{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

reciprocalLattice+BrillouinZone

# reciprocalLattice+BrillouinZone - Brillouin Zones Physics...

This preview shows pages 1–8. Sign up to view the full content.

Brillouin Zones Physics 3P41 Chris Wiebe

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Direct space to reciprocal space ij j i a a πδ 2 * = Reciprocal space Real (direct) space Note: The real space and reciprocal space vectors are not necessarily in the same direction
Laue Equations ° Another way of expression the diffraction condition k = G is by the Laue equations, which can be derived by taking the scalar product of k and G with a 1 , a 2 , and a 3 ° These equations have a simple interpretation: for a Bragg reflection, k must lie on a certain cone about the direction of a 1 (for example). Likewise, it must be on a cone for a 2 and a 3 . Thus, a Bragg reflection which satisfies all three conditions must lie at the intersection of these three cones, which is at a point in reciprocal space. a 1 ° k = 2 πν 1 a 2 ° k = 2 πν 2 a 3 ° k = 2 πν 3 (Laue Equations)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Single crystal diffraction Ewald sphere k Each time k = G, a reciprocal lattice vector, you get a Bragg reflection. This is a point of intensity at some 2 θ angle, and some Φ angle in space Bragg reflections
Actual single crystal diffraction patterns

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Experimental setup
Powder vs. Single crystals ° So, Bragg peaks are usually at a single spot in real space for single crystals. For powder samples, however, which are composed of many tiny single crystals randomly oriented, the G vectors exist on a cone of scattering (think of taking the Ewald circle, and rotating about k).

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 19

reciprocalLattice+BrillouinZone - Brillouin Zones Physics...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online