Comparing Melting Curves of Metals Using the Equation of State and Lindemann's Law

Our study’s primary goal is to accurately predict the equation of state required for calculating the pressure-dependent melting curves of metals. We introduce a unique model for the melting curve, utilizing various equations of state (EOS) such as Murnaghan EOS, Kholiya EOS, Goyal-Gupta EOS, Usual-Tait EOS, Singh and Kao EOS, and Modified Lennard–Jones EOS. This model, rigorously tested and compared with Lindemann’s and available experimental data, establishes the relationship among pressure, bulk modulus, pressure derivative of bulk modulus, and volume compression. Our findings conclusively demonstrate that a significant increase in melting temperature is directly linked to a substantial rise in bulk modulus and a gradual decrease in the first-order pressure derivative of bulk modulus. This study provides unprecedented insights into the fundamental understanding of the effect of pressure on melting temperature. The model we have developed is highly reliable for extrapolating melting temperature to high pressure, instilling confidence in its application. Notably, our study finds that Murnaghan EOS is more suitable for predicting the melting temperature of the metal. Importantly, our results agree with Lindemann’s law and experimental values, validating our approach.