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The defects and the lattice perfection of an AlN (0001) single crystal grown by the physical vapor transport (PVT) method were investigated by wet etching, X-ray diffraction (XRD), and infrared absorption, respectively. A regular hexagonal etch pit density (EPD) of about 4000 cm~(-2) is observed on the (0001) A1 surface of an AlN single crystal. The EPD exhibits a line array along the slip direction of the wurtzite structure, indicating a quite large thermal stress born by the crystal in the growth process. The XRD full width at half maximum (FWHM) of the single crystal is 35 arcsec, suggesting a good lattice perfection. Pronounced infrared absorption peaks are observed at wave numbers of 1790, 1850, 2000, and 3000 cm~(-1), respectively. These absorptions might relate to impurities O, C, Si and their complexes in AlN single crystals.