Absolute Measurement of the Atomic Scattering Factors of Iron, Copper, and Aluminum

Abstract

The x-ray atomic scattering factors of iron, copper, and aluminum were carefully remeasured to obtain more reliable information on the outer electron charge densities in these elements. The scattering factors were obtained from measurements of the integrated Bragg intensities of powder samples using monochromatic Mo $K_{\alpha }$ radiation. The intensities were put on an absolute scale by direct measurements of the power in the primary x-ray beam. Extinction, surface roughness, and preferred orientation effects were shown to be negligible in the samples used. The ratios of the measured scattering factors of the three elements agree with those calculated from Hartree-Fock theory to within 1%. This substantiates the findings of Batterman, and, in contrast with the previous results of Weiss and DeMarco, indicates that there is no large discrepancy between the electronic structures of copper and iron. The absolute values of the measured scattering factors, however, lie about 4% below theory in the region of low $\frac{sin\theta }{\lambda }$. It is pointed out that the high theoretical values for iron and copper could result from known differences in electronic structure between a free atom and one in the solid, but that present theory probably cannot account for the discrepancy in the case of aluminum.