently from molecular dynamics simulations. The adiabatic bulk moduli of CaSiO3 perovskite along lower mantle geotherms are further calculated using the Keane and the Mie-Grüneisen–Debye equations of state. They are found to be constantly higher than those of the PREM by ~5%, and also very similar to those of the MgSiO3 perovskite. Our results support the view that CaSiO3 perovskite remains invisible in the Earth’s lower mantle.

Keywords

CaSiO3 perovskite Molecular dynamics Molar volume Bulk modulus Lower mantle 

Notes

Acknowledgements

This work is supported by a grant (No.40221402) to R. Zhu and Y. Zhang from the National Natural Science Foundation of China, grants (Kiban-B 11440134, Kiban-A 17204037) to D. Zhao, and a grant (No. 16540442) to M. Matsui from Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (Monkasho), Japan. The first author (YZ) appreciates the visiting professorship at Geodynamics Research Center, Ehime University. D. Zhao received a special grant for Center of Excellence (COE) from the President of Ehime University. We appreciate the helpful discussions with Prof. T. Tsuchiya and Drs. Zhigang Zhang and Jiawen Hu. Very careful and thoughtful reviews by the two anonymous reviewers greatly improved the quality of the paper.

References

  1. Akber-Knutson S, Bukowinski MST, Matas J (2002) On the structure of compressibility of CaSiO3 perovskite. Geophys Res Lett 29:1034–1037CrossRefGoogle Scholar
  2. Anderson OL (1995) Equations of state of solids for geophysics and ceramic science. Oxford University Press, New YorkGoogle Scholar
  3. Anderson OL (1999) The volume dependence of thermal pressure in perovskite and other minerals. Phys Earth Planet Inter 112:267–283CrossRefGoogle Scholar
  4. Bass JD (1984) Elasticity of single-crystal SmAlO3, GdAlO3 and ScAlO3 perovskites. Phys Earth Planet Inter 36:145–156CrossRefGoogle Scholar
  5. Birch F (1952) Elasticity and constitution of the Earth’s interior. J Geophys Res 57:227–286CrossRefGoogle Scholar
  6. Brown JM, Shankland TJ (1981) Thermodynamic parameters in the Earth as determined from seismic profiles. Geophys J R astr Soc 66:579–596Google Scholar
  7. Caracas R, Wentzcovitch R, Price GD, Brodholt J (2005) CaSiO3 perovskite at lower mantle pressures. Geophys Res Lett 32:L06306CrossRefGoogle Scholar
  8. Chizmeshya AVG, Wolf GH, McMillan PF (1996) First-principles calculation of the equation-of-state, stability and polar optic modes of CaSiO3 perovskite. Geophys Res Lett 23:2725–2728CrossRefGoogle Scholar
  9. Cohen RE, Gülseren O, Hemley RJ (2000) Accuracy of equation-of-state formulations. Am Mineral 85:338–344Google Scholar
  10. Dziewonski AM, Anderson D (1981) Preliminary reference Earth model. Phys Earth Planet Inter 25:297–356CrossRefGoogle Scholar
  11. Hama J, Suito K (1996) The search for a universal equation of state correct up to very high pressures. J Phys: Condens Matter 8:67–81CrossRefGoogle Scholar
  12. Hama J, Suito K (1998) High-temperature equation of state of CaSiO3 perovskite and its implications for the lower mantle. Phys Earth Planet Inter 105:33–46CrossRefGoogle Scholar
  13. Hama J, Suito K (2001) Thermoelastic models of minerals and the composition of the Earth’s lower mantle. Phys Earth Planet Inter 125:147–166CrossRefGoogle Scholar
  14. Hemley RJ, Jackson MD, Gordon RG (1987) Theoretical study of the structure, lattice dynamics, and equations of state of perovskite-type MgSiO3 and CaSiO3. Phys Chem Miner 14:2–12CrossRefGoogle Scholar
  15. Holzapfel WB (1996) Physics of solids under strong compression. Rep Prog Phys 59:29–90CrossRefGoogle Scholar
  16. Holzapfel WB (1998) Equations of state for solids under strong compression. High Press Res 16:81–126CrossRefGoogle Scholar
  17. Holzapfel WB (2004) Equation of state and thermodynamical properties of solids under pressure. In: Katrusiak P (ed) High-pressure crystallography. McMillan, Kluwer, Dordrecht, HollandGoogle Scholar
  18. Jackson I, Rigden SM (1996) Analysis of P–V–T data: constraints on the thermoelastic properties of high-pressure minerals. Phys Earth Planet Inter 96:85–112CrossRefGoogle Scholar
  19. Jeanloz R (1989) Shock wave equations of state and finite strain theory. J Geophys Res 94:5873–5886CrossRefGoogle Scholar
  20. Jung DY, Oganov AR (2005) Ab initio study of the high-pressure behavior of CaSiO3 perovskite. Phys Chem Miner 32:146–153CrossRefGoogle Scholar
  21. Karki BB, Crain J (1998) First-principles determination of elastic properties of CaSiO3 perovskite at lower mantle pressures. Geophys Res Lett 25:2741–2744CrossRefGoogle Scholar
  22. Karki BB (2000) Thermal pressure in MgO and MgSiO3 perovskite at lower mantle conditions. Am Mineral 85:1447–1451Google Scholar
  23. Karki BB, Stixrude L, Wentzcovitch RM (2001) High-pressure elastic properties of major materials of Earth’s mantle from first-principles. Rev Geophys 39:507–534CrossRefGoogle Scholar
  24. Keane A (1954) An investigation of finite strain in an isotropic material subjected to hydrostatic pressure and its seismological applications. Aust J Phys 7:322–333Google Scholar
  25. Kesson SE, Fitz JD, Shelly JM (1998) Mineralogy and dynamics of a pyrolite lower mantle. Nature 393:252–255CrossRefGoogle Scholar
  26. Koito S, Akaogi M, Kubota O, Suzuki T (2000) Calorimetric measurements of perovskites in the system CaTiO3–CaSiO3 and experimental and calculated phase equilibria for high-pressure dissociation of diopside. Phys Earth Planet Inter 120:1–10CrossRefGoogle Scholar
  27. Kurashina T, Hirose K, Ono S, Sata N, Ohishi Y (2004) Phase transition in Al-bearing CaSiO3 perovskite: implications for seismic discontinuities in the lower mantle. Phys Earth Planet Inter 145:67–74CrossRefGoogle Scholar
  28. Li B, Kung J, Liebermann RC (2004) Modern techniques in measuring elasticity of Earth materials at high pressure and high temperature using ultrasonic interferometry in conjunction with synchrotron X-radiation in multi-anvil apparatus. Phys Earth Planet Inter 143–144:559–574CrossRefGoogle Scholar
  29. Li B, Zhang J (2005) Pressure and temperature dependence of elastic wave velocity of MgSiO3 perovskite and the composition of the lower mantle. Phys Earth Planet Inter 151:143–154Google Scholar
  30. Liu LG (1978) High pressure Ca2SiO4, the silicate K2NiF4-isotype with crystalchemical and geophysical implications. Phys Chem Miner 3:291–299CrossRefGoogle Scholar
  31. Liu LG, Ringwood AE (1975) Synthesis of a perovskite-type polymorph of CaSiO3. Earth Planet Sci Lett 28:209–211CrossRefGoogle Scholar
  32. Magyari-Köpe B, Vitos L, Grimvall G, Johansson B, Kollár J (2002) Low-temperature crystal structure of CaSiO3 perovskite: an ab initio total energy study. Phys Rev B 65:193107CrossRefGoogle Scholar
  33. Mao HK, Chen LC, Hemley RJ, Jephcoat AP, Wu Y (1989) Stability and equation of state of CaSiO3-perovskite to 134 GPa. J Geophys Res 94:17889–17894CrossRefGoogle Scholar
  34. Marcus PM, Qiu SL (2004) Reply to comment on ‘On the importance of the free energy for elasticity under pressure’. J Phys: Condens Matter 16:8787–8790CrossRefGoogle Scholar
  35. Matsui M (1989) Molecular dynamics study of the structural and thermodynamic properties of MgO crystal with quantum correction. J Chem Phys 91:489–494CrossRefGoogle Scholar
  36. Matsui M (1998) Breathing shell model in molecular dynamics simulations: Application to MgO and CaO. J Chem Phys 108:3304–3309CrossRefGoogle Scholar
  37. Matsui M (2000) Molecular dynamics simulation of MgSiO3 perovskite and the 660-km seismic discontinuity. Phys Earth Planet Int 121:77–84CrossRefGoogle Scholar
  38. Matsui M, Parker S C, Leslie M (2000) The MD simulation of the equation of state of MgO: application as a pressure calibration standard at high temperature and high temperature. Am Miner 85:312–316Google Scholar
  39. Murakami M, Hirose K, Sata N, Ohishi Y (2005) Post-perovskite phase transition and mineral chemistry in the pyrolitic lowermost mantle. Geophys Res Lett 32:L03304CrossRefGoogle Scholar
  40. Nishiyama N, Yagi T (2003) Phase relation and mineral chemistry in pyrolite to 2200°C under the lower mantle pressures and implications for dynamics of mantle plumes. J Geophys Res 108(B5):2255CrossRefGoogle Scholar
  41. Nosé S (1984) A unified formulation of the constant temperature molecular dynamics method. J Chem Phys 81:511–519CrossRefGoogle Scholar
  42. Nye J F (1985) Physical properties of crystals. Clarendon, OxfordGoogle Scholar
  43. Ono S, Ito E, Katsura T (2001) Mineralogy of subducted basaltic crust (MORB) from 25 to 37 GPa, and chemical heterogeneity of the lower mantle. Earth Planet Sci Lett 190:57–63CrossRefGoogle Scholar
  44. Ono S, Ohishi Y, Mibe K (2004) Phase transition of Ca-perovskite and stability of Al-bearing Mg-perovskite in the lower mantle. Am Mineral 89:1480–1485Google Scholar
  45. Parrinello M, Rahman A (1981) Polymorphic transitions in single crystals: a new molecular dynamics method. J Appl Phys 52:7182–7190CrossRefGoogle Scholar
  46. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in C. Cambridge University Press, CambridgeGoogle Scholar
  47. Reid AF, Ringwood AE (1975) High-pressure modification of ScAlO3 and some geophysical implications. J Geophys Res 80:3363–3370CrossRefGoogle Scholar
  48. Rydberg R (1932) Graphishe Darstellung einiger bandspektroskopisher Ergebnisse. Z Phys 73:376–385CrossRefGoogle Scholar
  49. Shanker J, Singh BP (2005) A comparative study of Keane’s and Stacey’s equations of state. Physica B 370:78–83CrossRefGoogle Scholar
  50. Sherman DM (1993) Equation of state, elastic properties, and stability of CaSiO3 perovskite: first principles (periodic Hartree–Fock results). J Geophys Res 98:19795–19805CrossRefGoogle Scholar
  51. Shieh SR, Duffy TS, Shen G (2004) Elasticity and strength of calcium silicate perovskite at lower mantle pressures. Phys Earth Planet Inter 143–144:93–105CrossRefGoogle Scholar
  52. Shim S, Duffy TS, Shen G (2000a) The equation of state of CaSiO3 perovskite to 108 GPa at 300 K. Phys Earth Planet Inter 120:327–338CrossRefGoogle Scholar
  53. Shim S, Duffy TS, Shen G (2000b) The stability and P–V–T equation of state of CaSiO3 perovskite in the Earth’s lower mantle. J Geophys Res 105(B11):25955–25968CrossRefGoogle Scholar
  54. Shim S, Jeanloz R, Duffy TS (2002) Tetragonal structure of CaSiO3 perovskite above 20 GPa. Geophys Res Lett 29:2166, DOI 10.1029/2002GL016148Google Scholar
  55. Sinelnikov YD, Chen G, Liebermann RC (1998) Elasticity of CaTiO3–CaSiO3 perovskites. Phys Chem Miner 25:515–521CrossRefGoogle Scholar
  56. Singh BP (2005) A comparison of equations of state including the generalized Rydberg EOS. Physica B 369:111–116CrossRefGoogle Scholar
  57. Stacey FD (2005) High pressure equations of state and planetary interiors. Rep Prog Phys 68:341–383CrossRefGoogle Scholar
  58. Stacey FD, Brennan BJ, Irvine RD (1981) Finite strain theories and comparisons with seismological data. Geophys Surv 4:189–132CrossRefGoogle Scholar
  59. Stacey FD, Davis PM (2004) High pressure equations of state with applications to the lower mantle and core. Phys Earth Planet Inter 142:137–184CrossRefGoogle Scholar
  60. Stacey FD, Isaak DG (2001) Compositional constraints on the equation of state and thermal properties of the lower mantle. Geophys J Int 146:143–154CrossRefGoogle Scholar
  61. Steinle-Neumann G, Cohen RE (2004) Comment on ‘On the importance of the free energy for elasticity under pressure’. J Phys: Condens Matter 16:8783–8786CrossRefGoogle Scholar
  62. Tamai H, Yagi T (1989) High-pressure and high-temperature phase relations in CaSiO3 and CaMgSi2O6 and elasticity of perovskite-type CaSiO3. Phys Earth Planet Inter 54:370–377CrossRefGoogle Scholar
  63. Tarrida M, Richet P (1989) Equation of state of CaSiO3 perovskite to 96 GPa. Geophys Res Lett 16:1351–1354CrossRefGoogle Scholar
  64. Vinet P, Ferrante J, Smith JR, Ross JH (1986) A universal equation of state for solids. J Phys: Condens Matter 19:L467–L473Google Scholar
  65. Wang Y, Weidner DJ (1994) Thermoelasticity of CaSiO3 perovskite and implications for the lower mantle. Geophys Res Lett 21(10):895–898CrossRefGoogle Scholar
  66. Wang Y, Weidner DJ, Guyot F (1996) Thermal equation of state of CaSiO3 perovskite. J Geophys Res 101(B1):661–672CrossRefGoogle Scholar
  67. Wentzcovitch RM, Ross NL, Price GD (1995) Ab initio study of MgSiO3 and CaSiO3 perovskites at lower-mantle pressures. Phys Earth Planet Inter 90:101–112CrossRefGoogle Scholar
  68. Wentzcovitch RM, Karki BB, Cococcioni M, de Gironcoli S (2004) Thermoelastic properties of MgSiO3-perovskite: insights on the nature of the Earth’s lower mantle. Phys Rev Lett 92(1):018501CrossRefPubMedGoogle Scholar
  69. Wolf GH, Jeanloz R (1985) Lattice dynamics and structural distortions of CaSiO3 and MgSiO3 perovskite. Geophys Res Lett 12:413–416CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Yigang Zhang
    • 1
    Email author
  • Dapeng Zhao
    • 2
  • Masanori Matsui
    • 3
  • Guangjun Guo
    • 1
  1. 1.State Key Laboratory of Lithospheric Evolution, Institute of Geology and GeophysicsChinese Academy of SciencesBeijingChina
  2. 2.Geodynamics Research CenterEhime UniversityMatsuyamaJapan
  3. 3.School of ScienceUniversity of HyogoHyogoJapan

Personalised recommendations