Wilhelm Röntgen discovered X-rays in 1895 and Max von Laue established X-ray crystal diffraction in 1912 using X-rays to analyze the structure of crystals. X-ray diffraction works by firing X-rays at a crystalline sample and observing the scattered rays, which can be used to determine the location of atoms in the crystal based on the Bragg condition of diffraction. There are two main methods for X-ray diffraction - the Laue method which uses a single crystal sample and front scattering, and powder diffraction which analyzes polycrystalline samples using Debye-Scherrer cameras or modern diffractometers. The patterns obtained from X-ray diffraction can be analyzed using Rietveld refinement to determine

1. X-Ray Diffraction
Colin McElroy
11/09/2012

2. OUTLINE
Historical account (partial)
Wilhelm Röntgen: X-Rays (1895)
Max von Laue: X-Ray diffraction (1912)
Paul Peter Ewald: Ewald Sphere (1969)
William Lawrence Bragg: Bragg condition (1912)
X-Ray Overview
Photons
Generators
Subtle Characteristics (Cuκα, Cuκβ, filters)
Diffraction
2-slit experiment
Reflection planes
Equipment/Method
Powder Diffraction
Laue
Laue Method
Powder Diffraction Method
Analysis/Tools

3. HISTORY (brief)
Wilhelm Röntgen
(1845-1923)
William Lawrence Bragg
(1890-1971)
Peter Debye (1884-1966)
Paul Scherrer (1890-1969)
Max von Laue (1879-1960)
Paul Peter Ewald (1888-1985)
Wilhelm Röntgen studies X-Rays
Crookes Tubes
Max von Laue establishes crystal diffraction
Paul Peter Ewald’s thesis
William Lawrence Bragg: Bragg’s Law
Peter Debye & Paul Scherrer
Debye Scherrer camera (technique)

4. X-RAYS (overview)
High energy (𝐸 = ℎν)
Diagnostic Tool
Penetration
Resolution

5. X-RAYS (subtleties)
Black Body Radiation
Broad spectrum (white)
Electron energy levels
Discrete Energies (monochromatic)
𝐼 ν, 𝑇 =
2ℎν3
𝑐2
1
𝑒
ℎν
𝑘 𝐵
𝑇 − 1

6. X-RAYS (subtleties continued)
Filters (absorption curve)
Truly Monochromatic
Monochromators
Expensive & Unnecessary

7. DIFFRACTION
Interference (Constructive/Destructive)
Relation of periodicity to slit spacing
Imaging limited by wavelength
𝑑 sin θ 𝑛 = 𝑛λ

8. EQUIPMENT
Laue (fingers crossed)
single crystal samples
easy
fast
D 8 Discover (Bruker)
polycrystalline samples
single crystal samples
Debye Scherrer camera

9. LAUE METHOD
Front scatter vs. Reflection
White X-Rays (satisfy Bragg’s condition)
Reciprocal space lattice
orientation
single phase?
𝑛λ = 2𝑑 sin θ

10. LAUE METHOD (continued)
Ewald sphere
incident wave vector
reflected wave vector
angle

11. θ
2θ
POWDER DIFFRACTION
Debye-Scherrer camera
polycrystalline sample
maps all reflection planes to 1-D
𝑛λ = 2𝑑 sin θ

12. θ θ
2θ
POWDER DIFFRACTION (continued)
All possible reflection planes present
Debye Scherrer rings
Multiple, simultaneous two-slit experiments

13. Lattice parameters
GSAS: Rietveld refinement
phase purity
atomic positions
ANALYSIS
1
𝑑2
=
ℎ2 + 𝑘2 + 𝑙2
𝑎2
Cubic
1
𝑑2
=
ℎ2 + 𝑘2
𝑎2
+
𝑙2
𝑐2
Tetragonal
1
𝑑2
=
4
3
ℎ2 + ℎ𝑘 + 𝑘2
𝑎2
+
𝑙2
𝑐2
Hexagonal

14. END
Thank you