  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.
