The shape of a crystal in equilibrium or during growth is determined by the surface free energy and its anisotropy, by transport phenomena and reactions. Inversely such type of experiments should in principle enable the determination of elementary surface quantities if they are made under well known conditions. Crystals which form the end of a tip seems to be in particular suitable for it, because (1) calculations on shape changes of tips do exists and are confirmed in important details, (2) the cleanliness of the surface or the presence of a special adsorbed layer can be controled by field emission microscopy, (3) the variation of geometrical data (tip length, curvature radius, diameter of faces) can be measured in situ in ultra high vacuum, (4) as such crystals are small (diameter roughly between 0.1 and 10 µ) one shape change experiment requires only a short time. In this paper a review is presented, mainly results on metal crystals obtained in recent years by Piquet, Vu Thien, Roux, Uzan, Pichaud and A. Müller in cooperation with the author. Described are new methods using scanning and field emission microscopes.
The theory of Nichols and Mullins on shape changes of conical tips by surface self-diffusion is confirmed experimentally, in particular the existence of the critical half cone angle α=3°, the formation of single crystal drops (α<3°), the evolution of "steady state" forms and the radius-time relation. Surface self-diffusion diffusivities and energies are measured. If an adsorbed layer is added to the clean surface, an essential increase or decrease of surface self-diffusion can occur. Shape changes can be considerably influenced by free evaporation and surface reactions (corrosion) which is shown theoretically as well as experimentally. The equilibrium shape and the surface free energy anisotropy is determined for several clean metals in agreement with calculated data.