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Structural Model of Phase Transitions in Manganese Determined by the Closest Spiral Packing of Tetrahedrons

  • STRUCTURE AND PHASE TRANSFORMATIONS
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Metal Science and Heat Treatment Aims and scope

A single structural model for the experimentally determined succession of phase transitions between cubic α-, β-, γ- and δ-modifications of Mn, in which the lattice constants of the modifications decrease with the temperature growth is suggested. The model is based on the definition of the Mn phases as successive periodic approximants of a linear substructure of a four-dimensional analog of an icosahedron. The model seems to be appropriate for an adequate description of structural transformations in close-packed metals and of variation of their structure-sensitive properties under heat treatment.

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References

  1. A. L. Talis, A. A. Everstov, and V. S. Kraposhin, “Crystal structures of alpha and beta modifications of Mn as packing of tetrahedral helices extracted from a four-dimensional {3,3,5} polytope,” Acta Cryst., B76, 948 – 954 (2020).

    Google Scholar 

  2. A. L. Talis, A. A. Everstov, and V. S. Kraposhin, “Spiral tetrahedral packing in the β-Mn crystal as the symmetry realization of the 8-dimensional E8 lattice,” Acta Cryst., A77,7– 18 (2021).

    Google Scholar 

  3. S. Lee, C. Leighton, and F. S. Batesb, “Sphericity and symmetry breaking in the formation of Frank-Kasper phases from one component materials,” PNAS, 111(50), 17723 – 17731 (2014).

    Article  CAS  Google Scholar 

  4. V. S. Urusov, Theoretical Crystal Chemistry [in Russian], Izd. MGU, Moscow (1987), pp. 212 – 213.

    Google Scholar 

  5. J. F. Sadoc and N. Rivier, “Boerdijk–Coxeter helix and biological helices,” Eur. Phys. J. B, 12, 3019 – 318 (1999).

    Article  Google Scholar 

  6. H. Nyman, C. E. Carroll, and B. C. Hyde, “Rectilinear rods of face-sharing tetrahedral and the structure of β-Mn,” Z. Kristallogr., 196, 39 (1991).

    Article  CAS  Google Scholar 

  7. W. Hornfeck and P. Kuhn, “Octagonal symmetry in low-discrepancy β-manganese,” Acta Cryst., A70, 441 – 447 (2014).

    Google Scholar 

  8. A. L. Talis, A. A. Everstov, and V. S. Kraposhin, “Spiral substructures of close-packed metals determined by a universal building unit (tetrablock),” Metalloved. Term. Obrab. Met., No. 3, 49 – 54 (2022).

  9. M. I. Gasik, N. P. Lyakishev, and B. I. Emlin, Theory and Technology of Production of Ferroalloys [in Russian], Metallurgiya, Moscow (1988), 783 p.

    Google Scholar 

  10. A. L. Talis, “Symmetry laws of the structure of ordered tetra-coordinated structures,” in: Investigation of Carbon: Successes and Problems [in Russian], Nauka, Moscow (2007), pp. 198 – 205.

  11. B. G. Livshits, V. S. Kraposhin, and Ya. L. Linetskii, Physical Properties of Metals and Alloys [in Russian], Metallurgiya, Moscow (1980), 320 p.

    Google Scholar 

  12. B. K. Vainshtein, Modern Crystallography. Vol. 1. Crystal Symmetry [in Russian], Nauka, Moscow (1979), 384 p.

  13. V. S. Kraposhin and A. L. Talis, “Noncrystallographic symmetries of the crystal structure of cementite and its transformations,” in: V. M. Schastlivstev (ed.), Cementite in Carbon Steels, Ch. 1 [in Russian], Izd. UMTs UPI, Ekaterinburg (2017), 375 p.

  14. V. L. Ljasotsky, N. B. Dyakonova, and D. L. Dyakonov, “Metastable primary precipitation phases in multicomponent glass forming Fe-base alloys with metalloids,” J. Alloys Compd., 586, 520 – 523 (2014).

    Google Scholar 

  15. N. B. Dyakonova, D. L. Dyakonov, and V. L. Ljasotsky, “Primary precipitation phase with b-Mn structure in FeSiBP base multicomponent metallic grasses,” J. Alloys Compd., 586, 41 – 45 (2014).

    Article  Google Scholar 

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Correspondence to A. L. Talis.

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Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 2, pp. 63 – 68, February, 2023.

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Talis, A.L., Kraposhin, V.S. Structural Model of Phase Transitions in Manganese Determined by the Closest Spiral Packing of Tetrahedrons. Met Sci Heat Treat 65, 122–126 (2023). https://doi.org/10.1007/s11041-023-00901-6

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