Skip to main content

Phonon Density of States and Thermodynamic Properties of Minerals

  • Chapter
Thermodynamic Data

Part of the book series: Advances in Physical Geochemistry ((PHYSICAL GEOCHE,volume 10))

Abstract

An important objective of the earth sciences is to develop the capability of predicting the thermodynamic properties of minerals and their phase relations under various pressure-temperature conditions in the earth, moon and the terrestrial planets. Experimentally, thermodynamic properties such as specific heat can be measured by adiabatic and differential scanning calorimetry. However, there are cases, in which the determination of the low temperature specific heat by adiabatic calorimetry is not feasible due to the paucity of materials. Such is the case for the high-pressure and high-temperature magnesium silicate phases: Mg2SiO4 (β- and γ-spinel) and MgSiO3 (ilmenite, perovskite and garnet) considered to be stable in the earth’s mantle. These phases are synthesized in cubic-anvil and split-sphere apparati in 10 to 20 mg quantities, that are barely adequate for the specific heat measurement by differential scanning calorimetry (DSC), usually in the range 300 to 900 K. Hence, the ability to correctly predict the low temperature specific heat of these phases would be extremely useful. Such a theoretical treatment should at the same time provide an understanding of the thermodynamic properties of minerals at the atomistic level. This was the goal aimed at the Mineralogical Society of America Short Course organized by S.W. Kieffer and A. Navrotsky on “Macroscopic to microscopic: Atomic environments to mineral thermodynamics” held at Washington College, Chestertown, Maryland in spring, 1985.

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., 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 

  • Ashida, T., Kume, S., Ito, E., and Navrotsky, A. (1988). MgSiO3 ilmenite: Heat capacity, thermal expansivity, and enthalpy of transformation. Phys. Chem. Miner., 16, 239–245.

    Article  Google Scholar 

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

    Google Scholar 

  • Born, M. and von Kármán, Th. (1912). Über Schwingungen in Raumgittern. Physik. Zeit.13, 297–309.

    Google Scholar 

  • Brockhouse, B.N. (1962). Interatomic forces from neutron scattering. J. Phys. Soc. Jap., Suppl. 17, BII, 363–367.

    Google Scholar 

  • Brüesch, P. (1982). Phonons: Theory and Experiment I. Springer-Verlag, Berlin.

    Google Scholar 

  • Bukowinski, M.S.T. and Wolf, G.H. (1988). Equation of state and possible critical phase transitions in MgSiO3 perovskite at lower mantle conditions, in Structural and Magnetic Phase Transitions in Minerals, S. Ghose, J.M.D. Coey, and E. Salje, eds., Springer-Veríag, New York, pp. 91–112.

    Google Scholar 

  • Chaplot, S.L. (1978). A computer program for external modes in complex molecular-ionic crystals. Re. 972, Bhabha Atomic Research Centre, Bombay, India.

    Google Scholar 

  • Choudhury, N., Chaplot, S.L., and Rao, K.R. (1989). Equation of state and melting point studies of forsterite. Phys. Chem. Miner.16, 599–605.

    Article  Google Scholar 

  • Choudhury, N., Chaplot, S.L., Rao, K.R. and Ghose, S. (1988). Lattice dynamics of MgSiO3 perovskite. Pramāna-J. Phys.30, 423–428.

    Article  Google Scholar 

  • Cohen, R.E. (1987). Elasticity and equation of state of MgSiO3 perovskite. Geophys. Res. Lett., 14, 1053–1056.

    Article  Google Scholar 

  • Debye, P. (1912). Zur Theorie der spezifíschen Wärmen. Ann. der Physik 39, 789.

    Article  Google Scholar 

  • Dorner, B. (1982). Coherent Inelastic Neutron Scattering in Lattice Dynamics. Springer-Verlag, Berlin.

    Google Scholar 

  • Fuess, H., Ballet, O., and Lottermoser, W. (1988). Magnetic phase transitions in olivines Mg2SiO4 (M = Mn, Fe, Co, FexMn1_x), in Structural and Magnetic Phase Transitions in Minerals, S. Ghose, J.M.D. Coey, and E. Salje, eds., Springer-Verlag, New York, pp. 185–207.

    Google Scholar 

  • Ghose, S. Hastings, J.M., Corliss, L.M., Rao, K.R., Chaplot, S.L., and Choudhury, N. (1987). Study of phonon dispersion relations in forsterite, Mg2SiO4 by inelastic neutron scattering. Solid State Comm.63, 1045–1050.

    Article  Google Scholar 

  • Ghose, S. (1988). Inelastic neutron scattering, in Spectroscopic Methods in Mineralogy and Geology, F.C. Hawthorne, ed., Reviews in Mineralogy, vol. 18, 161–192. Mineralogical Society America, Washington, D.C.

    Google Scholar 

  • Ghose, S., Hastings, J.M, Choudhury, N, Chaplot, S.L., and Rao, K.R. (1991) Phonon dispersion relation in fayalite, Fe2SiO4. Physica B 174, 83–86.

    Article  Google Scholar 

  • Hemley, R.J., Cohen, R.E., Yeganeh-Haeri, A., Mao, H.K., Weidner, D.J., and Ito, E. (1989). Raman spectroscopy and lattice dynamics of MgSiO3 perovskite at high pressure, in Perovskite: A Structure of Great Interest to Geophysics and Materials Science, pp. 35–44. American Geophysical Union, Washington, D.C.

    Google Scholar 

  • Hemley, R.J., Jackson, M.D., and Gordon, R.G. (1987). Theoretical study of the structure, lattice dynamics and equation of state of perovskite-type MgSiO3 and CaTiO3. Phys. Chem. Miner.14, 2–12.

    Article  Google Scholar 

  • Horiuchi, H., Ito, E., and Weidner, D.J. (1987). Perovskite-type MgSiO3: Single crystal x-ray diffraction study. Amer. Mineral 72, 357–360.

    Google Scholar 

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

    Google Scholar 

  • Iishi, K., Salje, E., and Werneke, C. (1979). Phonon spectra and rigid-ion model calculations on andalusite. Phys. Chem. Miner.4, 173–188.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Kieffer, S.W. (1985). Heat capacity and entropy: Systematic relations to lattice vibrations, in Microscopic to Macroscopic: Atomic Environments to Mineral Thermodynamics, S.W. Kieffer and A. Navrotsky, eds., Reviews in Mineralogy, vol. 14, pp. 65–126, Mineralogical Society of America, Washington, D.C.

    Google Scholar 

  • Knittle, E. and Jeanloz, R. (1987). Synthesis and equation of state of (Mg,Fe)SiO3 perovskite to over 100 GPa. Science 235, 669–670.

    Article  Google Scholar 

  • Placzek, G. and Van Hove, L. (1955). Interference effects in total neutron scattering cross-section of crystals. Nuovo Cimento 1, 233–244.

    Article  Google Scholar 

  • Price, D.L., Ghose, S, Choudhury, N, Chaplot, S.L., and Rao, K.R. (1991). Phonon density of states in fayalite, Fe2SiO4. Physica B174, 87–90.

    Article  Google Scholar 

  • Price, G.D., Parker, S.C., and Leslie, M. (1987a). The lattice dynamics of forsterite. Mineral Mag. 51, 157–170.

    Article  Google Scholar 

  • Price, G.D., Parker, S.C., and Leslie, M. (1987b) The lattice dynamics and thermodynamics of the Mg2SiO4 polymorphs. Phys. Chem. Miner 15, 181–190.

    Article  Google Scholar 

  • Rao, K.R., Chaplot, S.L, Choudhury, N., Ghose, S., and Price, D.L. (1987). Phonon density of states and specific heat of forsterite, Mg2SiO4. Science 236, 64–65.

    Article  Google Scholar 

  • Rao, K.R., Chaplot, S.L., Choudhury, N., Ghose, S., Hastings, J.M., Corliss, L.M., and Price, D.L. (1988). Lattice dynamics and inelastic neutron scattering from forsterite, Mg2SiO4; phonon dispersion relations, phonon density of states and specific heat. Phys. Chem. Miner.16, 83–97.

    Article  Google Scholar 

  • Robie, R.A., Finch, C.B., and Hemingway, B.S. (1982a). Heat capacity and entropy of fayalite (Fe2SiO4) between 5.1 and 383 K: Comparison of calorimetric and equilibrium values for the QFM buffer. Amer. Mineral 67, 463–469.

    Google Scholar 

  • Robie, R.A., Hemingway, B.S., and Takei, H. (1982b). Heat capacities and entropies of Mg2SiO4, Mn2SiO4 and Co2SiO4 between 5 and 380 K. Amer. Mineral 67, 470–482.

    Google Scholar 

  • Robie, R.A. and Hemingway, B.S. (1984). Entropies of kyanite, andalusite and sillimanite: additional constraints on pressure and temperature of the A12SiO5 triple point. Amer. Mineral 69, 298–306.

    Google Scholar 

  • Salje, E. and Werneke, C. (1982). The phase equilibrium between sillimanite and andalusite as determined from lattice vibrations. Contrib. Mineral Petrol 79, 56–76.

    Article  Google Scholar 

  • Sköld, K. and Price, D.L., eds. (1986). Neutron Scattering, Part I. Methods of Experimental Physics, vol. 15, Academic Press, New York.

    Google Scholar 

  • Smyth, J.R. (1975). High temperature crystal chemistry of fayalite. Amer. Mineral 60, 1092–1097.

    Google Scholar 

  • Sumino, Y. (1979). The elastic constants of Mn2SiO4, Fe2SiO4 and CO2SiO4, and the elastic properties of olivine group minerals at high temperature. J. Phys. Earth 27, 209–238.

    Article  Google Scholar 

  • Wang, Y., Guyot, F., Yeganeh-Haeri, A., and Lieberman, R.C. (1990). Twinning in MgSiO3 perovskite. Science 248, 468–471.

    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, S. Akimoto and M.H. Manghnani, eds., Center for Academic Publications, Tokyo, pp. 441–464.

    Google Scholar 

  • Winkler, B. and Buehrer, W. (1990). Lattice dynamics of andalusite: Prediction and experiment. Phys. Chem. Miner.17, 453–461.

    Article  Google Scholar 

  • Winkler, B., Dove, M.T., and Leslie, M. (1991). Static lattice energy minimization and lattice dynamics calculations on aluminosilicate minerals. Amer. Mineral 76, 313–331.

    Google Scholar 

  • Wolf, G. and Bukowinski, M. (1985). Ab initio structural and thermoelastic properties of orthorhombic MgSiO3 perovskite. Geophys. Res. Lett.12, 809–812.

    Article  Google Scholar 

  • Wolf, F.H. and Jeanloz, R. (1985). Lattice dynamics and structural distortions of CaSiO3 and MgSiO3 perovskites. Geophys. Res. Lett.12, 413–416.

    Article  Google Scholar 

  • Yeganeh-Haeri, A., Weidner, D.J., and Ito, E. (1989). Single-crystal elastic moduli of magnesium metasilicate perovskite, in Perovskite: A Structure of Great Interest to Geophysics and Materials Science, A. Navrotsky and D.J. Weidner, eds., pp. 13–25. American Geophysical Union, Washington, D.C., pp. 13–25.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Ghose, S., Choudhury, N., Chaplot, S.L., Rao, K.R. (1992). Phonon Density of States and Thermodynamic Properties of Minerals. In: Saxena, S.K. (eds) Thermodynamic Data. Advances in Physical Geochemistry, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2842-4_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2842-4_11

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7692-0

  • Online ISBN: 978-1-4612-2842-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics