Abstract
The correlation between the structure and thermodynamic properties of minerals has long been considered fundamental. Besides the first-law functions, it is possible to calculate entropy and free energy for a pure ideal crystal if the vibrational properties are taken into account. These calculations imply the precise evaluation of spectroscopic data (Raman, IR, phonon dispersion curves) and allow good estimates of elastic properties and atomic displacement parameters.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Au, A.Y. and Weidner, D.J. (1986). Theoretical modelling of the elastic properties of forsterite: A polyhedral approach. Phys. Chem. Miner. 13, 360–370.
Bertaut, F. (1952). L’Energie electrostatique de reseaux ioniques. J. Phys. 13, 499–505.
Bertaut, F. (1978a). The equivalent charge concept and its application to the electrostatic energy of charges and multipoles. J. Phys. 39, 1331–1348.
Bertaut, F. (1978b). Electrostatic potentials, fields and field gradients. J. Phys. Chem. Solids 39, 97–102.
Bertaut, F. (1983). Energie dipolaire ďune structure modulee. C. R. Acad. Sci. Ser. II 296, 1123–1127.
Bertaut, F. (1985). Analyse de representation de la phase incommensurable de K2SeO4, cas ďun groupe ďespace non symmorphe. C.R. Acad. Sci. Ser. II 300, 589–594.
Bertaut, F. (1986). Champs, energies coulombienne, dipolaire et de polarisation dans une structure incommensurable. C.R. Acad. Sci. Ser. II 302, 1137–1142.
Birle, J.D., Gibbs, G.V., Moore, P.B., and Smith, J.V. (1968). Crystal structures of natural olivines. Amer. Mineral. 53, 807–824.
Bocchio, R., Brajkovic, A., and Pilati, T. (1986). Crystal chemistry of the olivines in the peridotites from the Ivrea-Verbano zone (Western Italian Alps). Neues Jahrb. Miner. Monatsh. 7, 313–324.
Born, M. and Huang, K. (1954). Dynamical Theory of Crystal Lattices. Oxford, Clarendon Press.
Burnham, C.W. (1990). The ionic model: Perceptions and realities in mineralogy. Amer. Mineral 75, 443–463.
Busing, W.R. (1981). WMIN, a computer program to model molecules and crystals in terms of potential energy functions. ORNL-5747, U.S. Technical Inform. Sev.
Busing, W.R. and Matsui, M. (1984). The application of external forces to computational models of crystals. Acta Cryst. A40, 532–538.
Catlow, C.R.A. and Mackrodt, W.C. (1982). Computer simulation of solids, in Lecture Notes in Physics, Vol. 166, Springer-Verlag, Berlin.
Catti, M. (1982). Atomic charges in Mg2SiO4 (forsterite), fitted to thermoelastic and structural properties. J. Phys. Chem. Solids 43, 1111–1118.
Catti, M. (1989). Modelling of structural and elastic changes of forsterite (Mg2SiO4) under stress. Phys. Chem. Miner. 16, 582–590.
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.
Cochran, W. (1971). Lattice dynamics of ionic and covalent crystals. C.R.C. Crit. Rev. Solid State Sci. 2, 1–83.
Cochran, W. (1973). The Dynamics of Atoms in Crystals. London, Arnold.
Eastman, E.D. and McGavock, W.C. (1937). The heat capacity and entropy of rhombic and monoclinic Sulfur. J. Amer. Chem. Soc. 59, 145–151.
Elcombe, M. (1967). Some aspects of the lattice dynamics of quartz. Proc. Phys. Soc. 91, 947–958.
Ewald, P.P. (1921). Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. (Leipzig) 64, 253–287.
Filippini, G., Gramaccioli, C.M., Simonetta, M., and Sufl’ritti, G. B. (1976). Lattice-dynamical applications to crystallographic problems: Consideration of the Brillouin zone sampling. Acta Cryst. A32, 259–264.
Fujino, K., Sasaki, S., Takeuchi, Y., and Sadanaga, R. (1981). X-ray determination of electron distributions in forsterite, fayalite and tephroite. Acta Cryst. B37, 513–518.
Ghose, S. (1985). Macroscopic to microscopic, in Lattice Dynamics, Phase Transitions and Soft Modes, Reviews in Mineralogy, S.W. Kieffer and A. Navrotsky, eds., Mineralogy Society of America, Washington, D.C.; Vol. 14, Chap. 4.
Ghose, S., Hastings, J.M., Corliss, L.M., Rao, K.R., Chaplot, S.L., and Choudhury, L. (1987). Study of phonon dispersion relations in forsterite, Mg2SiO4 by inelastic neutron scattering. Solid State Commun. 63, 1045–1050.
Gramaccioli, C.M. (1987). Spectroscopy of molecular crystals and crystallographic implication. Int. Rev. Phys. Chem. 6 (4), 337–349.
Gramaccioli, C.M. and Filippini, G. (1983). Lattice-dynamical evaluation of temperature factors in non-rigid molecular crystals: A first application to aromatic hydrocarbons. Acta Cryst. A39, 784–791.
Gramaccioli, C.M. and Filippini, G. (1984). Lattice-dynamical calculations for orthorhombic sulfur: A non-rigid molecular model. Chem. Phys. Lett. 108, 585–588.
Gramaccioli, C.M. and Filippini, G. (1985). Thermal motion for non-rigid molecules in crystals: Symmetry of the generalized mean-square displacement tensor W.Acta Cryst. A41, 356–361.
Guthrie, G.B., Jr., Scott, D.W., and Waddington, G. (1954). Thermodynamic functions and heat of formation of S 8 (gas). J. Amer. Chem. Soc. 76, 1488–1493.
Hazen, R.N. (1976). Effects of temperature and pressure on the crystal structure of forsterite. Amer. Mineral. 61, 1280–1293.
Iishi, K. (1976). The analysis of the phonon spectrum of α-quartz based on a polarizableion model. Z. Krist. 144, 289–303.
Iishi, K. (1978a). Lattice-dynamical study of the β -quartz phase transition. Amer. Mineral. 63, 1190–1197.
Iishi, K. (1978b). Lattice Dynamics of Corundum. Phys. Chem. Miner. 3, 1–10.
Iishi, K. (1978c). Lattice dynamics of forsterite. Amer. Mineral. 63, 1198–1208.
Iishi, K., Salje, E., and Werneke, C. (1979). Phonon spectra and rigid-ion model calculations on andalusite. Phys. Chem. Miner. 4, 173–186.
Iishi, K., Miura, M., Shiro, Y., and Murata, H. (1983). Lattice dynamics of α-quartz including the effect of the width of the atomic electron distribution. Phys. Chem. Miner. 9, 61–66.
Johnson, C.K. (1976). ORTEPII: A FORTRAN thermal-ellipsoid plot program for crystal structure illustrations. Rept. ORNL-5138. Oak Ridge Nat. Lab. Tenn.
Kellermann, E.W. (1940). Theory of the vibrations of the sodium chloride lattice. Phil. Trans. R. Soc. Lond. 238, 513–548.
Kiefl’er, S.W. (1985). Macroscopic to microscopic, in Heat Capacity and Entropy: Systematic Relations to Lattice Vibrations, Reviews in Mineralogy, 14, S.W. Kieffer and A. Navrotsky, eds., Mineralogy Society of America, Washington, D.C.; Vol. 14, Chap. 3.
Kroon, P. A. and Vos, A. (1978). Convergence of Brillouin zone summations. Acta Cryst. A34, 823–824.
Kroon, P.A. and Vos, A. (1979). Thermal diffuse scattering for molecular crystals: Error in X-ray diffraction intensities and atomic parameters. Acta Cryst. A35, 675–684.
Lam, P.K., Rici, Y., Lee, M.W., and Sharma, S.K. (1990). Structural distorsions and vibrational modes in Mg2SiO4. Amer. Mineral. 75, 109–119.
Langen, R. (1987). Ph.D. Thesis, Die Abhängigkeit der Kationenverteilung in einem Mg-Fe-Olivin (Som Carlos, Arizona vom Sauerstofîpartialdruck. Rheinisches Friedrich-Wilhelm Universität, Bonn.
Matsui, M. and Busing, W.R. (1984a). Computational modeling of the structure and elastic constants of the olivine and spinel forms of Mg2SiO4. Phys. Chem. Miner. 11, 55–59.
Matsui, M. and Busing, W.R. (1984b). Calculation of the elastic constants and high-pressure properties of diopside, CaMgSi2O6. Amer. Mineral. 69, 1090–1095.
Matsui, M. and Matsumoto, T. (1982). An interatomic potential-function model for Mg, Ca and CaMg olivines. Acta Cryst. A38, 513–515.
Miyamoto, M., Takeda, H., Fujino, K., and Takeuchi, Y. (1982). The ionic compressibilities and radii estimated for some transition metals in olivine structure. Miner. J. 11, 172–179.
Ottonello, G. (1986). Energetics of multiple oxides with spinel structure. Phys. Chem. Miner. 13, 79–90.
Parker, S.C., Catlow, C.R.A., and Cormack, A.N. (1983). Prediction of mineral structure by energy minimisation techniques. J. Chem. Soc., Chem. Commun. 529, 936–938.
Pawley, G.S. and Rinaldi, R.P. (1972). Constrained refinement of orthorhombic sulphur. Acta Cryst. B28, 3605–3609.
Pilati, T., Bianchi, R., and Gramaccioli, C.M. (1990a). Evaluation of atomic displacement parameters by lattice-dynamical calculations: Efficiency in Brillouin-zone sampling. Acta Cryst. A46, 485–489.
Pilati, T., Bianchi, R., and Gramaccioli, C.M. (1990b). Evaluation of Coulombic lattice sums for vibrational calculations in crystals: An extension of Bertauťs method. Acta Cryst. A46, 309–315.
Pilati, T., Bianchi, R., and Gramaccioli, C.M. (1990c). Lattice-dynamical estimation of atomic thermal parameters in silicates: Forsterite α-Mg2SiO4. Acta Cryst. B46, 301–311.
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. Miner. 10, 209–216.
Price, G.D., Parker, S.C., and Leslie, M. (1987a). The lattice dynamics of forsterite. Miner. Magazine 51, 157–170.
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.
Price, G.D., Parker, S.C., and Yeomans, J. (1985). The energetics of polytypic structures: A computer simulation of magnesium silicate spinelloids. Acta Cryst. B41, 231–239.
Rao, K.R., Chaplot, S.L., Choudhury, L., Ghose, S., Hastings. J.M. and Corliss L.M. (1988). Lattice dynamics and inelastic neutron scattering from forsterite, Mg2SiO4: Phonon dispersion relation, density of states and specific heat. Phys. Chem. Miner. 16, 83–97.
Reid, J.S. and Smith, T. (1970). Improved Debye-Waller factors for some alkali halides. J. Phys. Chem. Solids 31, 2689–2697.
Rinaldi, R. and Pawley, G.S. (1975). An investigation of the intermolecular modes in orthorhombic sulphur. J. Phys. C 8, 599–616.
Robie, R.A., Hemingway, B.S., and Takei, H. (1982). Heat capacities and entropies of Mg2SiO4, Mn2SiO4, and Co2SiO4 between 5 and 380 K. Amer. Miner. 67, 470–482.
Vieillard, P. (1982). Modele de Calcul des Energies de Formation des Mineraux, Bati sur la Connoissance Raffinée des Structures Cristallines. Memoire 69, Université Louis Pasteur de Strasbourg, Institut de Geologie.
Willis, B.T.M. and Pryor, A.W. (1975). Thermal Vibrations in Crystallography. Cambridge University Press, Cambridge, U.K.
Woods, A.D.B., Cochran, W., and Brockhouse, B.N. (1960). Lattice dynamics of alkali halide crystals. Phys. Rev. 119, 980–999.
Woods, A.D.B., Brockhouse, B.N., and Cowley, R.A. (1963). Lattice dynamics of alkali halide crystals. II. Experimental studies of KBr and Nal. Phys. Rev. 131, 1025–1029.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Gramaccioli, C.M., Pilati, T. (1992). Practical Problems in Calculating Thermodynamic Functions for Crystalline Substances from Empirical Force Fields. 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_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2842-4_8
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