On the growth of grains

Growth of single crystalline seeds into polycrystalline strontium titanate: Anisotropy of the mobility, intrinsic drag effects and kinetic shape of grain boundaries

“…where P is the driving force, c m is the mean grain boundary energy of the polycrystalline matrix, R m ðtÞ is the mean grain radius of the matrix at time t, and k % 1 corresponds to a geometric constant, which accounts for the deviation of the grain shape from a sphere [44]. Grain growth occurs in the polycrystalline matrix during annealing ( Fig.…”

“…with a geometric constant b [3,43,44]. Hence at all times the driving force of the polycrystal is smaller compared to the single crystal.…”

Monte Carlo Simulations of Grain Growth in Metals

“…Furthermore, because they are usually of a simple form, they are generally not suitable for describing more complicated microstructural phenomena. Due to these shortcomings of empirical models, microstructural modeling approaches at the mesoscopic scale such as the Cellular Automaton (Feppon & Hutchinson, 2002) and the Monte Carlo Potts Model have been developed. In these approaches, the continuous material structure is discretized into a lattice that typically comprises thousands of grains.…”

A multi-scale approach for microstructure prediction in thermo-mechanical processing of metals

“…Due to these shortcomings, microstructural modeling approaches at the mesoscopic scale, such as the Cellular Automaton [10] and the Monte Carlo (MC) Potts Model [11] have been developed, wherein the continuous material structure is discretized into a lattice, which typically comprises thousands of grains. Physical laws (such as the surface energy reduction law governing normal grain growth, the site-saturated nucleation law for recrystallization, etc.)…”