“A Study on the Theoretical Model for Pressure Dependence of the Melting Curve for Some Metals Using Lindemann’s Melting Law.”

Authors: NAND KISHOR

DOI: https://doi.org/10.37082/IJIRMPS.v13.i6.232854

Short DOI: https://doi.org/hbft6p

Country: India

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Abstract: The melting behaviour of metals under varying pressure conditions is a fundamental problem in condensed matter physics and materials science, with important implications for geophysics, metallurgy, and high-pressure technology. In this study, a theoretical model is developed to analyze the pressure dependence of the melting temperature for selected metals based on Lindemann’s melting law. Lindemann’s criterion relates the melting temperature to the amplitude of atomic vibrations and interatomic spacing, suggesting that a solid melts when the root-mean-square atomic displacement reaches a critical fraction of the interatomic distance[1]. By combining this principle with the equations of state (EOS) for metals, the study derives an analytical expression that links melting temperature with pressure. The model incorporates parameters such as atomic volume, Grüneisen parameter, and bulk modulus, allowing for a detailed description of melting behavior under compression[2].The theoretical results are compared with available experimental data for several representative metals, including aluminum, copper, iron, and nickel. The comparison demonstrates good agreement, validating the reliability of the developed model across a broad range of pressures. The findings confirm that the melting temperature increases with pressure in a nonlinear manner, consistent with both experimental observations and thermodynamic expectations[3]. Moreover, deviations observed at extreme pressures are discussed in terms of anharmonic effects and changes in electronic structure[4].This work contributes to a deeper understanding of the thermodynamic and vibrational properties governing melting transitions. It also provides a simple yet powerful theoretical framework for predicting melting curves of metals where experimental data are scarce or difficult to obtain. The results have potential applications in high-pressure physics, planetary core modeling, and materials design under extreme environment[5].

Keywords: Lindemann’s melting law; Pressure dependence; Melting curve; Theoretical model; Metals; Equation of state; Grüneisen parameter; High-pressure physics; Melting temperature; Thermodynamic properties.

Paper Id: 232854

Published On: 2025-12-16

Published In: Volume 13, Issue 6, November-December 2025

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