{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

123B_1_EE123B W 11 Lecture3

# 123B_1_EE123B W 11 Lecture3 - Lecture 3 Kittel Chapter 2...

This preview shows pages 1–12. Sign up to view the full content.

Lecture 3 Kittel Chapter 2 January 11, 2010 Hand in HW#1.

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

View Full Document
Homework #2 due 1/18 Tuesday Kittel Chapter 2 2.1 – interplanar distance 2.2 – primitive cell calculations volume, vectors, Brillouin zone sketch for HCP 2.4 – examine scattering linewidth F, K, G 2.5 – structure factor
Last lecture Chapter 1 cont’d More BCC, FCC lattice characteristics More diamond, zincblende lattices Chapter 2 Diffraction in a crystal Bragg’s law Fourier Analysis Reciprocal lattice

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

View Full Document

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

View Full Document
Constructive Interference Constructive interference occurs when reflected beam path lengths differ by nλ 2dsinθ=nλ Bragg Law dsinθ θ θ θ d
Today’s lecture Chapter 2 Reciprocal Space Brillouin Zone Scattering amplitude, F Structure factor Atomic form factor

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

View Full Document
Diffraction Conditions – map real to reciprocal Reciprocal lattice vectors G determines possible reflection We want an expression to relate Bragg Condition to G. Next define G using reciprocal lattice vectors 3 3 2 2 1 1 b v b v b v G + + = 3 2 1 3 2 1 2 a a a a a b × × = π Translates reciprocal to real 3 2 1 1 3 2 2 a a a a a b × × = π 3 2 1 2 1 3 2 a a a a a b × × = π
Laue Equations – also derive E.S. Laue equations relate to real lattice to reciprocal lattice 3 2 1 , a a b ij j i a b πδ 2 = 1 3 2 , a a b 2 1 3 , a a b 3 3 2 2 1 1 b v b v b v G + + = 3 2 1 3 2 1 2 a a a a a b × × = π 3 2 1 1 3 2 2 a a a a a b × × = π 3 2 1 2 1 3 2 a a a a a b × × = π Axis vectors of the reciprocal lattice: Each vector is orthogonal to two axis vectors of the crystal lattice: Thus: j i ij = = if 1 δ j i ij = if 0 δ Points in the reciprocal lattice are: are integers, is a reciprocal lattice vector 3 2 1 , , v v v G

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

View Full Document
Laue condition contd. Thus can be rewritten in terms of k G , G a k a = 1 1 1 3 3 2 2 1 1 1 2 ) ( v b v b v b v a π = + + 2 3 3 2 2 1 1 2 2 ) ( v b v b v b v a π = + + 3 3 3 2 2 1 1 3 2 ) ( v b v b v b v a π = + + Relates back to Ewald Sphere 3 2 1 , , a a a k G ' k θ θ 2 1 2 But why a.G?
Brillouin Zone Provide geometrical, visual interpretation of Use Wigner-Seitz primitive cell in reciprocal space.

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 ]}