We have modelled the microstructures that result from grain nucleation and growth-to-impingement in two dimensions, using various nucleation and growth conditions. Nucleation conditions include simultaneous nucleation at a fixed number of sites, continuous nucleation at a constant rate per unit of untransformed area, cases in which the nucleation rate declines with time, and cases in which nucleation is excluded in a zone surrounding each pre-existing grain. The growth rate for each grain is taken to be a simple function of the grain radius, either increasing with radius, decreasing with radius, or remaining constant. These different conditions result in markedly different structures, with different geometric and topological properties. We have also modelled the effect of grain boundary migration and grain growth following impingement.
H. J. Frosts,
C. V. Thompson,
"Development Of Microstructure In Thin Films", Proc. SPIE 0821, Modeling of Optical Thin Films, (2 February 1988); doi: 10.1117/12.941844; https://doi.org/10.1117/12.941844