Recent developments in the modeling of grain growth and coarsening are briefly considered. Common characteristics of both these phenomena are briefly pointed out. A formulation based on stochastic consideration is proposed. This formulation assumes that the rate of growth of an individual grain or a precipitate is not entirely determined by its size but has a random component to it. This leads to a Fokker-Planck Equation for the size distribution. It can then be shown that there is indeed a unique state (the self-similar state) which is in general reached from an arbitrary initial state. The case of two dimensional grain growth is treated in detail as an example. Grain size distribution is obtained from these considerations, which is in good agreement with experiments.

Non random nucleation processes are a subject of much interest in the study of first order phase transformations. However, the theory available to obtain the time evolution of the transformation for a nucleation and growth process, the well known Kolmogorov, Johnson-Mehl and Avrami kinetic equation (KJMA), is not accomplished if the nucleation process is nonrandom. Therefore, KJMA does not give an adequate description of the transformation kinetics.

In the present paper, a non-random nucleation protocol resulting from a reduced nucleation rate due to the nearby presence of other growing grains is considered. Monte-Carlo simulations of such processes are performed, and the deviations from the Avrami kinetics observed are analyzed in detail.

A model is developed that is capable of simulating simultaneous nucleation, growth, and coarsening. Growth and coarsening are simulated with a 2-D Phase Field model and nucleation is simulated by a stochastic algorithm. The actual nucleation events are simulated by placing ordered particles in the matrix, according to the local supersaturation, with the mean rate of introduction matching that of the nucleation rate. The nucleation rates are input parameters that could, for example, be supplied by experiment or atomistic modeling. Isothermal results for this model under conditions approaching constant nucleation show excellent agreement with the Johnson-Mehl- Avrami-Kolmogorov (JMAK) theory of isothermal transformations involving nucleation and growth. Because the Phase Field simulation is interrupted in order to put particles in, problems can arise due to the mismatch of the assumed diffusion field about the nucleating particles and that would be obtained as a result of growth. This can lead to numerical instabilities as the simulation parameters are adjusted to approach the site saturation extreme as well as underestimating the transformation rate by a small transient time. Preliminary step quench results showed the method to be stable enough to simulate non-isothermal transformations with a series of step quench operations.

We reported a scanning tunneling microscopy(STM) observation on the growth mode transition from 2D-nucleation to spiral growth in the epitaxial Fe films on MgO(001). As the growth temperature is increased to above 493 K, a temperature region where the Schwoebel barrier is overcome, the Fe films grow in a 2D-nucleation and growth mode formed atomically flat films. The 2D-nucleation transformed into a spiral growth as increasing film thickness. At a growth temperature of 493 K, the transition of 2D nucleation to the spiral growth was observed at a film thickness of 75 Å. The critical thickness of the emergence of growth transition decreased as the growth temperature is increased.