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Investigation of melting point, Debye frequency and temperature of iron at high pressure

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Abstract

The Debye model has been developed to investigate the pressure effects on melting point, Debye frequency and Debye temperature of iron metal. The analytical expressions of these thermodynamic quantities have been derived as functions of crystal volume compressibility. The pressure dependence of them is studied based on the well-established equation-of-state which includes the contributions of the anharmonic and electronic thermal pressures. We performed numerical calculations for iron up to pressure 350 GPa and compared with experimental data when possible. Our results show that the Debye frequency and Debye temperature increase rapidly with compression, and beyond 150 GPa they behave like linear functions of pressure. From the pressure-dependent melting point of iron, we deduce the temperatures of the Earth’s inner-outer core boundary (ICB) and core-mantle boundary (CMB). The temperatures of the Earth’s ICB and CMB are predicted lower than 5540(±170) K and about 4060 K, respectively.

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References

  1. L. Stixrude, Phys. Rev. Lett. 108, 055505 (2012)

    ADS  Google Scholar 

  2. M. Pozzo, D. Alfè, Phys. Rev. B 88, 024111 (2013)

    ADS  Google Scholar 

  3. L. Burakovsky, N. Burakovsky, M.J. Cawkwell, D.L. Preston, D. Errandonea, S.I. Simak, Phys. Rev. B 94, 094112 (2016)

    ADS  Google Scholar 

  4. S. Baty, L. Burakovsky, D. Preston, Crystals 10, 20 (2020)

    Google Scholar 

  5. D. Alfé, Rev. Mineral. Geochem. 71, 337 (2010)

    Google Scholar 

  6. H.K. Hieu, T.T. Hai, N.T. Hong, N.D. Sang, N.V. Tuyen, J. Electron. Mater. 46, 3702 (2017)

    ADS  Google Scholar 

  7. D. Errandonea, Phys. Rev. B 87, 054108 (2013)

    ADS  Google Scholar 

  8. J.H. Nguyen, N.C. Holmes, Nature 427, 339 (2004)

    ADS  Google Scholar 

  9. N.W. Ashcroft, N.D. Mermin,Solid State Physics, 1st edn. (Cengage Learning, Boston, 1976)

  10. O.L. Anderson, L. Dubrovinsky, S.K. Saxena, T. LeBihan, Geophys. Res. Lett. 28, 399 (2001)

    ADS  Google Scholar 

  11. D. Santamaria-Perez, M. Ross, D. Errandonea, G.D. Mukherjee, M. Mezouar, R. Boehler, J. Chem. Phys. 130, 124509 (2009)

    ADS  Google Scholar 

  12. D. Errandonea, S.G. MacLeod, L. Burakovsky, D. Santamaria-Perez, J.E. Proctor, H. Cynn, M. Mezouar, Phys. Rev. B 100, 094111 (2019)

    ADS  Google Scholar 

  13. S. Anzellini, V. Monteseguro, E. Bandiello, A. Dewaele, L. Burakovsky, D. Errandonea, Sci. Rep. 9, 13034 (2019)

    ADS  Google Scholar 

  14. Y. Ping, F. Coppari, D.G. Hicks, B. Yaakobi, D.E. Fratanduono, S. Hamel, J.H. Eggert, J.R. Rygg, R.F. Smith, D.C. Swift et al., Phys. Rev. Lett. 111, 065501 (2013)

    ADS  Google Scholar 

  15. S. Anzellini, A. Dewaele, M. Mezouar, P. Loubeyre, G. Morard, Science 340, 464 (2013)

    ADS  Google Scholar 

  16. T.T. Hai, H.K. Hieu, VNU Journal of Science: Mathematics - Physics 33, 1 (2017)

    Google Scholar 

  17. H.K. Hieu, N. Viet Tuyen, V.N. Nguyen, B.D. Nguyen, Q.T. Vu, T.H. Tran, Q.K. Doan, Curr. Appl. Phys. 19, 55 (2019)

    ADS  Google Scholar 

  18. H.K. Hieu, N.T. Hong, D.Q. Khoa, J. Phys. Soc. Jpn. 88, 105002 (2019)

    ADS  Google Scholar 

  19. R. Boehler, Nature 363, 534 (1993)

    ADS  Google Scholar 

  20. D. Alfè, Phys. Rev. B 79, 060101 (2009)

    ADS  Google Scholar 

  21. G. Aquilanti, A. Trapananti, A. Karandikar, I. Kantor, C. Marini, O. Mathon, S. Pascarelli, R. Boehler, Proc. Natl. Acad. Sci. U.S.A. 112, 12042 (2015)

    ADS  Google Scholar 

  22. D. Zhang, J.M. Jackson, J. Zhao, W. Sturhahn, E.E. Alp, M.Y. Hu, T.S. Toellner, C.A. Murphy, V.B. Prakapenka, Earth Planet. Sci. Lett. 447, 72 (2016)

    ADS  Google Scholar 

  23. R. Boehler, Phys. Rev. B 27, 6754 (1983)

    ADS  Google Scholar 

  24. M. Kumari, N. Dass, Phys. Status Solidi B 133, 101 (1986)

    ADS  Google Scholar 

  25. H.K. Hieu, Vacuum 109, 184 (2014)

    ADS  Google Scholar 

  26. M.J. Graf, C.W. Greeff, J.C. Boettger, AIP Conf. Proc. 706, 65 (2004)

    ADS  Google Scholar 

  27. H.K. Hieu, N.N. Ha, AIP Adv. 3, 112125 (2013)

    ADS  Google Scholar 

  28. L. Burakovsky, D.L. Preston, J. Phys. Chem. Solids 65, 1581 (2004)

    ADS  Google Scholar 

  29. H.K. Hieu, Vacuum Part A 120, 13 (2015)

    ADS  Google Scholar 

  30. H.K. Hieu, T.T. Hai, N.T. Hong, N.D. Sang, N.V. Tuyen, High Pressure Res. 37, 267 (2017)

    ADS  Google Scholar 

  31. L.V. Al’tshuler, S.E. Brusnikin, E.A. Kuz’menkov, J. Appl. Mech. Tech. Phys. 28, 129 (1987)

    ADS  Google Scholar 

  32. A. Dewaele, P. Loubeyre, F. Occelli, M. Mezouar, P.I. Dorogokupets, M. Torrent, Phys. Rev. Lett. 97, 215504 (2006)

    ADS  Google Scholar 

  33. M.J. Brown, Geophys. Res. Lett. 28, 4339 (2001)

    ADS  Google Scholar 

  34. E. Sevillano, H. Meuth, J.J. Rehr, Phys. Rev. B 20, 4908 (1979)

    ADS  Google Scholar 

  35. L. Burakovsky, D.L. Preston, R.R. Silbar, J. Appl. Phys. 88, 6294 (2000)

    ADS  Google Scholar 

  36. D. Errandonea, Physica B 357, 356 (2005)

    ADS  Google Scholar 

  37. F. Lindemann, Physik Z. 11, 609 (1910)

    Google Scholar 

  38. D. Errandonea, J. Appl. Phys. 108, 033517 (2010)

    ADS  Google Scholar 

  39. H.K. Hieu, J. Appl. Phys. 116, 163505 (2014)

    ADS  Google Scholar 

  40. Y. Wang, R. Ahuja, B. Johansson, Phys. Rev. B 65, 014104 (2001)

    ADS  Google Scholar 

  41. O.L. Anderson, Equations of State for Solids in Geophysics and Ceramic Science, Oxford Monographs on Geology and Geogphysics (Oxford University Press, Oxford, 1995)

  42. P. Dorogokupets, A. Oganov, Dokl. Earth Sci. 410, 1091 (2006)

    ADS  Google Scholar 

  43. P.I. Dorogokupets, A.R. Oganov, Phys. Rev. B 75, 024115 (2007)

    ADS  Google Scholar 

  44. D. Alfè, G.D. Price, M.J. Gillan, Phys. Rev. B 64, 045123 (2001)

    ADS  Google Scholar 

  45. A. Basu, M.R. Field, D.G. McCulloch, R. Boehler, Geosci. Front. 11, 565 (2020)

    Google Scholar 

  46. R. Sinmyo, K. Hirose, Y. Ohishi, Earth Planet. Sci. Lett. 510, 45 (2019)

    Google Scholar 

  47. J.M. Brown, R.G. McQueen, J. Geophys. Res. Solid Earth 91, 7485 (1986)

    Google Scholar 

  48. T.J. Ahrens, K.G. Holland, G.Q. Chen, Geophys. Res. Lett. 29, 54 (2002)

    Google Scholar 

  49. Y. Ma, M. Somayazulu, G. Shen, H. kwang Mao, J. Shu, R.J. Hemley, Phys. Earth Planet. Inter. 143-144, 455 (2004)

    ADS  Google Scholar 

  50. G. Shen, H.k. Mao, R.J. Hemley, T.S. Duffy, M.L. Rivers, Geophys. Res. Lett. 25, 373 (1998)

    ADS  Google Scholar 

  51. R. Boehler, D. Santamaria-Perez, D. Errandonea, M. Mezouar, J. Phys.: Conf. Ser. 121, 022018 (2008)

    Google Scholar 

  52. J.M. Jackson, W. Sturhahn, M. Lerche, J. Zhao, T.S. Toellner, E.E. Alp, S.V. Sinogeikin, J.D. Bass, C.A. Murphy, J.K. Wicks, Earth Planet. Sci. Lett. 362, 143 (2013)

    ADS  Google Scholar 

  53. J. Bouchet, S. Mazevet, G. Morard, F. Guyot, R. Musella, Phys. Rev. B 87, 094102 (2013)

    ADS  Google Scholar 

  54. D. Alfe, M. Gillan, G. Price, Earth Planet. Sci. Lett. 195, 91 (2002)

    ADS  Google Scholar 

  55. H. Terasaki, S. Kamada, T. Sakai, E. Ohtani, N. Hirao, Y. Ohishi, Earth Planet. Sci. Lett. 304, 559 (2011)

    ADS  Google Scholar 

  56. G. Morard, D. Andrault, D. Antonangeli, Y. Nakajima, A. Auzende, E. Boulard, S. Cervera, A. Clark, O. Lord, J. Siebert et al., Earth Planet. Sci. Lett. 473, 94 (2017)

    ADS  Google Scholar 

  57. J. Badro, A.S. Côté, J.P. Brodholt, Proc. Natl. Acad. Sci. U.S.A. 111, 7542 (2014)

    ADS  Google Scholar 

  58. K. Umemoto, K. Hirose, Geophys. Res. Lett. 42, 7513 (2015)

    ADS  Google Scholar 

  59. H. Ozawa, K. Hirose, K. Yonemitsu, Y. Ohishi, Earth Planet. Sci. Lett. 456, 47 (2016)

    ADS  Google Scholar 

  60. A. Laio, S. Bernard, G.L. Chiarotti, S. Scandolo, E. Tosatti, Science 287, 1027 (2000)

    ADS  Google Scholar 

  61. D. Andrault, G. Pesce, M.A. Bouhifd, N. Bolfan-Casanova, J.M. Hénot, M. Mezouar, Science 344, 892 (2014)

    ADS  Google Scholar 

  62. G.K. Pradhan, G. Fiquet, J. Siebert, A.L. Auzende, G. Morard, D. Antonangeli, G. Garbarino, Earth Planet. Sci. Lett. 431, 247 (2015)

    ADS  Google Scholar 

  63. R.E. Silber, R.A. Secco, W. Yong, J.A.H. Littleton, Sci. Rep. 8, 10758 (2018)

    ADS  Google Scholar 

  64. I.C. Ezenwa, R.A. Secco, Crystals 9, 359 (2019)

    Google Scholar 

  65. S. Japel, B. Schwager, R. Boehler, M. Ross, Phys. Rev. Lett. 95, 167801 (2005)

    ADS  Google Scholar 

  66. W.B. Holzapfel, High Pressure Research 16, 81 (1998)

    ADS  Google Scholar 

  67. R. Hrubiak, Y. Meng, G. Shen, https://arXiv:1804.05109 (2018)

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Authors and Affiliations

  1. Tan Trao University, Km 6, Yen Son, Tuyen Quang, 301910, Vietnam

    Nguyen Ba Duc

  2. Institute of Research and Development, Duy Tan University, 03 Quang Trung, Hai Chau, Da Nang, 550000, Vietnam

    Ho Khac Hieu

  3. Faculty of Natural Sciences, Duy Tan University, 03 Quang Trung, Hai Chau, Da Nang, 550000, Vietnam

    Ho Khac Hieu

  4. Hanoi Pedagogical University No2, Nguyen Van Linh, Vinh Phuc, 15900, Vietnam

    Pham Thi Minh Hanh

  5. Hong Duc University, 565 Quang Trung, Dong Ve, Thanh Hoa, 441430, Vietnam

    Tran Thi Hai

  6. VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Ha Noi, 120000, Vietnam

    Nguyen Viet Tuyen

  7. Laboratory of Advanced Materials Chemistry, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, 758307, Vietnam

    Tran Thi Ha

  8. Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, 758307, Vietnam

    Tran Thi Ha

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  1. Nguyen Ba Duc
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Duc, N.B., Hieu, H.K., Hanh, P.T.M. et al. Investigation of melting point, Debye frequency and temperature of iron at high pressure. Eur. Phys. J. B 93, 115 (2020). https://doi.org/10.1140/epjb/e2020-10083-8

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