Calculation of Upper Bounds to the Small‐Angle Scattering from Crystallite Models of Amorphous Materials

摘要

The inability of experimentalists to observe small‐angle x‐ray scattering from single‐phase liquids and amorphous solids has been considered, by many workers in the field, to invalidate a crystallite model for these materials. In this work we calculate the intensity of small‐angle x‐ray scattering from two crystallite models which are designed to yield upper bounds to the actual scattering. The calculated upper bounds are, in general, considerably lower in intensity than the scattering from isolated particles. The results are extremely sensitive to the density and average crystallite size of the sample, so that general conclusions about the observability of such scattering cannot be made. The particular case of vitreous SiO2, which was examined experimentally by Warren and Weinberg, has been studied in detail. For this case, the calculated scattering intensity is of the same order of magnitude as that observed by these authors. Thus, it is concluded that the failure to observe small‐angle scattering from vitreous SiO2 does not invalidate a crystallite model for that material. It should be noted that the calculation does not, on the other hand, offer any evidence for the existence of crystallites.