The relative intensities of the ED spots in a cross-grating pattern can be calculated using N-beam electron diffraction theory. The scattering matrix formulation of N-beam ED theory has been previously applied to imperfect microcrystals of gold containing stacking disorder (coherent twinning) in the (111) crystal plane. In the present experiment an effort has been made to grow single-crystalline, defect-free (111) gold films of a uniform and accurately know thickness using vacuum evaporation techniques. These represent stringent conditions to be met experimentally; however, if a meaningful comparison is to be made between theory and experiment, these factors must be carefully controlled. It is well-known that crystal morphology, perfection, and orientation each have pronounced effects on relative intensities in single crystals.The double evaporation method first suggested by Pashley was employed with some modifications. Oriented silver films of a thickness of about 1500Å were first grown by vacuum evaporation on freshly cleaved mica, with the substrate temperature at 285° C during evaporation with the deposition rate at 500-800Å/sec.
On the existence of the poles of the scattering matrix for several convex bodies