X-Ray Bragg Diffraction in Asymmetric Backscattering Geometry

We observe three effects in the Bragg diffraction of x rays in backscattering geometry from asymmetrically cut crystals. First, exact Bragg backscattering takes place not at normal incidence to the reflecting atomic planes. Second, a well-collimated () beam is transformed after the Bragg reflection into a strongly divergent beam () with reflection angle dependent on x-ray wavelength—an effect of angular dispersion. The asymmetrically cut crystal thus behaves like an optical prism, dispersing an incident collimated polychromatic beam. The dispersion rate is . Third, parasitic Bragg reflections accompanying Bragg backreflection are suppressed. These effects offer a radically new means for monochromatization of x rays not limited by the intrinsic width of the Bragg reflection.

Figure 1

Schematic drawing illustrating Bragg diffraction in the asymmetric backscattering geometry, with the asymmetry angle $\eta \ne 0$. Exact backscattering ($\theta ={\theta }^{\prime }$) is attained in the transition from (a) to (b) while increasing $\theta$.

Figure 2

Transformation of the Bragg reflection region from the ($\lambda$, $\theta$) space of incident waves in the vicinity of normal incidence, into the ($\lambda$, ${\theta }^{\prime }$) space of exit waves. (s) Symmetrically cut crystal: $\eta =0$. (a) Asymmetrically cut crystal: $\eta \ne 0$. The red line is a locus of points obeying exact backscattering condition in asymmetric scattering geometry, given by Eq. (3). It is a borderline between scattering geometries of Figs. 1a, 1b. $\Omega =0.1°=1.7\mathrm{mrad}$.

Figure 3

Top: schematic of the experimental arrangement for studying exact Bragg backscattering of x rays from a single crystal, $D$. Other components: crystal collimator, $C$; selector, $S$; x-ray detector, Det. Bottom: fragment of Fig. 2a illustrating operation of the three crystal arrangement.

Figure 4

Bragg reflectivity from crystal $D$ of 9.1315 keV x rays, exactly backwards, as a function of the angle of incidence $\Theta =\pi /2-\theta$ to the reflecting atomic planes.