Resolution correction for surface X-ray diffraction at high beam exit angles

Owing to the two-dimensional periodicity of a superstructure on the crystal surface, the intensity in reciprocal space is continuously distributed along rods normal to the sample surface. The analysis of rod scans in surface X-ray diffraction provides information about the structure parameters normal to the sample surface. For high resolution to be achieved, the measurements must extend to momentum transfers q_⊥ that are as large as possible. At large exit angles, the conventional Lorentz factor must be modified to take account of the finite aperture of the detector and the continuous intensity along the lattice rod. For two types of Z-axis diffractometer used in surface X-ray crystallography, an analytical expression for the resolution correction of rod-scan intensity data has been developed. It takes into account an anisotropic detector resolution T(ΔΘ, ΔΦ), the finite width of the diffracted beam and the primary-beam divergence parallel to the sample surface, Δτ. The calculation of the convolution functions is simplified by a projection onto the q_⊥ = 0 plane. The effects of different detector settings and the influences of the primary-beam divergence and the sample quality on the measured intensity are demonstrated for several examples.