Abstract
Based on the Mie–Lennard-Jones interatomic pair potential and the Einstein crystal model, the thermal equation of state and the pressure dependences of the thermophysical properties of niobium are obtained. The pressure dependences of the Debye temperature, the first, second, and third Grüneisen parameters, isothermal compression modulus, isochoric and isobaric heat capacity, thermal expansion coefficient, and the pressure derivatives of these parameters along the 300 and 3000 K isotherms are studied. The calculations showed good agreement with experimental data. Based on the results obtained, the pressure dependence of the melting point of niobium and its pressure derivative are calculated.
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REFERENCES
P. I. Dorogokupets, T. S. Sokolova, B. S. Danilov, and K. D. Litasov, “Near-absolute equations of state of diamond, Ag, Al, Au, Cu, Mo, Nb, Pt, Ta, and W for quasi-hydrostatic conditions,” Geodinamika i Tektonofizika 3, No. 2, 129–166 (2012).
M. R. Fellinger, H. Park, and J. W. Wilkins, “Force-matched embedded-atom method potential for niobium,” Phys. Rev. B 81, No. 14, 144119-1–144119-15 (2010).
M. N. Magomedov, The study of Interatomic Interaction, Formation of Vacancies, and Self-Diffusion in Crystals (Fizmatlit, Moscow, 2010) [in Russian].
M. N. Magomedov, “On self-diffusion in iron at very strong compression of crystal,” Phys. Met. Metallogr. 114, No. 3, 207–216 (2013).
M. N. Magomedov, “On self-diffusion and surface energy under compression of diamond, silicon, and germanium,” Tech. Phys. 83, No. 12, 1789–1799 (2013).
M. N. Magomedov, “Change in the thermophysical properties of BCC iron during isothermal compression,” Tech. Phys. 85, No. 11, 1619–1625 (2015).
M. N. Magomedov, “Change in the lattice properties and melting temperature of a face-centered cubic iron under compression,” Tech. Phys. 87, No. 4, 569–576 (2017).
M. N. Magomedov, “Variations in thermal properties of diamond under isothermal compression,” Tech. Phys. 87, No. 5, 661–668 (2017).
M. N. Magomedov, “State equations and properties of various polymorphous modifications of silicon and germanium,” Phys. Solid State 59, No. 6, 1085–1093 (2017).
E. N. Akhmedov, “Molybdenum lattice properties at high pressure,” J. Phys. Chem. Solids 121, 62–66 (2018).
M. N. Magomedov, “The calculation of the parameters of the Mie–Lennard-Jones potential,” High Temp. 44, No. 4, 513–529 (2006).
S. I. Novikova, Thermal Expansion of Solids (Nauka, Moscow, 1974) [in Russian].
R. G. McQueen, S. P. Marsh, J. W. Taylor, J. N. Fritz, and W. J. Carter, “The equation of state of solids from shock wave studies”, In High-Velocity Impact Phenomena, Ed. by R. Kinslow (Academic, New York, 1970).
T. Kenichi and A. K. Singh, “High-pressure equation of state for Nb with a helium-pressure medium: Powder X-ray diffraction experiments,” Phys. Rev. B 73, No. 22, 224 119(9) (2006).
L. V. Al’tshuler, S. E. Brusnikin, and E. A. Kuz’menko, “Isotherms and Grüneisen functions of 25 metals,” Zh. Prikladnoi Mekhaniki i Tekhnicheskoi Fiz., No. 1, 134–146 (1987).
Y. Zou, X. Qi, X. Wang, T. Chen, X. Li, D. Welch, L. Baosheng, “High-pressure behavior and thermoelastic properties of niobium studied by in situ X-ray diffraction,” J. Appl. Phys. 116, No. 1, 013 516(6) (2014).
A. Karbasi, S. K. Saxena, and R. Hrubiak, “The thermodynamics of several elements at high pressure,” Calphad Comput. Coupling Phase Diagrams Thermochem. 35, No. 1, 72–81 (2011).
C. Nie, B. Zong, and J. Wang, “Pressure dependency Grüneisen parameter γ for bcc Mo,” Appl. Phys. Res. 6, No. 4, 26–30 (2014).
Z. Y. Zeng, C. E. Hu, X. R. Chen, X. L. Zhang, L. C. Cai, and F. Q. Jing, “Density functional theory investigation of the phonon instability, thermal equation of state and melting curve of Mo,” Phys. Chem. Chem. Phys. 13, No. 4, 1669–1675 (2011).
S. N. Vaidya and G. C. Kennedy, “Compressibility of 22 elemental solids to 45 kb,” J. Phys. Chem. Solids 33, No. 7–9, 1377–1389 (1972).
A. K. Singh and T. Kenichi, “Measurement and analysis of nonhydrostatic lattice strain component in niobium to 145 GPa under various fluid pressure-transmitting media,” J. Appl. Phys. 90, No. 7, 3269–3275 (2001).
Y. Song, R. Yang, D. Li, W. T. Wu, and Z. X. Guo, “Calculation of theoretical strengths and bulk moduli of bcc metals,” Phys. Rev. B 59, No. 22, 14 220–14 225 (1999).
L. Koči, Y. Ma, A. R. Oganov, P. Souvatzis, and R. Ahuja, “Elasticity of the superconducting metals V, Nb, Ta, Mo, and W at high pressure,” Phys. Rev. B 77, No. 21, 214 101(5) (2008).
Q. Jiang, H. M. Lu, and M. Zhao, “Modelling of surface energies of elemental crystals,” J. Phys.: Condens. Matter 16, No. 4, 521–530 (2004).
X. D. Dai, J. H. Li, and Y. Kong, “Long-range empirical potential for the bcc structured transition metals,” Phys. Rev. B 75, No. 5, 052 102(4) (2007).
M. N. Magomedov, “On the criterion of the crystal-liquid phase transition,” Phys. Met. Metallogr. 105, No. 2, 116–125 (2008).
ACKNOWLEDGMENTS
We are grateful to M.N. Magomedov, N.Sh. Gazanova, and A.A. Aliverdiev for fruitful discussions and assistance in this work.
Funding
This work was supported by the Russian Foundation for Basic Research (project no. 18-29-11013_mk) and the Presidium of the Russian Academy of Sciences (program no. I.13).
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Translated by E. Chernokozhin
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Kramynin, S.P., Akhmedov, E.N. Change in Thermophysical Properties and Melting Temperature of Niobium with Increasing Pressure. Phys. Metals Metallogr. 120, 1027–1032 (2019). https://doi.org/10.1134/S0031918X19110097
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DOI: https://doi.org/10.1134/S0031918X19110097