A statistical theory of grain growth

Abstract

By extending the theory of Kurtz and Carpay, a detailed statistical theory of normal grain growth has been developed. The theory utilizes their concept of multiple distributions, i.e. the division of grains into topological classes (14 planar, 34 spatial) but unlike their treatment it does not require the individual distributions of each class to be lognormal. An alternate multiple distribution of grain sizes, where the grains are classified according to a given value of size, rather than a given value of sides, or faces is also proposed. The overall distributions (both in grain shapes and sizes) are then obtained by summing the individual distributions, and are shown to be approximately lognormal. Alternate origins of lognormality are also discussed.