Electron Diffraction Studies of Thin Films. II. Anomalous Powder Patterns Produced by Small Crystals

Abstract

The (200) ring has been observed to be relatively very weak in electron diffraction patterns produced by extremely small crystals of face-centered cubic type. To study this anomaly we have obtained microphotometer curves from copper films in which the mean linear dimensions of the crystals, as estimated from half-breadths of diffraction rings, varied from 20A to 67A. From each curve the ratio of intensities of the (200) and (111) rings has been determined, and this ratio is found to vary from 0.14 for the 20A crystals to 0.42 for the 67A crystals, the latter figure agreeing within experimental error with 0.48 the theoretical value calculated for large crystals of copper. In order to find what to expect from extremely small crystals, we have carried through the usual calculation to determine the scattering from gas molecules, assuming for each molecule $N$ similar atoms with a face-centered cubic arrangement and nearly spherical shape. For $N=55\mathrm{}$ no (200) ring can be detected in the scattering pattern, while for $N=379\mathrm{}$ the (200) ring is very plain and all of the rings have relative intensities appropriate to large crystals. The previously reported intensity anomaly is thus accounted for on the basis of smallness of the individual crystals. The very smallest crystals which we have produced give ring intensity ratios intermediate between those calculated for crystals of 55 and 379 atoms each. This is a somewhat smaller size than that estimated from half-breadths of diffraction rings produced by these smallest crystals.