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Relaxation Contribution of a System of Jahn–Teller Complexes to the Elastic Moduli of Doped Fluorites

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Abstract

The results of the study of the temperature dependence of attenuation and velocity of ultrasonic waves are presented for CaF2:Cr and CaF2:Ni crystals in which Cr2+ and Ni2+ ions substitute calcium ions, forming Jahn–Teller (JT) complexes [CrF8]6– and [NiF8]6–. The Cr2+ and Ni2+ ions in the fluorite structure have threefold orbital degeneracy in the ground state, are described by the T \( \otimes \) (e + t2) Jahn–Teller effect (JTE) problem, and have an adiabatic potential energy surface (APES) defined in the five-dimensional space of trigonal and tetragonal symmetrized coordinates whose lower sheet is a simply connected surface with orthorhombic minima separated by potential energy barriers. The temperature dependence of the ultrasonic attenuation and velocity exhibits anomalies typical of the relaxation contributions of systems of JT complexes in the low-temperature region. The effect of tunneling relaxation mechanisms (direct and two-phonon transitions) on the JT contribution to the complex elastic moduli and to the error in determining the relaxation time is analyzed. Based on the approach that takes into account both tunneling and activation mechanisms of relaxation, the activation energies and the constants characterizing these relaxation mechanisms are determined in CaF2:Cr2+ and CaF2:Ni2+ crystals.

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Funding

At the Ural Federal University, the research was supported by the Russian Foundation for Basic Research (project no. 18-02-00332a), by the Center of Excellence of the Ural Federal University “Radiation and Nuclear Technologies,” and by the Ministry of Science and Higher Education of the Russian Federation within the State Assignment no. FEUZ-2020-0060. At the South Ural State University, the research was supported by the Government of the Russian Federation (Act 211, contract no. 02.A03.21.0011, Program 5-100). The research at the Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, was carried out within the State Assignment no. AAAA-A18-118020190098-5. The research at the Zavoisky Physical–Technical Institute, Federal Research Center Kazan Scientific Center, Russian Academy of Sciences, was carried out within the State Assignment no. АААА-А18-118030690040-8.

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Authors and Affiliations

  1. Institute of Physics and Technology, Ural Federal University, 620002, Yekaterinburg, Russia

    M. N. Sarychev, A. S. Bondarevskaya, I. V. Zhevstovskikh & V. V. Gudkov

  2. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 620137, Yekaterinburg, Russia

    I. V. Zhevstovskikh

  3. Kazan State Power Engineering University, 420066, Kazan, Russia

    V. A. Ulanov

  4. Zavoisky Physical–Technical Institute, Federal Research Center Kazan Scientific Center, Russian Academy of Sciences, 420029, Kazan, Russia

    V. A. Ulanov & G. S. Shakurov

  5. Vinogradov Institute of Geochemistry, Siberian Branch, Russian Academy of Sciences, 664033, Irkutsk, Russia

    A. V. Egranov

  6. Irkutsk State University, 664003, Irkutsk, Russia

    A. V. Egranov

  7. Institute of Solid State Chemistry, Ural Branch, Russian Academy of Sciences, 620990, Yekaterinburg, Russia

    V. T. Surikov

  8. Ioffe Institute, 194021, St. Petersburg, Russia

    N. S. Averkiev

  9. South Ural State University, 454080, Chelyabinsk, Russia

    V. V. Gudkov

Authors
  1. M. N. Sarychev
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  2. A. S. Bondarevskaya
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  3. I. V. Zhevstovskikh
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  4. V. A. Ulanov
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  5. G. S. Shakurov
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  6. A. V. Egranov
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  7. V. T. Surikov
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  8. N. S. Averkiev
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  9. V. V. Gudkov
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Corresponding author

Correspondence to V. V. Gudkov.

Additional information

Translated by I. Nikitin

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Sarychev, M.N., Bondarevskaya, A.S., Zhevstovskikh, I.V. et al. Relaxation Contribution of a System of Jahn–Teller Complexes to the Elastic Moduli of Doped Fluorites. J. Exp. Theor. Phys. 132, 790–799 (2021). https://doi.org/10.1134/S106377612105006X

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  • DOI: https://doi.org/10.1134/S106377612105006X

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