Absolute measurement of the x-ray scattering factor of iron: An analysis of the scattering factor and crystal structure of3delements

Absolute measurements have been performed to determine the x-ray scattering factor of iron. This study has been made using an imperfect single crystal in symmetrical transmission and applying a measured secondary-extinction correction to the integrated intensities obtained with Mo $K\alpha$ radiation. A measurement of the incident-beam power placed the measurements on an absolute scale. As in previous measurements on nickel and chromium the apparent scattering factors of iron have been found to depend on the reflection half-width, thus indicating the presence of primary extinction. The true scattering factors for the (110) and (200) reflections determined from an extrapolation to zero reciprocal half-width have been found to be considerably lower than the corresponding theoretical free-atom values. From an analysis of the published absolute data for the upper half of the first transitional series, it is suggested that the percent difference between crystal and free-atom scattering factors decreases with filling of the $3d$ band and that the room-temperature structures of $3d$ metals can be related to the measured asphericities of charge density.