X-Ray Diffraction

1. X-Ray Diffraction Dr. T. Ramlochan March 2010

2. Public service announcement… Radiation warning symbol New IAEA Radiation warning symbol Radiation is dangerous, so run away!

3. Crystals • A crystal is a solid material where the constituent atoms are arranged in an orderly repeating pattern extending in all three spatial dimensions CaSO4·2H2O SrTiO3

4. Crystallography • Crystals are divided into 7 lattice systems → all crystalline materials must fit in one of these unit cells • lengths of edges (a, b, c) of unit cell and the angles (α, β, γ) between them are the lattice parameters • The space group of a crystal is a description of the symmetry of the crystal → the unit cells do not just repeat side-by-side • Space groups in three dimensions are made from combinations of different symmetry operations (reflection, rotation and improper rotation, the screw axis and glide plane) • 230 unique space groups

5. Crystallography • The atoms in a crystal lattice form planes (described by Miller indices) that repeat

6. X-rays and diffraction • X-rays were discovered in 1895 by Röntgen • X-rays are electromagnetic radiation with wavelengths in the range of 0.5-2.5 Å • As with visible light X-rays will undergo diffraction when they encounter an obstacle • If the diffracting obstacle is on the order of the size of the wavelength, the propagating waves will have interference due to different waves having travelled different path lengths X-ray diffraction image of DNA by Rosalind Franklin (1952)

7. X-rays and diffraction • Differences in the length of the path travelled lead to differences in phase • The introduction of phase differences produces a change in amplitude → summed amplitude of the waves can have any value between zero and the sum of the individual amplitudes

8. Scattering of X-rays • Atoms (or their electrons) will scatter X-rays in all directions • If atoms are arranged in space in a regular periodic fashion, as a crystal, some of the scattered X-rays will undergo reinforcement in certain directions and cancellation in other directions producing diffracted beams • Diffraction is essentially reinforced scattering

9. Bragg’s Law • For a particular condition of scattering where the angle (θ) of the incident beam and the ‘reflected’ X-rays are the same, the scattered X-rays will be completely in phase and undergo reinforcement if the path difference is equal to a whole number of n wavelengths, such that nλ = 2d sin θ • This was first identified by W.L. Bragg and is called Bragg’s Law

10. Bragg’s Law • For a fixed wavelength (λ) and value of d, there will be an angle theta (θ) where diffraction (complete reinforcement) occurs • Diffractogram is a plot of the intensity of the diffracted X-rays vs. 2θ over a range of angles • Each peak represents a plane in the crystal lattice with a given ‘d-spacing’ • Basis for powder diffraction

11. X-ray production • X-ray are produced when electrically charged particles (e.g., electrons) with sufficient kinetic energy give up some energy • Non-characteristic (continuous) X-rays → electrons decelerated in an electromagnetic field (Bremsstrahlung) • Characteristic X-rays → if electrons have high enough kinetic energy can knock electrons out of their shells → when an electron moves from an outer shell to an inner one it is ‘excited’ and releases excess energy directly as X-rays with eV/wavelength characteristic of the atom released from

12. X-ray production • X-rays named according to shell being filled and number of shells changed (e.g., K shell filled by L shell (Kα radiation) or M shell (Kß radiation)) • Each peak represents a transition; more than one peak (‘family of X-rays’); Kα(highest probability) is ~5 times stronger than Kß • Kα is a doublet (Kα1 and Kα2) → different spin states • Kα1 always about twice the intensity of Kα2 • For Cu Kα1 1.540598 Å Kα2 1.544426 Å Kα1.541874 Å Kß1.392250 Å

13. X-ray production • For XRD we want monochromatic X-rays (i.e., X-rays of a single wavelength travelling in the same direction/plane) • Can filter the beam by passing through a material with an absorption edge between Kα and Kß wavelengths • For Cu radiation use Ni filter → Kß reduced to 1/500; Kα reduced by 1/2

14. X-ray generation • To generate X-rays → a) source of electrons, b) high accelerating voltage, and c) a metal target • Use a water-cooled X-ray tube • Evacuated glass tube with an anode (Cu target) and cathode maintained at high negative potential (HT transformer) • Filament is heated to emit electrons → accelerated towards target • X-rays emitted through (X-ray-transparent) beryllium windows

15. X-ray diffractometer • Diffractometer has two parts: • Generator → to generate X-rays • Goniometer → to scan sample through a range of angles

16. Diffraction optics/geometry • X-rays diverge from source → pass through Soller slits and divergence slits to define and collimate incident beam • Incident beam diffracted by ‘flat’ powder specimen • Diffracted beam passed through receiving slits • Secondary monochromator reduces background radiation from sample • X-rays collected by detector (proportional, Geiger, scintillation, semiconductor)

17. Diffractograms • Gives information about peak positions, intensity, and shape