Synchrotron-radiation measurements of forbidden reflections in silicon and germanium

The (442) and (662) reflections in both Si and Ge were measured using synchrotron radiation from the Wilson 12-GeV Synchrotron. These reflections, which are basis forbidden in diamond-structure materials, arise from two distinct effects: antisymmetric charge buildup due to covalent bonding of the valence electrons and anharmonic thermal vibrations of the core electrons. Because these reflections are sensitive only to deviations from a centrosymmetric charge density, their integrated intensities are extremely small. The measured structure factors for these reflections at room temperature were $F\left(442\right)=0.042\mathrm{}\pm 0.003$, $F\left(622\right)=0.005\mathrm{}\pm 0.004$, and $F\left(442\right)=0.0630\mathrm{}\pm 0.0016$, $F\left(622\right)=0.0558\mathrm{}\pm 0.0023$ in silicon and germanium, respectively. The anharmonic contribution can be removed from these values leaving the scattering amplitude due solely to the bond change. We compare these values to empirical and theoretical predictions. New techniques utilizing the inherent properties of synchrotron radiation will also be discussed.