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

TL;DR

This paper analyzes how x-ray and gamma-ray beams propagate through bent crystals with flat or cylindrical surfaces, focusing on strain effects and diffraction peak positions using analytical and numerical methods.

Contribution

It introduces solutions to the Takagi-Taupin equations for crystals with strain gradients and applies them to a double-crystal diffractometer setup, confirming peak location dependencies.

Findings

Strain in the analyzer crystal affects diffraction peak positions.

The peak location is determined solely by the diffracting plane spacing at the entrance surface.

Validated the analytical solutions with numerical methods.

Abstract

In this paper we investigate x-ray and $\gamma$-ray propagation in crystals having a constant strain gradient and flat or cylindrical surfaces. When a displacement field is present, we solve the Takagi-Taupin equations either by the Riemann-Green method or by a numerical method. We apply the results to study the operation of a double-crystal Laue-Laue diffractometer having a flat collimating crystal followed by a bent analyzer crystal. In particular, we examine the effect of the analyzer strain on the location of the diffraction peaks in the dispersive and non-dispersive setup, thus confirming our previously reported peak-location as being set only by the diffracting plane spacing on the analyzer entrance surface.