High-pressure Melting Curves of and Phases of Iron
Main Article Content
Abstract
In this study, statistical moment method (SMM) was applied in combination with Lindemann melting criterion to investigate pressure effects on melting temperature of iron. Melting curves of phase with body-centered cubicstructure and phase with face-centered cubicstructure of iron were derived up to pressure 13 GPa and 90 GPa, respectively. The study results show that melting curves of these two phases of iron increased functions of pressure, and the higher the pressure was the lower the slopes of melting curves were. The results were compared with the available experimental data to verify the developed theory. The efficiency of the SMM on the investigation of melting temperatures of and phases of iron suggests that the present SMM scheme can be developed extensively to determine melting temperatures of other phases of iron as well as other materials.
Keywords:
Melting; High pressure; Iron; Lindemann criterion; Statistical 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] C. S. Yoo, J. Akella, A. J. Campbell, H. K. Mao, R. J. Hemley, Phase Diagram of lron by in Situ X-ray Diffraction: Implications for Earth's Core, Science 270 (1995) 1473-1475.
[3] O. L. Anderson, Iron: Beta Phase Frays, Science 278 (1997) 821-822.
[4] K. Ohta, Y. Kuwayama, K. Shimizu, T. Yagi, K. Hirose, Y. Ohishi, Measurements of electrical and thermal conductivity of iron under Earth’s core conditions, AGU abstract MR21B-06, AGU Fall Meeting, San Francisco, (2014) Dec 15–19.
[5] D. Andrault, G. Fiquet, M. Kunz, F. Visocekas, D. Hausermann, The Orthorhombic Structure of iron: An in Situ Study at High-Temperature and High-pressure , Science 278 (1997) 831.
[6] M. Mattesini, A. B. Belonoshko, E. Buforn, M. Ramírez, S. I. Simak, A. Udías, H. K. Mao, and R. Ahuja, Hemispherical anisotropic patterns of the Earth’s inner core, Proc. Natl. Acad. Sci. U.S.A. 107 (2010) 9507-9512.
[7] M. Monnereau, M. Calvet, L. Margerin, A. Souriau, Lopsided Growth of Earth's Inner Core, Science 328 (2010) 1014.
[8] A. B. Belonoshko, R. Ahuja, B. Johansson, Stability of the body-centred-cubic phase of iron in the Earth’s inner core, Nature 424 (2003) 1032.
[9] Y. Wu, L. Wang, Y. Huang, D. Wang, Melting of copper under high pressures by molecular dynamics simulation, Chem. Phys. Lett. 515 (2011) 217-220.
[10] D. Zhang, J.M. Jackson, J. Zhao, W. Sturhahn, E.E. Alp, M.Y. Hu, T.S. Toellner, C.A. Murphy, V.B. Prakapenka, Temperature of Earth’s core constrained from melting of Fe and Fe0.9Ni0.1 at high pressures, Earth Planet. Sci. Lett. 447 (2016) 72–83.
[11] H.K. Hieu, Melting of solids under high pressure, Vacuum 109 (2014) 184–186.
[12] H.K. Hieu, T.T. Hai, N.T. Hong, N.D. Sang, N.V. Tuyen, Pressure dependence of melting temperature and shear modulus of hcp-iron, High Pressure Res. 37 (2017) 267-277.
[13] S. Anzellini, A. Dewaele, M. Mezouar, P. Loubeyre, G. Morard, Diffraction Melting of Iron at Earth's Inner Core Boundary Based on Fast X-ray, Science 340 (2013) 464–466.
[14] Q. Williams, R. Jeanloz, J. Bass, B. Svendsen, T.J. Ahrens, The Melting Curve of Iron to 250 Gigapascals: A Constraint on the Temperature at Earth's Center, Science 236 (1987) 181–182.
[15] C.S. Yoo, N.C. Holmes, M. Ross, D.J. Webb, C. Pike, Shock Temperatures and Melting of Iron at Earth Core Conditions, Phys. Rev. Lett. 70 (1993) 3931–3934.
[16] N.H. Jeffrey, H.C. Neil, Melting of iron at the physical conditions of the Earth’s core, Nature 427 (2004) 339–342.
[17] H.K. Hieu, Volume and pressure-dependent thermodynamic properties of sodium, Vacuum. 120 (2015) 13–16.
[18] H.K. Hieu and N. N. Ha, High pressure melting curves of silver, gold and copper, AIP Adv. 3 (2013) 112125.
[19] F. Lindemann, The calculation of molecular vibration frequencies, Phys. Z. 11 (1910) 609-612.
[20] H.K. Hieu, Systematic prediction of high-pressure melting curves of transition metals, J. Appl. Phys. 116 (2014) 163505-1 - 16305-6.
[21] V.V. Hung, Statistical moment method in studying thermodynamic and elastic property of crystal, HNUE Publishing House, Hanoi, 2009.
[22] V.V. Hung, N.T. Hoa, Equation of state and thermodynamic properties of BCC metals, ASEAN J. Sci. Tech. Dev. 23 (2006) 27-42.
[23] M. Magomedov, The Calculation of the Parameters of the Mie–Lennard-Jones Potential, High Temp. 44 (2006) 513-529.
[24] T.J. Ahrens, K.G. Holland, G.Q. Chen, Phase diagram of iron, revised-core temperatures, Geophys. Res. Lett. 29 (2002) 54-1 – 54-4.
[25] T. Komabayashi, Y.W. Fei, Internally consistent thermodynamic database for iron to the Earth’s core conditions, J. Geophys. Res. Solid Earth 115 (2010) B03202.
[26] 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 atomic dynamics, Earth Planet. Sci. Lett. 362 (2013) 143–150.
[27] R.Sinmyo, K. Hirose, Y. Ohishi, Melting curve of iron to 290 GPa determined in a resistance-heated diamond-anvil cell, Earth Planet. Sci. Lett. 510 (2019) 45–52.
[2] C. S. Yoo, J. Akella, A. J. Campbell, H. K. Mao, R. J. Hemley, Phase Diagram of lron by in Situ X-ray Diffraction: Implications for Earth's Core, Science 270 (1995) 1473-1475.
[3] O. L. Anderson, Iron: Beta Phase Frays, Science 278 (1997) 821-822.
[4] K. Ohta, Y. Kuwayama, K. Shimizu, T. Yagi, K. Hirose, Y. Ohishi, Measurements of electrical and thermal conductivity of iron under Earth’s core conditions, AGU abstract MR21B-06, AGU Fall Meeting, San Francisco, (2014) Dec 15–19.
[5] D. Andrault, G. Fiquet, M. Kunz, F. Visocekas, D. Hausermann, The Orthorhombic Structure of iron: An in Situ Study at High-Temperature and High-pressure , Science 278 (1997) 831.
[6] M. Mattesini, A. B. Belonoshko, E. Buforn, M. Ramírez, S. I. Simak, A. Udías, H. K. Mao, and R. Ahuja, Hemispherical anisotropic patterns of the Earth’s inner core, Proc. Natl. Acad. Sci. U.S.A. 107 (2010) 9507-9512.
[7] M. Monnereau, M. Calvet, L. Margerin, A. Souriau, Lopsided Growth of Earth's Inner Core, Science 328 (2010) 1014.
[8] A. B. Belonoshko, R. Ahuja, B. Johansson, Stability of the body-centred-cubic phase of iron in the Earth’s inner core, Nature 424 (2003) 1032.
[9] Y. Wu, L. Wang, Y. Huang, D. Wang, Melting of copper under high pressures by molecular dynamics simulation, Chem. Phys. Lett. 515 (2011) 217-220.
[10] D. Zhang, J.M. Jackson, J. Zhao, W. Sturhahn, E.E. Alp, M.Y. Hu, T.S. Toellner, C.A. Murphy, V.B. Prakapenka, Temperature of Earth’s core constrained from melting of Fe and Fe0.9Ni0.1 at high pressures, Earth Planet. Sci. Lett. 447 (2016) 72–83.
[11] H.K. Hieu, Melting of solids under high pressure, Vacuum 109 (2014) 184–186.
[12] H.K. Hieu, T.T. Hai, N.T. Hong, N.D. Sang, N.V. Tuyen, Pressure dependence of melting temperature and shear modulus of hcp-iron, High Pressure Res. 37 (2017) 267-277.
[13] S. Anzellini, A. Dewaele, M. Mezouar, P. Loubeyre, G. Morard, Diffraction Melting of Iron at Earth's Inner Core Boundary Based on Fast X-ray, Science 340 (2013) 464–466.
[14] Q. Williams, R. Jeanloz, J. Bass, B. Svendsen, T.J. Ahrens, The Melting Curve of Iron to 250 Gigapascals: A Constraint on the Temperature at Earth's Center, Science 236 (1987) 181–182.
[15] C.S. Yoo, N.C. Holmes, M. Ross, D.J. Webb, C. Pike, Shock Temperatures and Melting of Iron at Earth Core Conditions, Phys. Rev. Lett. 70 (1993) 3931–3934.
[16] N.H. Jeffrey, H.C. Neil, Melting of iron at the physical conditions of the Earth’s core, Nature 427 (2004) 339–342.
[17] H.K. Hieu, Volume and pressure-dependent thermodynamic properties of sodium, Vacuum. 120 (2015) 13–16.
[18] H.K. Hieu and N. N. Ha, High pressure melting curves of silver, gold and copper, AIP Adv. 3 (2013) 112125.
[19] F. Lindemann, The calculation of molecular vibration frequencies, Phys. Z. 11 (1910) 609-612.
[20] H.K. Hieu, Systematic prediction of high-pressure melting curves of transition metals, J. Appl. Phys. 116 (2014) 163505-1 - 16305-6.
[21] V.V. Hung, Statistical moment method in studying thermodynamic and elastic property of crystal, HNUE Publishing House, Hanoi, 2009.
[22] V.V. Hung, N.T. Hoa, Equation of state and thermodynamic properties of BCC metals, ASEAN J. Sci. Tech. Dev. 23 (2006) 27-42.
[23] M. Magomedov, The Calculation of the Parameters of the Mie–Lennard-Jones Potential, High Temp. 44 (2006) 513-529.
[24] T.J. Ahrens, K.G. Holland, G.Q. Chen, Phase diagram of iron, revised-core temperatures, Geophys. Res. Lett. 29 (2002) 54-1 – 54-4.
[25] T. Komabayashi, Y.W. Fei, Internally consistent thermodynamic database for iron to the Earth’s core conditions, J. Geophys. Res. Solid Earth 115 (2010) B03202.
[26] 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 atomic dynamics, Earth Planet. Sci. Lett. 362 (2013) 143–150.
[27] R.Sinmyo, K. Hirose, Y. Ohishi, Melting curve of iron to 290 GPa determined in a resistance-heated diamond-anvil cell, Earth Planet. Sci. Lett. 510 (2019) 45–52.