Abstract
Prediction of phase stabilities in geological systems represents one of the fundamental problems challenging earth scientists today. Phase equilibria can be studied directly under controlled pressure and temperature conditions in laboratory experiments. In some cases, however, it is not possible to determine phase stabilities from experiments, because, for example, the pressures and temperatures of interest may not be attainable in the laboratory, samples may be non-quenchable, or equilibrium may not be attainable. Under such circumstances, a different approach is needed to study mineral stability. The purpose of this chapter is to describe how mineral stabilities can be studied from direct consideration of the mineral’s lattice vibrations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Akaogi M., Ross, N. L., McMillan, P., et al. (1984) The Mg2SiO4 polymorphs (olivine, modified spinel and spinel)-thermodynamic properties from oxide melt solution calorimetry, phase relations, and models of lattice vibrations. American Mineralogist, 69, 499–512.
Born, M. and Huang, K. (1954) Dynamical Theory of Crystal Lattices, Oxford University Press, New York.
Born, M. and Von Karman, T. (1912) Über Schwingungen in Raumgittern. Physikalische Zeitschrift, 13, 297–309.
Born, M. and Von Karman T. (1913) Theory of specific heat. Physikalische Zeitschrift, 14, 15–71.
Catlow, C. R. A. (1977) Point defect and electronic properties of uranium dioxide. Proceedings of the Royal Society of London, A353, 533–61.
Catlow, C. R. A. and Mackrodt, W. C. (1982) Theory of simulation methods for lattice and defect energy calculations in crystals, (eds C. R. A. Catlow and W. C. Mackrodt), in Lecture Notes in Physics 166: Computer Simulation of Solids, Springer-Verlag, Berlin, pp. 3–20.
Chopelas, A. (1990) Thermal properties of forsterite at mantle pressures derived from vibrational spectroscopy. Physics and Chemistry of Minerals, 17, 149–56.
Cochran, W. (1973) The Structures and Properties of Solids 3: The Dynamics of Atoms in Crystals, Edward Arnold Ltd, London.
Cohen, R. E., Boyer, L. L., and Mehl M. J. (1987) Lattice dynamics of the potential-induced breathing model: phonon dispersion in the alkaline-earth oxides. Physical Review B, 35, 5749–60.
Cowley, R. A., Woods, A. D. B., and Dolling G. (1966) Crystal dynamics of potassium. I. Pseudopotential analysis of phonon dispersion curves at 9°K. Physical Review, 150, 487–94.
Debye, P. (1912) Zur Theorie der spezifischen Wärmen. Annalen der Physik (Leipzig), 39, 789–839.
Dick, B. G. and Overhauser, A. W. (1958) Theory of dielectric constants of alkali halide crystals. Physical Review, 112, 90–103.
Dugdale, J. S., Morrison, J. A., and Patterson, D. (1954) The effect of particle size on the heat capacity of titanium dioxide. Proceedings of the Royal Society of London, A224, 228–35.
Elcombe, M. M. (1967) Some aspects of the lattice dynamics of quartz. Proceedings of the Physical Society, 91, 947–58.
Galeener, F.L., Leadbetter, A. J., and Stringfellow, M. W. (1983) Comparison of neutron, Raman, and infrared vibrational spectra of vitreous SiO2, GeO2, and BeF2. Physical Review B, 27, 1052–78.
Ghose, S. (1988) Inelastic neutron scattering, in Reviews in Mineralogy, vol. 18: Spectroscopic Methods in Mineralogy and Geology, (ed. F. C. Hawthorne), Mineralogical Society of America, pp. 161–92.
Gibbs, G. V. (1982) Molecules as models for bonding in silicates. American Mineralogist, 67, 421–50.
Gilat, G. (1972) Analysis of methods for calculating spectral properties in solids. Journal of Computational Physics, 10, 432–65.
Hofmeister, A. M. (1987) Single-crystal absorption and reflection infrared spectroscopy of forsterite and fayalite. Physics and Chemistry of Minerals, 14, 499–513.
Kieffer, S. W. (1979a) Thermodynamics and lattice vibrations of minerals: 1. Mineral heat capacities and their relationships to simple lattice vibrational models. Reviews of Geophysics and Space Physics, 17, 1–19.
Kieffer, S. W. (1979b) Thermodynamics and lattice vibrations of minerals: 2. Vibrational characteristics of silicates. Reviews of Geophysics and Space Physics, 17, 20–34.
Kieffer, S. W. (1979c) Thermodynamics and lattice vibrations of minerals: 3. Lattice dynamics and an approximation for minerals with application to simple substances and framework silicates. Reviews of Geophysics and Space Physics, 17, 35–59.
Kieffer, S. W. (1980) Thermodynamics and lattice vibrations of minerals: 4. Application to chain and sheet silicates and orthosilicates. Reviews of Geophysics and Space Physics, 18, 862–86.
Kieffer, S. W. (1982) Thermodynamics and lattice vibrations of minerals: 5. Applications to phase equilibria, isotope fractionation, and high-pressure thermodynamic properties. Reviews of Geophysics and Space Physics, 20, 827–49.
Ko, J. and Prewitt C. T. (1988) High-pressure phase transition in MnTiO3 from the ilmenite to the LiNbO3 structure. Physics and Chemistry of Minerals, 15, 355–62.
Ko, J., Brown, N. E., Navrotsky, A., el al. (1989) Phase equilibrium and calorimetric study of the transition of MnTiO3 from the ilmenite to the lithium niobate structure and implications for the stability field of perovskite. Physics and Chemistry of Minerals, 16, 727–33.
Leadbetter, A. J. (1969) Inelastic cold neutron scattering from different forms of silica. Journal of Chemical Physics, 51, 779–86.
Leinenweber, K., Utsumi, W., Tsuchida, Y. et al. (1991) Unquenchable high-pressure perovskite polymorphs of MnSnO3 and FeTiO3. Physics and Chemistry of Minerals, 18, 244–250.
Lewis, G. V. and Catlow, C. R. A. (1985) Potential models for ionic oxides. Journal of Physics C, 18, 1149–61.
Lord, R. C. and Morrow, J. C. (1957) Calculation of heat capacity of α-quartz and vitreous silica from spectroscopic data. Journal of Chemical Physics, 26, 230–2.
Maradudin, A. A., Montroll, E. W., and Weiss, G. H. (1963) Lattice Dynamics in the Harmonic Approximation, Academic Press, New York.
Megaw, H. (1969) A note on the structure of LiNbO3. Acta Crystallographica, A24, 583–8.
Montroll, E. W. (1942) Frequency spectrum of crystalline solids. Journal of Chemical Physics, 10, 218–29.
Montroll, E. W. (1943) Frequency spectrum of crystalline solids II: general theory and applications to simple cubic lattices. Journal of Chemical Physics, 11, 481–95.
Navrotsky, A. (1980) Lower mantle phase transitions may generally have negative pressure-temperature slopes. Geophysical Research Letters, 7, 709–11.
Parker, S. C. and Price, G. D. (1989) Computer modelling of phase transitions in minerals, in Advances in Solid-State Chemistry, vol. 1, JAI Press Inc., London, pp. 295–327.
Placzek, G. and Van Hove, L. (1954) Crystal dynamics and inelastic scattering of neutrons. Physical Review, 93, 1207–14.
Price, G. D., Parker, S. C., and Leslie, M. (1987) The lattice dynamics of forsterite. Mineralogical Magazine, 51, 157–70.
Price, G. D., Wall, A., and Parker, S. C. (1989) The properties and behaviour of mantle minerals: a computer simulation approach. Philosophical Transactions of the Royal Society of London, A328, 391–407.
Rao, K. R., Chaplot, S. L., Choudhury, N., et al. (1988) Lattice dynamics and inelastic neutron scattering from forsterite, Mg2SiO4: phonon dispersion relation, density of states and specific heat. Physics and Chemistry of Minerals, 16, 83–97.
Robie, R. A., Hemingway, B. S., and Fischer, J. R. (1975) Thermodynamic properties of minerals and related substances at 298.15 K and 1 bar (105 pascals) pressure and at higher temperatures. US Geological Survey Bulletin 1452, US Government, Washington D.C.
Ross, N. L. and Navrotsky, A. (1987) The Mg2GeO4 olivine-spinel phase transition. Physics and Chemistry of Minerals, 14, 473–81.
Ross, N. L. and Navrotsky, A. (1988) Study of the MgGeO3 polymorphs (orthopyroxene, clinopyroxene, and ilmenite structures) by calorimetry, spectroscopy, and phase equilibria. American Mineralogist, 73, 1355–65.
Ross, N. L., and Price, G. D. (1989) Factors determining the stability of LiNbO3 and ilmenite structures. Transactions of the American Geophysical Union, 70, 350.
Ross N. L., Ko, J., and Prewitt C. T. (1989) A new phase transition in MnTiO3:LiNbO3 to perovskite structure. Physics and Chemistry of Minerals, 16, 621–9.
Ross, N. L., Akaogi, M., Navrotsky, A., et al. Phase transitions among the GaGeO3 polymorphs (wollastonite, garnet, and perovskite structures): studies by high-pressure synthesis, high-temperature calorimetry, and vibrational spectroscopy and calculation. Journal of Geophysical Research, 91, 4685–96.
Salje, E. and Viswanathan, K. (1976) The phase diagram calcite-aragonite as derived from the crystallographic properties. Contributions to Mineralogy and Petrology, 55, 55–67.
Salje, E. and Werneke, C. (1982a) How to determine phase stabilities from lattice vibrations, in High-Pressure Researches in Geoscience, (ed. W. Schreyer), E. Schwiezer. Verlag, Stuttgart, pp. 321–48.
Salje, E. and Werneke, C. (1982b) The phase equilibrium between sillimanite and andalusite as determined from lattice vibrations. Contributions to Mineralogy and Petrology, 79, 56–67.
Shomate, C. H. (1947) Heat capacities at low temperatures of titanium dioxide (rutile and anatase). Journal of the American Chemical Society, 69, 218–19.
Striefler, M. E. and Barsch, G. R. (1975) Lattice dynamics of a-quartz. Physical Review B, 12, 4553–66.
Traylor, J.G., Smith, H. G., Nicklow, R. M., et al (1971) Lattice dynamics of rutile. Physical Review B, 3, 3457–72.
Watanabe, H. (1982) Thermochemical properties of synthetic high-pressure compounds relevant to the earth’s mantle, in High Pressure Research in Geophysics, (eds S. Akimoto and M. H. Manghnani), D. Reidel, Boston, pp. 441–64.
Woods, A. D. B., Brockhouse, B. N., Cowley, R. A., et al. (1963) Lattice dynamics of alkali halide crystals II: experimental studies of KBr and Nal. Physical Review. 131, 1025–39.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Geoffrey D. Price, Nancy L. Ross and the contributors
About this chapter
Cite this chapter
Ross, N.L. (1992). Lattice vibration and mineral stability. In: Price, G.D., Ross, N.L. (eds) The Stability of Minerals. The Mineralogical Society Series, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-0-585-27578-9_4
Download citation
DOI: https://doi.org/10.1007/978-0-585-27578-9_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-412-44150-9
Online ISBN: 978-0-585-27578-9
eBook Packages: Springer Book Archive