The change in lattice spacing at a crystal boundary

Abstract

Some recent experiments of Davisson and Germer on the scattering of electrons by a crystal have drawn attention to the conditions at a crystal boundary. In interpreting their results in terms of de Broglie waves, the authors have to postulate a contraction of the crystal lattice at the surface— in some cases of as much as 30 per cent.f It is, therefore, important that other independent methods should be devised to indicate what change (if any) takes place at a crystal surface. Unfortunately X-rays are unable to help in this respect as several hundred atomic layers are necessary to produce a Bragg reflection pattern ; nor is theory able to provide an answer in the case of metallic crystals such as are used by Davisson and Germer because little is known of the forces which hold a metal together. Certain other cases can, however, be considered theoretically, and these may indicate the order of the effect to be expected in metallic crystals. In this paper we consider the change in spacing at a (100) boundary of a crystal of the NaCl type, this boundary being considered because it is a natural plane of crystal. Two effects are to be anticipated: (1) a change of spacing between planes at the boundary; (ii) a change of spacing between atoms in the surface layer itself. These effects are considered separately and independently. Actually, of course, each affects the other, but this is assumed to be a correction of the second order.