Dr. Andreas Bill     

CSU Long Beach     

"Development of the Grain Size Distribution During the Crystallization of a Solid"

The microstructure of a solid impacts in important ways its electronic, optical or magnetic properties. A quantitative characterization of a material’s granularity is thus essential for tailoring its functionality. We propose a theory for the grain size distribution of an amorphous solid undergoing crystallization, and derive an analytic expression for the case of random nucleation and growth processes in d dimensions (d = 1,2,3). The solution describes the time-dependence of the distribution from early stages to full crystallization. Both isotropic and anisotropic growth rates are considered. Particular emphasis is set on analyzing how the time-dependence of both the effective nucleation and growth rates affects the final distribution. Remarkably, for certain effectives rates the distribution evolves into a lognormal form in the asymptotic limit of large times. An application of the theory to semiconductors is also presented.