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.

GIDInd: an automated indexing software for grazing-incidence X-ray diffraction data.

Grazing-incidence X-ray diffraction (GIXD) is a widely used technique for the crystallographic characterization of thin films. The identification of a specific phase or the discovery of an unknown polymorph always requires indexing of the associated diffraction pattern. However, despite the importance of this procedure, only a few approaches have been developed so far. Recently, an advanced mathematical framework for indexing of these specific diffraction patterns has been developed. Here, the successful implementation of this framework in the form of an automated indexing software, named GIDInd, is introduced. GIDInd is based on the assumption of a triclinic unit cell with six lattice constants and a distinct contact plane parallel to the substrate surface. Two approaches are chosen: (i) using only diffraction peaks of the GIXD pattern and (ii) combining the GIXD pattern with a specular diffraction peak. In the first approach the six unknown lattice parameters have to be determined by a single fitting procedure, while in the second approach two successive fitting procedures are used with three unknown parameters each. The output unit cells are reduced cells according to approved crystallographic conventions. Unit-cell solutions are additionally numerically optimized. The computational toolkit is compiled in the form of a MATLAB executable and presented within a user-friendly graphical user interface. The program is demonstrated by application on two independent examples of thin organic films.