Reciprocal Lattice & Diffraction

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Objectives By the end of this section you should:

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Presentation transcript:

Reciprocal Lattice & Diffraction Crystallography H. K. D. H. Bhadeshia Reciprocal Lattice & Diffraction

Weiss Zone Rule proven!

Cubic P, section of reciprocal lattice normal to [001]

Cubic P, section of reciprocal lattice normal to [110]

Cubic P, section of reciprocal lattice normal to [111]

For 100 keV accelerating voltage, the wavelength of electrons is 0 For 100 keV accelerating voltage, the wavelength of electrons is 0.0037 nm. If the d spacing is 0.2 nm, then the Bragg angle is just 0.5° Ewald sphere has a large diameter in reciprocal space.

Cubic P Cubic F

Cubic P Cubic F

Cubic P Cubic F

Lattice: face-centred cubic Motif: Si at 0,0,0 Si at 1/4,1/4,1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 Lattice: face-centred cubic Motif: Si at 0,0,0 Si at 1/4,1/4,1/4

diffraction from thin crystals

100 nm thick foil 20 nm thick foil

[111] [0.99 0.99 1.02]

(R. Herring)