X-ray standing waves at grazing angles

X-ray diffraction from crystal surfaces at grazing angles gives rise to X-ray standing waves above and below the surface. Expressions are derived for the fluorescence observed from atoms located on or in a crystal as a result of excitation by the grazing-angle X-ray standing waves. In addition to the dependence of the fluorescence on the position of the atom with regard to the crystal plane that is responsible for the diffraction, the standing-wave amplitude also depends on the distance from the surface. We present standing-wave measurements from I on Ge(111) and the Ge atoms themselves which illustrate these effects.