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GaInN layers are often grown on a sapphire substrate, with a low-temperature-deposited AlN layer and a thick GaN buffer layer. High-resolution X-ray diffraction experiments were conducted on BL20-B at the Photon Factory (Tsukuba, Japan), to investigate the structural quality of the AlN and GaN layers. Reciprocal space mapping was used to study samples ar each stage of the growth process and for various layer thicknesses. Two analysis techniques were compared. The first utilised broadening of reflections in reciprocal space, and the second was based on statistical diffraction theory (SDT). Both techniques yield information about the mosaic-blocks and layer thicknesses: however, simulations based on SDT give information on strain and tilt distribution within the AlN layer, evident in off centre, non-symmetric, peaks. This suggests a possible mechanism by which AlN buffer layers can be exploited to improve device characteristics. Our work also demonstrates the efficacy of SDT for the analysis of these structures.