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

The energy saving resulting from the equalization of Fermi energies of a crystal and its melt is added to the Gibbs free-energy change ΔG_2ls 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 T_m in agreement with a thermodynamics constraint. The homogeneous nucleation critical temperature T₂, the nucleation critical barrier ΔG_2ls∗/k_BT and the critical radius R∗_2ls are determined as functions of ε_ls(T). In bulk metallic glass forming melts, ε_ls(T) and T₂ only depend on the free-volume disappearance temperature T_0l, and ε_ls(T_m) is larger than 1 (T_0l>T_m/3); in conventional undercooled melts ε_ls(T_m) is smaller than 1 (T_0l>T_m/3). Unmelted intrinsic crystals act as growth nuclei reducing ΔG_2ls∗/k_BT and the nucleation time. The temperature-time transformation diagrams of Mg₆₅Y₁₀Cu₂₅, Zr_41.2Ti_13.8Cu_12.5Ni₁₀Be_22.5, 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 ΔG_2ls∗/k_BT. The energy-saving coefficient ε _nm(T) of an unmelted crystal of radius R_nm is reduced when R_nm ≪R∗_2ls; ε_nm 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.