Investigation of melting point, Debye frequency and temperature of iron at high pressure
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Investigation of melting point, Debye frequency and temperature of iron at high pressure Nguyen Ba Duc 1 , Ho Khac Hieu 2,3 , Pham Thi Minh Hanh 4 , Tran Thi Hai 5 , Nguyen Viet Tuyen 6 , and Tran Thi Ha 7,8,a 1 2
3 4 5 6 7
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Tan Trao University, Km 6, Yen Son, Tuyen Quang 301910, Vietnam Institute of Research and Development, Duy Tan University, 03 Quang Trung, Hai Chau, Da Nang 550000, Vietnam Faculty of Natural Sciences, Duy Tan University, 03 Quang Trung, Hai Chau, Da Nang 550000, Vietnam Hanoi Pedagogical University No2, Nguyen Van Linh, Vinh Phuc 15900, Vietnam Hong Duc University, 565 Quang Trung, Dong Ve, Thanh Hoa 441430, Vietnam VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Ha Noi 120000, Vietnam Laboratory of Advanced Materials Chemistry, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam Received 14 February 2020 / Received in final form 17 April 2020 Published online 22 June 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 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.
1 Introduction Investigation of thermodynamic properties of iron at high pressure is a subject attracting the interest of many scientists in planetary science, geophysics and nuclear physics. This comes from a fact that iron is a main component in the Earth’s core in which it combines with a small amount of light elements such as Si, C, H, O,... Furthermore, the temperature of Earth’s inner-outer core boundary (ICB) is proposed to be closed to the melting point of iron at pressure of 330 GPa. Hence, the high-pressure thermomechanical properties of iron are of primarily important information to explain geochemical observations and seismic data. Therefore, the understanding of physical properties of iron as well as its alloys at extreme conditions permits us to model the dynamic properties, the composition, the evolution process, the
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