Enhancing the Energy Resolution in Inelastic X-ray Scattering Experiments

An X-ray crystal spectrometer uses a perfect crystal (mostly Si or Ge) to select X-rays of a certain energy, which depends on the chosen angle of incidence via Bragg's law¹. To increase overall efficiency, i.e. to increase the angular acceptance, analyzer crystals with cylindrical or spherical shapes are widely used. This allows the focussing of X-rays scattered by a point source (i.e. the sample under investigation) onto the small sensitive area of an X-ray detector. For experiments requiring the highest energy resolution, the analyzer crystal is often built by gluing several thousands of single crystallites ("dices") on a spherical substrate. Since the single crystallites are flat, the surface of their composition follows the desired curved shape rather approximately. Thus the angle of incidence varies along the crystallite surface, leading to a broadening of the energy range accepted by each dice and thus a degradation of the energy resolution. Although each dice transmits a certain energy band, the problem can be overcome by exploiting the fact that it sorts the photons in space according to their energy, since the energy and the diffraction angle are coupled by Bragg's law.

The ID16 team combined a high-efficiency position-sensitive pixel detector with a crystal spectrometer (Figure 1) by registering not only the number of photons reaching the detector, but also their exact position on the detector surface. In this way, the photon energy within the energetical bandpass transmitted by the dices could be deduced with a high accuracy. By this procedure the energy resolution of the existing spectrometers operating in the 6-10 keV energy range can be enhanced by an order of magnitude without otherwise affecting their performance. In the first experiments of this type (Figure 2), a remarkably good resolution of 23 meV at 9.9 keV was achieved with a spectrometer based on a spherical diced analyzer crystal with a 1-m bending radius in nearly backscattering conditions utilizing a Medipix2 detector. If equipped with a standard position-insensitive detector, the instrument would have a resolution of 190 meV. These novel results may affect the design of future high-resolution X-ray spectrometers. They also show an exciting new area to which pixel detectors are ideally suited.

Fig. 1: Experimental arrangement. The diced analyzer crystal projects a point source into a square which is an image of an individual dice magnified by a factor of two. Due to an energy gradient within the focus, it is possible to measure the photon energy using the information on its position.

Fig. 2: Panels (1)-(6): Series of images collected with the position-sensitive detector (PSD) while tuning the incident-photon energy, E denoting the energy transferred to the sample. Each pixel is found to be illuminated at a well-specified photon energy, making it possible to infer the photon energy from the pixel position with an accuracy 8-fold better than with a standard position-insensitive detector (PISD), as can be seen from the respective resolution functions depicted in the panel (7).

See also: an animated example of an inelastic X-ray scattering experiment with position-sensitive detectors: Phonons in Be

¹Bragg's law states that the energy of a radiation reflected by the crystal is , where d is the lattice spacing corresponding to the reflection and the angle of incidence .

Authors and Principal Publication
S. Huotari, Gy. Vanko, F. Albergamo, C. Ponchut, H. Graafsma, C. Henriquet, R. Verbeni, G. Monaco, Journal of Synchrotron Radiation 20, 467-472 (2005).
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