X-ray and γ-ray propagation in bent crystals with flat and cylindrical surfaces

In this paper, X-ray and γ-ray propagation in crystals having a constant strain gradient and flat or cylindrical surfaces is investigated. When a displacement field is present, the Takagi–Taupin equations are solved either by the Riemann–Green method or by a numerical method. The results are applied to study the operation of a double-crystal Laue–Laue diffractometer having a flat collimating crystal followed by a bent analyzer crystal. In particular, the effect of the analyzer strain on the location of the diffraction peaks in the dispersive and non-dispersive set-up is examined, thus confirming the previously reported peak location as being set only by the diffracting-plane spacing on the analyzer entrance surface.