The Bain and Orthorhombic Paths of the Bcc–fcc Transformation in a Bcc Metal

A. R. Kuznetsov; S. A. Starikov

doi:10.17804/2410-9908.2023.6.035-044

A. R. Kuznetsov, S. A. Starikov

THE BAIN AND ORTHORHOMBIC PATHS OF THE BCC–FCC TRANSFORMATION IN A BCC METAL

DOI: 10.17804/2410-9908.2023.6.035-044

The energy of the Bain and orthorhombic paths in niobium and the instability of phonons during uniaxial deformation along <001> are studied with the application of the ab initio method. The orthorhombic transformation path is refined with regard to its symmetry. The calculation of the phonon spectrum in the entire irreducible Brillouin zone depending on deformation makes it possible to find the softest branches of the phonon spectrum responsible for the loss of stability of the structure. The nature of the loss of stability is revealed, and the strain at which stability is lost both in tension and compression is evaluated. Possible mechanisms determining the stability of the structure and theoretical strength of niobium are discussed. The results obtained can relate to experimental situations when small defect-free regions are deformed, for example, in nanostructured materials, when surface layers are modified by modern methods of plastic deformation, and during nanoindentation.

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

Keywords: first-principles calculation, Bain and orthorhombic paths, phonon spectrum, structure stability

References:

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А. Р. Кузнецов, С. А. Стариков

БЕЙНОВСКИЙ И ОРТОРОМБИЧЕСКИЙ ПУТИ ОЦК-ГЦК ПРЕВРАЩЕНИЯ В ОЦК-МЕТАЛЛЕ

В работе ab initio методом изучена энергетика бейновского и орторомбического путей в ниобии и нестабильности фононов в ходе одноосной деформации вдоль <001>. Уточнен орторомбический путь превращения с учетом его симметрии. Расчет фононного спектра во всей неприводимой зоне Бриллюэна в зависимости от деформации позволил найти наиболее мягкие ветви фононного спектра, 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. Обсуждаются возможные механизмы, определяющие устойчивость структуры и теоретическую прочность ниобия. Полученные результаты могут относиться к ситуациям в эксперименте, когда деформируются малые свободные от дефектов области, например, в наноструктурированных материалах, при модифицировании поверхностных слоев современными методами пластического деформирования, при наноиндентировании.

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:

Bain E. C. The Nature of Martensite // Trans. AIME. – 1924. – Vol. 70. – P. 25–35.
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, No. 9. – P. 094111–094115. – DOI: 10.1103/RevModPhys.84.945.
Lattice instabilities in metallic elements / G. Grimvall, B. Magyari-Köpe, V. Ozoliņš, K. A. Persson // Review of Modern Physics. – 2012. – Vol. 84, No. 3. – P. 945–986. – DOI: 10.1103/PhysRevB.79.094111.
Kuznetsov A. R., Starikov S. A., Sagaradze V. V. Phonon instabilities in a metal on the Bain fcc–bcc transformation path // Diagnostics, Resource and Mechanics of materials and structures. – 2022. – Iss. 6. – P. 86–94. – DOI: 10.17804/2410-9908.2022.6.086-094. – URL: http://dream-journal.org/issues/2022-6/2022-6_385.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, No. 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.
Ab initio calculations of mechanical properties: methods and applications / J. Pokluda, M. Černý, M. Sob, Y. Umeno // Progress in Materials Science. – 2015. – Vol. 73. – P. 127–158. – DOI: 10.1016/j.pmatsci.2015.04001.
Li Ju, Yip S. Atomistic measures of materials strength // CMES-Computer Modeling in Engineering and Sciences. – 2002. – Vol. 3. – P. 219. – DOI: 10.3970/cmes.2002.003.219.
Ideal strength of bcc molybdenum and niobium / W. Luo, D. Roundy, M. L. Cohen, J. W. Morris Jr. // Physical Review B. – 2002. – Vol. 66, iss. 9. – P. 094110. – DOI: 10.1103/PhysRevB.66.094110.
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, iss. 2. – P. 024115. – DOI: 10.1103/PhysRevB.76.024115.
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 // Phys. Rev. B. – 2010. – Vol. 81, iss. 9. – P. 094108. – DOI: 10.1103/PhysRevB.81.094108.
First-principles investigation of elastic anomalies in niobium at high pressure and temperature / Y. X. Wang, H. Y. Geng, Q. Wu, X. R. Chen, Y. Sun // Journal of Applied Physics. – 2017. – Vol. 122, iss. 23. – P. 235903. – DOI: 10.1063/1.5006396.
Kohn anomaly and phase stability in group VB transition metals / A. Landa, P. Söderlind, I. I. Naumov, J. E. Klepeis, L. Vitos // Computation. – 2018. – Vol. 6 (29). – P. 1–19. – DOI: 10.3390/computation6020029.
Discrete and continuous deformation during nanoindentation of thin films / A. Gouldstone, H. J. Koh, K. Y. Zeng, A. E. Giannakopoulos, S. Suresh // Acta Materialia. – 2000. – Vol. 48, No. 9. – P. 2277–2295. – DOI: 10.1016/S1359-6454(00)00009-4.
Dislocation emission around nanoindentations on a (001) fcc metal surface studied by scan-ning 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, No. 3. – P. 036101–036104. – DOI: 10.1103/PhysRevLett.88.036101.
Молекулярно-лучевая эпитаксия и гетероструктуры / под ред. Л. Ченга, К. Плога; пер. с англ. под ред. Ж. И. Алферова, Ю. В. Шмарцева. – Москва : Мир, 1989. – 582 с.
Phonon instabilities in uniaxially compressed fcc metals as seen in molecular dynamics sim-ulations / G. Kimminau, P. Erhart, E. M. Bringa, B. Remington, J. S. Wark // Physical Review B. – 2010. – Vol. 81. – P. 092102. – DOI: 10.1103/PhysRevB.81.092102.
URL: arXiv:cond-mat/0504077 [cond-mat.supr-con]
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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, iss. 21. – 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.
Numerical Data and Functional Relationships in Science and Technology / ed. by O. Madelung. – Landolt-Börnstein New Series. – Group III : Crystal and Solid State Physics. – Vol. 14 : Structure Data of Elements and Intermetallic Phases. – Berlin : Springer Verlag, 1988.
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 (11). – P. 773. – DOI: 10.1088/0305-4608/9/11/008.
James A. M., Lord M. P. Macmillan’s Chemical and Physical Data. – London, UK : Macmillan, 1992.

Библиографическая ссылка на статью

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/content/article_423.html
(accessed: 30.12.2024).