Bragg reflection from single crystals is commonly applied to define monochromatic beams in neutron and X-ray scattering. In general, mosaic crystals provide a significantly higher particle flux than perfect crystals, at the expense of a deterioration in the beam divergence. This disadvantage can be overcome by using gradient crystals, which are characterized by a continuous variation in the crystal lattice spacing. Diffraction from a gradient crystal can be described by simple mirror reflection for a desired wavelength band. We synthesized various Si1-xGex single crystals with both fixed and continuously varying concentrations. They were grown on silicon substrates from a mixture of SiH4, GeH4, H2, HCl in a low pressure chemical vapor deposition reactor. The lattice spacing gradient was obtained by controlled variation of the gas flows. The various characterization techniques employed emphasize in particular the aspects of growth rate, crystallinity and mixing of the components, A test on a neutron diffractometer of a 0.85 mm thick crystal, grown for 24 h, showed the expected performance.