DOI: 10.11648/j.wjmst.20260303.12 ISSN: 3070-1546

Study the Melting Curves of Metals to Very High Pressure and Temperature Can Be Predicted by the Theoretical Model in Lindemann’s Melting Law

Nand Kishor, Amar Kumar
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The study of melting curves of metals under very high pressures and temperatures is essential for understanding their thermodynamic and structural behavior in extreme conditions. In this research, a theoretical model has been developed to predict the pressure dependence of the melting temperature for selected metals based on the Lindemann’s melting law and its modifications. The model relates the melting temperature to vibrational properties of the lattice, atomic volume, and Grüneisen parameter, enabling estimation of melting points at pressures beyond experimental limits. The theoretical framework assumes that melting occurs when the amplitude of atomic vibrations reaches a critical fraction of the interatomic spacing, and this criterion is used to derive a quantitative relationship between pressure and melting temperature. The proposed model has been applied to various metals such as aluminum, copper, iron, and nickel to compute their melting curves up to several hundred gigapascals. The calculated results show a strong agreement with available experimental and simulation data, indicating that the model effectively captures the essential physics of the melting process. The study reveals that the melting temperature increases nonlinearly with pressure, primarily due to the compression of atomic volume and enhanced lattice stability at high pressures. Furthermore, the model provides valuable insights into the influence of atomic mass, bulk modulus, and an harmonic effects on the melting behavior of metals. Such theoretical predictions are particularly important for fields like materials science, geophysics, and planetary science, where direct experimental measurements at extreme conditions are challenging. Overall, the developed model offers a reliable and simplified approach to estimate melting curves, contributing to a deeper understanding of phase stability and thermodynamic properties of metals under extreme environments.

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