Advertisement

Petrology

, Volume 27, Issue 4, pp 386–394 | Cite as

First-Principles Determination of Oxygen and Silicon β-Factors for Zircon

  • D. P. KrylovEmail author
Article
  • 4 Downloads

Abstract

The temperature dependence of the β-factors of zircon was determined for 18O/16O and 30Si/28Si isotopic substitutions. Calculations were performed on the basis of the density functional theory (DFT) using the frozen phonon approach. The obtained geometric parameters of the zircon crystal lattice and vibrational frequencies are in good agreement with experimental data. The results were approximated by the following cubic polynomials in x = 106/T(K)2: 1000 ln βzrn(18O/16O) = 9.83055x – 0.19499x2 + 0.00388x3 and 1000 ln βzrn(30Si/28Si) = 7.89907x – 0.17978x2 + 0.00377x3. The obtained relations can be used in combination with the β-factors of other phases for the construction of geothermometers. New calibrations of the quartz–zircon isotope geothermometer were proposed. The obtained 1000 ln βzrn values and isotope fractionation factors between quartz and zircon (1000 ln βqtz – 1000 ln βzrn) are significantly different from those obtained by previous experimental, empirical, and semiempirical calibrations of isotope equilibria.

Notes

ACKNOWLEDGMENTS

The author thanks V.B. Polyakov (Institute of Experimental Mineralogy, Russian Academy of Sciences) for carefully reviewing the manuscript and helpful comments. Calculations of β-factors from inelastic neutron scattering data were conducted using a program of the reviewer.

FUNDING

This study was financially supported by the Russian Foundation for Basic Research, project no. 19-05-00175. Computer resources were provided by the Resource Center “Computer Center of the St. Petersburg State University” (http://cc.spbu.ru).

CONFLICT OF INTEREST

The authors declare that they have no conflict of interest.

REFERENCES

  1. 1.
    Bigeleisen, J. and Mayer, M.G., Calculation of equilibrium constants for isotopic exchange reactions, J. Chem. Phys., 1947, vol. 15, no. 5, pp. 261–267.CrossRefGoogle Scholar
  2. 2.
    Blanchard, M., Poitrasson, F., Méheut, M., et al., Iron isotope fractionation between pyrite (FeS2), hematite (Fe2O3) and siderite (FeCO3): a first-principles density functional theory study, Geochim. Cosmochim. Acta, 2009, vol. 73, no. 21, pp. 6565–6578.CrossRefGoogle Scholar
  3. 3.
    Chacko, T., Cole, D.R., and Horita, J., Equilibrium oxygen, hydrogen and carbon isotope fractionation factors applicable to geologic systems, Rev. Mineral. Geochem., 2001, vol. 43, no. 1, pp. 1–81.CrossRefGoogle Scholar
  4. 4.
    Chaplot, S.L., Pintschovius, L., Choudhury, N., and Mittal, R., Phonon dispersion relations, phase transitions, and thermodynamic properties of ZrSiO4: inelastic neutron scattering experiments, shell model, and first-principles calculations, Phys. Rev. B:, 2006, vol. 73, no. 9, p. 094308.CrossRefGoogle Scholar
  5. 5.
    Clayton, R.N. and Kieffer, S.W., Oxygen isotopic thermometer calibrations, Geochem. Soc. Spec. Publ., 1991, vol. 3, pp. 3–10.Google Scholar
  6. 6.
    CRYSTAL14 : A program for the ab initio investigation of crystalline solids, Int. J. Quantum Chem., 2014, vol. 114, no. 19, pp. 1287–1317.Google Scholar
  7. 7.
    Dawson, P., Hargreave, M.M., and Wilkinson, G.R., The vibrational spectrum of zircon (ZrSiO4), J. Phys. C: Solid St. Phys, 1971, vol. 4, no. 2, pp. 240–256.CrossRefGoogle Scholar
  8. 8.
    Dovesi, R., Orlando, R., Erba, A., et al., CRYSTAL14. User’s Manual (2016).Google Scholar
  9. 9.
    Evarestov, R.A. and Smirnov, V.P., Symmetrical transformation of basic translation vectors in the supercell model of imperfect crystals and in the theory of special points of the Brillouin zone, J. Phys. Condens. Matter, 1997, vol. 9, no. 14, pp. 3023–3031.CrossRefGoogle Scholar
  10. 10.
    Finch, R.J. and Hanchar, J.M., Structure and chemistry of zircon and zircon-group minerals, Rev. Mineral. Geochem., 2003, vol. 53, no. 1, pp. 1–25.CrossRefGoogle Scholar
  11. 11.
    Grimme, S., Semiempirical GGA-type density functional constructed with a long-range dispersion correction, J. Comput. Chem., 2006, vol. 27, no. 15, pp. 1787–1799.CrossRefGoogle Scholar
  12. 12.
    Heyd, J., Peralta, J.E., Scuseria, G.E., and Martin, R.L., Energy band gaps and lattice parameters evaluated with the Heyd–Scuseria–Ernzerhof screened hybrid functional, J. Chem. Phys., 2005, vol. 123, no. 17, p. 174101.CrossRefGoogle Scholar
  13. 13.
    Hoffbauer, R., Hoernes, S., and Fiorentini, E., Oxygen isotope thermometry based on a refined increment method and its applications to granulite-grade rocks from Sri Lanka, Precambrian Res., 1994, vol. 66, nos. 1–4, pp. 199–220.CrossRefGoogle Scholar
  14. 14.
    Hofmeister, A.M. and Mao Ho-kwang, Redefinition of the mode Grüneisen parameter for polyatomic substances and thermodynamic implications, Proc. Natl. Acad. Sci. USA, 2002, vol. 99, no. 2, pp. 559–564.CrossRefGoogle Scholar
  15. 15.
    Horita, J. and Clayton, R.N., Comment on the studies of oxygen isotope fractionation between calcium carbonates and water at low temperatures by Zhou and Zheng (2003; 2005), Geochim. Cosmochim. Acta, 2007, vol. 71, no. 12, pp. 3131–3135.CrossRefGoogle Scholar
  16. 16.
    Kieffer, S.W., Thermodynamics and lattice vibrations of minerals: 5. Applications to phase equilibria, isotopic fractionation, and high-pressure thermodynamic properties, Rev. Geophys., 1982, vol. 20, no. 4, pp. 827–849.CrossRefGoogle Scholar
  17. 17.
    Krylov D.P. and Evarestov R.A. Ab-initio (DFT) calculations of corundum (α-Al2O3) oxygen isotope fractionation, Eur. J. Mineral., 2018, vol. 30, no. 6, pp. 1063–1070.CrossRefGoogle Scholar
  18. 18.
    Krylov, D.P., Zagnitko, V.N., Hoernes, S., et al., Oxygen isotope fractionation between zircon and water: experimental determination and comparison with quartz-zircon calibrations, Eur. J. Mineral., 2002, vol. 14, no. 4, pp. 849–853.CrossRefGoogle Scholar
  19. 19.
    Meheut, M., Lazzeri, M., Balan, E., and Mauri, F., Equilibrium isotopic fractionation in the kaolinite, quartz, water system: prediction from first-principles density-functional theory, Geochim. Cosmochim. Acta, 2007, vol. 71, no. 13, pp. 3170–3181.CrossRefGoogle Scholar
  20. 20.
    Monkhorst, H. and Pack, J., Special points for Brillouin zone integrations, Phys. Rev. B:, 1976, vol. 13, no. 12, pp. 5188–5192.CrossRefGoogle Scholar
  21. 21.
    Montanari, B., Civalleri, B., Zicovich-Wilson, C.M., and Dovesi, R., Influence of the exchange-correlation functional in all-electron calculations of the vibrational frequencies of corundum (α-Al2O3), Int. J. Quantum Chem., 2006, vol. 106, no. 7, pp. 1703–1714.CrossRefGoogle Scholar
  22. 22.
    Mursi, Z., Vogt, T., Boysen, H., and Frey, F., Single-crystal neutron diffraction study of metamict zircon up to 2000 K, J. Appl. Crystallogr., 1992, vol. 25, no. 4, pp. 519–523.CrossRefGoogle Scholar
  23. 23.
    Nipko, J.C. and Loong, C.-K., Inelastic neutron scattering from zircon, Physica B. Condens. Matt., 1997, vol. 241–243, pp. 415–417.CrossRefGoogle Scholar
  24. 24.
    Ozkan, H., Correlations of the temperature and pressure dependencies of the elastic constants of zircon, J. Europ. Ceram. Soc., 2008, vol. 28, no. 16, pp. 3091–3095.CrossRefGoogle Scholar
  25. 25.
    Ozkan, H. and Jamieson, J.C., Pressure dependence of the elastic constants of nonmetamict zircon, Phys. Chem. Mineral., 1978, vol. 2, no. 3, pp. 215–224.CrossRefGoogle Scholar
  26. 26.
    Polyakov, V.B., On anharmonic and pressure corrections to the equilibrium isotopic constants for minerals, Geochim. Cosmochim. Acta, 1998, vol. 62, no. 18, pp. 3077–3085.CrossRefGoogle Scholar
  27. 27.
    Polyakov, V.B. and Kharlashina, N.N., Effect of pressure on equilibrium isotopic fractionation, Geochim. Cosmochim. Acta, 1994, vol. 58, no. 21, pp. 4739–4750.CrossRefGoogle Scholar
  28. 28.
    Porter, A.R., Towler, M.D., and Needs, R.J., Muonium as a hydrogen analogue in silicon and germanium; quantum effects and hyperfine parameters, Phys. Rev. B:, 1999, vol. 60, no. 19, pp. 13534–13546.CrossRefGoogle Scholar
  29. 29.
    Qin, T., Wu, F., Wu, Z., and Huang, F., First-principles calculations of equilibrium fractionation of O and Si isotopes in quartz, albite, anorthite, and zircon, Contrib. Mineral. Petrol., 2016, vol. 171, no. 11, pp. 1–14.CrossRefGoogle Scholar
  30. 30.
    Schauble, E.A., First-principles estimates of equilibrium magnesium isotope fractionation in silicate, oxide, carbonate and hexaaquamagnesium(2+) crystals, Geochim. Cosmochim. Acta, 2011, vol. 75, no. 3, pp. 844–869.CrossRefGoogle Scholar
  31. 31.
    Schauble, E., Rossman, G.R., and Taylor, H.P., Theoretical estimates of equilibrium chromium-isotope fractionations, Chem. Geol., 2004, vol. 205, nos. 1–2, pp. 99–114.CrossRefGoogle Scholar
  32. 32.
    Smyth, J.R., Electrostatic characterization of oxygen sites in minerals, Geochim. Cosmochim. Acta, 1989, vol. 53, no. 5, pp. 1101–1110.CrossRefGoogle Scholar
  33. 33.
    Sophia, G., Baranek, P., Sarrazin, C., et al., First-principles study of the mechanisms of the pressure-induced dielectric anomalies in ferroelectric perovskites, Phase Transitions: A Multinational J., 2013, vol. 86, no. 11, pp. 1069–1084.Google Scholar
  34. 34.
    Trail, D., Bindeman, I.N., Watson, E.B., and Schmitt, A.K., Experimental calibration of oxygen isotope fractionation between quartz and zircon, Geochim. Cosmochim. Acta, 2009, vol. 73, no. 23, pp. 7110–7126.CrossRefGoogle Scholar
  35. 35.
    Valley, J.W., Bindeman, I.N., and Peck, W.H., Empirical calibration of oxygen isotope fractionation in zircon, Geochim. Cosmochim. Acta, 2003, vol. 67, no. 17, pp. 3257–3266.CrossRefGoogle Scholar
  36. 36.
    Valley, J.W., Cavosie, A.J., Ushikubo, T., et al., Hadean age for a post-magma-ocean zircon confirmed by atom-probe tomography, Nature Geoscience, 2014, vol. 7, no. 3, pp. 219–223.CrossRefGoogle Scholar
  37. 37.
    Widanagamage, I.H., Schauble, E.A., Scher, H.D., and Griffith, E.M., Stable strontium isotope fractionation in synthetic barite, Geochim. Cosmochim. Acta, 2014, vol. 147, no. 1, pp. 58–75.CrossRefGoogle Scholar
  38. 38.
    Zheng, Y.-F., Calculation of oxygen isotope fractionation in anhydrous silicate minerals, Geochim. Cosmochim. Acta, 1993, vol. 57, no. 5, pp. 1079–1091.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Precambrian Geology and Geochronology, Russian Academy of SciencesSt. PetersburgRussia

Personalised recommendations