Analysis of transformations nucleated on non-random sites simulated by cellular automata in three dimensions

Abstract

Cellular automata simulation in three dimensions is carried out to simulate microstrutural evolution for nuclei distribution ranging from a periodic arrangement to clusters of nuclei. The effect of clustering in three dimensions is found to be much more difficult to detect using conventional microstructural path analysis than in two dimensions. Microstructural path equations fit simulated data well, even when the nuclei are non-randomly located. However, the parameters obtained by means of this fitting lead to erroneous time dependent velocities. Therefore, measuring a descriptor that is sensitive to non-randomness such as the contiguity is even more important in three than in two dimensions

Simulation of recrystallization in iron single crystals

“…Such an analysis may yield good curve fitting, but will obtain fitting parameters that are inaccurate. For example, in previous works, Rios et al 15,29,31 showed that CA simulations with non-randomly located nuclei yield a fitted value of the number of nuclei per unit of volume, N V , and a time exponent for the velocity from Equation 6 that were different from the number of nuclei per unit of volume and time exponent used in the simulation. Consequently, in the present work, the fact that we reproduced experimental results using quantities extracted from analytical models validates the CA simulation and the analytical treatment by V&R. However, in studies in which one has less experimental data this could become an issue.…”

“…Therefore, it is not surprising that CA is the choice of many researchers simulating recrystallization, including Gottstein 17,18 and Raabe 19,20 and many others [21][22][23][24][25][26] . We too have published a series of papers using CA simulations 15,[27][28][29][30][31] . In those papers CA simulation was shown to be geometrically sound in 2-d 28 and 3-d 30 by comparing the results with exact analytical theory available for recrystallization of randomly located nuclei.…”

“…In those papers CA simulation was shown to be geometrically sound in 2-d 28 and 3-d 30 by comparing the results with exact analytical theory available for recrystallization of randomly located nuclei. Moreover, we also used CA simulations to study the influence of non-randomness of nuclei distribution 15,27,29,31 . Nevertheless, our studies lacked direct comparison of CA simulation to experimental data, as is provided here.…”

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

“…The shape of CA is compared with a sphere in Figure 2. The analytical expression equivalent to Equation 3 for CA was derived by Rios et al 22 .…”

“…In previous papers [18][19][20][21][22][23][24] , cellular automata (CA) simulation of phase transformation/recrystallization in 2-d and 3-d were carried out and compared with KJMA analytical solutions. The purpose of the present paper is to simulate phase transformations/recrystallization in by cellular automata (CA) in order to compare the simulation with the analytical solution by Rios and Villa.…”