The resolution function of a spectrometer based on a strongly bent single crystal (bending radius of 10 cm or less) is evaluated. It is shown that the resolution is controlled by two parameters, (i) the ratio of the lattice spacing of the chosen reflection to the crystal thickness and (ii) a single parameter comprising crystal thickness, its bending radius, and anisotropic elastic constants of the chosen crystal. Diamond, due to its unique elastic properties, can provide notably higher resolution than silicon. The results allow to optimize the parameters of bent crystal spectrometers for the hard X-ray free electron laser sources.
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