This paper presents the elastic deformation and thermodynamic theory for crystals with HCP structure on the basis of the statistical moment method (SMM) together with numerical results and discussions for metals Mg, Zn, Dy, Er and Gd. Some numerical results are compared with experiments and other calculations.

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References

1. E. Y. Tonkov and E. G. Ponyatovsky, Phase Transformations of Elements Under High Pressure (CRC Press, 2005). Google Scholar
2. D. Errandonea, R. Boehler and M. Ross, Phys. Rev. B 65 (2002) 012108/1-4. https://doi.org/10.1103/PhysRevB.65.012108 Crossref, Web of Science, ADS, Google Scholar
3. H. Olijnyk and W. B. Holzapfel, Phys. Rev. B 31 (1985) 4682. https://doi.org/10.1103/PhysRevB.31.4682 Crossref, Web of Science, ADS, Google Scholar
4. J. A. Moriarty and A. K. McMahan, Bull. Am. Phys. Soc. 27 (1982) 324. Google Scholar
5. J. A. Moriarty and A. K. McMahan, Phys. Rev. Lett. 48 (1982) 809. https://doi.org/10.1103/PhysRevLett.48.809 Crossref, Web of Science, ADS, Google Scholar
6. J. A. Moriarty, First-principles pressure-temperature phase diagrams in metals, in High-pressure Science and Technology-1993, eds. S. C. Schmidt et al. (AIP Press, New York, 1994), pp. 233–236. Crossref, Google Scholar
7. J. A. Moriarty and J. D. Althoff, Phys. Rev. B 51 (1995) 5609. https://doi.org/10.1103/PhysRevB.51.5609 Crossref, Web of Science, ADS, Google Scholar
8. J. D. Althoff, P. B. Allen, R. M. Wentscovitch and J. A. Moriarty, Phys. Rev. B 48 (1993) 13253. https://doi.org/10.1103/PhysRevB.48.13253 Crossref, Web of Science, ADS, Google Scholar
9. R. M. Wentscovitch, Phys. Rev. B 50 (1994) 10358, https://doi.org/10.1103/PhysRevB.50.10358; In Quantum Theory of Real Materials, eds. J. R. Chelikowsky and S. R. Louie, (Kluwer Academic Publishers), pp. 113–128. Google Scholar
10. D. A. Young, Phase Diagrams of the Elements (University of California Press, Berkeley, 1991). Crossref, Google Scholar
11. C. W. Greff and J. A. Moriarty, Phys. Rev. B 59 (1999) 3427. https://doi.org/10.1103/PhysRevB.59.3427 Crossref, Web of Science, ADS, Google Scholar
12. K. Takemura, High-pressure X-ray study of Zn, in High-Pressure Science and Technology (Warsaw, 1995), ed. W. A. Trzeciakowski (World Scientific, Singapore, 1996), pp. 748–750. Google Scholar
13. S. Meenakshi, V. Vijayakumar, B. K. Godwal and S. K. Sikka, Pressure variation of the c/a ratio of zinc from the first principles electron band theory, in Recent Trends in High Pressure Research, ed. by A. K. Singh (Oxford and IBH Publication, 1992), pp. 328–330. Google Scholar
14. H. Olijnyk, A. P. Jephcoat, D. L. Novikov and N. E. Christensen, Phys. Rev. B 62 (2000) 5508. https://doi.org/10.1103/PhysRevB.62.5508 Crossref, Web of Science, ADS, Google Scholar
15. G. C. Kennedy and R. C. Newton, Melting and phase transformations in solid state of some pure metals at high temperatures and pressures, in Solids Under Pressure, eds. W. Paul and D. M. Warshauer (McGraw-Hill Book Co, New York, 1963), pp. 63–78. Google Scholar
16. P. A. Urtiew and R. Grover, J. Appl. Phys. 48 (1977) 1222. https://doi.org/10.1063/1.323789 Crossref, Web of Science, Google Scholar
17. Y. Nie and Y. Xie, Phys. Rev. B 75 (2007) 174117. https://doi.org/10.1103/PhysRevB.75.174117 Crossref, Web of Science, ADS, Google Scholar
18. K. Chen and K. P. Boyle, Metall. Mater. Trans. A 40A (2009) 2751. https://doi.org/10.1007/s11661-009-9954-6 Crossref, Web of Science, ADS, Google Scholar
19. T. G. Naghiyev and R. M. Rzayev, Mod. Phys. Lett. B 35 (2021) 2150469. https://doi.org/10.1142/S0217984921504698 Link, Web of Science, ADS, Google Scholar
20. T. G. Naghiyev, Mod. Phys. Lett. B 37 (2023) 2350021. https://doi.org/10.1142/S0217984923500215 Link, Web of Science, ADS, Google Scholar
21. E. M. Huseynov and T. G. Naghiyev, Appl. Phys. A 128 (2022) 115. https://doi.org/10.1007/s00339-022-05265-x Crossref, Web of Science, ADS, Google Scholar
22. E. M. Huseynov and T. G. Naghiyev, Vacuum 212 (2023) 111990. https://doi.org/10.1016/j.vacuum.2023.111990 Crossref, Web of Science, ADS, Google Scholar
23. T. G. Naghiyev, U. R. Rzayev, E. M. Huseynov, I. T. Huseynov and S. H. Jabarov, UNEC J. Eng. Appl. Sci. 2 (2022) 85. Google Scholar
24. K. Masuda-Jindo, S. R. Hishitani and V. V. Hung, Phys. Rev. B 79 (2004) 184122. https://doi.org/10.1103/PhysRevB.70.184122 Crossref, Web of Science, ADS, Google Scholar
25. N. Tang and V. V. Hung, Phys. Status Solidi B 149 (1988) 511. https://doi.org/10.1002/pssb.2221490212 Crossref, ADS, Google Scholar
26. T. D. Cuong, N. Q. Hoc, N. D. Trung, N. T. Thao and D. P. Anh, Phys. Rev. B 106 (2022) 094103. https://doi.org/10.1103/PhysRevB.106.094103 Crossref, Web of Science, ADS, Google Scholar
27. V. V. Hung and N. T. Hai, Comput. Mater. Sci. 14 (1999) 261. https://doi.org/10.1016/S0927-0256(98)00117-7 Crossref, Web of Science, Google Scholar
28. M. N. Magomedov, High Temp. 44 (2006) 513. https://doi.org/10.1007/s10740-006-0064-5 Crossref, Web of Science, Google Scholar
29. A. Dinsdale, A. Khvan, E. A. Smirnova, A. V. Ponomareva and I. A. Abrikosov, Calphad 72 (2021) 102253. Crossref, Google Scholar
30. G. V. Sin’ko and N. A. Smirnov, J. Phys. Condens. Matter 17 (2005) 559. https://doi.org/10.1088/0953-8984/17/3/014 Crossref, Web of Science, ADS, Google Scholar
31. K. Takemura, Phys. Rev. B 65 (2002) 132107. https://doi.org/10.1103/PhysRevB.65.132107 Crossref, Web of Science, Google Scholar
32. A. Dewaele, M. Torrent, P. Loubeyre and M. Mezouar, Phys. Rev. B 78 (2008) 104102. https://doi.org/10.1103/PhysRevB.78.104102 Crossref, Web of Science, ADS, Google Scholar
33. M. Griffel, R. E. Skochdopole and F. H. Spedding, J. Chem. Phys. 25 (1956) 75. https://doi.org/10.1063/1.1742851 Crossref, Web of Science, ADS, Google Scholar
34. F. H. Spedding, S. Legvold, A. H. Daane and L. D. Jennings, Prog. Low Temp. Phys. 2 (1957) 368. Crossref, Google Scholar
35. F. J. Jelinek, B. C. Gerstein, M. Griffel, R. E. Skochdopole and F. H. Spedding, Phys. Rev. 149 (1966) 489. https://doi.org/10.1103/PhysRev.149.489 Crossref, Web of Science, ADS, Google Scholar