Lindemann melting criterion and the Gaussian core model

A series of molecular-dynamics calculations has been carried out to examine melting in the classical Gaussian core model at reduced density ${\rho }^{*}=0.2\mathrm{}$. The stable crystal form at this density is body-centered cubic. Thermal equilibrium values of mean-square particle displacement have been evaluated over the entire temperature range below melting. As a result the Lindemann ratio $f$ (of rms displacement to lattice spacing at the melting point) was found to be 0.160±0.005, considerably larger than Shapiro's estimate for several bcc metals. This finding further undermines the Lindemann hypothesis that $f$ should be constant for all solids of a given crystal structure at their melting points.