Abstract
Equilibrium grain structures and grain growth processes have been investigated in ordered two-dimensional polycrystals, containing three types of grain based on a regular hexagonal unit cell. In particular, the family of structures with one central, two vertex, and three edge grains, all meeting at threefold grain edge nodes, has been examined in detail. It has been found convenient and instructive to present the energies as contours on a ternary diagram of grain areas, and grain growth can be shown as paths on the same diagram. Four regions representing topologically distinct trimodular structures arise within this diagram, and the boundaries and corners correspond to degenerate bimodular and unimodular structures respectively. Although the lowest energy state is the unimodular array of regular hexagons, other structures are also locally stable. A pseudorandom distribution of grains can be generated by combining different variants of some of the unit cells. The study is considered to be relevant to thin film technology and to provide guidelines for a corresponding three-dimensional analysis.
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