The structure of atomically smooth spherical surfaces

Abstract An infinite lattice is assumed to be cut by a sphere and the distance between the surface of this ideal sphere and all points slightly inside it have been computed for face-centered and body-centered cubic lattices. The lattice positions are plotted orthographically and patterns are given of the points which lie within the surface of the sphere by 0.05 lattice distances in the {100} plane, for a sphere of diameter equivalent to 969 A for platinum or 951 A for tungsten. They are very similar to field ion microphotographs obtained by M uller (e.g. Ref. 2) and suggest that the atoms which form the image in field ion microscopy can be specified by their distance from an ideal sphere.