A. R. Kuznetsov, S. A. Starikov

THE BAIN AND ORTHORHOMBIC PATHS OF STRUCTURAL-PHASE TRANSFORMATIONS IN A TRANSITION METAL (V)

The energy of the Bain and orthorhombic paths of structural-phase transformations in a transition metal (V) under uniaxial deformation is studied by the ab-initio method. The orthorhombic path of transformation is refined in view of its symmetry. The softest branches of the phonon spectrum for the Bain path, responsible for the loss of structure stability, are found from the calculation of the phonon spectrum as a function of strain. The nature of the loss of stability is revealed, and the strain at which stability is lost under both tension and compression is evaluated. The most probable mechanisms determining the structure stability and the theoretical strength of the transition metal V are discussed. The results can relate to experimental situations of the deformation of small, defect-free regions, for example, in nanostructured materials, when surface layers are modified by plastic deformation, during nanoindentation, and during ultra-high plasticity of V-based alloys.

Acknowledgment: The work was performed under the state assignment from the Russian Ministry of Science and Higher Education (theme Structure, No 122021000033-2). The Uran supercomputer, IMM UB RAS, was used for the calculations.

References:

1. Bain, E.C. The Nature of martensite. Trans. AIME, 1924, 70, 25–35.
2. Okatov, S.V., Kuznetsov, A.R., Gornostyrev, Yu.N., Urtsev, N.V., and Katsnelson, M.I. Effect of magnetic state on the α–γ transition in iron: first-principles calculations of the Bain transformation path. Physical Review B, 2009, 79 (9), 094111–094115. DOI: 10.1103/RevModPhys.84.945.
3. Grimvall, G., Magyari-Kope, B., Ozolins, V., and Persson, K.A. Lattice instabilities in metallic elements. Review of Modern Physics, 2012, 84 (3), 945–986. DOI: 10.1103/PhysRevB.79.094111.
4. Kuznetsov, A.R., Starikov, S.A., and Sagaradze, V.V. Phonon instabilities in a metal on the Bain fcc–bcc transformation path. Diagnostics, Resource and Mechanics of materials and structures, 2022, 6, 86–94. DOI: 10.17804/2410-9908.2022.6.086-094. Available at: http://dream-journal.org/issues/2022-6/2022-6_385.html
5. Kuznetsov, A.R. and Starikov, S.A. The Bain and orthorhombic paths of the bcc–fcc transformation in a bcc metal. Diagnostics, Resource and Mechanics of materials and structures, 2023, 6, 35–44. DOI: 10.17804/2410-9908.2023.6.035-044. Available at: http://dream-journal.org/issues/2023-6/2023-6_423.html
6. Clatterbuck, D.M., Krenn, C.R., Cohen, M.L., and Morris, J.W., Jr. Phonon instabilities and the ideal strength of aluminum. Physical Review Letters, 2003, 91 (13), 135501–135504. DOI: 10.1103/PhyaRevLett.91.135501.
7. Pokluda, J., Cern, M., Sandera, P., and Sob, M. Calculations of theoretical strength: state of the art and history. Journal of Computer-Aided Materials Design, 2004, 11, 1–28. DOI: 10.1007/s10820-004-4567-2.
8. Pokluda, J., Černý, M., Šob, M., and Umeno, Y. Ab initio calculations of mechanical properties: methods and applications. Progress in Materials Science, 2015, 73, 127–158. DOI: 10.1016/j.pmatsci.2015.04.001.
9. Li, J. and Yip, S. Atomistic measures of materials strength. CMES-Computer Modeling in Engineering and Science, 2002, 3, 219. DOI: 10.3970/cmes.2002.003.219.
10. Nagasako, N., Jahnátek, M., Asahi, R., and Hafner, J. Anomalies in the response of V, Nb, and Ta to tensile and shear loading: ab initio density functional theory calculations. Physical Review B, 2010, 81, 094108–094121. DOI: 10.1103/PhysRevB.81.094108.
11. Landa, A., Söderlind, P., Naumov, I.I., Klepeis, J.E., and Vitos, L. Kohn anomaly and phase stability in group VB transition metals. Computation, 2018, 6, 29. DOI: 10.3390/computation6020029.
12. Gouldstone, A., Koh, H.J., Zeng, K.Y., Giannakopoulos, A.E., and Suresh, S. Discrete and continuous deformation during nanoindentation of thin films. Acta Materialia, 2000, 48 (9), 2277–2295. DOI: 10.1016/S1359-6454(00)00009-4.
13. De la Fuente, O.R., Zimmerman, J.A., Gonzales, M., De la Figuera, A.J., Hamilton, J.C., Pai, W.W., and Rojo, J.M. Dislocation emission around nanoindentations on a (001) fcc metal surface studied by scanning tunneling microscopy and atomic simulation. Physical Review Letters, 2002, 88 (3), 036101–036104. DOI: 10.1103/PhysRevLett.88.036101.
14. Molecular Beam Epitaxy and Heterostructures, NATO Science Series E, L.L. Chang and K. Ploog, eds., Springer, Dordrecht, 728 p. DOI: 10.1007/978-94-009-5073-3.
15. Tyumentsev, A.N., Ditenberg, I.A., Tsverova, A.S., Chernov, V.M., Potapenko, M.M., and Drobyshev, V.A. Regularities of V–4Ti–4Cr alloy microstructure formation in conditions of ultrahigh technological plasticity. Voprosy Atomnoy Nauki i Tekhniki. Ser. Termoyadernyi Sintez, 2018, 41 (4), 48–64. (In Russian). DOI: 10.21517/0202-3822-2018-41-4-48-64.
16. Tyumentsev, A.N., Korotaev, A.D., Ditenberg, I.A., Pinzhin, Yu.P., and Chernov, V.M. Zakonomernosti plasticheskoy deformatsii v vvysokoprochnykh i nanokristallicheskikh metallicheskikh materiaakh [Plastic Deformation of High-Strength Metallic Materials]. SO RAN Publ., Novosibirsk, 256 p. (In Russian).
17. Tyumentsev, A.N., Litovchenko, I.Yu., Ditenberg, I.A., Pinzhin, Yu.P., Grinyaev, K.V., Smirnov, I.V., and Chernov, V.M. Plasticheskaya deformatsiya v usloviyakh fazovoy nestabilnosti [Plastic Deformation Under the Phase Instability of the Crystal Lattice]. NTL Publ., Tomsk, 2024, 212 p. (In Russian).
18. Kimminau, G., Erhart, P., Bringa, E.M., Remington, B., and Wark, J.S. Phonon instabilities in uniaxially compressed fcc metals as seen in molecular dynamics simulations. Physical Review B, 2010, 81, 092102. DOI: 10.1103/PhysRevB.81.092102.
19. Colella, R. and Batterman, B.W. X-ray determination of phonon dispersion in vanadium. Physical Review B, 1970, 1, 3913. DOI: 10.1103/PhysRevB.1.3913.
20. Savrasov, S.Y. and Savrasov, D.Y. Electron-phonon interactions and related physical properties of metals from linear-response theory. Physical Review B, 1996, 54, 16487. DOI: 10.1103/PhysRevB.54.16487.
21. Li, X., Schonecker, S., Zhao, J., Johansson, B., and Vitos, L. Ideal strength of random alloys from first principles. Physical Review B, 2013, 87, 214203. DOI: 10.1103/PhysRevB.87.214203.
22. Suzuki, N. and Otani, M. The role of the phonon anomaly in the superconductivity of vanadium and selenium under high pressures. Journal Physics: Condensed Matter, 2007, 19, 125206. DOI: 10.1088/0953-8984/19/12/125206.
23. Černý, M. and Pokluda, J. Influence of superimposed biaxial stress on the tensile strength of perfect crystals from first principles. Physical Review B, 2007, 76, 024115. DOI: 10.1103/PhysRevB.76.024115.
24. Bolef, D.I., Smith, R.E., and Miller, J.G. Elastic properties of vanadium. I. Temperature dependence of the elastic constants and the thermal expansion. Physical Review B, 1971, 3, 4100. DOI: 10.1103/PhysRevB.3.4100.
25. Takemura, K. High-pressure X-ray study of Zn with a helium pressure medium. In: Proceedings of the International Conference on High Pressure Science and Technology (AIRAPT-17), Honolulu, Hawaii, July 25–30, 1999, eds., M.H. Manghnani, W.J. Nellis, and M.F. Nicol, Universities Press, Hyderabad, India, 2000, vol. 1, pp. 440–442.
26. Koči, L., Ma, Y., Oganov, A.R., Souvatzis, P., and Ahuja, R. Elasticity of the superconducting metals V, Nb, Ta, Mo, and W at high pressure. Physical Review B, 2008, 77, 214101. DOI: 10.1103/PhysRevB.77.214101.
27. Söderlind P., Eriksson O., Wills J.M., and Boring A.M. Theory of elastic constants of cubic transition metals and alloys. Physical Review B, 1993, 48, 5844. DOI: 10.1103/PhysRevB.48.5844.
28. Katahara, K.W., Manghnani, M.H., and Fisher, E. Elastic moduli of paramagnetic chromium and Ti-V-Cr alloys. Journal of Physics F: Metal. Physics, 1979, 9, 773. DOI: 10.1088/0305-4608/9/11/008.
29. Kittel, C. Introduction to Solid State Physics, Wiley, New York, 1996, 674 p.
30. Luo, W., Roundy, D., Cohen, M.L., and Morris Jr., J.W. Ideal strength of bcc molybdenum and niobium. Physical Review B, 2002, 66, 094110. DOI: 10.1103/PhysRevB.66.094110.

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