1. Theory of diffraction
Peter Ballo

5. Ka
L-series Ka Fe Cr Kb Kb Ka Kb Ni

6. Diffraction and destructive interference
Incoming, coherent wavefront (all rays have same phase – both rays have crests at same time)
Outgoing wave: crests match troughs across the planar wavefront darkness
Destructive interference
(This diagram shows the electric field of the EM radiation as it oscillates with time and distance travelled by the ‘ray’. They make the simplifying assumption that scattering from atoms does not change phase of radiation, i.e. the incoming and outgoing rays have the same value of electric field at the scattering atom.)

7. Bragg’s Law n  = 2 d sin   d Constructive interference –
Optical path difference = 2 (d sin  )
Constructive interference –
optical path difference equals whole number, n , of wavelengths, .
n  = 2 d sin 

8. Detector Divergence Receiving slit Anti-scatter Beam Attenuator knifeq 2
Divergence
slit
Attenuator
Sample
Detector
Graphite
monochromator
Anti-scatter
Beam
knife
Receiving

12. Crystal Structures Can be described by crystallographic “unit cell”
Crystal structure: characterized by regularity of atomic arrangement.
Atomic positions repeat periodically
“structure unit” can be specified.
Can be described by crystallographic “unit cell”

13. All structures shown here have the same lattice !!
Lattices
All structures shown here have the same lattice !!
Unit cell
N.b. identical environment

14. Close Packing Crystal Structures
APF = 0.74
FCC: ABCABC..
HCP: ABAB...

15. Diffraction Patterns in FCC and BCC
X-rays
Simple cubic:
All combinations of h, k and l are seen in diffraction
FCC and BCC:
Systematic absences of some reflections (certain combinations of h, k, l)
Centred atoms lead to destructive interference in some cases
out of phase
The (100) reflection from an F-centred cubic lattice
Smart, Moore “Solid State Chemistry”

16. Looking down on Young’s slit (interference) experiment
Learning outcomes:
Appreciation of importance and prevalence of metallic bonding in elemental solids.
Apart from intermediate cases (which in general behave as large covalent molecules), everything else is a gas
H atom is exception

17. Diffraction gratings Diffraction patterns

18. Ewald Construction

19. First Brillouin Zone: Two Dimensional Oblique Lattice

20. Primitive Lattice Vectors: FCC

21. Brillouin Zones: FCC

22. First Brillouin Zone FCC