Chapter 2: Structural Analysis Flashcards
1
Q
Bragg Condition
(3 points)
A
- Simple explanation for discrete spots in diffraction patterns
- Constructive interference occurs only when Bragg condition is met
- 2d sin θ = nλ
2
Q
Wave Diffraction of Periodic Solids
(Assumptions: 2 points)
A
- Wavelength of incident radiation on the order of lattice constant
- λ ≈ A
- Elastic scattering
3
Q
Bragg Condition Take-Away
(2 points)
A
- Bragg peaks occur where scattering angle meets condition
- Allows for determination of interplanar spacing d
4
Q
Fourier Analysis
(2 points)
A
- Fourier series of function with periodicity or Bravais lattice can only contain wave vectors which belong to reciprocal lattice
- Allows translation between reciprocal and real space
5
Q
Lattice Planes and Miller Indices
(2 points)
A
- For every set of parallel planes, there exists lattice vector G that are perpendicular to the planes.
- For shortest one Gmin
- |Gmin| = 2π/d
6
Q
Bragg Condition Restriction
A
- λ < 2d
7
Q
Laue Condition Take-Away
(2 points)
A
- Allows for discovery of reciprocal lattice basis
- Real lattice can be found from reciprocal lattice
8
Q
Ewald Construction
(3 points)
A
- Origin of crystal at center
- Create circle with radius r = 2π/λ = |k|
- Lattice points on perimeter indicate constructive interference
9
Q
General Refraction Theory
A
Allows resolution of crystal structure from diffraction patterns
10
Q
Reciprocal Lattice
(3 points)
A
- Sell of all vectors k which lead to plane waves with the periodicity of the Bravais lattice
- All k = G such that exp(iGR) = 1, where R is a real space lattice vector
- G is wave vector of reciprocal space
11
Q
Reciprocal Lattice Vectors
(3 points)
A
- G = hb1 + k b2 + lb3
- Requirement: G·R = 2πn
- Reciprocal lattice of reciprocal lattice is original lattice
12
Q
Ewald Construction Purpose
(3 points)
A
Used to determine:
- Wave vector of incident and refracted beams
- Diffraction angle
- Reciprocal lattice of crystal
13
Q
Debye-Waller Factor
A
Used to describe the attenuation of scattering peaks due to thermal motion
14
Q
Bragg Condition Assumptions
(2 points)
A
- Crystal consists of parallel planes with separation distance d
- Incident wave partially reflected at each plane
15
Q
Bragg-Laue Equivalence
(2 points)
A
- Bragg condition is special case of Laue condition
- For minimum reciprocal lattice vector Gmin
