PhaseDiff

PhaseDiff - Path Length and Phase Differences d δ α φ...

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Unformatted text preview: Path Length and Phase Differences d δ α φ (h,k) a A a/h a xa xa _____________________________________________________________________________________________________________________ Unit cell side = a Set of diffraction planes = (h,k) New atom in unit cell at position = xa Path length difference for rays reflecting from old and new planes = δ _____________________________________________________________________________________________________________________ a2 2 for large ∆: d = h2 -A 2 _____________________________________________________________________________________________________________________ for small ∆: δ2 = x2a2 - α2 _____________________________________________________________________________________________________________________ α = xa sin φ a A = h sin φ _____________________________________________________________________________________________________________________ δ2 = x2a2 (1 - sin2θ) a2 2 d = 2 (1 - sin2θ) h } δ xa = a = hx d h _____________________________________________________________________________________________________________________ δ = (hx) d in general: δ = (hx + ky + lz) d _____________________________________________________________________________________________________________________ diffraction angle: 2 d sinθ = λ sinθ = λ/2d _______________________________________________________________ extra path length: ∆x = 2 δ sinθ = δλ/d θ δ sinθ δ _______________________________________________________________ ∆φ 2π δ phase difference: ∆x = 2π d λ phase difference: ∆φ = 2π (hx + ky + lz) _______________________________________________________________ δ sinθ plane wave amplitude: e2πi (hx + ky + lz) ...
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This document was uploaded on 02/22/2012.

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