The 80 Diperiodic Groups in Three Dimensions

Abstract

The law-energy electron diffraction work of L. H. Germer, J. J. Lander, A. U. MacRae, J. Morrison and others is resulting in new information about surface structures. These three-dimensional structures have periodicity only in two dimensions. The 230 triperiodic space groups are not applicable to the solution of these structures. The 17 strictly two-dimensional groups do not admit the existence of a third dimension and may therefore not be appropriate for these structures which are not strictly planar. The useful space groups for these structures are the 80 diperiodic groups in three dimensions. Nowhere in the literature have these been put into a form convenient for use, as have the other two sets of space groups. This has now been done and the tables are available on request from the Circulation Manager, Bell System Technical Journal, Bell Telephone Laboratories, Incorporated, 463 West Street, New York 14, N. Y. Sample tables are given in this paper.