DOI: 10.11648/j.wjmst.20260302.12 ISSN: 3070-1546

Lindemann’s Ratio Pressure Dependence of the Melting Temperature for Some Metals in Geothermal at High Pressure and High Temperature

Nand Kishor, Amar Kumar
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The study of melting behavior under extreme conditions of pressure and temperature is essential for understanding the physical properties of metals within Earth’s interior and industrial high-pressure applications. This research investigates the pressure dependence of the melting temperature for selected metals using Lindemann’s melting law, which establishes a relationship between vibrational amplitudes of atomic lattices and melting phenomena. The Lindemann’s ratio, defined as the critical amplitude of atomic vibrations relative to interatomic spacing, serves as the foundation for evaluating how pressure influences the melting process. In this study, the melting curves of metals such as iron (Fe), copper (Cu), aluminum (Al), and magnesium (Mg) are theoretically modeled under high-pressure conditions. The model incorporates modifications to Lindemann’s law to account for the anharmonic effects and compressional behavior of lattice parameters at elevated pressures. Using the pressure-dependent Grüneisen parameter and the Mie Grüneisen equation of state, the variation of melting temperature with pressure is derived and analyzed. The results reveal that melting temperature increases nonlinearly with pressure for all investigated metals, consistent with experimental and geophysical observations. Iron, a major component of Earth’s core, exhibits the highest melting slope due to its dense atomic packing and strong interatomic bonding. Conversely, metals with lower bulk moduli, such as magnesium, show a relatively moderate increase in melting temperature. The findings provide critical insights into the thermodynamic stability of metals under extreme conditions, supporting applications in geothermal studies, planetary modeling, and materials science. Overall, this work demonstrates that Lindemann’s ratio remains a reliable theoretical framework for predicting melting behavior at high pressures, highlighting the importance of vibrational dynamics in understanding phase stability and the melting mechanisms of metals under extreme environments.

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