X-ray and $\gamma$-ray propagation in bent crystals with flat and cylindrical surfaces

摘要

In this paper we investigate x-ray and $\gamma$-ray propagation in crystalshaving a constant strain gradient and flat or cylindrical surfaces. When adisplacement field is present, we solve the Takagi-Taupin equations either bythe Riemann-Green method or by a numerical method. We apply the results tostudy the operation of a double-crystal Laue-Laue diffractometer having a flatcollimating crystal followed by a bent analyzer crystal. In particular, weexamine the effect of the analyzer strain on the location of the diffractionpeaks in the dispersive and non-dispersive setup, thus confirming ourpreviously reported peak-location as being set only by the diffracting planespacing on the analyzer entrance surface.