Phase modulation effects in X-ray diffraction from a highly deformed crystal with variable strain gradient

The X-ray interbranch scattering by lattice distortions is studied for a thin crystal whose thickness is appreciably less than the conventional X-ray extinction length. The concept of interbranch phase modulation of the X-ray wavefield is extended to the case of a large gradient which depends on depth inside the crystal. The prominent interbranch features of the diffracted intensity are also established within this concept. Numerical calculations of the diffracted intensity are presented for an exponential strain gradient model to illustrate this. Diffraction (extinction) contrast is discussed for a strongly deformed specimen containing a single dislocation. It is predicted that for large values of the X-ray extinction length the extinction contrast may arise even in the case of a very thin crystal. This effect, owing to the interbranch phase changes of the waves scattered in the deformed matrix, is observed in experiments with protein crystals.