Abstract
The electron-gas theory of crystals is extended to include the effects of many-body forces that arise from both electrostatic and overlap interactions. These effects are incorporated through a self-consistent spherical relaxation of the ionic charge distributions such that the crystal binding energy is minimized. This variational model is used to compute the elastic constants and equations of state of MgO and CaO, and we compare its results to those derived from earlier electron-gas models. In the variational model, the anion charge distributions are markedly more sensitive to the local crystal environment than they are in the PIB or other electron-gas models. We find that for these oxides the variational model gives the best overall agreement with experiment for lattice constants, equations of state, dissociation energies, and elastic moduli.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aidun J, Bukowinski MST, Ross M (1984) Equation of state and metallization of CsI. Phys Rev B 29:2611–2622
Birch F (1978) Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300 K. J Geophys Res 83:1257–1268
Born M, Huang K (1954) Dynamical theory of crystal lattices. Oxford Press, London
Boyer LL (1980) Calculations of thermal expansion compressibility, and melting in alkali halides. Rev Lett 45:1858–1862
Boyer LL (1981) First-principles equation-of-state calculations for alkali halides. Phys Rev B23:3673–3685
Boyer LL (1984) Parameter-free equation of state calculation for CsCaF3. J Phys C: Solid State Phys 17:1825–1832
Boyer LL, Hardy JR (1981) Theoretical study of the structural phase transition in RbCaF3. Phys Rev B 24:2577–2591
Boyer LL, Mehl MJ, Feldman JL, Hardy JR, Flocken JW, Fong CY (1985) Beyond the rigid-ion approximation with spherically symmetric ions. Phys Rev Lett 54:1940–1943
Bukowinski MST (1985) First principles equations of state of MgO and CaO. Geophys Res Lett 12:536–539
Bukowinski MST, Aidun J (1985) First-principles vs spherical ion models of the B1 and B2 phase of NaCl. J Geophys Res 90:1794–1800
Cantor S (1973) Lattice energies of cubic alkaline-earth oxides. Affinity of oxygen for two electrons. J Chem Phys 59:5189–5194
Chang KJ, Cohen ML (1984) High-pressure behavior of MgO: Structural and electronic properties. Phys Rev B30:4774–4781
Chang ZP, Graham EK (1977) Elastic properties of oxides in the NaCl-structure. J Phys Chem Solids 38:1355–1362
Clementi E, Roetti C (1974) Atomic data and nuclear tables. Academic Press, New York
Cohen AJ, Gordon RG (1975) Theory of the lattice energy, equilibrium structure elastic constants, and pressure-induced phase transitions in alkali-halide crystals. Phys Rev B 12:3228–3241
Cohen AJ, Gordon RG (1976) Modified electron-gas study of the stability, elastic properties, and high-pressure behavior of MgO and CaO crystals. Phys Rev B14:4593–4605
Cohen RE, Boyer LL, Mehl MJ (1987) Lattice dynamics of the potential induced breathing model: Phonon dispersion in the alkaline earth oxides. Phys Rev B35:5749–5760
Ewald PP (1921) The calculation of optical and electrostatic lattice potentials. Ann Phys (Leipzig) 64:253–287
Gordon RG, Kim YS (1972) A theory for the forces between closed shell atoms and molecules. J Chem Phys 56:3122–3133
Green S, Gordon RG (no date) Quantum Chemistry Program Exchange. QCPE program 251: Chemistry Department, Indiana University (unpublished)
Hemley RJ, Jackson MD, Gordon RG (1985) First-principles theory for the equations of state of minerals at high pressures and temperatures: Application to MgO. Geophys Res Lett 12:247–250
Hemley RJ, Gordon RG (1985) Theoretical study of solid NaF and NaCl at high pressures and temperatures. J Geophys Res 90:7803–7813
Jackson J, Niesler H (1982) The elasticity of periclase to 3 GPa and some geophysical implications. In: Akimoto S, Manghani MH (eds) High pressure research in geophysics. Center for Academic Publications, Tokyo, Japan
Jeanloz R, Ahrens TJ, Mao HK, Bell PM (1979) B1-B2 transitions in CaO from shock-wave and diamond-cell experiments. Science 206:829–830
Kim YS, Gordon RG (1974) Theory of binding of ionic crystals: Application to alkali-halide and alkaline-earth-dihalide crystals. Phys Rev B9:3548–3554
Mammone JF, Mao HK, Bell PM (1981) Equation of state of CaO under static pressure conditions. Geophys Res Lett 8:140–142
Mao HK, Bell PM (1979) Pressure-volume equation of state of MgO and ε—Fe under static pressure conditions. J Geophys Res 84:4533–4536
Marsh SP (1980) LASL Shock Hugoniot Data. University of California Press, Berkeley
Mehl MJ, Hemley RJ, Boyer LL (1986) Potential-induced breathing model for the elastic moduli and high-pressure behavior of the cubic alkaline-earth oxides. Phys Rev B33:8685–8696
Muhlhausen C, Gordon RG (1981) Electron-gas theory of ionic crystals, including many-body effects. Phys Rev B23:900–923
Perez-Albuerne EA, Drickamer HG (1965) Effect of high pressures on the compressibilities of seven crystals having the NaCl or CsCl structure. J Chem Phys 43:1381–1387
Press WH, Flanery BP, Teukolsky SA, Vetterling WT (1986) Numerical Recipes. Cambridge University Press, New York
Roothaan CCJ, Bagus PJ (1963) Atomic self-consistent field calculations by the expansion method. In: Methods in computational physics, Vol 2. Pergamon Press, New York
Touloukian YS, Kirby RK, Taylor RE, Lee TYR (1977) Thermophysical properties. IFI/Plenum, New York
Vassiliou MS, Ahrens TJ (1981) Hugoniot equation of state of periclase. Geophys Res Lett 8:729–732
Waldman M, Gordon RG (1979) Scaled electron-gas approximation for intermolecular forces. J Chem Phys 71:1325–1339
Wallace DC (1972) Thermodynamics of crystals. John Wiley, New York
Wallace DC (1965) Lattice dynamics and elasticity of stressed crystals. Rev Mod Physics 37:57–67
Watson RE (1958) Analytic Hartree-Fock solutions for O −2. Phys Rev 111:1108–1110
Wolf GH, Bukowinski MST (1985) Ab initio structural and thermoelastic properties of orthorhombic MgSiO3 perovskite. Geophys Res Lett 12:809–812
Wolf GH, Bukowinski MST (1987) Theoretical study of the structural and thermoelastic properties of the MgSiO3 and CaSiO3 perovskites: Implications for lower mantle composition. In: Manghnanai M, Akimoto S (eds) US-Japan Joint Seminar on High Pressure Research: Applications in geophysics and geochemistry
Yamashita J, Asano S (1983) Cohesive properties of alkali halides and simple oxides in the local-density formalism. J Phys Soc Japan 52:3506–3513
Yin MT, Cohen ML (1981) Ground-state properties of diamond. Phys Rev B24:6121–6124
Author information
Authors and Affiliations
Additional information
Paper from Conference on Quantum Theory and Experiment
Rights and permissions
About this article
Cite this article
Wolf, G.H., Bukowinski, M.S.T. Variational stabilization of the ionic charge densities in the electron-gas theory of crystals: Applications to MgO and CaO. Phys Chem Minerals 15, 209–220 (1988). https://doi.org/10.1007/BF00307509
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00307509