Crystal growth nucleation and Fermi energy equalization of intrinsic spherical nuclei in glass-forming melts

Abstract

The energy saving resulting from the equalization of Fermi energies of a crystal and its melt is added to the Gibbs free-energy change ΔG2ls associated with a crystal formation in glass-forming melts. This negative contribution being a fraction ε ls(T) of the fusion heat is created by the electrostatic potential energy −U0 resulting from the electron transfer from the crystal to the melt and is maximum at the melting temperature Tm in agreement with a thermodynamics constraint. The homogeneous nucleation critical temperature T2, the nucleation critical barrier ΔG2ls∗/kBT and the critical radius R∗2ls are determined as functions of εls(T). In bulk metallic glass forming melts, εls(T) and T2 only depend on the free-volume disappearance temperature T0l, and εls(Tm) is larger than 1 (T0l>Tm/3); in conventional undercooled melts εls(Tm) is smaller than 1 (T0l>Tm/3). Unmelted intrinsic crystals act as growth nuclei reducing ΔG2ls∗/kBT and the nucleation time. The temperature-time transformation diagrams of Mg65Y10Cu25, Zr41.2Ti13.8Cu12.5Ni10Be22.5, Pd43Cu27 Ni10P20, Fe83B17 and Ni melts are predicted using classic nucleation models including time lags in transient nucleation, by varying the intrinsic nucleus contribution to the reduction of ΔG2ls∗/kBT. The energy-saving coefficient ε nm(T) of an unmelted crystal of radius Rnm is reduced when Rnm ≪R∗2ls; εnm is quantified and corresponds to the first energy level of one s-electron moving in vacuum in the same spherical attractive potential −U0 despite the fact that the charge screening is built by many-body effects.