Correlation of the Mössbauer Isomer Shift and the Residual Electrical Resistivity forAu197Alloys

The Mössbauer isomer shift, which is simply related to the charge density at the Mössbauer nucleus, has been measured for pure ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ and for ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ as an impurity in Cu, Ag, Ni, Pd, and Pt. Since the isomer shift associated with an impurity and the residual electrical resistance due to that impurity are properties of a common conduction-band wave function, one may expect a correlation of the residual resistance with the isomer shift through a suitable model. We have thus made residual-resistance as well as isomer-shift measurements at 4.2°K for the above dilute gold alloys. These measurements have been correlated through a theoretical model using (a) the residual electrical resistivity and the Friedel sum rule to specify the asymptotic wave function at the Fermi level and (b) a pseudopotential which will produce this asymptotic wave function and which is used to continue the $s$ partial wave inward to the gold nucleus at the origin. The correlation of our experimental results using the theoretical model is good if we assume that a gold impurity presents an attractive potential to the $s$ partial wave of the host $s$-band conduction electrons, and if we assume the $s$-band fillings to have the values 1, 1, 0.58, and 0.37 for Cu, Ag, Pd, and Pt.