This paper generalizes previous work of Rios and Villa on spherical growth. The generalized equation applies to nucleation of ellipsoids according to an inhomogeneous Poisson point process. Microstructural evolution in three dimensions of nucleation and growth transformations of ellipsoids is simulated using the causal cone method. In the simulation, nuclei are located in space according to an inhomogeneous Poisson point process. The transformed regions grow with prolate and oblate ellipsoidal shapes. The ellipsoids have their corresponding axes parallel. The simulation and the exact analytical solution are in excellent agreement. Microstructures generated by the computer simulation are displayed. From these generated microstructures one can obtain the contiguity. In the contiguity against volume fraction plot, data from the sphere and all ellipsoids fall on the same curve. The contiguity curve for nucleation according to an inhomogeneous Poisson point process falls above the contiguity curve for nucleation according to a homogeneous Poisson point process. This behavior indicates that nucleation according to an inhomogeneous Poisson point process introduced a nucleus clustering effect.

Nucleation is a phenomenon associated to the start of the new phase, from a primary phase, named matrix. Growth is the increase in size of this new phase over time. In metallic materials, the nucleation may take place on the grain boundaries of the primary phase. A network of Kelvin polyhedra was used in this paper to represent the grains. A computer simulation was performed in which nucleation took places at the faces, edges and vertices of this polyhedral network. The Causal cone method was employed in the simulations. The results of the present computational simulations were compared with the classical Johnson Mehl-Avrami-Kolmogorov (JMAK) as well as with Cahn model for nucleation at the grain boundaries. JMAK theory considers nuclei to be uniform randomly located within the matrix. Cahn analytical model specifies that nucleation takes place on random planes. For a small number of nuclei, the simulations approached the JMAK model whereas as the number of nuclei increased the simulation results agree with Cahn's theory. Reasons for this are fully discussed.

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Resumo Uma das etapas mais importantes do processo de transformação de fases é a chamada nucleação. Estapode ocorrer por saturação de sítios, onde todos os núcleos surgem no instante inicial da transformação, ou, por taxa de nucleação constante, onde uma determinada quantidade de núcleos surge por unidade de tempo. Neste trabalho estudou-se o efeito da taxa constante denucleação nas interfaces de uma rede poliédrica de Kelvin. Rios e Villa, revisitaram o trabalho clássico de Cahn, e propuseram uma equação exata para nucleação em planos paralelos. Utilizou-se então essa abordagem para comparar as simulações computacionais realizadas com o modelo proposto. Comparou-se também essas simulações com o modelo de JMAK. Para pequenas taxas de nucleação, a simulação obteve boa concordância com JMAK, enquanto que, a partir de uma determinada taxa, esta concordância não pode ser observada, uma vez que este modelo contempla núcleos distribuídos aleatoriamente em uma matriz. Por outro lado, a simulação se mostrou correspondente ao modelo de Cahn. Obteve-se também as possíveis microestruturas para os casos estudados.