Absolute X-Ray Measurement of the Atomic Scattering Factor of Chromium

Absolute measurements were made to determine the atomic scattering factor of chromium by x-ray diffraction. This study was made at room temperature, using an imperfect single crystal in transmission and applying a measured secondary-extinction correction to the integrated intensities obtained with monochromatic $\mathrm{Mo}K\alpha$ radiation. The measurements were placed on an absolute scale using a value of the Debye temperature of 525°K and a measured mass-absorption coefficient of 30.15 ${\mathrm{cm}}^2$/g. As in previous measurements on nickel, the apparent scattering factors of the (110) and (200) reflections were found to depend linearly on the reciprocal of the reflection half-width, thus indicating the presence of primary extinction. The true atomic scattering factors for the (110) and (200) reflections, determined from an extrapolation to zero reciprocal half-width, were found to be considerably lower than the theoretical values obtained from free-atom Hartree-Fock calculations. From the paired reflections (330)-(411) and (600)-(442) the $t_{2g}$ population of $3d$ electrons was found to be about 72%, thus indicating a marked departure from spherical symmetry.