  Two theoretical models for the description of the diffraction properties of
gradient crystals have been developed, one in the framework of the kinematic
theory, the other within a transfer matrix formalism based on the dynamical
theory of diffraction. A matrix describes the coupling and the propagation of
the forward- and the Bragg-diffracted wave functions through a plane, parallel
crystal lamella. It applies for the description of any crystalline medium with
changes of the diffraction properties along the direction of the surface
normal. Experimentally a crystal growth technique has been set up to produce
novel Si1-xGex gradient crystals with 0 < x < 0.4 on a large surface and with
growth rates of up to 0.6 um/min. Layer thicknesses of several 100 um have been
achieved. A tetragonal distortion attributed to different thermal expansion
coefficients has been discovered. The anisotrope mosaic distribution gives
evidences for the existence of misfit dislocations. The reflection curves
calculated by the transfer matrix method fit well the experimental results. The
diffraction data show an intensity increase of 25 related to the experimental
resolution function. Comparing this value with the calculated reflectivity for
perfect silicon, this factor increases to 40.
