Determination of magnitude, phase, and temperature dependence of forbidden reflections in silicon and germanium

The temperature dependence of the quasiforbidden reflections (442) and (622) in Si and Ge were measured with the use of synchrotron radiation. The absolute phase was determined in a novel way by using multiple reflections as a reference phase. The anharmonic vibrational amplitudes of the atoms were also determined directly from the temperature-dependent x-ray intensities. The phase of the (442) bonding-electron structure factor changes sign between silicon and germanium and is a manifestation of the difference in their antisymmetric bond-charge distribution.