DARWIN SPHERICAL-WAVE THEORY OF KINEMATIC SURFACE DIFFRACTION

In 1912, von Laue first described X-ray diffraction by approximating a s plane waves the spherical waves radiated by atoms in a crystal. Darw in recognized that this approximation is valid only in the limit of ve ry small crystals, and published in 1914 the more general spherical-wa ve theory based on the reflectivity of individual atomic planes. The D arwin theory is extended here to surface Bragg diffraction from a sing le-crystalline monolayer, including the rederivation of a 'surface' Br agg's law and the reflected intensity versus phi, the angle of inciden ce. This more general theory demonstrates how the intensity along a re ciprocal-lattice rod associated with diffraction from a semi-infinite crystal is modified by the phi dependence of the length over which ato ms in a plane emit spherical waves that constructively interfere at th e detector. The diffracted amplitude is not proportional to the Fourie r transform of the charge density. The plane- and spherical-wave model s yield identical results for the integrated intensity across a finite detector area, even for incident angles far from a Bragg reflection.