The scaling of nucleation rates
- PDF / 579,554 Bytes
- 6 Pages / 597 x 774 pts Page_size
- 11 Downloads / 207 Views
I.
INTRODUCTION
S C A L E D models for nucleation allow the plotting and analysis of experimental data for a spectrum of materials simultaneously. In some applications, the scaled models can provide quick estimates of critical supersaturation ratios, Scr, or supercoolings required for onset of nucleation; the latter estimates are particularly useful when numerical substance data are unavailable. But the models offer something more far-reaching: they allow one to isolate the universal temperature dependences and to focus on the substance parameters which dominate the nucleation process. As used here, the term "scaled nucleation model" refers to a formalism in which the nucleation rate, J, (and all expressions derived from J ) is expressed in terms of T/Tc, P / P c , and if/tic, m The latter are the reduced temperature, pressure, and number density, respectively, and the subscript r denotes critical point quantities. From the critical point quantities, one can form factors (such as Pc/~ckTc "~ 3/8) having numerical values nearly substance independent. Finally, scaled functional forms (generally available in the literature f5,61) for equilibrium vapor pressure, surface tension, and number density are substituted into the formalism. [L2,7] The final result is an expression for J which explicitly displays the "corresponding states" properties of nucleating substances. The scaling of J is not a new idea. Near the critical point (at T ~ T~), such scaling of the nucleation rate has been considered extensively, t8-141 In particular, Binder ~81 presented a scaled form for the (slightly modified) classical nucleation rate valid near Tc. The major difference between Binder's form and the scaled models described here is the applicable temperature range: the expressions BARBARA N. HALE, Professor of Physics, is with the University of Missouri-Rolla, Rolla, MO 65401. 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. METALLURGICAL TRANSACTIONS A
presented here for J and S are not intended for use near Tc but, rather, for T ~ Tc--where most of the data exists. We point out that the temperature dependence used in the present models, [ T J T - 1], is different from the e = - [ 1 - T/Tel of critical point formalisms. Both forms are equivalent (for all practical purposes) in the standard analysis near Tc. However, for T r To, there appears to be no advantage to a series expansion in e, and the [ T c / T - 1] form emerges naturally from the placement of T in the exponential denominator of the Boltzmann factor. It is interesting that use of [ T J T - 1], rather than e, in some critical point formalisms can dramatically extend the range of applicability, t151 This result is not widely used (although recognized) by those working with critical point phenomena. Some time ago, Wu et al. 1161plotted In Scr v s
Data Loading...
