COMPARISON OF SEVERAL POWDER DIFFRACTION GEOMETRIES

D. Rafaja, R. Kuzel, Jr.

Symmetrical Bragg-Brentano geometry has been dominating in powder diffraction for many years and it can be called as conventional powder diffraction technique. However, other asymmetrical geometries have also been used for a long time as for example -- the so-called $\Omega$ and $\Psi $ -- goniometers applied to the stress and texture measurements. Recently, significantly growing interest in thin films resulted in the development of different techniques of the grazing incidence type : historically old Seemann-Bohlin geometry and its relatively new alternative, the parallel beam technique. Theoretical descriptions of instrumental factors for all the techniques have already been published. This small contribution compares diffraction patterns, especially profiles, of standard powder samples and ferroelectric thin films obtained with conventional powder diffraction geometries on the XRD-7 (Seifert-FPM) and HZG-4 goniometers (FPM) with those measured by the Seemann-Bohlin goniometer (HUBER) and parallel beam (XRD-7) arrangements with different inclination angles. Basic features of the techniques can be summarized briefly as follows :

Bragg-Brentano symmetric case, $\theta - 2\theta$ scan

• for each reflection only the planes parallel to the surface are diffracting, so that the information corresponding to different hkl diffraction peaks is related to different crystallite groups
• consequently, the method is suitable for quick texture estimation
• the penetration depth of radiation significantly increases with increasing diffraction angle
• the intensities of diffraction peaks are relatively high depending, of course, on the slits, source and the type and amount of material used (e.g. thin film)
• the instrumental XRD line broadening varies with the diffraction angle and it is relatively low and nearly independent of experimental set-up, with exception of the receiving slit width

• only the planes inclined with the angle $\psi$, the deviation from the symmetric position, are diffracting
• therefore, the method is appropriate for the investigation of deformations in specimen as well as for a more precise determination of the preferred orientation
• line broadening is significantly higher, mainly because of defocusation
• the technique is sensitive to the alignment

• for each reflection the planes differently inclined to the surface are diffracting
• consequently, the method is suitable for stress measurement
• for low angle of incidence, the penetration depth does not vary much with the diffraction angle but it is strongly dependent on the angle of incidence
• due to the focusing geometry, the diffraction intensities are relatively high
• as the penetration depth is rather low (that is approximately ten times less than in the Bragg--Brentano method), the technique is especially suitable for thin films
• the instrumental broadening is higher than in the B-B case; it is relatively low at higher angle of incidence $\gamma$ (e.g. 10 degrees), but it increases rapidly with decreasing $\gamma$
• the large line broadening is caused by the defocusation; as the whole focusation needs cylindrically curved samples, the large divergence (i.e. the large irradiated area) combined with a flat specimen can be the origin of the large instrumental broadening
• the technique is extremely sensitive to the alignment; for precise quantitative evaluation of lattice parameter the usage of an internal standard in the form of very thin powder layer covering the sample surface is inevitable

• the diffraction intensities are relatively low, because only a part of the diffracted intensity is transmitted to the detector
• the line broadening is higher than in the conventional B-B geometry; for low incidence angles $\gamma$, the instrumental broadening is nearly constant and lower than in the SB case but it increases with the increasing angle of incidence
• the technique is less sensitive to the alignment but care must be given to the correct inclination of the long Soller slits in the diffracted beam as well as to the setting of the secondary monochromator