Diffractogram
A diffractogram (from Latin diffraction : "diffraction" and Greek. ... grámma : "written", "letter") is the graphic recording of a diffraction experiment , for example an electron, neutron or X-ray diffraction.
construction
In a (one-dimensional) diffractogram, the measured radiation intensities are plotted against the angle between the radiation source, sample and detector (2 θ angle).
For recording a polycrystalline sample with a powder diffractometer is usually monochromatic Cu -Kα radiation used. During the measurement, the specified angular range, usually for 2θ = 10 ° - 90 °, is traversed in defined steps. Due to the purely random orientation of the individual crystals in the sample, enough crystals under a certain Bragg angle θ fulfill the Bragg equation , i.e. the X-rays are reflected at a certain lattice plane in the crystal lattice and the reflex can be observed as a peak in the diffractogram. The intensity of the reflections is primarily dependent on the atoms on the lattice plane. However, the intensity can also be weakened by destructive interference with waves scattered on other lattice planes. The intensities can also vary due to texture effects if the individual crystals within the sample have a preferred orientation, for example due to a needle-like crystal habit .
While relatively few reflections can be observed with simple and highly symmetrical compounds, as in the example of the diffractogram of the cubic sodium bromide (NaBr) shown on the right , more complicated compounds with lower symmetry ( triclinic or monoclinic ) show a significantly larger number of reflections (see example below ).
Every crystalline compound has a characteristic diffractogram based on the position and intensity of the reflections and can thus be clearly identified. In addition to measured diffractograms, these can also be simulated, provided that data on the lattice parameters and atomic positions of the compound are available from measurements of single crystals ( crystal structure analysis ).
Intensity distribution in X-ray powder diffractograms and in neutron diffraction
In an X-ray powder diffractogram, a decrease in the intensity of the reflections towards larger diffraction angles can be observed. This is due to the fact that the atomic form factors become smaller with larger diffraction angles and therefore their share in the total intensity is also smaller at larger angles. This decrease in intensity does not occur with neutron diffraction, since the atomic shape factors are replaced by the scattering lengths (b values) of the atomic nuclei. Because of the small size of the atomic nuclei, these are almost constant and distributed around an average value.
geometry
A receiver moving along a line creates a one-dimensional diffraction diagram. A two-dimensional receiver, typically a photo plate, shows the diffraction maxima as circles. If the powders show a preferred orientation, individual diffraction points emerge. A single crystal produces only discrete diffraction points.
Use of X-ray powder diffractograms
In addition to crystallography, the creation and evaluation of diffractograms is used today in many other areas, such as solid-state chemistry and solid-state physics or materials science , and for various purposes.
preparation
Crystalline powders are usually prepared as thick as a fingernail between two adhesive strips (which do not cause reflections) to record an X-ray powder diffractogram. Clamped in a sample carrier, the sample is then examined in the diffractometer. The use of glass capillaries instead of adhesive strips is also possible and generally enables better diffractograms.
Problems and solutions of X-ray powder diffractometry
Various preparation and measurement difficulties can occur with X-ray powder diffraction.
Particle size and location statistics
Based on the location statistics alone (according to Smith (1992) ) there are approx. 38,000 crystallites in the reflection position in a phase-pure sample of crystallites with a grain diameter of 1 μm. The grain diameter increases tenfold - the mean grain diameter is 10 μm - there are only 760 crystallites in the reflection position. The measured intensities are therefore largely determined by the particle statistics; they continue to vary greatly in the case of texture effects (e.g. with platelets or needles), which cannot always be avoided even with careful preparation.
For optimal preparation, the sample should have a grain diameter of 1–10 μm. If the crystallites are too large to measure this sample, no continuous line is recorded, but a group of individual points. Crystals that are too large are noticeable through irregular reflections. If the crystallites are too small, the signal is broadened; if a sample consists of nanoparticles, it is usually X-ray amorphous.
If the crystallites are too large, they have to be crushed, which can be done by using a mortar or grinding. This process can be problematic due to the pressure applied and the increase in temperature, as this can lead to phase changes or chemical reactions. This can e.g. B. can be avoided by cooling with liquid nitrogen, another advantage of this method is the increase in brittleness caused by the cold. For the sake of simplicity, a solvent which evaporates easily and does not react with the sample can also be selected.
Texture effects
Texture effects result from a preferred orientation of the crystalline particles. If the crystallites are anisotropic in a powder sample, e.g. B. have plate-like or needle-like shapes, it can be very difficult to get them to adopt random orientations that are important for diffractometry. So are z. B. needle-shaped crystallites are not randomly distributed, but in a preferred orientation (preferred orientation). Needle-shaped crystallites are very likely to lie on their side and finding one crystallite standing perpendicular to the other is unlikely (like dropping Mikado sticks). Texture effects are a major problem in qualitative and quantitative phase analysis. Rotating the sample in the X-ray diffractometer only improves the particle statistics ; preferred orientations can be reduced by oscillating the sample in an additional spatial direction ( wobbled scan ).
Texture leads to greatly reduced reflex intensities or missing reflexes in comparison to a calculated powder diffractogram.
For mica z. B. the 00l reflexes increased by a factor of 5-10 compared to the other reflexes. This effect is only desirable here because it can be used for the analysis of clay minerals, so the texture effect is intentionally increased during preparation.
Underground
The background of an X-ray powder diffraction pattern is, among other things, strongly dependent on the quality of the radiation source: the fewer foreign wavelength components there are in the monochromatic radiation, the lower the background. At best, measurements should therefore be made with synchrotron radiation, but at least with a high-quality X-ray tube with the aid of a monochromator crystal (e.g. germanium (111)). Gas particles in the beam path also increase the background content in the powder data, so evacuation is advisable. The sample carrier (the diaphragm) also provides a background; Apertures from z. B. Quartz have a very low background. Last but not least, the Compton scattering must be mentioned here. The inelastic scattering of the radiation on the sample can increase the wavelength of the radiation; this effect occurs especially when fluorescence is possible (e.g. for iron atoms when CuK α radiation is used).
Asymmetrical reflections
Asymmetrical reflections can occur due to axial divergence or transparency of the sample. The axial divergence can be prevented by using so-called Soller slits (a special diaphragm made of stacked lamellae) , a reduction in the sample transparency can be achieved by different preparations.
evaluation
Crystallinity, particle size and stress
With the help of a diffractogram, a statement can be made about the crystallinity of a sample. A high product crystallinity is reflected in a good signal-to-noise ratio and a low half-width of the reflections. Poorly crystallized samples show strongly broadened reflections in the diffractogram and a very restless course of the curve. Broadened reflections can also occur due to a small particle size (e.g. due to strong mortaring of the sample) or lattice tension. Lattice tensions, i.e. different d-values, lead to different reflex positions (which cannot be resolved) and thus to wider reflexes. If stress acts on the crystal, the reflexes shift to higher or smaller diffraction angles, depending on the type of stress, because the unit cell becomes larger or smaller.
Phase purity
A diffractogram can also be used to examine the phase purity of a crystalline powder, ie whether the sample consists of only one crystalline ( single phase ) or several ( multi-phase ) compounds. In pure-phase powders, all reflections can be observed and assigned to the connection, in multi-phase powders at least some of the reflections can be clearly assigned to a connection, and some reflections from different compounds can also overlap. In practice, phase purity is usually checked by comparing a measured and a calculated powder diffraction pattern (see example on the right). Compared to the calculated powder diffractogram, there must never be more than the expected reflections so that a sample can be regarded as phase-pure, but there can be fewer (texture effect).
Additional, forbidden reflexes can be triggered by various methods, e.g. B. the search with the SearchMatch function of WinXPOW or the comparison with the powder data of the starting materials of the product can be identified.
In the case of phase-pure, crystalline products for which no single-crystal structure analysis is possible, it is possible to determine the cell parameters and the space group by means of indexing from the X-ray powder data. This can e.g. E.g. with the Topas Academic program .
Lattice parameters
Based on the position of the reflections, according to the Bragg equation, the spacing between the lattice planes of the crystals contained in the sample and thus the different crystalline phases to which they belong can be determined. At least in the case of simple, highly symmetrical compounds, the lattice parameters of the unit cell of the crystal structure can also be determined from the diffractogram . With the help of the Rietveld method , the individual atomic layers can ideally also be determined, although in the experiment the diffraction intensity of a few atomic layers is too low for a measurement.
literature
- R. Allmann (1994): X-ray powder diffractometry , Verlag Sven von Loga, ISBN 3-87361-029-9
- L. Smart, E. Moore (1995): Introduction to Solid State Chemistry , Vieweg Verlag, Braunschweig, ISBN 3-528-06773-X
- AR West (2000): Fundamentals of Solid State Chemistry. Wiley-VCH, Weinheim. ISBN 3527281037
Individual evidence
- ↑ Massa, Werner: Crystal structure determination . 4th edition Teubner, Wiesbaden 2005, ISBN 978-3-8351-0113-5 , pp. 48 f .
- ↑ a b c d e Allmann, Rudolf .: X-ray powder diffractometry: computer-aided evaluation, phase analysis and structure determination . 2nd, corrected and enlarged edition. Springer Berlin Heidelberg, Berlin, Heidelberg 2003, ISBN 978-3-540-43967-7 .
- ↑ a b c Detlef Beckers: QPA instrumentation, sample and validation aspects. PANalytical BV, 2015, accessed September 14, 2018 .
- ↑ Allmann, Rudolf .: X-ray powder diffractometry: computer-aided evaluation, phase analysis and structure determination . 2nd, corrected and advanced Edition Springer, Berlin 2003, ISBN 3-540-43967-6 .