[en] Detailed measurements of the X-ray scattering from a 400 AA thin film of Nb grown on sapphire have been performed using synchrotron radiation from a bending magnet. Bragg reflections from Nb planes perpendicular to the surface normal have a two-component lineshape: a sharp, essentially resolution-limited peak, superimposed on a diffuse Lorentzian-squared component. In contrast, Bragg peaks with a finite wavevector transfer in the plane of the film display the broad component only. These measurements indicate that the lattice mismatch between the metallic overlayer and substrate is relieved by the formation of domains randomly rotated in the plane of the film. (author)