Calibration of the isomer shift for the $14.4\text{−}\mathrm{keV}$ transition in ${}^{57}\mathrm{Fe}$ using the full-potential linearized augmented plane-wave method

Full-potential linearized augmented plane-wave method has been used to calibrate isomer shift for the $14.4\text{−}\mathrm{keV}$ resonant transition in ${}^{57}\mathrm{Fe}$. Augmented plane waves and local orbitals were used for the valence electrons. For the correlation and exchange potentials, a generalized gradient approximation has been adopted. Calculations have been performed for the following compounds: $\mathrm{Fe}{\mathrm{F}}_2(P{4}_2∕mnm)$, $\mathrm{Fe}{\mathrm{Cl}}_2\left(R\overline{3}m\right)$, $\mathrm{Fe}{\mathrm{Br}}_2\left(P\overline{3}m1\right)$, $\mathrm{Fe}{\mathrm{I}}_2\left(P\overline{3}m1\right)$, $\mathrm{Fe}{\mathrm{F}}_3\left(R\overline{3}c\right)$, $\mathrm{Ti}\mathrm{Fe}\left(Pm\overline{3}m\right)$, and $\mathrm{Fe}\left(Im\overline{3}m\right)$. Strong on-site Coulomb interactions in the $\mathrm{Fe}3d$ shell of halides were taken into account by applying the Hubbard repulsion parameter $U$ and the on-site exchange interaction constant $J$. The isomer shift calibration constant of $\alpha =-0.291{\mathrm{a.u.}}^3\mathrm{mm}{\mathrm{s}}^{-1}$ has been obtained. The nuclear quadrupole moment of the excited nuclear state involved was found to be $Q=+0.17\mathrm{b}$.

Figure 1

Relative experimental shift plotted versus difference in electron density for various compounds.

Figure 2

Experimental quadrupole splitting is plotted versus calculated effective electric field gradient.