Characteristics of the X-ray tunable source on the basis of parametric radiation from non-relativistic electrons in a crystal are considered. Theoretical interpretation of experimental X-ray spectra in the transmitted electron microscope with the crystal foil as a target is considered. Conditions for the kinematical decrease of the radiation line width due to electron multiple scattering are also described. (c) 2005 Elsevier B.V. All rights reserved.