We report on the growth and characterization of sapphire single crystals for X-ray optics applications. Structural defects were studied by means of laboratory double-crystal X-ray diffractometry and white-beam synchrotron-radiation topography. The investigations confirmed that the main defect types are dislocations. The best quality crystal was grown using the Kyropoulos technique. Therein the dislocation density was 10$^2$–10$^3$ cm$^{-2}$ and a small area with approximately 2*2 mm$^2$ did not show dislocation contrast in many reflections. This crystal has suitable quality for application as a backscattering monochromator. A clear correlation between growth rate and dislocation density is observed, though growth rate is not the only parameter impacting the quality.