Contrast Asymmetries in Lang Topographs of Crystals Strained by Thin Films

Causes of contrast asymmetries between (h k l) and (h k l) Lang topographs of crystals strained by thin films are discussed. The images of film edges are approximated by direct and dynamical components, and experimental separation of these components is illustrated. The direct component, dominant for low μ t, is identical in (h k l) and (h k l) topographs, while the dynamical component, dominant for larger μ t, is asymmetrical and is responsible for the Lang topograph asymmetries. The asymmetries are due to the anomalous absorption or Borrmann effect, where waves belonging to one branch of the dispersion surface undergo less than normal absorption, while waves belonging to the other branch undergo more than normal absorption. It is shown that the absorption properties of these two branches can be reversed by suitable reflections from some crystals, leading to image asymmetry reversal.