Correlations and fluctuations in phase coarsening.

Three-dimensional phase coarsening at various volume fractions is simulated by employing multiparticle diffusion methods. The dynamic process of phase coarsening is visualized through a three-dimensional movie. The present study also characterizes interparticle spacings in polydispersed particle systems and clarifies the controversial mathematical expressions for interparticle spacings used in the literature for 30 years. Consequently, this study reveals spatial, temporal, and nearest-neighbor correlations in polydispersed particle systems. A new three-dimensional movie of a Voronoi network demonstrating these correlations is provided. Our simulation and experiments show that growth rates of individual particles deviate from those of the mean-field theory, which is caused by their differing local environments. Multiplicative noise provides a good basis to describe the stochastic nature of fluctuations during phase coarsening.

Modeling and simulation for phase coarsening: a comparison with experiment.

The phase coarsening of precipitates is modeled in the framework of Debye-Hückel theory. The interactions observed among a population of precipitates dispersed throughout a matrix can be described by diffusion screening. The relationship between the maximum particle radius and the volume fraction of the phases is established, and the rate of coarsening is related to the volume fraction and the self-similar particle size distribution. We simulated the dynamics of late-stage phase separation using multiparticle diffusion methods. Experimental measurements on the rates of coarsening of delta(') ( Al3 Li) precipitates in binary Al-Li alloys are compared with our results using modeling and simulation. The theoretically predicted particle size distributions and the maximum radius expected for particles in the microstructure agree well with recent experimental results.

Noise of microstructural environments in late-stage phase coarsening.

Multiparticle diffusion equations were modeled to simulate the dynamics of late-stage phase coarsening in the region of lower volume fractions. Local environmental information and particle interactions within each coarsening "locale" are included in our simulations. These studies reveal that locale fluctuations occur in the growth rates of particles due to their differing environments. Multiplicative noise provides a sound basis to describe locale fluctuation in late-stage coarsening. A Fokker-Planck equation for the particle size distribution and its asymptotic solution are obtained.

Evidence for tip velocity oscillations in dendritic solidification.

Dendritic growth experiments were conducted in the reduced-convection environment aboard the space shuttle Columbia on STS-87. Spectral analysis was performed on 30-frame/s video data during growths of isothermal dendrites. Results indicate that pivalic acid dendrites exhibit a subtle oscillatory behavior of the axial growth velocity near the tip, with a frequency component that is associated with the sidebranch formation process.

Experimental measurements of sidebranching in thermal dendrites under terrestrial-gravity and microgravity conditions.

We perform sidebranch measurements on pure succinonitrile dendrites grown in both microgravity and terrestrial-gravity conditions for a set of supercoolings within the range 0.1-1.0 K. Two distinct types of sidebranch regions, uniform and coarsening, exist, and are characterized by the distance from the tip at which the region began, D(i), and the average spacing of sidebranches within that region, lambda(i). There does not appear to be any significant dependence on either gravity level or supercooling when D(i) or lambda(i) are normalized with respect to the radius of curvature of the tip, R. The apparently constant normalized proportionality factor between D(i), lambda(i), and R, regardless of the relative importance of diffusion and convective heat transport, demonstrates self-similarity between dendrites of different length scales propagating under various heat transfer conditions. However, when the form of the sidebranch envelope is defined by a power law relating the amplitude and relative positions of the sidebranches normalized to the radius of the tip, the form is seen to have significant variations with supercooling between the terrestrial gravity and microgravity growth dendrites. Furthermore, both the amplitude coefficient and exponent from the power-law regressions of the microgravity data are statistically different (95% confidence level) than their terrestrial counterparts.