The Bain and Orthorhombic Paths of Structural-Phase Transformations in a Transition Metal (v)

A. R. Kuznetsov; S. A. Starikov

doi:10.17804/2410-9908.2024.6.119-130

A. R. Kuznetsov, S. A. Starikov

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

DOI: 10.17804/2410-9908.2024.6.119-130

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.

Acknowledgement: 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.

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

References:

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А. Р. Кузнецов, С. А. Стариков

БЕЙНОВСКИЙ И ОРТОРОМБИЧЕСКИЙ ПУТИ СТРУКТУРНО-ФАЗОВЫХ ПРЕВРАЩЕНИЙ В ПЕРЕХОДНОМ МЕТАЛЛЕ (ВАНАДИИ)

Первопринципным методом изучена энергетика бейновского и орторомбического путей структурно-фазовых превращений при одноосной деформации переходного металла (ванадия). Уточнен орторомбический путь превращения с учетом его симметрии. В результате расчета фононного спектра в зависимости от деформации найдены наиболее мягкие ветви фононного спектра для бейновского пути, ответственные за потерю устойчивости структуры. Выявлен характер потери устойчивости, а также оценена величина деформации, при которой теряется устойчивость как при растяжении, так и при сжатии. Отмечены наиболее вероятные механизмы, определяющие устойчивость структуры и теоретическую прочность переходного металла V. Результаты могут относиться к ситуациям в эксперименте, когда деформируются малые, свободные от дефектов области, например, в наноструктурированных материалах при модифицировании поверхностных слоев пластическим деформированием, при наноиндентировании, при сверхвысокой пластичности сплавов на основе V.

Благодарность: Работа выполнена в рамках государственного задания Минобрнауки России по теме «Структура» № 122021000033-2. Расчеты проведены с использованием суперкомпьютера «Уран» ИММ УрО РАН.

Ключевые слова: первопринципный расчет, бейновский и орторомбический пути, фононный спектр, стабильность структуры

Библиография:

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Effect of magnetic state on the α–γ transition in iron: first-principles calculations of the Bain transformation path / S. V. Okatov, A. R. Kuznetsov, Yu. N. Gornostyrev, V. N. Urtsev, M. I. Katsnelson // Physical Review B. – 2009. – Vol. 79 (9). – P. 094111–094115. – DOI: 10.1103/RevModPhys.84.945.
Lattice instabilities in metallic elements / G. Grimvall, B. Magyari-Kope, V. Ozolins, K. A. Persson // Review of Modern Physics. – 2012. – Vol. 84 (3). – P. 945–986. – DOI: 10.1103/PhysRevB.79.094111.
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Kuznetsov A. R., 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. – Iss. 6. – P. 35–44. – DOI: 10.17804/2410-9908.2023.6.035-044. – URL: http://dream-journal.org/issues/2023-6/2023-6_423.html
Phonon instabilities and the ideal strength of aluminum / D. M. Clatterbuck, C. R. Krenn, Marvin L. Cohen, J. W. Morris, Jr. // Physical Review Letters. – 2003. – Vol. 91 (13). – P. 135501–135504. – DOI: 10.1103/PhyaRevLett.91.135501.
Calculations of theoretical strength: State of the art and history / J. Pokluda, M. Cern, P. Sandera, M. Sob // Journal of Computer-Aided Materials Design. – 2004. – Vol. 11. – P. 1–28. – DOI: 10.1007/s10820-004-4567-2.
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Li J., Yip S. Atomistic measures of materials strength // CMES-Computer Modeling in Engineering and Science. – 2002. – Vol. 3. – P. 219. – DOI: 10.3970/cmes.2002.003.219.
Anomalies in the response of V, Nb, and Ta to tensile and shear loading: ab initio density functional theory calculations / N. Nagasako, M. Jahnátek, R. Asahi, J. Hafner // Physical Review B. – 2010. – Vol. 81. – P. 094108–094121. – DOI: 10.1103/PhysRevB.81.094108.
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Dislocation emission around nanoindentations on a (001) fcc metal surface studied by scanning tunneling microscopy and atomic simulation / O. R. de la Fuente, J. A. Zimmerman, M. A. Gonzales, J. de la Figuera, J. C. Hamilton, W. W. Pai, J. M. Rojo // Physical Review Letters. – 2002. – Vol. 88 (3). – P. 036101–036104. – DOI: 10.1103/PhysRevLett.88.036101.
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Colella R., Batterman B. W. X-ray determination of phonon dispersion in vanadium // Physical Review B. – 1970. – Vol. 1. – P. 3913. – DOI: 10.1103/PhysRevB.1.3913.
Savrasov S. Y., Savrasov D. Y. Electron-phonon interactions and related physical properties of metals from linear-response theory // Physical Review B. – 1996. – Vol. 54. – P. 16487. – DOI: 10.1103/PhysRevB.54.16487.
Ideal strength of random alloys from first principles / X. Li, S. Schonecker, J. Zhao, B. Johansson, L. Vitos // Physical Review B. – 2013. – Vol. 87. – P. 214203. – DOI: 10.1103/PhysRevB.87.214203.
Suzuki N., Otani M. The role of the phonon anomaly in the superconductivity of vanadium and selenium under high pressures // Journal Physics: Condensed Matter. – 2007. – Vol. 19. – P. 125206. – DOI: 10.1088/0953-8984/19/12/125206.
Černý M., Pokluda J. Influence of superimposed biaxial stress on the tensile strength of perfect crystals from first principles // Physical Review B. – 2007. – Vol. 76. – P. 024115. – DOI: 10.1103/PhysRevB.76.024115.
Bolef D. I., Smith R. E., Miller J. G. Elastic properties of vanadium. I. Temperature dependence of the elastic constants and the thermal expansion // Physical Review B. – 1971. – Vol. 3. – P. 4100. – DOI: 10.1103/PhysRevB.3.4100.
Takemura K. High-pressure X-ray study of Zn with a helium pressure medium // Proceedings of the International Conference on High Pressure Science and Technology (AIRAPT-17), Honolulu, Hawaii, July 25–30, 1999 / ed. by M. H. Manghnani, W. J. Nellis, M. F. Nicol. – Hyderabad, India : Universities Press, 2000. – Vol. 1. – P. 440–442.
Elasticity of the superconducting metals V, Nb, Ta, Mo, and W at high pressure / L. Koči, Y. Ma, A. R. Oganov, P. Souvatzis, R. Ahuja // Physical Review B. – 2008. – Vol. 77. – P. 214101. – DOI: 10.1103/PhysRevB.77.214101.
Theory of elastic constants of cubic transition metals and alloys / P. Söderlind, O. Eriksson, J. M. Wills, A. M. Boring // Physical Review B. – 1993. – Vol. 48. – P. 5844. – DOI: 10.1103/PhysRevB.48.5844.
Katahara K. W., Manghnani M. H., Fisher E. Elastic moduli of paramagnetic chromium and Ti-V-Cr alloys // Journal of Physics F: Metal Physics. – 1979. – Vol. 9. – P. 773. – DOI: 10.1088/0305-4608/9/11/008.
Kittel C. Introduction to Solid State Physics. – New York : Wiley, 1996. – 674 p.
Ideal strength of bcc molybdenum and niobium / W. Luo, D. Roundy, M. L. Cohen, J. W. Morris, Jr. // Physical Review B. – 2002. – Vol. 66. – P. 094110. – DOI: 10.1103/PhysRevB.66.094110.

Библиографическая ссылка на статью

Kuznetsov A. R., 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. - Iss. 6. - P. 119-130. -
DOI: 10.17804/2410-9908.2024.6.119-130. -
URL: http://dream-journal.org/issues/content/article_490.html
(accessed: 21.01.2025).