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Internal energy and parameters of the order-disorder phase transition in titanium monoxide TiO y

  • Solids and Liquids
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Abstract

Quantum-mechanical ab initio calculations are used to simulate the free energy functions for titanium monoxide TiO y . The effect of the long-range order of the Ti5O5 type superstructure on the internal energy of the compound is studied by the supercell method. The dependences of the configuration entropy and free energy on the long-range order parameter are determined. It is found that the order-disorder phase transition in titanium monoxide must occur in accordance with the mechanism of the first-order phase transition with a critical value of the long-range order parameter of 0.971. The calculated parameters of the phase transition are compared with the experimental data and the results obtained using the model of point charges and by calculating the Madelung energy. It is concluded that the short-range order and the phonon entropy must be taken into account in calculating the equilibrium phase diagrams for strongly nonstoichiometric compounds.

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References

  1. A. I. Gusev and A. A. Rempel’, Nonstoichiometry, Disorder, and Order in Solids (Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 2001) [in Russian].

    Book  Google Scholar 

  2. R. Kikuchi, Phys. Rev. 81, 988 (1951).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. M. Kurata, R. Kikuchi, and T. Watari, J. Chem. Phys. 21, 434 (1953).

    Article  MathSciNet  ADS  Google Scholar 

  4. J. Hijmans and J. de Boer, Physica (Amsterdam) 21, 471 (1955).

    Article  ADS  Google Scholar 

  5. R. Kikuchi and S. G. Brush, J. Chem. Phys. 47, 195 (1967).

    Article  ADS  Google Scholar 

  6. A. A. Rempel’, Effects of Ordering in Nonstoichiometric Interstitial Compounds (Nauka, Yekaterinburg, 1992).

    Google Scholar 

  7. A. A. Valeeva and A. A. Rempel’, JETP Lett. 88(3), 172 (2008).

    Article  ADS  Google Scholar 

  8. M. G. Kostenko, A. A. Valeeva, and A. A. Rempel, Mendeleev Commun. 22, 245 (2012).

    Article  Google Scholar 

  9. M. G. Kostenko and A. A. Rempel, JETP 115(6), 999 (2012).

    Article  ADS  Google Scholar 

  10. A. I. Gusev and A. A. Rempel, Phys. Status Solidi B 131, 43 (1985).

    Article  ADS  Google Scholar 

  11. A. I. Gusev and A. A. Rempel’, Zh. Fiz. Khim. 60, 1349 (1986).

    Google Scholar 

  12. A. I. Gusev and A. A. Rempel, Phys. Status Solidi B 140, 335 (1987).

    Article  ADS  Google Scholar 

  13. A. I. Gusev and A. A. Rempel’, Zh. Fiz. Khim. 65, 625 (1991).

    Google Scholar 

  14. A. I. Gusev and A. A. Rempel, J. Phys. Chem. Solids 55, 299 (1994).

    Article  ADS  Google Scholar 

  15. A. I. Gusev and A. A. Rempel, Phys. Status Solidi A 163, 273 (1997).

    Article  ADS  Google Scholar 

  16. A. I. Gusev and A. A. Rempel, in Materials Science of Carbides, Nitrides, and Borides, Ed. by Y. G. Gogotsi and R. A. Andrievski (Kluwer, Dordrecht, 1999), p. 47.

  17. M. G. Kostenko, A. V. Lukoyanov, V. P. Zhukov, and A. A. Rempel’, JETP Lett. 95(12), 647 (2012).

    Article  ADS  Google Scholar 

  18. G. L. Humprey, J. Am. Chem. Soc. 73, 1587 (1951).

    Article  Google Scholar 

  19. D. A. Andersson, P. A. Korzhavyi, and B. Johansson, Phys. Rev. B: Condens. Matter 71, 144101–1 (2005).

    Article  ADS  Google Scholar 

  20. M. G. Kostenko and A. A. Rempel’, Phys. Solid State 53(9), 1909 (2011).

    Article  ADS  Google Scholar 

  21. D. Watanabe, J. R. Castles, A. Jostsons, and A. S. Marlin, Acta Crystallogr. 23, 307 (1967).

    Article  Google Scholar 

  22. D. Watanabe, O. Terasaki, A. Jostsons, and J. R. Castles, in The Chemistry of Extended Defects in Non-Metallic Solids, Ed. by L. Eyring and M. O’Keefe (North-Holland, Amsterdam, 1970), p. 238.

  23. A. A. Valeeva, A. A. Rempel’, and A. I. Gusev, Inorg. Mater. 37(6), 603 (2001).

    Article  Google Scholar 

  24. D. Watanabe, O. Terasaki, A. Jostsons, and J. R. Castles, J. Phys. Soc. Jpn. 25, 292 (1968).

    Article  ADS  Google Scholar 

  25. W. Kohn and L. J. Sham, Phys. Rev. [Sect.] A 140, 1133 (1965).

    MathSciNet  ADS  Google Scholar 

  26. R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).

    Article  ADS  Google Scholar 

  27. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).

    Article  ADS  Google Scholar 

  28. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, J. Phys. Condens. Matter 21, 395502 (2009).

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Solid-State Chemistry, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620090, Russia

    M. G. Kostenko & A. A. Rempel

  2. Ural Federal University, Yekaterinburg, 620002, Russia

    A. A. Rempel & A. V. Lukoyanov

  3. Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, 620990, Russia

    A. V. Lukoyanov

Authors
  1. M. G. Kostenko
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  2. A. A. Rempel
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  3. A. V. Lukoyanov
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Correspondence to A. A. Rempel.

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Original Russian Text © M.G. Kostenko, A.A. Rempel, A.V. Lukoyanov, 2013, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2013, Vol. 143, No. 6, pp. 1097–1104.

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Kostenko, M.G., Rempel, A.A. & Lukoyanov, A.V. Internal energy and parameters of the order-disorder phase transition in titanium monoxide TiO y . J. Exp. Theor. Phys. 116, 945–951 (2013). https://doi.org/10.1134/S1063776113060071

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  • DOI: https://doi.org/10.1134/S1063776113060071

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