Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation

Abstract

Microstructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata (CA). In the simulation, nuclei are located in space according to a heterogeneous Poisson point processes. The simulation is compared with exact analytical solution recently obtained by Rios and Villa supposing that the intensity is a harmonic function of the spatial coordinate. The simulated data gives very good agreement with the analytical solution provided that the correct shape factor for the growing CA grains is used. This good agreement is auspicious because the analytical expressions were derived and thus are exact only if the shape of the growing regions is spherical.

Generalizing Ellipsoidal Growth

“…The intensity was equal to λ(x) = λ(x 1 , x 2 , x 3 ) = mx 1 + n where "m" and "n" are constants equal to 596 and 2, respectively. The same values of "m" and "n" were used in an earlier work of in which growth was equiaxed 15 . For dimensional purposes, we consider that each the side of a cell measures 1µm.…”

“…We can compare the present work with previous work 15 that used cellular automata to simulate the transformation nucleated according to an inhomogeneous Poisson point process. In the previous work 15 , the growing regions were not spherical but equiaxed owing to the use of cellular automata. In that work, analytical theory and experiment were also in good agreement.…”

Kinetics of Phase Transformation of Indium in the Presence of Polytetrafluoroethylene: Implications for DSC Measurements on Polymers and Their Composites

“…Equation (3) is based on postulates which often result in overestimations of the volume of the transformation product [29]. Amongst the assumptions, there is also that of uniform randomly nucleation [30]. This condition may not be respected even for rapidly quenched thin metal layers [31], meaning that practically nucleation is a process time and space dependent [28,32] and therefore the Avrami equation can be only seemingly fitted by data collected in limited time intervals for specimens with very small thickness.…”

Simulation of CP-Ti Recrystallization and Grain Growth by a Cellular Automata Algorithm: Simulated Versus Experimental Results

“…Stiko 2 and Davies 6 modified the rules of transition between neighboring cells using growth models related to a realistic time scale. Others researchers investigated the influence of initial microstructure topologies on the kinetics of static recrystallization in simulations by CA 1,2,7 , and static recrystallization in cold-worked copper 8 and in iron 9 were recently simulated by a CA algorithm. Dynamic recrystallization models using cellular automata were proposed by Goetz and Seetharaman 10 , Qian…”