Electron Binding in Metals: Grey and White Tin

Core-electron binding-energy-shift data, obtained from photoelectron spectroscopy, are presented for $\beta -\mathrm{Sn}$ and $\alpha -\mathrm{Sn}$. These data and published results for the Mössbauer isomer shift and for internal conversion of ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$ in the $\beta$ form have been analyzed in terms of free-atom valence-electron wave functions renormalized to the Wigner-Seitz radii characteristic of the two solids. The three sets of experimental data are readily accounted for in this analysis: $\beta -\mathrm{Sn}$ turns out to have 1.6 ± 0.3 $5s$ electrons; and the transition $\beta -\mathrm{Sn}\to \alpha -\mathrm{Sn}$ is associated with a surprisingly small change, 0.1e to 0.2e, of valence-$s$ to valence-$p$ character. The concepts embodied in this analysis must be applied to the analysis of electron-binding-energy shifts observed in alloys and compounds, both insulating and metallic.