Charge-transfer effect on the linewidth of Fe<i>K</i>α x-ray fluorescence spectra

Abstract

High-resolution K\ensuremath{\alpha} x-ray fluorescence spectra of FeO, ${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$, ${\mathrm{Fe}}_{3}$${\mathrm{O}}_{4}$, ${\mathrm{K}}_{3}$[Fe(CN${)}_{6}$]\ensuremath{\cdot}${3\mathrm{H}}_{2}$O, ${\mathrm{K}}_{4}$[Fe(CN${)}_{6}$], and Fe (metal) are measured. It is found that the linewidth of Fe K${\mathrm{\ensuremath{\alpha}}}_{1}$ (K-${\mathit{L}}_{3}$) does not follow Van Vleck's theorem for oxides, but it follows Van Vleck's theorem for cyanides; the line shapes of FeO, ${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$, and ${\mathrm{Fe}}_{3}$${\mathrm{O}}_{4}$ are nearly identical. These results are rationalized by the spin-unrestricted DV-X\ensuremath{\alpha} molecular-orbital calculations of model clusters. The model clusters we tried are [${\mathrm{FeO}}_{6}$${]}^{10\mathrm{\ensuremath{-}}}$, [${\mathrm{FeO}}_{6}$${]}^{9\mathrm{\ensuremath{-}}}$, [Fe(CN${)}_{6}$${]}^{3\mathrm{\ensuremath{-}}}$, and [Fe(CN${)}_{6}$${]}^{4\mathrm{\ensuremath{-}}}$ as model clusters of FeO, ${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$, ${\mathrm{K}}_{3}$[Fe(CN${)}_{6}$]\ensuremath{\cdot}${3\mathrm{H}}_{2}$O, and ${\mathrm{K}}_{4}$[Fe(CN${)}_{6}$], respectively. The electronic structures of these clusters are calculated for their ground states and 1${\mathit{s}}^{\mathrm{\ensuremath{-}}1}$ hole states. It is concluded from these calculations that the charge-transfer effect induced by the creation of the 1${\mathit{s}}^{\mathrm{\ensuremath{-}}1}$ core hole, which is the initial state of the K\ensuremath{\alpha} x-ray emission, reduces the effective number of 3d unpaired electrons of iron oxides, resulting in the K${\mathrm{\ensuremath{\alpha}}}_{1}$ width being reduced from that expected from Van Vleck's theorem. On the other hand, the effective number of 3d unpaired electrons of cyanides in the ground state is conserved in the 1${\mathit{s}}^{\mathrm{\ensuremath{-}}1}$ core-hole state. Thus Van Vleck's theorem holds for cyanides.