CHE-20031 (Structural Inorganic Chemistry) X-ray Diffraction & Crystallography lecture 3 Dr Rob Jackson LJ1.16, 01782 733042

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CHE (Structural Inorganic Chemistry) X-ray Diffraction & Crystallography lecture 3 Dr Rob Jackson LJ1.16, Twitter: #che20031

X-ray Diffraction & Crystallography: lecture 3 plan What have we covered so far? –Key points Single crystal and powder diffraction Simulated patterns How to obtain positions of atoms A further example of indexing a pattern (revision from lecture 2) che-20031: XRD & Crystallography lecture 3 2

Key points from lectures 1 and 2 We can index an X-ray diffraction pattern to get the Miller indices and lattice parameters of a crystal. The peak positions therefore enable us to calculate the crystal lattice parameters. How do we get the atomic positions? che-20031: XRD & Crystallography lecture 3 3

Measurements on single crystals The data we have seen so far have come from single crystals. However it is not always possible to grow perfect single crystals. Samples are often in the form of powders. che-20031: XRD & Crystallography lecture 3 4 A single crystal of CaF 2

What about powder samples? Usually you don’t have single crystals to analyse. Powder samples contain many small crystallites, of dimension to m, and they will be orientated randomly. We still need the 2  angles for each lattice spacing, but they are more difficult to measure.. che-20031: XRD & Crystallography lecture 3 5

Scattering an X-ray beam from a powder sample The diagram shows an X-ray beam incident on a sample of randomly-orientated crystallites. che-20031: XRD & Crystallography lecture 3 6

A real powder XRD pattern che-20031: XRD & Crystallography lecture 3 7

Indexing powder patterns The X-ray diffraction pattern on slide 7 can be indexed in the same way as the single crystal patterns we have seen, but some of the peaks may be less sharp, so harder to measure. However, for powder patterns of many materials, library patterns are available for comparison. che-20031: XRD & Crystallography lecture 3 8

Using library patterns Using a pattern like the one on slide 7, experimental powder patterns can be compared with library patterns, and if identification is successful, automatic indexing is possible. This information is obtained from the PDF (powder diffraction file) published by the International Centre for Diffraction Data: (the site will be shown) che-20031: XRD & Crystallography lecture 3 9

A simulated powder XRD pattern Intensity vs 2θ 10 che-20031: XRD & Crystallography lecture 3

How atom positions are obtained For completeness, we need to consider how to get the atomic positions. What information has not been used so far? The atomic positions are obtained from the peak intensities, but the procedure involved is beyond the scope of this module. che-20031: XRD & Crystallography lecture 3 11

Exercise: a further example of indexing a pattern for a cubic material 22 sin 2  ratiohkla Assign hkl values assuming the lowest ratio value is 3. Calculate ‘a’ for each reflection and explain any differences in the values. What is the lattice type? che-20031: XRD & Crystallography lecture 3 12