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Featured Application: laser surface-processing. Monocrystalline barium fluoride (BaF2) slab targets were irradiated by focused 46.9-nm laser radiation at various fluence levels above the ablation threshold. Well-developed ablation patterns with sharp edges were studied by AFM (atomic force microscopy). Their inner surfaces were uniformly covered by periodic structures. The spatial period of the ripples depends on the laser fluence. When the sample is rotated by 45°, the orientation of the grating-like structure changes accordingly. Thus, the grating vector of the periodic structure seems to be coupled to the crystallographic planes of the single crystal. This means that the XUV-laser induced ripples reported here differ from LIPSS (laser-induced periodic surface structures) associated with interference phenomena occurring on illuminated surfaces. Therefore, other mechanisms are discussed to explain the formation of the periodic nanostructures reported in this article. [ABSTRACT FROM AUTHOR]