Microstructural evolution in two-phase alloys: Experimental investigation and modeling of stochastic effects at finite volume fractions.

摘要

The study of microstructural evolution in two-phase alloy systems has been a vital component of modern materials science over the past few decades. The ability to understand and effectively control the microstructure of a material provides control over mechanical, physical and chemical properties during processes such as casting and liquid phase sintering. Phase coarsening, or Ostwald ripening, is a kinetic process occurring during the later stages of microstructural evolution. This is a competitive multiparticle diffusion process typically occurring among a dispersion of domains (particles) randomly distributed throughout a continuous matrix phase. Understanding the evolution of the average particle size and particle size distribution (PSD) is essential in order to accurately predict the final microstructures. In 1961, Lifshitz, Slyozov, and Wagner (TLSW) [1] formulated the classical theory of phase coarsening kinetics by relying on a variety of simplifying assumptions, such as spherical particles and, most importantly, an infinitely small volume fraction of the coarsening phase. In order to more accurately model the phase coarsening process, theories need to account for the effects of particle-particle interactions and of the “local” environment of each particle has on the overall kinetics of the system.; The first part of this study provides new experimental results on the liquid-solid phase coarsening of Ag-Cu alloys. Isothermal annealing of several different alloy compositions for various periods of time resulted in significant phase coarsening of the nearly spherical solid particles within the melt phase. Large areas of the annealed microstructures were analyzed using digital image processing techniques to provide statistically large amounts of raw data. The growth rate of the average particle volume was found to scale linearly with the cube-root of time, in agreement with theoretical predictions and other experimental studies. The experimental PSD's showed a strong deviation from theory, following the same behavior reported in other coarsening studies. The shape of the 3-D PSD's is somewhat erratic and the indication of time invariance and time-invariant behavior, present in the 2-D PSD's, is not as clear after applying the stereological transformation process.; Coarsening rates based on radii measurements exhibited a slight volume fraction dependence but did not agree with the theoretical predictions. By contrast, the coarsening rates derived from the analysis involving the surface area density showed close agreement with the predictions from mean-field theories. These results, along with the particle size distribution results, suggest that the kinetic analysis based on the radii measurements contains significant uncertainties and sources of error. However, the analysis based on the decay of the surface area is more robust and provides a straightforward method by which to quantify microstructural evolution. Experimental results for the coarsening rate behavior also provide the first significant experimental support for the validity of the mean-field approach proposed by Marsh and Glicksman [2] and their suggestion that “direct Laplacian screening” limits interaction distances among particles in a dense microstructure, in clear distinction with diffusional “Debye screening” that occurs in microstructures with relatively low volume fractions.; The second part of the study focuses on computer simulations of phase coarsening in very dilute two-phase systems. Computer simulations based on a multiparticle diffusion model, which incorporates the effect of the ‘local’ environment on the individual particle growth rates was performed for systems of 500 particles. The results reveal that the growth rates of particles with the same radii can differ, in contrast to the mean-field theoretical predictions. A stochastic flux function is used in an effort to quantify the stochastic behav