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Melting Temperature of Iron at High Pressure: Statistical Moment Method Approach

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. | VNU Journal of Science: Mathematics – Physics, Vol. 33, No. 3 (2017) 30-35 Melting Temperature of Iron at High Pressure: Statistical Moment Method Approach Tran Thi Hai1,* Ho Khac Hieu2 1 Hong Duc University, Thanh Hoa, Vietnam 2 Duy Tan University, Da Nang, Vietnam Received 08 June 2017 Revised 15 August 2017; Accepted 15 September 2017 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. 1. Introduction In recent years, the investigation of melting of materials under high pressure is motivated by the remarkable developments of experimental techniques. Researchers could utilize various methods to measure the melting temperature up to hundreds of GPa [1]. However, up to now, the prediction of high-pressure melting curves of transition metals has been under debate and disagreement among different methods such as diamond-anvil cell experiments [2], X-ray diffraction measurements (XRD) [3], shock-wave experiments [4], computer simulations [5] and theoretical approaches [6]. Consequently, building a theory for determining the melting of materials under high pressure is still the inspiring subjects in physics, especially in geophysics, planet physics, shock physics, and nuclear physics. In this paper, the melting curve of iron is investigated basing on