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The recent increase of activity in the field of slow-electron diffraction has resulted in a need for agreement on conventions of terminology in the description of a diperiodic surface structure relative to a triperiodic substrate. Vector description of the surface structure net in terms of the substrate surface net is suggested. Fractional Miller indices result when the surface structure mesh is larger than the substrate surface mesh. The surface structure may be either that of a deposit or that of the selvedge of the substrate. With the relaxation of one of the diffraction conditions in the diperiodic structure the reciprocal lattice becomes a set of parallel rods intersecting the Ewald sphere continuously with change of wavelength of the incident radiation or change of orientation of the crystal. The paper discusses the applicability of the seventeen two-dimensional space groups and the eighty diperiodic groups in three dimensions to these diperiodic structures. A comparison is made between the different effects of surface symmetry on etch pits and epitaxial deposits on the cleavage face of muscovite.

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deficiency of one-third of eighteen, namely six, represents the six negative charges on the complex anion.This structure, like that of the 6-heteropoly compounds, involves octahedral coordination of oxygen atoms around the central ion, whereas the structure of the upper limiting series of 12-compounds and the structure recently published by Dawson (1953) for the more highly condensed 18-anions or doubled 9-anions is based on tetrahedral coordination of the central ion.We thank Prof. W. N. Lipscomb of the University of Minnesota for the piezo-electric determination and Dr S. Weinbaum, Miss Linda Pauling, and Mrs Nan Arp for computational work.