Role of lattice structure on the Lindemann fusion theory of metals

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Abstract
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 A1 (FCC), A2 (BCC) and A3 (HCP) type crystals. The lattice factors Lj of these metals and a new physical quantity rho j identical to Lj delta j= alpha /Lj 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)12/. Vibration amplitudes of atoms Aj (root-mean-square displacements Aj (DWL)=((Ui2))12/), 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 Lj. The L1.2 and rho 1.2 are constants, L3( gamma ) and rho 3( gamma ) for HCP metals are smoothly varying functions of the axial ratio gamma =c/a, although L3 (HCP) and delta 3 (HCP) are not. A firm conclusion is made that the Lindemann constants Lj 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.

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