Diffraction in the Transmission Electron Microscope Vidhya Sagar Jayaseelan
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Transcript of Diffraction in the Transmission Electron Microscope Vidhya Sagar Jayaseelan
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Diffraction in the
Transmission Electron Microscope
Vidhya Sagar Jayaseelan
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TEM- What is it?
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Advantages of TEM
1. High Resolution images 1,000,000 X
2. Sub-micron level diffraction
3. Defect imaging – dislocations, twins, stacking faults, point defects, antiphase boundaries
4. Simultaneous imaging, structural and compositional analysis
5. Orientation studies possible
6. Identifying the phases and crystal structures
7. Site occupancy of atoms/ions
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Disadvantages of TEM
1. Sample size
2. Preparation
3. Instrument issues
4. Operation
5. Interpretation
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Wavelength of electrons
Wavelength – magnificationq*U = ½ mv2, λ = h/ (m * v )
where:
λ = wavelength h = Planck's constant (6.6 X 10-27) m = mass of the electron (9.1 X 10-28) v = velocity of the electron
U = Potential drop
λ = (1.23 nm)/ U1/2
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Electron Sample Interaction
Incident electron beam
Transmitted beam
Elastic scattering-DiffractionInelastic scattering
Auger Electrons
Backscattered electrons-Elastic
Characteristic X rays
Inelastic- Secondary electrons
2θ
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Optics of the TEM
•Gun
•Lenses
Focal length
•Apertures
•Screen
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Image Contrast in TEM
• Thickness
• Composition – Atomic number/phases
• Diffraction (orientation)
• Strain fields
• Fringe Effects
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Diffraction in TEM
Reciprocal lattice –What is it?Equations- Bragg, Laue, Fourier Transform
Real Reciprocal
Ewald Sphere
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Zone axis for SC
<100> <100>
<111>
<110>
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Real to Reciprocal lattice equationsThe relationship
– Bragg’s law nλ = 2d sinθ
– Laue equation r = (S-S0) / λ
– Fourier Transform F(s) = ∫ dx f(x) exp(–i2πsx)
Structure factor
Fhkl = ∑ fn exp { 2πi (hx1 +ky1+ lz1)}
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Single vs Polycrystal
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Electron vs XRay Diffraction
2θ
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TEM Diffraction- What can we infer?
• Phases and crystal structure types• Crystal symmetry and space group• Orientation relationships between phases• Determining growth directions, interface
coherency• Identifying defects , i.e. twinning, SFs,
Dislocations• Ordering behavior of crystal structures and
the site occupancy preferences
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Dark field imaging
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Dark field imaging
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Kikuchi lines
θ
Inelastic scattering without significant
wavelength change leads to formation of Kikuchi lines by
diffraction. Incoming beam has
every possible direction. Outgoing strong beam is at
Bragg angle. This is particularly seen in
thick samples
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Kikuchi Maps
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More….
• Transmission Electron Microscopy- Dr. Vasudevan’s Graduate Course
• Transmission Electron Microscopy – David B. Williams and C. Barry Carter
• Transmission Electron Microscopy – Ludwig Reimer• WWW