Crystal growth nucleation and equalization of Fermi energies of intrinsic nuclei and glass-forming melts

Abstract

The energy saving produced by the equalization of Fermi energies of a crystal and its melt is determined by adding a negative fraction ϵsl(T) of the fusion heat to the Gibbs free energy change ΔG2ls associated to a charged crystal formation in glass-forming melts. In bulk metallic glasses, ϵls(Tm) is larger than 1 at the melting temperature Tm and only determined by the knowledge of the free volume disappearance temperature. When the unmelted intrinsic crystals have a radius Rnm much smaller than the critical radius R*2ls, ϵsl(T) is strongly reduced by the quantification of electronic levels in the large electrostatic potential created by the electron transfer from the crystal to the melt. The reduced value ϵnm0 of ϵsl(Tm) for Rnm=3.2E-10m in Zr41.2Ti13.8Cu12.5Ni10Be22.5 is determined by comparing the experimental Time-Temperature-Transformation diagram measured by electrostatic levitation to the calculated one. It exactly corresponds to the first energy level of one s state electron moving in the same spherical attractive potential and in vacuum in spite of the fact that, in a metal, the charge screening is built by many-body effects.