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 G 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 −U 0 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 T 2 , the nucleation critical barrier G * 2ls /k B T and the critical radius R * 2ls are determined as functions of ε ls (T ). In bulk metallic glass forming melts, ε ls (T ) and T 2 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 G * 2ls /k B T and the nucleation time. The temperature-time transformation diagrams of Mg 65 Y 10 Cu 25 , Zr 41.2 Ti 13.8 Cu 12.5 Ni 10 Be 22.5 , Pd 43 Cu 27 Ni 10 P 20 , Fe 83 B 17 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 G * 2ls /k B T . 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 −U 0 despite the fact that the charge screening is built by many-body effects.

Crystallization of Supercooled Liquid Elements Induced by Superclusters Containing Magic Atom Numbers

“…The homogeneous nucleation temperature T 2 is equal to T m /3 (or θ 2 = −2/3) in liquid elements and ε ls (θ) is equal to zero at this temperature [15,24].…”

“…where ε nm0 is the quantified energy saving coefficient of an n-atom cluster at T m depending on the spherical nucleus radius R [24]. This thermal variation has for consequence that the fusion entropy per mole of a cluster of radius R is equal to the fusion entropy ΔS m of the bulk solid [15,24] …”

“…This thermal variation has for consequence that the fusion entropy per mole of a cluster of radius R is equal to the fusion entropy ΔS m of the bulk solid [15,24] …”

“…Equations (21)- (24) are now used to calculate the homogeneous formation reduced temperature θ 13c of 13-atom clusters in a melt cooled below T m from thermodynamic equilibrium state at T m and the crystallization reduced temperature θ c that they induce in liquid droplets of 10 micrometers in diameter. In Table 2, 38 liquid elements are considered.…”

“…In this article, each cluster having a radius smaller than the critical radius has its own energy saving coefficient ε nm depending on θ 2 , n and its radius R nm . In this case too, the cluster surface energy is a linear function of ε nm instead of a function of θ or T [20][21][22][23][24][25]. The Gibbs free energy change derivative [d(ΔG 2ls )/dT] p = −ΔS m at T m continues to be equal to the entropy change whatever the particle radius is because (dε ls /dT) T=Tm is equal to zero.…”