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A. R. Kuznetsov, S. A. Starikov

THE BAIN AND ORTHORHOMBIC PATHS OF THE STRUCTURAL AND PHASE TRANSFORMATIONS AND THEORETICAL STRENGTH OF MOLYBDENUM

DOI: 10.17804/2410-9908.2025.5.053-065

An ab initio method is used to study the energy of the Bain and orthorhombic paths of the structural and phase transformations in molybdenum and phonon instability during uniaxial deformation along <001>. The calculation of the phonon spectrum in the whole irreducible Brillouin zone as dependent on strain for the Bain path makes it possible to find the softest phonon spectral regions, responsible for the loss of structural stability. The nature of the stability loss is revealed, and the strain at which stability is lost under both tension and compression is evaluated. The most probable mechanisms governing the structural stability and theoretical strength of molybdenum are discussed. The results can concern experiment situations when small defect-free regions are strained, e. g., in nanostructured materials, or when surface layers are modified by state-of-the-art plastic deformation techniques, or during nanoindentation, or for super-high ductility of Mo-based alloys.

Acknowledgment: The work was performed under the state assignment for the IMP UB RAS from the Russian Ministry of Science and Higher Education. The Uran supercomputer of the IMM UB RAS was used for the calculations.

Keywords: ab initio calculation, Bain and orthorhombic paths, phonon spectrum, structural stability

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, V.N., 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-Köpe, B., Ozoliņš, 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. Clatterbuck, D.M., Krenn, C.R., Cohen, M.L., and Morris Jr., J.W. Phonon instabilities and the ideal strength of aluminum. Physical Review Letters, 2003, 91 (13), 135501–135504. DOI: 10.1103/PhyaRevLett.91.135501.
  5. 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.
  6. 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.2015.04001.
  7. 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
  8. 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
  9. Kuznetsov, A.R. and Starikov, S.A. The Bain and orthorhombic paths of structural-phase transformations in a transition metal (V). Diagnostics, Resource and Mechanics of materials and structures, 2024, 6, 119–130. DOI: 10.17804/2410-9908.2024.6.119-130. Available at: http://dream-journal.org/issues/2024-6/2024-6_490.html
  10. Luo, W., Roundy, D., Cohen, M.L., and Morris, J.W. Ideal strength of bcc molybdenum and niobium. Physical Review B, 2002, 66, 094110. DOI: 10.1103/PhysRevB.66.094110.
  11. Liu, Z. and Shang, J. First principles calculations of electronic properties and mechanical properties of bcc molybdenum and niobium. Rare Metals, 2011, 30 (suppl. 1), 354–358. DOI: 10.1007/s12598-011-0302-9.
  12. Available at: arXiv:2406.16634 [cond-mat.mtrl-sci]
  13. 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 kristallicheskoy reshetki [Plastic Deformation Under the Phase Instability of the Crystal Lattice]. NTL Publ., Tomsk, 2024, 212 p. (In Russian).
  14. Dewaele, A., Torrent, M., Loubeyre, P., and Mezouar, M. Compression curves of transition metals in the Mbar range: experiments and projector augmented-wave calculations. Physical review B: Condensed Matter, 2008, 78 (10), 104102. DOI:10.1103/PhysRevB.78.104102.
  15. Haas, P., Tran, F., and Blaha, P. Calculation of the lattice constant of solids with semilocal functionals. Physical Review B, 2009, 79 (8), 085104. DOI: 10.1103/physrevb.79.085104.
  16. Ming, L. and Manghnani, M.H. Isothermal compression of BCC transition metals to 100 kbar. Journal of Applied Physics, 1978, 49, 208–212. DOI: 10.1063/1.324325.
  17. 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.
  18. 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.
  19. Dickinson, J.M. and Armstrong, P.E. Temperature dependence of the elastic constants of molybdenum. Journal of Applied Physics, 1967, 38, 602–606. DOI: 10.1063/1.1709381.
  20. Bolef, D.I. and De Klerk, J. Elastic constants of single crystal Mo and W between 77° and 500°K. Journal of Applied Physics, 1962, 33, 2311–2314. DOI: 10.1063/1.1728952.
  21. Zeng, Z.-Y., Hu, C.-E., Cai, L.-C., Chen, X.-R., and Jing, F.-Q. Lattice dynamics and thermodynamics of molybdenum from first-principles calculations. The Journal of Physical Chemistry B, 2010, 114, 298–310. DOI: 10.1021/jp9073637.
  22. Kittel, C. Introduction to Solid State Physics, Wiley, New York, 1996, 674 p.
  23. Molekulyarno-luchevaya epitaksiya i geterostruktury [Molecular Beam Epitaxy and Heterostructures]. Mir Publ., Moscow, 1989, 582 p. (In Russian).
  24. 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.
  25. 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.
  26. Johannes, M.D. and Mazin, I.I. Fermi surface nesting and the origin of Charge Density Waves in metals. Physical Review. B, Condensed Matter, 2007, 77 (16), 165135. DOI: 10.1103/PhysRevB.77.165135.


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Article reference

Kuznetsov A. R., Starikov S. A. The Bain and Orthorhombic Paths of the Structural and Phase Transformations and Theoretical Strength of Molybdenum // Diagnostics, Resource and Mechanics of materials and structures. - 2025. - Iss. 5. - P. 53-65. -
DOI: 10.17804/2410-9908.2025.5.053-065. -
URL: http://eng.dream-journal.org/issues/content/article_531.html
(accessed: 04/20/2026).

 

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