Abstract
Using the ab initio molecular dynamics method, the dynamics of the bcc titanium lattice and its response to high temperature deformations are studied. The results of calculation of phonon spectra with use of the harmonic Hamiltonian and the Hamiltonian containing third-order force constants are compared. It is shown that the lattice dynamics of bcc titanium cannot be correctly described without taking into account the anharmonic terms. Stress–strain curves are calculated for specified deformation scheme η1 = η11 = η, η6 = 2η12= η. Analytical expressions of the dependence of the nonzero components of the stress tensor on the strain magnitude are given for this deformation scheme, which take into account the elastic constants up to the fourth order inclusive. All second-order elastic constants, three third-order elastic constants, and four fourth-order elastic constants of bcc titanium are calculated.
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REFERENCES
M. Bartosik, C. Rumeau, R. Hahn, Z. L. Zhang, and P. H. Mayrhofer, Sci. Rep. 7, 16476 (2017).
I. Polmear, D. St. John, J.-F. Nie, and M. Qian, Light Alloys (Elsevier, Oxford, 2017), p. 369.
M. Peters, J. Kumpfert, C. H. Ward, and C. Leyens, Adv. Eng. Mater. 5, 419 (2003).
T. M. Pollock, Nat. Mater. 15, 809 (2016).
Q. Zhang, M. Zheng, Y. Huang, H. J. Kunte, X. Wang, Y. Liu, and C. Zheng, Sci. Rep. 9, 3195 (2019).
P. Souvatzis, O. Eriksson, M. I. Katsnelson, and S. P. Rudin, Phys. Rev. Lett. 100, 095901 (2008).
G. Grimvall, B. Magyari-Köpe, V. Ozolinš, and K. A. Persson, Rev. Mod. Phys. 84, 945 (2012).
A. V. Shapeev, E. V. Podryabinkin, K. Gubaev, F. Tasnádi, and I. A. Abrikosov, New J. Phys. 22, 113005 (2020).
Y. Hiki, Ann. Rev. Mater. Sci. 11, 51 (1981).
H. Ledbetter, H. Ogi, S. Kai, S. Kim, and M. Hirao, J. Appl. Phys. 95, 4642 (2004).
E. Fisher and D. Dever, Science, Technology, and Application of Titanium (Pergamon, New York, 1970), p. 373.
W. Petry, A. Heimig, J. Trampenau, M. Alba, C. Herzig, H. Schrober, and G. Vogl, Phys. Rev. B 43, 10933 (1991).
G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).
G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996).
G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
P. E. Blochl, Phys. Rev. B 50, 17953 (1994).
G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
M. Methfessel and A. T. Paxton, Phys. Rev. B 40, 3616 (1989).
S. Nosé, J. Chem. Phys. 81, 511 (1984).
S. Nosé, Prog. Theor. Phys. Suppl. 103, 1 (1991).
O. Hellman, I. A. Abrikosov, and I. A. Simak, Phys. Rev. B 84, 180301 (2011).
O. Hellman and I. A. Abrikosov, Phys. Rev. B 88, 144301 (2013).
R. A. Cowley, Rep. Prog. Phys. 31, 123 (1968).
A. A. Maradudin and A. E. Fein, Phys. Rev. 128, 2589 (1962).
Yu. Kh. Vekilov, O. M. Krasilnikov, A. V. Lugovskoy, and Yu. E. Lozovik, Phys. Rev. B 94, 104114 (2016).
F. F. Voronov, V. M. Prohorov, E. L. Gromnickaya, and G. G. Ilina, Phys. Met. Metallogr. 45, 1263 (1978).
O. M. Krasilnikov, M. P. Belov, A. V. Lugovskoy, I. Y. Mosyagin, and Y. K. Vekilov, Comput. Mater. Sci. 81, 313 (2014).
Funding
This study was supported by the Russian Science Foundation (project no. 21-72-10105). The calculations were performed using the computer cluster of National University of Science and Technology “MISiS.”
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Translated by O. Kadkin
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Belov, M.P., Sinyakov, R.I. Lattice Dynamics of BCC Titanium and Its Nonlinear Response to High Temperature Deformations in Ab Initio Molecular Dynamics. Phys. Solid State 64, 229–233 (2022). https://doi.org/10.1134/S1063783422060014
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DOI: https://doi.org/10.1134/S1063783422060014