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Volume 16 Issue 4
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“Extension of Lindemann’s formula to study the Pressure dependence of melting temperature for some metals”

Author(s) Mr. NAND KISHOR, Prof. Dr. AMAR KUMAR
Country India
Abstract The melting behavior of metals under high pressure has been a subject of considerable interest in solid-state physics and materials science due to its fundamental and technological importance. Lindemann’s melting law, proposed in 1910, provides one of the earliest semi-empirical approaches to correlate the melting temperature of a crystalline solid with the amplitude of atomic vibrations. According to Lindemann’s, melting occurs when the root-mean-square amplitude of lattice vibrations exceeds a critical fraction of the [1]interatomic spacing. While the classical form of the Lindemann’s formula has been successful in predicting ambient-pressure melting points for many metals, its direct applicability at elevated pressures remains limited, primarily due to the neglect of pressure-induced changes in elastic and vibrational properties.[2]In the present work, an extended form of Lindemann’s formula is employed to study the pressure dependence of melting temperatures for selected metals[3]. The modification involves incorporating pressure-dependent variations of volume, Grüneisen parameter, and bulk modulus into the melting criterion, thereby improving its predictive accuracy for high-pressure conditions. Using an equation of state (EOS) to describe the compression behavior of metals, the revised model establishes a more realistic relationship between melting temperature and pressure. Calculations are carried out for representative metals such as aluminum, copper, iron, and nickel, covering a wide range of compressions relevant to both laboratory and geophysical conditions.[4,5] The results indicate that the modified Lindemann’s approach successfully reproduces the experimentally observed positive pressure dependence of melting temperature, with values that are in close agreement with available high-pressure melting data and other theoretical models. For transition metals like iron and nickel, which are crucial in planetary core studies, the model yields melting curves that align with geophysical estimates [6] for the Earth’s inner core boundary conditions. Moreover, the study highlights the sensitivity of the predicted melting curve to the choice of Grüneisen parameter formulation and EOS, suggesting that accurate thermodynamic input data are essential for reliable predictions.[7] This extended application of Lindemann’s law not only bridges the gap between classical melting theory and modern high-pressure physics but also provides a computationally simple yet effective tool for estimating melting curves of metals under extreme conditions. Such insights are valuable for understanding phase stability, material processing, and planetary interior modeling, where knowledge of melting behavior at high pressures plays a critical role.[8]
Keywords Lindemann’s melting law; extended Lindemann formula; pressure dependence of melting temperature; high-pressure physics; metals; aluminum; copper; iron; nickel; Grüneisen parameter; bulk modulus; equation of state (EOS); lattice vibrations; atomic displacement; melting curve; phase transition; geophysics; planetary core modeling; thermodynamics; solid-state physics; crystallography; high-pressure melting; material science; elastic properties; vibrational amplitude; compression behavior.
Field Physical Science
Published In Volume 16, Issue 4, October-December 2025
Published On 2025-10-25
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