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The scaling of nucleation rates

Metallurgical Transactions A volume 23, pages 1863–1868 (1992)Cite this article

Abstract

The homogeneous nucleation rate,J, forT → T c can be cast into a “corresponding states” form by exploiting scaled expressions for the vapor pressure and for the surface tension, δ. In the vapor-to-liquid case with δ= δ0[T c -T], the classical cluster energy of formation /kT = [16π/3] • Ώ3 [T c -1]3/(lnS)2 = [x0/x]2, where Ώ ≡ δ0/[k ñ2/3] and ñ is liquid number density. [1] The Ώ≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications ofσ and Ώ.[2]) The above [x0/x]2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data.[3,4] In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with lnJ ≈ const. -[x0/x]2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γc), whereT c is the inverse thermal wavelength cubed per second atT =T c . The ln (Γc) is ≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at smalln, the discrete integer behavior ofn, and a configurational entropy term, τ ln (n), is presented.

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Authors and Affiliations

  1. University of Missouri-Rolla, 65401, Rolla, MO

    Barbara N. Hale (Professor of Physics)

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  1. Barbara N. Hale
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Additional information

This paper is based on a presentation made in the “G. Marshall Pound Memorial Symposium on the Kinetics of Phase Transformations” presented as part of the 1990 fall meeting of TMS, October 8–12, 1990, in Detroit, MI, under the auspices of the ASM MSD Phase Transformations Committee.

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Hale, B.N. The scaling of nucleation rates. Metall Mater Trans A 23, 1863–1868 (1992). https://doi.org/10.1007/BF02647536

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Keywords

  • Surface Tension
  • Metallurgical Transaction
  • Nonane
  • Nucleation Rate
  • Free Energy Difference