GRAIN COORDINATION IN PLANE SECTIONS OF POLYCRYSTALS

The description of isotropic polycrystalline structures such as those encountered in normal grain growth, is approached from a probabilistic point of view. The discussion is restricted to the distribution of grain shapes in two dimensional sections, as characterized by the topological parameter n, i.e. the number of sides or nearest neighbours, which is also known to be somehow related to grain dimensions. Assuming that only two elementary transformations (interchange of grain neighbours and creation or annihilation of 3-sided grains) can take place in the array, it is predicted that the mean coordination number mn of the nearest neighbours of all n-sided grains is related to n through Weaire's relation: mn = 5 + (6 + μ2)/n in which μ2 is the second central moment of the overall distribution of grain coordination numbers. The latter is generated by Monte-Carlo simulation and it is suggested that a 'normal polycrystalline structure' may be viewed as that grain array most likely to develop when both elementary transformations repeatedly occur at random. Since their relative proportions remain a priori unknown, at least one degree of freedom is available in the model and evolutionary processes, e.g. grain growth can be accounted for within its framework. It is shown with a particular example, that actual microstructures may be found, which can be adequately described by the present model. © 1979.