We present a treatise on solving the Takagi-Taupin equations in the case of a strain field with an additional, spatially slowly varying component (owing to e.g. heat expansion or angular compression). We show that the presence of such a component in a typical case merely shifts the reflectivity curve as a function of wavelength or incidence angle, while having a negligible effect on its shape. On the basis of the derived result, we develop a computationally efficient method to calculate the reflectivity curve of a large deformed crystal. The validity of the method is demonstrated by compared computed reflectivity curves with experimental ones for bent silicon wafers. An excellent agreement is observed.
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