Thermodynamic formula for evaluating the reversible work to form a critical nucleus and influence of critical nucleus si
- PDF / 1,160,868 Bytes
- 13 Pages / 597 x 774 pts Page_size
- 115 Downloads / 165 Views
I.
INTRODUCTION
U N D E R the steady-state approximation, nucleation rate J, per unit time and per unit volume of the parent phase, is given by J = ZKN*
[1]
where Z denotes the Zeldovich or the nonequilibrium factor, K the rate of atomic transfer into a critical nucleus from the parent phase, and N* the metastable equilibrium concentration of the critical nucleus. For condensed parent phases, N* is given by N* = N exp ( - WreV/kT)
[2]
with N the number of nucleation sites per unit volume, for which the number density of atoms or molecules is usually taken in homogeneous nucleation, W rev the reversible work to form a critical nucleus from the parent phase, k the Boltzmann constant, and T the absolute temperature. For the nucleation of condensed phases from the vapor, N* is given by I~,2] N* = ~I~pN exp ( - wrr
[3]
where dPLp denotes the Lothe-Pound factor. The value for qbLpis estimated to be about 1017 in a typical case by Pound and co-workers, [m,3] but Reiss and Katz, [4] Reiss, tSl and Kikuchi t61 estimated much smaller values for ~L~. For the details of the consideration and the related articles, we refer the reader to the review articles. T M 7] The factor similar to qbLp in Eq. [3] is conceptually required also in Eq. [2], but it will not be numerically significant.
K. NISHIOKA, Professor, is with the Division of Mechanical Sciences, Department of Mechanical Engineering, University of Tokushima, 2-1 Minamijosanjima, Tokushima 770, Japan. 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
Since J in Eq. [1] is exponentially dependent o n W rev, the dependence of the steady-state nucleation rate on the supersaturation is largely determined by that of W ~ev. This influence of the supersaturation on the value of W rev is, in turn, mainly through that on the size of the critical nucleus. Thus, as long as the nucleation may be assumed to be in steady state, the concept of the critical nucleus plays the principal role and the evaluation of the reversible work to form a critical nucleus is the main problem in predicting the nucleation rate. Note that the information on the subcritical or the supercritical clusters is needed only in evaluating the factor Z, which does not depend strongly on supersaturation. The first part of this articles summarizes, incorporating the recent developments, t81 the interfacial thermodynamics which is applicable to small nuclei as well as to macroscopic interfaces. Then, recent works i9,~~ on the size and the composition dependence of the interfacial tension are presented. The value of the interfacial tension is the most important quantity in evaluating W rev accurately. Lastly, we clarify the relation between the Gibbs formulae and the commonly used ones for determining the size and the composition of the critical nucl
Data Loading...
