Homogeneous Nucleation in Metal Vapors
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Homogeneous Nucleation in Metal Vapors. 4. Cluster Growth Rates from Light Scattering D. J. Frurip and S. H. Bauer' Department of Chemistry, Cornell University, Ithaca, New York 14853 (Received July 19, 1976; Revised Manuscript Received March 7, 1977)
We describe an experimental arrangement for recording the turbidity developed in a metal vapor while it is undergoing homogeneous nucleation and condensation,and concurrently recording the intensity of light scattered at 90' by the growing clusters. The supersaturated vapors were generated by shock heating metalloorganics from which the attached groups (CH,; CO) were stripped within the first few microseconds after passage through a shock front. The turbidity and scattered intensity data were collected with a time resolution of approximately 2 ps. Absolute time dependent scattering cross sections were evaluated for lead (vapor e clusters). The experimental configuration was calibrated with gases for which the scattering cross section are available (Ar and CHFZC1). From the ratio of [I,,,/ln(lo/Z)] we deduced separately the mean radii as a function of time, and the corresponding cluster densities. Our results are well accounted for by a simple kinetic theory model. As a consequence, we have an indirect procedure for estimating the condensation flux (nuclei generated sec-' ~ m - at ~ critical ) supersaturation and the time-dependent parameters for the cluster size distribution function.
Introduction Among the various diagnostics we tested for observing nucleation-condensation processes in metal vapors, we found four which proved generally applicable. The onset of avalanche condensation can be established by recording a sudden rise either in the black-body radiation emitted from the tiny particles or in the turbidity of the sample. Thus we determined the variation of the critical supersaturation ratio with temperature for iron,' lead, and bismuth.2 The dependence of the heat of condensation on cluster size for iron was estimated from measurements of post-shock density gradients3 [applied to clusters: 40 < n < 20001. In this report we demonstrate the use of light scattering to follow growth rates of clusters of lead [applied to lo4 < n < 2 X lo6]. As a consequence we obtained approximate net condensation fluxes and cluster size distributions. The latter were verified by electron microscopic examination of the final metallic powders. Turbidity data provide values for the product of the number density, N = EN,, and the average volume, ( u ) . To uncouple the two magnitudes one must either estimate the density directly or introduce an assumption. In a procedure described by Kerkeq4 generally used for static systems, one assumes that the total mass of material is in the condensed phase; then, knowledge of the initial concentration is sufficient to uncouple N from ( u ) . In the present experiments, since we do not have a priori knowledge of N ( t ) , we measured simultaneously the turbidity and the intensity of light scattered from the growing clusters. For absorbing spheres, the latter is proportional to the product N ( u'), thereby providing the means for estimating N ( t ) and ( u ) separately. Although light scattering measurements have been applied extensivelyto a variety of systems few studies were made of homogeneous nucleation from the gas phase. Vietti and Schuster5determined the growth rates of large (- lo4A) water droplets in air by detection of oscillations in the intensity of scattered light from a He-Ne source. Stein' investigated the angular and wavelength dependence of scattered light from a cloud of ice particles formed by homogeneous nucleation in nozzle expansion, and determined the average particle size and the density as a function of the supersaturation ratio. Ethyl alcohol droplets were similarly studied by Clumpner. He mea-
sured the angular dependence of Rayleigh scattering. Graham and Homer' investigated Rayleigh scattering from lead particles generated by shock pyrolysis of Pb(CH3)4. They were primarily interested in the coagulation process, after all the monomer had entered the condensed phase and did not investigate the early growth regime.
Scattering-Turbidity Theory (A Brief Summary) The ratio of transmitted to incident light intensity is
I l l o = exp[-NICext] (1) where the extinction coefficient is given by Mie theory,' for small absorbing spheres.
(3) For Rayleigh scattering from spherical particles (size nt is not dependent on the presence of a maximum in the free-energy function, but is sensitive to the supersaturation ratio. The time to attain steady state was estimated, and we formulated an expression for the condensation flux at that condition. I. Introduction In this report we present a self-consistent kinetic model for homogeneous nucleation and condensation of liquid droplets from a vapor. The specific example used to illustrate our procedure is the condensation of atomic iron generated under supersaturated conditions by shock heating Fe(COI5highly diluted in argon.’ While several kinetic models for homogeneous nucleation have been
described,’ in our opinion these are hybrids because they incorporated relations based on the liquid-drop model, and utilized undefinable quantities such as a surface free energy for clusters of the order of 10 monomer units. This obscured a significant feature of the approach to steady state. The self-consistent kinetic model (SCKM) will be contrasted with those previously published. As initially formulated, all models have many aspects of similarity. The Journal of Physical Chemistry, Vol. 81, No. 10, 1977
