Exact Bragg backscattering of x rays

Exact 180° Bragg scattering of pulsed synchrotron radiation was observed by using a semitransparent detector and a time-of-flight technique. The angular dependences of Bragg scattering of monochromatic 14.413 keV x rays with only 0.5 $\mu$eV bandwidth were studied by utilizing the $\left(1\mathrm{}3\overline{4}28\right)$ reflection of an ${\mathrm{Al}}_2{\mathrm{O}}_3$ crystal at different temperatures. By heating the crystal first the exact backscattering shows up achieving maximum intensity and 1.7 mrad angular width at 372.40 K. By increasing the temperature it develops into the usual Bragg reflection with much narrower angular profile. The measured dependences are in agreement with the theory. The fit is sensitive to a $5\times {10}^{-9}$ Å variation of interplanar distance.