Skip to main content
SpringerLink
Log in

Seismic wave velocities of rare gas solids through elastic properties in Earth’s lower mantle

  • Published:
Science in China Series D: Earth Sciences Aims and scope Submit manuscript

Abstract

The expressions for second (SOE) and third order elastic (TOE) constants for rare gas solids are derived for comparative study of elastic behavior within the framework of many body potentials including the effect of pressure. The derived expressions are used to obtain the relations for pressure derivatives of bulk and shear moduli of RGS solids. The values of SOE, TOE constants and pressure derivative of bulk and shear modulus for Ne up to 100 GPa, Ar up to 75 GPa, for Kr up to 136 GPa and Xe up to 53.4 GPa pressure are computed. The results are in agreement with available experimental results. The computed results are then used to analyze the pressure up to high compression and the elastic and seismic wave velocities (P & S) in Earth’s deep interior.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Tsuchiya T, Kawamura J. Systematics of elasticity: Ab initio study in B1-type alkaline Earth oxides? Chem Phys, 2001, 114: 10086–10093

    Google Scholar 

  2. Tsuchiya T, Kawamura J. Ab initio study of pressure effect on elastic properties of crystalline Au. Chem Phys, 2002, 116: 2121–2124

    Google Scholar 

  3. Tsuchiya T, Kawamura J. First-principles study of systematics of high-pressure elasticity in rare gas solids, Ne, Ar, Kr, and Xe. Chem Phys, 2002, 117: 5859–5865

    Google Scholar 

  4. Karasevskii A L, Holzapfel W B. Equations of state and thermodynamic properties of rare-gas solids under pressure calculated using a self-consistent statistical method. Phy Rev, 2003, 67: 224301.1–224301.9

    Google Scholar 

  5. Barsch G R. Relation between third order elastic constants of single crystal and polycrystals. J Appl Phys, 1967, 39: 3780–3793

    Article  Google Scholar 

  6. Barsch G R, Chang Z P. Second and higher order effective elastic constants of cubic crystals under hydrostatic pressure. J Appl Phys, 1968, 39: 3276–3284

    Article  Google Scholar 

  7. Hollinger R C, Barsch G R. Higher order elastic constants of alkaline halides. J Phys Chem Solid, 1976, 37: 845

    Article  Google Scholar 

  8. Garg V K, Puri D S, Verma M P. On the second- and third-order elastic constants of ZnS structure solids. Phys Stat Sol, 1978, 87: 401

    Article  Google Scholar 

  9. Thakur K P. Third-order elastic constants for 2:2 chalcide crystals possessing the sodium chloride structure. J Phys Chem Solids, 1979, 41: 465–472

    Article  Google Scholar 

  10. Axilrod B M, Teller E. Interaction of the van der waals type between three atoms. J Chem Phys, 1943, 11: 299, doi: 10.1063/1.1723844

    Article  Google Scholar 

  11. Lehri S, Verma M P. Phonon dispersion in rare gas solids. Phys Status Solidi, 1976, 92: 363

    Article  Google Scholar 

  12. Lehri S, Verma M P. Third-order elastic constants and the pressure derivatives of the second-order elastic constants of rare gas solids. Phys Status Solidi, 1980, 98: 789

    Article  Google Scholar 

  13. Singh R K, Neb D K. Debye-waller factors for alkaline Earth oxides. Phys Status Solidi, 1982, 98: 735

    Article  Google Scholar 

  14. Singh R K, Neb D K, Sanyal S P. Effect of three-body forces on thermophysical and anharmonic properties of rare gas solid mixtures. Phys Status Solidi, 1983, 116: 389

    Article  Google Scholar 

  15. Verma M P, Singh R K. The contribution of three-body overlap forces to the dynamical matrix of Alkali Halides. Phy Stat Sol, 1969, 33: 769

    Article  Google Scholar 

  16. Gupta S, Goyal S C. Pressure derivatives of isothermal bulk modulus of rare gas solids. Sol Stat Commun, 2003, 126: 297–300

    Article  Google Scholar 

  17. Gupta S, Goyal S C. Pressure derivatives of bulk and shear modulus of rare gas solids. J Phys Chem Solids, 2003, 64: 1125–1130

    Article  Google Scholar 

  18. Gupta S, Gupta P, Goyal S C. Elastic Properties of Argon under High Pressure. Proc APFB, 2005. 05, Bangkok

  19. Brugger K, Fritz T C. Gruneisen gamma from elastic data. Phy Rev, 1967, 157: 514

    Article  Google Scholar 

  20. Tosi M P. Solid State Physics. Oxford: Clarendon Press, 1964. 16

    Google Scholar 

  21. Anderson O L. Equations of State of Solids for Geophysics and Cermic Science. New York: Oxford University Press, 1995

    Google Scholar 

  22. Birch F. Finite elastic strain of cubic crystals. Phys Rev, 1947, 71: 809

    Article  Google Scholar 

  23. Gupta S, Goyal S C. Effect of temperature on elastic properties of rare gas solids. Physica B, 2004, 352: 24–35

    Article  Google Scholar 

  24. Klein M L, Venables J A. Rare Gas Solids. New York: Academic, 1976. 2

    Google Scholar 

  25. Cocharn W. CRC Crit. Rev Solid State Sci, 1971, 2: 1

    Article  Google Scholar 

  26. Shimizu H, Saitoh N, Sasaki S. High-pressure elastic properties of liquid and solid krypton to 8 GPa. Phys Rev B, 1998, 57: 230–233

    Article  Google Scholar 

  27. Shimizu H, Tashiro H, Kume T, et al. High-pressure elastic properties of solid argon to 70 GPa. Phys Rev Lett, 2001, 86: 4568–4571

    Article  Google Scholar 

  28. Tse J S, Shpakov V P, Belosludov V R. High-pressure elastic constants of solid krypton from quasiharmonic lattice-dynamics calculations. Phy Rev B, 1998, 58(5): 2365–2368

    Article  Google Scholar 

  29. Grimsditch M, Loubeyre P, Polian A. Brillouin scattering and three-body forces in argon at high pressures. Phys Rev B, 1986, 33: 7192

    Article  Google Scholar 

  30. Iitaka T. et al. First-principles calculation of elastic properties of solid argon at high pressures. Phys Rev B, 2001, 65: 012103

    Article  Google Scholar 

  31. Hirschfelder J O, Curtiss C F, Bird R B. Molecular Theory of Gases and Liquids. New York: Wiley, 1954

    Google Scholar 

  32. Birch F J. The effect of pressure upon the elastic parameters of isotropic solids, according to Murnaghan’s Theory of finite strain. Appl Phys, 1938, 9: 279

    Article  Google Scholar 

  33. Anderson O L. Equation of State of Solids for Geophysics and Ceramic Science. Oxford: Oxford University Press, 1995

    Google Scholar 

  34. Robert R W, Smith C S. Ultrasonic parameters in the born model of the sodium and potassium halides. J Phys Chem Solids, 1970, 31: 619

    Article  Google Scholar 

  35. Sikka S K. Empirical equation of state theories at ultra-high pressures. Phys Lett A, 1989, 135: 129

    Article  Google Scholar 

  36. Shanker J, Kumar M. Ion-dependent and crystal-independent interionic potentials. Phys Stat Sol B, 1987, 142: 325

    Article  Google Scholar 

  37. Freund J, Ingalls R. Inverted isothermal equations of state and determination of B0, B’0 and B0. J Phys Chem Solids, 1989, 50: 263

    Article  Google Scholar 

  38. Stacey F D, Brennan B J, Irvine R D. Finite strain theories and comparisons with seismological data. Geophys Surveys, 1981, 4: 189

    Article  Google Scholar 

  39. Misra G, Goyal S C. Bulk modulus and its pressure derivatives of cuprous halides. Sol Stat Comm, 2005, 134(9): 637–640

    Article  Google Scholar 

  40. Hama, Suiot K. The search for a universal equation of state correct up to very high pressures. J Phys-Condens Matt, 1996, 8: 67

    Article  Google Scholar 

  41. Jephcoat A W. Rare gas solids in the Earth’s deep interior. Nature, 1998, 393: 355–358

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Agra College, Agra, 282002, India

    Seema Gupta

  2. Faculty of Engineering and Technology, Raja Balwant Singh College, Bichpuri, Agra, India

    Suresh C. Goyal

Authors
  1. Seema Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Suresh C. Goyal
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gupta, S., Goyal, S.C. Seismic wave velocities of rare gas solids through elastic properties in Earth’s lower mantle. Sci. China Ser. D-Earth Sci. 52, 1599–1611 (2009). https://doi.org/10.1007/s11430-009-0092-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11430-009-0092-1

Keywords

Search

Navigation