The Electromagnetic Spectrum

Electromagnetic Plane Wave H E

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

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

Diffraction Angles cubic: orthorhombic hexagonal rhombohedral

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

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