Ewald Sphere Construction Research Articles

A spherical viewing screen for diffraction patterns

Fraunhofer diffraction from a planar diffracting object is explained in terms of spatial Fourier transforms and the Ewald sphere construction from solid-state physics. It is found that the most meaningful view of such a diffraction pattern is obtained by letting it fall on a spherical screen centered upon the diffracting object and then observing the pattern from a distance along the normal to the plane. This visual projection yields a circular portion of the two-dimensional spatial transform of the diffracting object without any geometrical distortion. A classroom demonstration using a laser and crossed gratings of good quality illustrates clearly the superiority of this viewing technique over the standard procedure of simply allowing the pattern to fall directly on a flat screen.

Explanation of the “Venetian blind” effect in holography, using the Ewald sphere concept

The Ewald sphere construction of X-ray diffraction theory is used to describe the “Venetian blind” effect which occurs in holography when changes in geometry occur between hologram formation and image reconstruction. The limitations on information storage in thick holograms, due to the existence of the effect, are pointed out. Experimental results are given.

LEED study of steps and facets on a Re surface

A rhenium single crystal with an initial (0001) orientation, recrystallized by twinning to yield {101̄ n} planes parallel to the surface. The LEED pattern displayed a one-dimensional superstructure which could be attributed to a system of regularly spaced steps. The 00 beam is diffracted from the (0001) plateaus of the steps, and not the high index plane. Heating the crystal in oxygen apparently modified the step system. Residual gas analysis showed that even after a “clean” LEED pattern has been obtained, carbon contamination is removed from the surface as CO by heating the sample in oxygen. Electropolishing of Re (0001) may result in basal plane etching. The faces of the rhombohedral pyramids thus formed were determined by analysis of LEED patterns and photomicrographs to be {112̄ n}, n = 2, 3, 4. The facet reflections are shifted in energy with respect to the normal reflections, due to a difference in inner potential. Also a dynamic interaction between the two sets of beams is suggested by observations. An intensity versus voltage plot for the normal 00 beam exhibits “forbidden” Laue maxima out to the 21st order. The absence of all but two secondary Bragg peaks may be explained with an Ewald sphere construction.