1. The Electromagnetic Spectrum

2. Electromagnetic Plane WaveH E

3. Bragg Reflection q a To satisfy both: c q = a e a b d’’ q Bragg’s Law
For constructive interference in the upper figure:
For constructive interference in the lower figure:
These two equations can only be satisfied if q = a, yielding Bragg’s Law:
Bragg’s Law a e d’ a c b
Figure 3-2, Cullity

4. Diffraction q q q q A C A C D F
(200)
(100) E B B
2nd order (100) diffraction = 1st order (200) diffraction

5. Diffraction Angles
cubic:
orthorhombic
hexagonal
rhombohedral

6. Diffraction Methods a S So·a a So S·a
So and S are unit vectors of the incident and reflected x-ray beams respectively. a So
S·a

7. Diffraction & Reciprocal Lattice
Diffracted beam
S/l
Hhkl = (S - So)/l q
Incident
beam q q
So/l
(hkl)
Reciprocal-lattice
origin
By geometry we know that (S-So) = 2 sin q. We also know that Hhkl = (S-So)/l, and Hhkl = 1/d
Therefore, (2 sin q)/l = (S-So)/l = Hhkl = 1/d, or (2 sin q)/l = 1/d (Bragg’s Law)
Ewald sphere
S and So are unit vectors