Electron density distribution in $\alpha$-iron: A $\gamma$-ray diffraction study

High-accuracy single-crystal structure factors, complete up to $\sin \theta ∕\lambda =1.9{\mathrm{\AA }}^{-1}$ have been measured from $\alpha$-iron at $295\mathrm{K}$ using $316.5\mathrm{keV}$ gamma radiation. A detailed description of the electron density distribution is presented in terms of a multipolar atomic deformation model. The charge asphericity due to preferential occupancy of the $t_{2g}$ subshell is much smaller than that reported hitherto from x-ray measurements but is in quantitative agreement with ab initio calculations, laying to rest discussions about failures of theory in reproducing the aspherical charge. The $3d^7$ electron distribution in the solid is contracted by 8.9% relative to the free atom. The atomic radial 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. The directed metallic bonds are characterized by topological parameters at the bond critical points. Attention is paid to the $3d\text{−}4s$ occupation problem. A consistent interpretation of the $3d$ spin and charge form factors favors the occupation $d^7$ in the metal as against $d^6$ for the atom.

Figure 1

Aspherical contributions to the static model density in the (110) plane. The density range is from $-0.84\text{to}0.56e{\mathrm{\AA }}^{-3}$. Solid lines represent regions of excessive density and 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

The difference between the spherically averaged spin form factor ($={⟨{\mathrm{j}}_o⟩}_{\mathrm{obs}}$ from Ref. 38 and experimental uncertainties from Ref. 39) and the radial charge form factors for $3d^7(\kappa =1.089)$ and $3d^6(\kappa =1.062)$ as deduced from neutron and $\gamma$-ray diffraction. The form factors are normalized to unity at $\sin \theta ∕\lambda =0$.