Skip to main content

Theoretical Computation of Physical Properties of Mantle Minerals

  • Conference paper
Chemistry and Physics of Terrestrial Planets

Part of the book series: Advances in Physical Geochemistry ((PHYSICAL GEOCHE,volume 6))

Abstract

Methods of direct sampling, as used for crustal rocks, unfortunately cannot be applied to the study of chemical and mineralogical composition of the Earth’s mantle; only in some cases for the uppermost mantle layers, which interact with the crust by exchange of matter, are fragments or relics inserted in crustal material subject to petrographic examination. However, in the last two decades much experimental work has been performed in laboratory simulations of pressure-temperature conditions in systems of reasonably probable mantle chemical compositions (cf., e.g., Ringwood, 1975; Liu, 1977; Yagi et al., 1979; Ito et al., 1984). On the basis of these results a model of the mantle can be proposed such that its physical properties are in accordance with those observed by seismological and other measurements. This scheme requires that the relevant physical data be known for all phases that are to be included in the model. In some cases an experimental determination is possible, and the relative account of methods and results is found in Chapter 7 of this book (Weidner, this volume). However, very often it is not, either because synthetic samples are not available in the physical conditions required by the measurement (adequate dimensions or amount, single-crystal state, etc.), or because data are desired for pressure- temperature fields that cannot be attained. In these cases theoretical methods of calculating or sometimes even just estimating the required data can be very useful. The methods that are presently available and the main results obtained so far are considered and reviewed here.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Akaogi, M., and Navrotsky, A. (1984) The quartz-coesite-stishovite transformations: new calorimetric measurements and calculation of phase diagrams, Phys. Earth Planet. Int. 36, 124–134.

    Article  Google Scholar 

  • Akaogi, M., Ross, N. L., McMillan, P., and Navrotsky, A. (1984) The Mg2SiO4 polymorphs (olivine, modified spinel and spinel)—thermodynamic properties from oxide melt solution calorimetry, phase relations, and models of lattice vibrations, Amer. Mineral. 69, 499–512.

    Google Scholar 

  • Anderson, D. L., and Bass, J. D. (1984) Mineralogy and composition of the upper mantle, Geophys. Res. Lett. 11, 637 - 640.

    Article  Google Scholar 

  • Bamford, D. (1976) Seismic anisotropy in the crust and upper manlte, in The Physics and Chemistry of Minerals and Rocks, pp. 223–237, edited by R. G. J. Strens. Wiley- Intersicence, London.

    Google Scholar 

  • Born, M., and Huang, K. (1954) Dynamical Theory of Crystal Lattices. Oxford Univ. Press, London.

    Google Scholar 

  • Boswarva, I. M. (1970) Semiempirical calculations of ionic polarizabilities and van der Waals potential coefficients for the alkaline-earth chalcogenides, Phys. Rev. B1, 1698– 1701.

    Google Scholar 

  • Busing, W. R. (1970) An interpretation of the structures of alkaline earth chlorides in terms of interionic forces, Trans. Amer. Crystallogr. Assoc. 6, 57–72.

    Google Scholar 

  • Busing, W. R. (1981) WMIN, a computer program to model molecules and crystals in terms of potential energy functions. ORNL-5747, U.S. National Technical Information Service, Washington, D.C.

    Google Scholar 

  • Busing, W. R., and Matsui, M. (1984) The application of external forces to computational models of crystals, Acta Crystallogr. A40, 532–538.

    Article  Google Scholar 

  • Catlow, C. R. A., Dixon, M., and Mackrodt, W. C. (1982) Interionic potentials in ionic solids, in Computer Simulation of Solids, pp. 130–161, edited by C. R. A. Catlow and W. C. Mackrodt. Springer-Verlag, Berlin.

    Chapter  Google Scholar 

  • Catlow, C. R. A., and Mackrodt, W. C. (1982) Theory of simulation methods for lattice and defect energy calculations in crystals, in Computer Simulation of Solids, pp. 3–20, edited by C. R. A. Catlow and W. C. Mackrodt. Springer-Verlag, Berlin.

    Chapter  Google Scholar 

  • Catti, M. (1981) A generalized Born-Mayer parametrization of the lattice energy in orthorhombic ionic crystals, Acta Crystallogr. A37, 72–76.

    Google Scholar 

  • Catti, M. (1982) Atomic charges in Mg2SiO4x (forsterite), fitted to thermoelastic and structural properties, J. Phys. Chem. Solids 43, 1111–1118.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Catti, M., and Ivaldi, G. (1983) Charge distribution from least-energy structure in Ca-Mg orthosilicates, Phys. Chem. Minerals 9, 160–166.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Gaffney, E. S. (1972) Crystal-field effects in mantle minerals, Phys. Earth Planet. Int. 6, 385–390.

    Article  Google Scholar 

  • Ghosh, P. K., and Das, A. R. (1979) Preparation and characterization of forsterite and measurement of its dielectric cconstant and loss factor in the frequency range 100 kc/sec to 25 Mc/sec, Trans. Indian Ceram. Soc. 38, 89–95.

    Google Scholar 

  • Gilbert, T. L. (1968) Soft-sphere model for closed shell atoms and ions, J. Chem. Phys. 49, 2640–2645.

    Article  Google Scholar 

  • Graham, E. K., and Barsch, G. R. (1969) Elasticc constants of single crystal forsterite as a function of temperature and pressure, J. Geophys. Res. 74, 5949–5960.

    Article  Google Scholar 

  • Hazen, R. M. (1976) Effects of temperature and pressure on the crystal structure of forsterite, Amer. Mineral. 61, 1280–1293.

    Google Scholar 

  • Hazen, R. M., and Prewitt, C. T. (1977) Effects of temperature and pressure on interatomic distances in oxygen-based minerals, Amer. Mineral. 62, 309–315.

    Google Scholar 

  • Horiuchi, H., and Sawamoto, H. (1981) β-Mg2SiO4: single-crystal X-ray diffraction study, Amer. Mineral. 66, 568–575.

    Google Scholar 

  • Horiuchi, H., Hirano, M., Ito, E., and Matsui, Y. (1982) MgSiO3 (ilmenite-type): single crystal X-ray diffraction study, Amer. Mineral. 67, 788–793.

    Google Scholar 

  • Ito, E., and Matsui, Y. (1977) Silicate ilmenites and the post-spinel transformations, in High-Pressure Research, Applications in Geophysics, pp. 193’208, edited by M. H. Manghnani and S. Akimoto. Academic Press, New York.

    Google Scholar 

  • Ito, E., Takahashi, E., and Matsui, Y. (1984) The mineralogy and chemistry of the lower mantle: an implication of the ultrahigh-pressure phase relations in the system MgO- FeO-SiO2, Earth Planet. Sci. Lett. 67, 238–248.

    Article  Google Scholar 

  • Kern, H., and Richter, A. (1981) Temperature derivatives of compressional and shear wave velocities in crustal and mantle rocks at 6 kbar confining pressure, J. Geophys. 49, 47–56.

    Google Scholar 

  • Kieffer, S. W. (1979) Thermodynamics and lattice vibrations of minerals: 1. Mineral heat capacities and their relationships to simple lattice vibrational models, Rev. Geophys. Space Phys. 17, 1–19.

    Article  Google Scholar 

  • Kieffer, S. W. (1980) Thermodynamics and lattice vibrations of minerals: 4. Appliccation to chain and sheet silicates and orthosilicates, Rev. Geophys. Space Phys. 18, 862–886.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Levien, L., and Prewitt, C. T. (1981) High-pressure structural study of diopside, Amer. Mineral. 66, 315–323.

    Google Scholar 

  • Levien, L., Weidner, D. J., and Prewitt, C. T. (1979) Elasticity of diopside, Phys. Chem. Minerals 4, 105–133.

    Article  Google Scholar 

  • Liu, L. (1977) Mineralogy and chemistry of the earth’s mantle above 1000 km, Geophys. J. Roy. Astron. Soc. 48, 53–62.

    Google Scholar 

  • Liu, L. (1979) The high-pressure phase transformations of monticellite and implications for upper mantle mineralogy, Phys. Earth Planet. Int. 20, P25–P29.

    Article  Google Scholar 

  • Matsui, M., and Busing, W. R. (1984a) Calculation of the elastic constants and high- pressure properties of diopside, CaMgSi2O6, Amer. Mineral. 69, 1090–1095.

    Google Scholar 

  • Matsui, M., and Busing, W. R. (1984b) Computational modeling of the structure and elastic constants of the olivine and spinel forms of Mg2SiO4, Phys. Chem. Minerals 11, 55–59.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Matsui, Y. (1982) Computer simulation of structures of actual and hypothetical silicate crystals, in Collected Papers on “The Materials Science of the Earth’s Interior” pp. 11–17, edited by I. Sunagawa and K. Aoki. Tohoku University, Sendai, Japan.

    Google Scholar 

  • Miyamoto, M., and Takeda, H. (1984) An attempt to simulate high pressure structures of Mg-silicates by an energy minimization method, Amer. Mineral. 69, 711–718.

    Google Scholar 

  • Mizukami, S., Ohtani, A., and Kawai, N. (1975) High-pressure X-ray diffraction studies on β- and γ-Mg2SiO4, Phys. Earth Planet. Int. 10, 177–182.

    Article  Google Scholar 

  • Orr, R. L. (1953) High temperature heat contents of magnesium orthosilicate and ferrous orthosilicate, Amer. Chem. Soc. 75, 528–529.

    Article  Google Scholar 

  • Parker, S. C., Catlow, C. R. A., and Cormack, A. N. (1984) Structure prediction of silicate minerals using energy minimization techniques, Acta Crystallogr. B40, 200–208.

    Google Scholar 

  • Price, G. D., and Parker, S. C. (1984) Computer simulations of the structural and physical properties of the olivine and spinel polymorphs of Mg2SiO4, Phys. Chem. Minerals 10, 209–216.

    Article  Google Scholar 

  • Ringwood, A. E. (1975) Composition and Petrology of the Eart’s Mantle. McGraw-Hill Book Company, New York.

    Google Scholar 

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

    Article  Google Scholar 

  • Schloessin, H. H., and Timco, G. W. (1977) The significance of ferroelectric phase transitions for the earth and planetary interiors, Phys. Earth Planet. Int. 14, P6–P12.

    Article  Google Scholar 

  • Tamada, O. (1980) Electrostatic energies of polymorphs of M2SiO4 stoichiometry (M = Ni, Mg, Co, Fe and Mn), Mineral. J. 10, 71–83.

    Article  Google Scholar 

  • Tosi, M. P. (1964) Cohesion of ionic solids in the Born model. Solid State Phys. 16, 1–113.

    Article  Google Scholar 

  • Watanabe, H. (1982) Thermochemical properties of synthetic high pressure compounds relevant to the Earth’s mantle, in High Pressure Research in Geophysics, pp. 441–464, edited by S. Akimoto and M. H. Manghnani. Center for Academic Publications, Tokyo.

    Google Scholar 

  • Weidner, D. J., Sawamoto, H., Sasaki, S., and Kumazawa, M. (1984) Single crystal elastic properties of the spinel phase of Mg2SiO4, J. Geophys. Res. 89, 7852–7860.

    Article  Google Scholar 

  • Yagi, T., Bell, P. M., and Mao, H. K. (1979) Phase relations in the system MgO-FeO- SiO2 between 150 and 700 kbar at 1000°C, Carnegie Inst. Wash. Yearb. 78, 614–618.

    Google Scholar 

  • Yagi, T., Mao, H. K., and Bell, P. M. (1982) Hydrostatic compression of pervskite-type MgSiO3, in Advances in Physical Geochemistry, pp. 317–325, edited by S. K. Saxena. Springer-Verlag, New York.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag New York Inc.

About this paper

Cite this paper

Catti, M. (1986). Theoretical Computation of Physical Properties of Mantle Minerals. In: Saxena, S.K. (eds) Chemistry and Physics of Terrestrial Planets. Advances in Physical Geochemistry, vol 6. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4928-3_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4928-3_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-9363-7

  • Online ISBN: 978-1-4612-4928-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics