Focal aberrations of large-aperture HOPG von-Hàmos x-ray spectrometers

Focal aberrations of large-aperture highly oriented pyrolytic graphite (HOPG) crystals in von-Hamos geometry are investigated by experimental and computational methods. A mosaic HOPG crystal film of 100 μm thickness diffracts 8 keV x-rays. This thickness is smaller than the absorption depth of the symmetric 004-reflection, which amounts to 257 μm. Cylindrically bent crystals with 110mm radius of curvature and up to 100 mm collection width produce a X-shaped halo around the focus. This feature vanishes when the collection aperture is reduced, but axial spectral profiles show that the resolution is not affected. X-ray topography reveals significant inhomogeneous crystallite domains of 2±1mm diameter along the entire crystal. Rocking curves shift by about ±20arcmin between domains, while their full width at half-maximum varies between 30 and 50 arcmin. These inhomogeneities are not imprinted at the focal spot, since the monochromatically reflecting area of the crystal is large compared to inhomogeneities. Ray-tracing calculations using a Monte-Carlo-based algorithm developed for mosaic crystals reproduce the X-shaped halo in the focal plane, stemming from the mosaic defocussing in the non-dispersive direction in combination with large apertures. The best achievable resolution is found by analyzing a diversity of rocking curve widths, source sizes and crystal thicknesses for 8 keV x-rays to be ΔE/E ~ 10−4. Finally a general analytic expression for the shape of the aberration is derived.