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 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.

• metallic glasses
• intrinsic growth nuclei
• crystal nucleation
• Fermi energy effects
• unmelted intrinsic crystals
• glass-forming melts

Acknowledgments

Thanks are due to Eric Beaugnon, Philippe Odier, Jean-Louis Soubeyroux, to the referees for manuscript review, and to Jacques Friedel for discussions. Commenting on this paper, Yoshihiko Hirotsu considers that intrinsic nuclei could be identified to ‘medium range order’ (MRO) clusters only if the interface cluster-matrix is very diffuse at room temperature. The MRO cluster size depends on the overheating rate and then, these entities exist above the melting temperature even if the cooling rate tends to slightly modify their radii [49]. The Fe₈₅–B₁₅ kinematic viscosity is irreversible between θ = 0 and θ≅0.23 after an overheating up to θ=0.27 in good agreement with our prediction θ≅ε_ls0=0.3 [50] corresponding to the melting temperature of all surviving crystals.