Development of anisotropic particle morphology in an isotropically transforming matrix

In the present work we consider the growth of a very dilute concentration of anisotropic particles, nucleated with random orientations, in a matrix of growing spherical particles. It is assumed that the matrix particles obey the usual JMAK kinetics. We concentrate on describing the change in anisotropic particle grain morphology as the transformation process proceeds. An eccentric shaped particle will have certain growth directions that are rapid and others that are slower. Faster growing directions impinge upon the matrix particles much sooner than slower growing directions, and this feature leads to an effective change in particle morphology as the transformation process progresses. We analyze such changes in particle morphology by deriving expressions for the probabilities that growth rays will travel a certain distance before encountering matrix particles and that the length ratio of fast-axis to slow-axis growth of the anisotropic particle will attain certain values. The changes in particle morphology are examined as a function of the relative speeds of growth of anisotropic particle growth rays to matrix particle growth rates.