Melting temperature of iron at high pressure: statistical moment method approach
Main Article Content
Abstract
The pressure effects on melting temperatures of iron have been studied based on the combination of the modified Lindemann criterion with statistical moment method in quantum statistical mechanics. Numerical calculations have been performed up to pressure 150 GPa. Our results are in good and reasonable agreements with available experimental data. This approach gives us a relatively simple method for qualitatively calculating high-pressure melting temperature. Moreover, it can be used to verify future experimental and theoretical works. This research proposes the potential of the combination of statistical moment method and the modified Lindemann criterion on predicting high-pressure melting of materials.
Keywords:
Melting, High-Pressure, Iron, Moment method
References
[1] Y. Mori, H. Ozawa, K. Hirose, R. Sinmyo, S. Tateno, G. Morard, Y. Ohishi, Melting experiments on Fe–Fe3S system to 254 GPa.Earth Planet. Sci. Lett.464 (2017) 135–141.
[2] D. Errandonea, High-pressure melting curves of the transition metals Cu, Ni, Pd, and Pt, Phys. Rev. B 87(2013)054108.
[3] D. Santamaría-Pérez, M. Ross, D. Errandonea, G. D. Mukherjee, M.Mezouar, and R. Boehler, X-ray diffraction measurements of Mo melting to 119 GPa and the high pressure phase diagram, J. Chem. Phys. 130, 124509 (2009).
[4] J. H. Nguyen and N. C. Holmes, Melting of iron at the physical conditions of the Earth's core, Nature 427, 339 (2004).
[5] M. Pozzo and D. Alfè, Melting curve of face-centered-cubic nickel from first-principles calculations, Phys. Rev. B 88, 024111 (2013).
[6] A. B. Belonoshko, L. Burakovsky, S. P. Chen, B. Johansson, A. S.Mikhaylushkin, D. L. Preston, S. I. Simak, and D. C. Swift, Molybdenum at High Pressure and Temperature: Melting from Another Solid Phase, Phys. Rev.Lett. 100, 135701 (2008).
[7] F. Lindemann, The calculation of molecular vibration frequencies, Phys. Z. 11, 609 (1910).
[8] H.K. Hieu, Melting of solids under high pressure, Vacuum. 109 (2014) 184–186.
[9] H. K. Hieu and N. N. Ha, High pressure melting curves of silver, gold and copper, AIP Adv. 3, 112125 (2013).
[10] N. Tang and V. V. Hung, Investigation of the Thermodynamic Properties of Anharmonic Crystals by the Momentum Method. I. General Results for Face-Centred Cubic Crystals, Phys. Status Solid B 149, 511 (1988).
[11] H. K. Hieu, Systematic prediction of high-pressure melting curves of transition metals, J. Appl. Phys. 116 (2014) 163505.
[12] N. Tang and V. V. Hung, Investigation of the Thermodynamic Properties of Anharmonic Crystals by the Momentum Method. III. Thermodynamic Properties of the Crystals at Various Pressures, Phys. Status Solidi B 162, 371 (1990).
[13] H. K. Hieu and V. V. Hung, Study of thermodynamic properties of zinc-blende-type semiconductors: Temperature and pressure dependences, Mod. Phys. Lett. B 25(2011) 1041.
[14] M. Magomedov, The calculation of the parameters of the Mie-Lennard-Jones potential, High Temp. 44, 513 (2006).
[15] T. J. Ahrens, K. G. Holland,G. Q. Chen. Phase diagram of iron, revised-core temperatures, Geophys. Res. Lett. 29 (2002) 54.
[16] T. Komabayashi, Y. W. Fei, Internally consistent thermodynamic database for iron to theEarth's core conditions, J. Geophys. Res. Solid Earth 115 (2010) b03202.
[17] Y. Ma, M. Somayazulu, G. Shen, H.-k Mao, J. Shu, R. J. Hemley, In situ X-ray diffractionstudies of iron to earth-core conditions, Phys. Earth Planet Inter.143-144 (2004) 455-467.
[18] G. Shen, H.-k. Mao, R. J. Hemley, T. S. Duy, M. L. Rivers, Melting and crystal structureof iron at high pressures and temperatures, Geophys. Res. Lett. 25 (3) (1998)373-376.
[19] S. Anzellini, A. Dewaele, M. Mezouar, P. Loubeyre, G. Morard, Melting of iron at Earth'sinner core boundary based on fast X-ray diffraction, Science 340 (2013) 464-466.
[20] 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, Melting of compressed iron by monitoring atomicdynamics, Earth Planet. Sci.Lett. 362 (2013), 143-150.
[21] G. Aquilanti, A. Trapananti, A. Karandikar, I. Kantor, C. Marini, O. Mathon, S. Pascarelli,R. Boehler, Melting of iron determined by X-ray absorption spectroscopy to 100 GPa, Proc. Natl. Acad. Sci. U.S.A. 112 (2015), 12042-12045.
[22] R. Boehler, Temperatures in the Earth's core from melting-point measurements of iron athigh static pressures, Nature 363 (1993) 534-536.
[23] Q. Williams, R. Jeanloz, J. Bass, B. Swendsen, T. J. Ahrens, The melting curve of iron to 250 gigapascals: A constraint on the temperature at Earth's center, Science 236 (1987), pp. 181-182.
[2] D. Errandonea, High-pressure melting curves of the transition metals Cu, Ni, Pd, and Pt, Phys. Rev. B 87(2013)054108.
[3] D. Santamaría-Pérez, M. Ross, D. Errandonea, G. D. Mukherjee, M.Mezouar, and R. Boehler, X-ray diffraction measurements of Mo melting to 119 GPa and the high pressure phase diagram, J. Chem. Phys. 130, 124509 (2009).
[4] J. H. Nguyen and N. C. Holmes, Melting of iron at the physical conditions of the Earth's core, Nature 427, 339 (2004).
[5] M. Pozzo and D. Alfè, Melting curve of face-centered-cubic nickel from first-principles calculations, Phys. Rev. B 88, 024111 (2013).
[6] A. B. Belonoshko, L. Burakovsky, S. P. Chen, B. Johansson, A. S.Mikhaylushkin, D. L. Preston, S. I. Simak, and D. C. Swift, Molybdenum at High Pressure and Temperature: Melting from Another Solid Phase, Phys. Rev.Lett. 100, 135701 (2008).
[7] F. Lindemann, The calculation of molecular vibration frequencies, Phys. Z. 11, 609 (1910).
[8] H.K. Hieu, Melting of solids under high pressure, Vacuum. 109 (2014) 184–186.
[9] H. K. Hieu and N. N. Ha, High pressure melting curves of silver, gold and copper, AIP Adv. 3, 112125 (2013).
[10] N. Tang and V. V. Hung, Investigation of the Thermodynamic Properties of Anharmonic Crystals by the Momentum Method. I. General Results for Face-Centred Cubic Crystals, Phys. Status Solid B 149, 511 (1988).
[11] H. K. Hieu, Systematic prediction of high-pressure melting curves of transition metals, J. Appl. Phys. 116 (2014) 163505.
[12] N. Tang and V. V. Hung, Investigation of the Thermodynamic Properties of Anharmonic Crystals by the Momentum Method. III. Thermodynamic Properties of the Crystals at Various Pressures, Phys. Status Solidi B 162, 371 (1990).
[13] H. K. Hieu and V. V. Hung, Study of thermodynamic properties of zinc-blende-type semiconductors: Temperature and pressure dependences, Mod. Phys. Lett. B 25(2011) 1041.
[14] M. Magomedov, The calculation of the parameters of the Mie-Lennard-Jones potential, High Temp. 44, 513 (2006).
[15] T. J. Ahrens, K. G. Holland,G. Q. Chen. Phase diagram of iron, revised-core temperatures, Geophys. Res. Lett. 29 (2002) 54.
[16] T. Komabayashi, Y. W. Fei, Internally consistent thermodynamic database for iron to theEarth's core conditions, J. Geophys. Res. Solid Earth 115 (2010) b03202.
[17] Y. Ma, M. Somayazulu, G. Shen, H.-k Mao, J. Shu, R. J. Hemley, In situ X-ray diffractionstudies of iron to earth-core conditions, Phys. Earth Planet Inter.143-144 (2004) 455-467.
[18] G. Shen, H.-k. Mao, R. J. Hemley, T. S. Duy, M. L. Rivers, Melting and crystal structureof iron at high pressures and temperatures, Geophys. Res. Lett. 25 (3) (1998)373-376.
[19] S. Anzellini, A. Dewaele, M. Mezouar, P. Loubeyre, G. Morard, Melting of iron at Earth'sinner core boundary based on fast X-ray diffraction, Science 340 (2013) 464-466.
[20] 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, Melting of compressed iron by monitoring atomicdynamics, Earth Planet. Sci.Lett. 362 (2013), 143-150.
[21] G. Aquilanti, A. Trapananti, A. Karandikar, I. Kantor, C. Marini, O. Mathon, S. Pascarelli,R. Boehler, Melting of iron determined by X-ray absorption spectroscopy to 100 GPa, Proc. Natl. Acad. Sci. U.S.A. 112 (2015), 12042-12045.
[22] R. Boehler, Temperatures in the Earth's core from melting-point measurements of iron athigh static pressures, Nature 363 (1993) 534-536.
[23] Q. Williams, R. Jeanloz, J. Bass, B. Swendsen, T. J. Ahrens, The melting curve of iron to 250 gigapascals: A constraint on the temperature at Earth's center, Science 236 (1987), pp. 181-182.