Structure and Evolution of Nano- and Microcrystalline Grain Aggregates

Abstract

Polycrystalline grain aggregates are cellular networks filling space at random, like soap froths. Their structure (in statistical equilibrium) and evolution (steady state coarsening) are universal, due to local elementary topological transformations (ETT), which are the “collisions” responsible for statistical equilibrium. The structure and its evolution can be represented as a many-body problem with short-ranged interactions. The bodies are paraboloids attached to the grains, with one additional degree of freedom beside their position in space. ETT are caused by simple and orthogonal motions of the bodies. The model describes quantitatively the sintering of polycrystalline mosaics, scaling, steady state distributions of grain sizes and shapes, with mean-field growth exponent. Individual grains obey von Neumann’s law. The difference in coarsening rates between nano- and microcrystalline mosaics is related to the grain size distribution. The structure (Laguerre froth) has remarkable symmetries, stereology (it is identical to its own cut, and can be cut or lifted to higher dimension while preserving its geometry and statistics), and conformal invariance in any dimension and at all times.