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Computational modeling of the structure and elastic constants of the olivine and spinel forms of Mg2SiO4

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Abstract

A computational model of a crystal consists of a description of the structure, a potential function for calculating its energy, and a way of adjusting the structure to minimize the calculated energy. External forces such as hydrostatic pressure or normal and shearing stresses can be simulated, and elastic constants can be calculated. A realistic model should reproduce both the experimental structure and the observed elastic properties.

Such a model has been developed for α Mg2SiO4, the olivine orthosilicate known as forsterite. Coulomb energy is calculated for a structure consisting of Mg2+ ions and rigid SiO 4−4 groups with partial charges on Si and O atoms. Both r −n and exponential expressions were tried for the repulsion energy, and the latter expression yields the best results. This model reproduces reasonably well the experimental structure, the observed elastic constants, and their pressure derivatives. The same model successfully describes γ Mg2SiO4, the cubic spinel polymorph related to ring-woodite. Comparison is made with similar calculations by other authors.

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References

  • Busing WR (1972) A computer program to aid in the understanding of interatomic forces in molecules and crystals. Acta Crystallogr A 28:S252

    Google Scholar 

  • Busing WR (1981) WMIN, a computer program to model molecules and crystals in terms of potential energy functions. Report ORNL-5747. Oak Ridge National Laboratory, Oak Ridge, TN

    Google Scholar 

  • Busing WR, Matsui M (1984) The application of external forces to computational models of crystals. Acta Crystallogr (Submitted)

  • Butterfield C, Carlson EH (1972) Ionic soft sphere parameters from Hartree-Fock-Slater calculations. J Chem Phys 56:4907–4910

    Google Scholar 

  • Catti M (1981) The lattice energy of forsterite. Charge distribution and formation enthalpy of the SiO 4−4 ion. Phys Chem Minerals 7:20–25

    Google Scholar 

  • Catti M (1982) Atomic charges in Mg2SiO4 (forsterite), fitted to thermoelastic and structural properties. J Phys Chem Solids 43:1111–1118

    Google Scholar 

  • Fujino K, Sasaki S, Takéuchi Y, Sadanaga R (1981) X-ray determination of electron distributions in forsterite, fayalite and tephroite. Acta Crystallogr B37:513–518

    Google Scholar 

  • Gilbert TL (1968) Soft-sphere model for closed-shell atoms and ions. J Chem Phys 49:2640–2642

    Google Scholar 

  • Graham EK, Barsch GR (1969) Elastic constants of single-crystal forsterite as a function of temperature and pressure. J Geophys Res 74:5949–5960

    Google Scholar 

  • Iishi K (1978) Lattice dynamics of forsterite. Am Mineral 63:1198–1208

    Google Scholar 

  • Kumazawa M, Anderson OL (1969) Elastic moduli, pressure derivatives, and temperature derivatives of single-crystal olivine and single-crystal forsterite. J Geophys Res 74:5961–5972

    Google Scholar 

  • Matsui M, Matsumoto T (1982) An interatomic potential-function model for Mg, Ca and CaMg olivines. Acta Crystallogr A38:513–515

    Google Scholar 

  • Miyamoto M, Takeda H (1980) An interpretation of the structures of mantle minerals at high pressure in terms of interionic forces. Geochem J 14:243–248

    Google Scholar 

  • Nye JF (1957) Physical Properties of Crystals. Oxford University Press, London, p 146

    Google Scholar 

  • Pauling L (1960) The Nature of the Chemical Bond, Third edition. Cornell University Press, Ithaca, p 321

    Google Scholar 

  • Price GD, Parker SC (1984) Computer simulations of the structural and physical properties of the olivine and spinel polymorphs of Mg2SiO4. Phys Chem Minerals 10:209–216

    Google Scholar 

  • Sasaki S, Prewitt CT, Sato Y, Ito E (1982) Single-crystal x ray study of γ Mg2SiO4. J Geophys Res 87:7829–7832

    Google Scholar 

  • Weidner DJ, Sawamoto H, Sasaki S, Kumazawa M (1984) Single-crystal elastic properties of the spinel phase of Mg2SiO4. J Geophys Res (To be submitted)

  • Yuen PS, Murfitt RM, Collin RL (1974) Interionic forces and ionic polarization in alkaline earth halide crystals. J Chem Phys 61:2383–2393

    Google Scholar 

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Author notes

  1. Masanori Matsui

    Present address: Chemical Laboratory, Kanazawa Medical University, Uchinada, 920-02, Ishikawa-ken, Japan

Authors and Affiliations

  1. Oak Ridge National Laboratory, Chemistry Division, 37831, Oak Ridge, Tennessee, USA

    Masanori Matsui & William R. Busing

Authors
  1. Masanori Matsui
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  2. William R. Busing
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Additional information

Research sponsored by the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under contract W-7405-eng-26 with the Union Carbide Corporation

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Matsui, M., Busing, W.R. Computational modeling of the structure and elastic constants of the olivine and spinel forms of Mg2SiO4 . Phys Chem Minerals 11, 55–59 (1984). https://doi.org/10.1007/BF00308005

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  • DOI: https://doi.org/10.1007/BF00308005

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