DOI: 10.11648/j.wjmst.20260303.11 ISSN: 3070-1546

The Melting Temperature of FCC Crystal Na Without the Criterion Lindemann's Melting Law

Nand Kishor, Amar Kumar
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The Lindemann’s melting criterion, which posits that a crystal melts when the root-mean-square atomic displacement reaches a critical fraction of the interatomic distance, has been a cornerstone of simple melting theory for over a century. However, its phenomenological nature and system-dependent critical value limit its predictive power from first principles. This work presents a determination of the melting temperature (T m ) of face-centered cubic (FCC) crystalline sodium using molecular dynamics (MD) simulations, deliberately bypassing the Lindemann’s criterion. We employ a well-established embedded-atom method (EAM) potential to model interatomic interactions. The melting point is identified directly from the collapse of long-range order by monitoring the evolution of potential energy, radial distribution function, and mean-squared displacement (MSD) upon heating. Furthermore, we utilize the rigorous coexistence method (or "solid-liquid interface" method), where a direct two-phase simulation of solid FCC Na in contact with liquid Na is performed at various temperatures to pinpoint the true thermodynamic melting point as the state where the interface remains stationary. Our results for FCC Na, a model alkali metal, provide a benchmark melting temperature derived solely from direct observation of the solid-liquid phase transition. This approach not only offers a more fundamental determination of T m but also allows for a critical assessment of the validity and limitations of the Lindemann’s rule when compared a posteriori with the computed atomic vibrational amplitudes at the predicted melting point.

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