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Solid State - Coggle Diagram
Solid State
Reciprocal
- reciprocal lattice represents Fourier transform of another lattice
- A beam of incident x-rays are diffracted in a material
- reciprocal lattice of Bravais lattice is the set of all vectors K
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X-ray
- Found by Wilhelm Conrad Rontagen
- Energy related to λ via Planck's hypothesis
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X-ray spectrum
Neutron
- used to study magnetic structure of materials
- neutron energy relate to λ via de Broglie equation
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Bragg's Law
- explained the diffracted rays from crystal
- cubic unit cell ( dimension a )
Derivation Bragg's law
How Diffraction Works?
1) Wave Interacting wit a single particle
- beams scattered uniformly in all direction
2) Wave Interacting with solid
- scattered beams interfere
- random arrangement cause beam randomly interfere
3) Crystalline material
Ewald Construction
Bragg & Laue Diffraction
- elastic scattering of periodic lattice
Bragg
- lattice is objects group in families of planes and radiation
Laue
- does not require of particular planes, spacings and reflection be specular
Laue Equation
Eward sphere
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- wave vector Ki, length = 2π/λ
- diffrated plane has Kf
- if no energy, Kf = Ki
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Bragg reflected ray
Bragg's rule
- reflection can be seen in reciprocal lattice
- incident wave vector and reflected wave vector are q and q'
- reflection is elastic
i) expand
ii) compress
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Electron
- short penetration power
- de Broglie relation for e
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XRD
- capable to interfere different atoms
- For crystal, atoms arranged in periodic fashion
- allows to deduce the distribution of atoms
- the amorphous, arrangement is not periodic and Bragg's law not obeyed
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Powder Diffractometers
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- ω : between x-ray source and sample
- 2θ : between the incident beam and the detector angle
Diffraction Technique
Powder technique
- single or polycrystals are ground
- orientation of the tiny powder crystal are randomly oriented
- sample powder is put into container in line monochromatic x-ray
Difractometer
- recording x-ray intensity as function of angle between incident and diffracted ray
- use Bragg to obtain diffraction single crystal
- measure diffraction from powder samples or in X-ray florescence spectroscopy