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Nucleation Catalysis

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Principles of Solidification

Abstract

Melting and solidification are reciprocal examples of first-order phase transformations, i.e., transformations exhibiting discontinuities in the first-order thermodynamic properties of the ‘parent’ and ‘daughter’ phases, such as the volume, entropy, and enthalpy. First-order phase changes can resist initiation—even from a highly supercooled or supersaturated metastable parent phase—as energetic barriers develop that inhibit the formation of viable embryos of the daughter phase, which once formed, can grow spontaneously. Stable nuclei require ordering of numerous atoms or molecules, composition change, creation of large interfacial area per unit volume, and elastic straining, all of which require the accumulation of ‘excess’ free energy. The additional free energy needed to accomplish nucleation is provided by thermodynamic fluctuations that momentarily allow a miniscule region of the metastable parent phase to depart significantly from its average order, composition, and free energy.

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Notes

  1. 1.

    Various models of interphase transition zones are described in Section 8.2.4, and the reader should also see the Gibbsian model of a sharp interface, portrayed in Fig. 8.5, and that for a diffuse interface in Fig. 8.7.

  2. 2.

    A negative interfacial energy, if it ever occurred, would have the bizarre effect of potentially promoting endless spontaneous area increase—a phenomenon, fortunately, never encountered in phase transformations.

  3. 3.

    Again, the reader is cautioned that classical nucleation theory makes no distinction between the phase comprising the nuclear volume and the bulk crystalline solid. That approximation of classical nucleation theory, as discussed in Section 12.3.1, works reasonably well even into the nanoscopic regime of nuclear clusters.

  4. 4.

    The simplified exponential form of the Maxwell-Boltzmann probability distribution used in Eq. (12.14) to calculate the probabilty of a successful fluctuation remains valid as long as \({\varDelta{G}^{\star}\gg{k_B}{T}\approx0.09}\) ev, at \({T=1,000}\) K, which is true as shown by the examples applied above to Eq. (12.15).

  5. 5.

    Clearly, over a large range of supercooling the three interfacial energies, \(\gamma_{s\ell}\), \(\gamma_{\ell \alpha}\), and \(\gamma_{s\alpha}\), shown as surface tension vectors in Fig. 12.5, can change individually, which would alter the equilibrium value of ψ ⋆.

  6. 6.

    Calculation of the nuclear strain energy density, E ε , in the free energy expressions, Eqs. (12.40) and (12.42), by applying linear elasticity requires stipulation of the shape of the nuclear volume, as well as knowing the elastic stiffnesses of both the crystalline nucleus and the substrate. Such data are difficult to obtain.

  7. 7.

    The verb ‘fragment’, used here is not meant to imply merely the mechanical breakage, or disruption, of the advancing dendrites, but also includes an array of thermo-chemical processes including dissolution, coarsening, and local re-melting of already solidified crystallites.

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Authors and Affiliations

  1. Materials Science and Engineering Department, University of Florida, Gainesville, FL, 32611-6400, USA

    Martin Eden Glicksman

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Correspondence to Martin Eden Glicksman .

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Glicksman, M.E. (2012). Nucleation Catalysis. In: Principles of Solidification. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7344-3_12

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