The generalized Lindemann melting coefficient

TL;DR

This paper uncovers a link between the Lindemann melting coefficient and periodic table groups, providing specific values that improve melting temperature predictions for elements.

Contribution

It reveals a periodic group-based pattern in the Lindemann coefficient, enabling more accurate melting temperature calculations for multiple elements.

Findings

Identified 12 distinct Lindemann coefficient values for periodic groups.

Recalculated melting temperatures match experimental data for 39 elements.

Suggests periodic group dependence of the Lindemann coefficient.

Abstract

Lindemann developed the melting temperature theory over 100 years ago, known as the Lindemann criterion. Its main assumption is that melting occurs when the root-mean-square vibration amplitude of ions and atoms in crystals exceeds a critical fraction, h of the inter-atomic spacing in crystals. The Lindemann coefficient h is undefined and scientific papers report different h values for different elements. Here we present previously unobserved data trends pointing to the fact that the Lindemann coefficient could be linked to the periodic groups of the periodic table, having an exact value for each element belonging to a given periodic group. We report 12 distinctive Lindemann coefficient values corresponding to 12 groups of the periodic table containing solid elements with identifiable melting temperature. Using these vales, the recalculation of the melting temperatures indicates a good match to the experimental values for 39 elements, corresponding to 12 out of 15 periodic groups. This newly observed result opens up the possibility of further refining the Lindemann melting criterion by stimulating analytical studies of the Lindemann coefficient in the light of this newly discovered result.