Electron density distribution inα-iron: Aγ-ray diffraction study

Abstract

High-accuracy single-crystal structure factors, complete up to $\mathrm{sin}\phantom{\rule{0.2em}{0ex}}\ensuremath{\theta}∕\ensuremath{\lambda}=1.9\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$ have been measured from $\ensuremath{\alpha}$-iron at $295\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ using $316.5\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ 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 $3{d}^{7}$ electron distribution in the solid is contracted by 8.9% relative to the free atom. The atomic radial scattering factor deduced from $\ensuremath{\gamma}$-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 $3d\text{\ensuremath{-}}4s$ 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.