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The Concentration of Crystal Structures in High-Symmetry Structural Types (Stencils) As a Consequence of Crystal Dynamics

  • THEORY OF CRYSTAL STRUCTURES
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Abstract—

The model of the occurrence of translational symmetry as a complex of standing plane elastic waves, forming three-dimensional lattices of their intersection nodes, is proposed based on the results of a crystallographic analysis of popular structure types. Criteria of crystal structure stability, characterizing the reduction of atomic degrees of freedom, are proposed taking into account the additional symmetric atomic ordering in the unit-cell volume. The characteristics of some highly symmetrical structures with cubic or hexagonal symmetry are compared. It is proposed to refer to the process of formation of stable states by creating symmetric spatial configurations, which is universal for material particles, as crystal dynamics.

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REFERENCES

  1. E. S. Fedorov, Zap. S.-Peterb. Mineral. O-va, Ser. 2, No. 4, 1 (1891).

  2. A. F. Wells, Structural Inorganic Chemistry (Clarendon Press, Oxford, 1986).

    Google Scholar 

  3. H. Strunz and E. Nickel, Mineralogical Tables. Chemical Structural Mineral Classification System (Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, 2002).

    Google Scholar 

  4. A. S. Povarennykh, Crystallochemical Classification of Mineral Species (Naukova Dumka, Kiev, 1966; Plenum, New York, 1972).

  5. I. Kostov, Mineralogy (Mir, Moscow, 1971) [in Russian].

  6. S. V. Borisov, N. V. Pervukhina, and S. A. Magarill, Crystallogr. Rep. 65 (4), 540 (2020). https://doi.org/10.31857/S0023476120040062

    Article  ADS  Google Scholar 

  7. S. V. Borisov, Zh. Strukt. Khim. 33 (6), 123 (1992).

    Google Scholar 

  8. E. Dieulesaint and D. Royer, Elastic Waves in Solids (Wiley, New York, 1980).

    MATH  Google Scholar 

  9. S. V. Borisov, S. A. Magarill, and N. V. Pervukhina, Russ. Chem. Rev. 84 (4), 393 (2015). https://doi.org/10.1070/RCR4479

    Article  ADS  Google Scholar 

  10. S. A. Gromilov, E. A. Bykova, and S. V. Borisov, Crystallogr. Rep. 56 (6), 947 (2011).

    Article  ADS  Google Scholar 

  11. S. V. Borisov, S. A. Magarill, and N. V. Pervukhina, J. Struct. Chem. 60 (8), 1191 (2019). https://doi.org/10.1134/S0022476619080018

    Article  Google Scholar 

  12. S. V. Borisov, S. A. Magarill, and N. V. Pervukhina, J. Struct. Chem. 61 (10), 1669 (2020). https://doi.org/10.26902/JSC_id61842

    Article  Google Scholar 

  13. S. V. Borisov, S. A. Magarill, and N. V. Pervukhina, Crystallogr. Rep. 64 (4), 535 (2019). https://doi.org/10.1134/S0023476119040064

    Article  Google Scholar 

  14. S. V. Borisov, N. V. Pervukhina, and S. A. Magarill, J. Struct. Chem. 62 (1), 86 (2021). https://doi.org/10.26902/JSC_id61842

    Article  Google Scholar 

  15. M. A. Leontovich, Introduction into Thermodynamics. Statistical Physics (Nauka, Moscow, 1983) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Nikolaev Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    S. V. Borisov, N. V. Pervukhina & S. A. Magarill

Authors
  1. S. V. Borisov
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  2. N. V. Pervukhina
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  3. S. A. Magarill
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Correspondence to S. V. Borisov.

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The authors declare that they have no conflicts of interest.

Additional information

Dedicated to the 130th anniversary of the publication of E.S. Fedorov’s study about 230 crystallographic symmetry groups

Translated by Yu. Sin’kov

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Borisov, S.V., Pervukhina, N.V. & Magarill, S.A. The Concentration of Crystal Structures in High-Symmetry Structural Types (Stencils) As a Consequence of Crystal Dynamics. Crystallogr. Rep. 67, 150–155 (2022). https://doi.org/10.1134/S106377452202002X

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  • DOI: https://doi.org/10.1134/S106377452202002X

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