Electron density distribution in paramagnetic chromium: A $\gamma$-ray diffraction study

High-accuracy single-crystal structure factors, complete up to $\sin \theta ∕\lambda =1.78{\mathrm{\AA }}^{-1}$ have been measured from paramagnetic chromium at $333\mathrm{K}$ using $316.5\mathrm{keV}$ $\gamma$ radiation. A detailed description of the electron density distribution is derived in terms of a multipolar atomic deformation model. There is pronounced charge asphericity in the valence region arising from preferential occupancy of the $t_{2g}$ subshell. The $3d$ charge distribution is contracted by 12.6% relative to the free atom, in accordance with magnetic synchrotron x ray and neutron measurements. By contrast, the atomic crystal scattering factor deduced from $\gamma$-ray diffraction is found to be in contradiction with earlier experimental and theoretical work. Achievement of a reliable Debye-Waller factor is of vital importance in this context. There is no evidence for an anharmonic term in the atomic potential. Real space and energetic features of the charge density topology are used to characterize the directed metallic bonds. Special attention is paid to the form factor approximation in diffraction data analysis.

Figure 1

Aspherical contributions to the static model density in the (110) plane. The density range is from $-1.11\text{to}0.74e{\mathrm{\AA }}^{-3}$. Solid lines represent regions of excessive density, dashed lines depleted regions in steps of $0.1e{\mathrm{\AA }}^{-3}$. The zero contour is omitted. The densities are truncated at $\pm 0.5e{\mathrm{\AA }}^{-3}$.

Figure 2

Static model valence density in the (110) plane. Contours are drawn at intervals of $0.5e{\mathrm{\AA }}^{-3}$.