Impact of sample misalignment on grazing incidence x-ray diffraction patterns and the resulting unit cell determination

Grazing incidence x-ray diffraction (GIXD) is a frequently used tool for the crystallographic characterization of thin films in terms of polymorph identification and determination of the crystallographic lattice parameters. Even full structure solutions are possible. To obtain highly accurate diffraction patterns, the thin film sample has to be aligned carefully with the center of the goniometer, which allows a defined incidence of the primary x-ray beam relative to the sample surface. This work studies the effect of misalignment of a thin film sample on the acquired diffraction pattern. Three potential types of misalignments are considered: the deviation of the sample surface from the center of the goniometer, an error in the incidence angle of the primary beam, and an inclination of the goniometer rotation axis from the normal of the substrate surface. The consequence of these types of sample misalignments is the shift of diffraction peaks toward specific directions in reciprocal space. Mathematical equations are given that relate the error in positions of Bragg peaks for each type of sample misalignment. Experiments with intentionally misaligned samples confirm the given formulas. In a subsequent step, the errors in the peak positions are translated to systematic errors in the estimation of the unit cell parameters. Depending on the type of misalignment, some alignment errors can be reduced or even corrected; in particular, azimuthal sample rotations prove to be advantageous in these cases. The results in this work improve the quality of GIXD measurements, in general, enabling deeper analysis like the full structure solution from the GIXD pattern on everyday basis.