Equilibrium shape of copper crystals grown on sapphire

The equilibrium crystal shape (ECS) of copper has been studied by scanning electron microscopy on pin-sized copper crystallites supported on single-crystals of a-alumina. In addition, the orientation relationships between copper crystals and the sapphire substrate were investigated by X-ray techniques. A detailed discussion of the kinetic factors that can inhibit equilibration is provided, and it is shown that only crystals ranging in radius from 3 to 4.5 mum can achieve equilibrium shapes under the conditions of the experiment. The maximum anisotropy of surface energy was found to be about 1.02, which is significantly lower than that of the other two fcc metals (lead and gold) for which reliable data are available. Another distinction between copper and those other fcc metals is that its ECS displays {110} facets, and possibly {311} facets, in addition to the commonly observed {111} and {100} facets, at temperatures where equilibration is possible. The observed facets connect tangentially to the curved parts of the ECS, so that all possible surface orientations are present on the copper ECS.