Role of lattice structure on the Lindemann fusion theory of metals

A simple atomistic model for the fusion process of metals is derived from a combination of the atomic model of the lattices and the simple theory of harmonic vibration of the atoms of A 1 (FCC), A 2 (BCC) and A 3 (HCP) type crystals. The lattice factors L j of these metals and a new physical quantity rho j identical to L j delta j = alpha /L j with j=1, 2 and 3 for the fusion transitions BCC to liquid, FCC to liquid and HCP to liquid, involved with the vibrational instability fusion hypothesis of Lindemann, are defined. The derived structure-dependent simple fusion equation is related to a similar equation obtained from the combination of the Debye-Waller-Lindemann (DWL) formulae through a numerical factor f=(3/2) 1 2/. Vibration amplitudes of atoms A j (root-mean-square displacements A j (DWL)=((U i 2 )) 1 2/), Lindemann parameters delta j and the physical quantities rho j of 54 metals are calculated through the simple and DWL sets of equations above by using the empirical Lindemann constants L j . The L 1.2 and rho 1.2 are constants, L 3 ( gamma ) and rho 3 ( gamma ) for HCP metals are smoothly varying functions of the axial ratio gamma =c/a, although L 3 (HCP) and delta 3 (HCP) are not. A firm conclusion is made that the Lindemann constants L j and Lindemann parameters delta j for the BCC, FCC and HCP metals are significantly different and the Lindemann law holds for each structure separately including the HCP metals.