K.C. Russell

Nucleation in solids: The induction and steady state effects

Abstract The processes of nucleation, growth and coarsening combine to dictate the final particle density produced by a phase transformation (ref. 1). The entire process, known as “umlosung,” is illustrated in Fig. 1, which depicts the number of particles vs. time, for a hypothetical phase transformation. The regions are: 1. The induction period, τ, required to establish steady-state nucleation conditions. 2. Steady state nucleation, where the number of particles increases linearly with time. 3. Decreasing nucletion rate, due to a reduction in supersaturation by growing particles. 4. Capillarity-induced coarsening (or Ostwald ripening), where the larger particles grow, but only by cannibalizing the smaller, less stable particles. The number of particles now decreases with time. In any particular situation, any of these four stages may be dominant--the microstructure may be dominated on one extreme by a long induction period (as in some glasses (ref. 2)), or by coarsening (as for some carbides in steels (ref. 3)). This manuscript will be concerned only with stages I and II, transient and steady-state nucleation. The reader is referred elsewhere for discussion of growth (refs. 4–6) and coarsening (refs. 7–9) phenomena.

Wetting of ceramic particulates with liquid aluminum alloys: Part II. Study of wettability

Wetting phenomena in ceramic particulate/liquid Al-alloy systems were investigated experimentally using a new pressure infiltration technique developed by the authors. Studies were performed on two different ceramic particulates, SiC and B4C, with four different liquid aluminum alloy matrices, pure Al, Al-Cu, Al-Si, and Al-Mg. Five major variables tested to study wetting phenomena in ceramic/Al-alloy systems were holding time, melt temperature, alloying element, gas atmosphere, and particulate. Metal: ceramic interfaces were investigated with optical microscopy, SEM, EPMA, and Auger Electron Spectroscopy (AES) in order to understand better the wetting process. The threshold infiltration pressure decreased with, temperature as well as with pressurization time for all the ceramic/metal systems. A strong correlation was found between the alloying effect on the threshold pressure and the free energy of formation of oxide phase of the alloying element. More reactive alloying elements were more effective in improving wettability. In air atmospheres, the threshold pressure usually increased markedly as a result of a thick oxide layer formation on the liquid front. Compacts of B4C particulates showed lower threshold pressures than those of SiC, particulates. Fracture occurred in a generally brittle manner in infiltrated SiC, specimens. AES element profiles on the fracture surfaces showed fast diffusion of Si, and pile-up of C at the metal∶SiC boundaries which promoted fracture through the carbon-rich layer. The fracture surfaces of infiltrated B4C specimens indicated plastic deformation, hence a more ductile failure mode.

Influence of crystallography on aspects of solid-solid nucleation theory

Expressions for the major variables in the general rate equation for solid-solid nucleation were developed on the basis of various models of the critical nucleus shape during homogeneous and heterogeneous nucleation. These models are based upon spheres, but in some a facet was incorporated at one boundary orientation to represent the presence of a partially or fully coherent structure. Gibbs’ relationship for the critical radius is applicable to all of the models. The other variables in the nucleation rate equation are affected by the model and by faceting. Reduction of AG* by faceting is concluded to be the primary cause for the presence of reproducible lattice orientation relationships and for the existence of transition phases during precipitation from solid solutions.

Wetting of ceramic particulates with liquid aluminum alloys: Part I. Experimental techniques

An experimental technique for evaluation of wettability of solid particulates with liquid metal was developed. Uniformly packed powder specimens were prepared with a tamping device specially made for the present experiment, and wetting tests were conducted by pressure infiltration of liquid Al-alloys into the powder specimens. The threshold pressure for infiltration was used as a measure of wettability. With this technique, wettabilities were measured for 10 μm diameter SiC and B4C particulates by several Al-based alloys. Threshold pressures obtained from this technique showed reproducibility to approximately ±7 kPa. Microstructures of infiltrated powder specimens indicated planar front infiltration with no disruption of powder compact during infiltration test and virtually no porosity.

Precipitation at interphase boundaries

Three problems in precipitation at interphase boundaries are examined. 1) The classu argument as to the particular phase in which such a precipitate nucleates is shown to be irrelevant; except in a special situation, the critical nucleus must normally penetrate both phases forming the interphase boundary. 2) The relative penetrations into the two phases achieved during growth can be very different than those expected during nucleation; hence, deductions about the nucleation process based upon observations on growth morphologies can be quite misleading. 3) The observations of Honeycombe and others that the nucleation of carbides at austenite: ferrite boundaries occurs predominantly at the low energy, immobile broad faces of ledges rather than at the higher energy, mobile risers of ledges are accounted for theoretically on the basis of the high velocities of the risers preventing nucleation. Example calculations on a Ti-Ni alloy indicate that precipitation at the risers of ledges may become possible in substitutional systems, but only at lower homologous temperatures, and if the migration of these boundaries is still controlled by volume diffusion while nucleation is controlled by interfacial diffusion.

Nucleation of Supersaturated Vapors in Nozzles. I. H2O and NH3

Measurements have been made of the results of homogeneous nucleation of NH3 and H2O vapors expanding in steady flow in a supersonic air nozzle. From the effect of the nucleation and growth of liquid from the vapor phase on the nozzle pressure distribution, the point of incidence of condensation is readily detected. Experimental results have been compared with the predictions of the classical nucleation rate equation and with the quantum‐statistical treatment of Lothe and Pound. While H2O nucleation rates are in agreement with the classical equation, NH3 nucleation follows the very much higher rates (12 to 18 orders of magnitude) of the Lothe–Pound equation. A mass accommodation coefficient of 0.01 < ξ < 0.1 for H2O was inferred from the experimental data.

The role of excess vacancies in precipitation

Excess vacancy concentrations are known to have a strong effect on rates of precipitation from solid solution. In quenched AI-4w/o Cu alloys, for example, precipitation rates are many orders of magnitude greater than predicted on the basis of extrapolated high temperature di f fusiv i t ies (1). Similar effects have been observed in other alloy systems (1,2,3). This enhancement is usually attributed to the increased growth rate of precipitates due to the quenched-in vacancies. Diffusion in most metals is by the vacancy mechanism, so an n-fold increase in vacancy concentration gives an n-fold increase in diffusion rate.

Nucleation of Supersaturated Vapors in Nozzles. II. C6H6, CHCl3, CCl3F, and C2H5OH

Measurements have been made of the results of homogeneous condensation in benzene, chloroform, Freon 11, and ethanol vapors expanding in steady flow in a supersonic air nozzle. Experimental results have been compared with the predictions of the classical nucleation rate equation and with the quantum‐statistical treatment of Lothe and Pound. Whereas the results on C2H5OH were inconclusive, nucleation rates in the other three vapors are in good agreement with the Lothe–Pound treatment over substantial temperature ranges. It is noted that generally fluids of polar or rod‐shaped molecules follow classical theory, and that fluids of compact molecules without a large permanent dipole follow the Lothe–Pound treatment. Mass accommodation coefficients were also inferred. For CHCl3, ξ ≃ 1; for CCl3F and C6H6, ξ ≃ 0.1.

Nucleation on Gaseous Ions

The homogeneous nucleation theory of Lothe and Pound is extended to condensation on ions. A rate equation is derived that gives the frequency of droplet formation on an attenuated concentration of gaseous ions in supersaturated unary vapors. This treatment predicts little catalytic effect of ions in contrast to the classical theories of Volmer and of Becker and Doering, which predict condensation on ions at supersaturations substantially below those needed for homogeneous nucleation. The predictions of classical theory and of the present treatment are compared with Scharrers cloud‐chamber measurements of homogeneous, positive‐ion, and negative‐ion rain limits in a number of fluids. Neither theory predicts the different catalytic potencies of positive and negative ions. The homogeneous rain limits in CHCl3, C6H6, CCl4, and C6H5Cl are in good agreement with the Lothe–Pound theory, and the catalytic effect of ions is small or nil, in agreement with the present treatment. Classical theory correctly predicts ...

NUCLEATION OF VOIDS IN IRRADIATED METALS. II. THE GENERAL CASE.

Abstract An attempt was made to calculate the co-precipitation rate of vacancies, interstitials, and gas atoms into voids, thus modelling processes occurring in the fast breeder reactor. In the co-precipitation of vacancies and interstitials, the existence of a pseudo-equilibrium distribution permitted the rate to be expressed in a form very similar to the usual nucleation equations; however, the presence of gas atoms creates severe problems. It was found that if a pseudo-equilibrium distribution is to exist, it must bear a particular functional relationship to the equilibrium distribution which obtains in the absence of excess interstitials. It is generally thought that gas atoms are present in substitutional sites; in this case the constraints are so severe that it is generally impossible to define a pseudo-equilibrium distribution. The constraints are not as severe for the less-likely case of interstitial gas atoms, but even so, the free energy of void formation must have a special functional form. A difference equation is presented that describes void nucleation in the breeder environment; we believe that a theoretical understanding of void formation in the breeder reactor will come from solution of this equation. Accordingly, we are at present attempting a numerical evaluation for the steady-state nucleation rate and incubation time.