Analysis of SAED patterns
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This document discusses techniques for analyzing electron diffraction patterns obtained via transmission electron microscopy (TEM). It begins by explaining what electron diffraction is and how it can be used to determine properties of crystalline samples like crystal structure, grain size, and orientation. Key points covered include indexing diffraction patterns, analyzing polycrystalline and single crystal patterns, and relating diffraction patterns to a sample's reciprocal lattice. The document provides detailed steps for measuring diffraction pattern features and indexing them to identify unknown materials.
![Reciprocal lattice
• Indexing diffraction pattern is just
application of the reciprocal lattice
and kinematical theory of electron
diffraction
• Laue Condition
• Diffraction occurs when the vector
of diffraction wave K is a vector the
reciprocal lattice, ghkl i.e. K=ghkl.
This condition is equivalent to
Bragg Law.
• Laue condition describes the
crystal diffraction in a rigorous
fashion
Indexing DP is just to look for a reciprocal lattice
of a zone axis [vuw] satisfying Laue condition
𝐾 = 𝑘𝐼 − 𝑘𝐷
From scattering theory 𝑘𝐼 = 𝑘𝐷 =
1
𝜆
sin 𝜃 =
𝐾
2
𝑘𝐼
or 𝑘𝐼 = 2 sin(θ)/𝜆](https://image.slidesharecdn.com/analysisofsaed-210701141811/85/Analysis-of-SAED-patterns-3-320.jpg)
![Zone axis at intersection of
plane (h1k1l1) and (h2k2l2)
• If (h1k1l1) and (h2k2l2) belong to zone
[uvw], then we can find the zone axis
[uvw], i.e. the direction of intersection of
two planes (h1k1l1) and (h2k2l2)](https://image.slidesharecdn.com/analysisofsaed-210701141811/85/Analysis-of-SAED-patterns-8-320.jpg)
Analysis of SAED patterns
- 1. Analysis of SAED Antilen Jacob G Research Scholar, NIT-Trichy
- 2. Diffraction in TEM • What is it? • What can we learn from it? • Why do we see it? • What determines the scale? An experimentally observed DP showing the central intense, direct beam and array of diffraction spots from different atomic planes. • Is the specimen crystalline or amorphous? • If it is crystalline: what are crystallographic characteristics of the specimen? • Is the specimen mono-crystalline? • If not what is the grain morphology and grain size distribution? • Is more than one phase presented, how are they oriented to each other? Comparison X-ray /Electrons: - Electrons have a much shorter wavelength than X-ray - Electrons are scattered more strongly - Electron beams are easily directed However, much of electron D follows directly from X-ray D
- 3. Reciprocal lattice • Indexing diffraction pattern is just application of the reciprocal lattice and kinematical theory of electron diffraction • Laue Condition • Diffraction occurs when the vector of diffraction wave K is a vector the reciprocal lattice, ghkl i.e. K=ghkl. This condition is equivalent to Bragg Law. • Laue condition describes the crystal diffraction in a rigorous fashion Indexing DP is just to look for a reciprocal lattice of a zone axis [vuw] satisfying Laue condition 𝐾 = 𝑘𝐼 − 𝑘𝐷 From scattering theory 𝑘𝐼 = 𝑘𝐷 = 1 𝜆 sin 𝜃 = 𝐾 2 𝑘𝐼 or 𝑘𝐼 = 2 sin(θ)/𝜆
- 4. Ring patterns a) Amorphous material b) crystalline material R L d Where R is the ring radius, d is a crystal d-spacing; – wave length of the electron; L – constant of the TEM.
- 5. Zero-order laue Zone (ZOLZ) put the zero-order Laue zone(ZOLZ) perfectly symetrical around the transmitted beam by centring the first - order Laue zone (FOLZ) when visible! High-symmetry zone axes through a crystal lattice
- 6. diffraction in 100 plane
- 7. Indices all other reflections: vector addition diffraction in 010 plane
- 8. Zone axis at intersection of plane (h1k1l1) and (h2k2l2) • If (h1k1l1) and (h2k2l2) belong to zone [uvw], then we can find the zone axis [uvw], i.e. the direction of intersection of two planes (h1k1l1) and (h2k2l2)
- 9. The addition rule You only need find two reciprocal lattice then you can construct whole pattern Angle ρ between plane normal (h1k1l1) and (h2k2l2) Inspecting the angle is easy to identify the crystal structure based on the DP database
- 10. Structure factor rule Using the structure factor rule to exclude the forbidden vectors from the candidate reciprocal lattices
- 11. Analysis of polycrystalline diffraction pattern • If the grains in a polycrystalline material are randomly oriented or weakly textured, then the reciprocal vector g to each diffracting plane will be oriented in all possible direction • Since the length of a particular g is a constant, these vectors g will describe a sphere with radius of |g| • The intersection of such a sphere with Ewald sphere is a circle, and therefore the diffraction pattern will consist of concentric rings
- 12. Texture DP If texture is present, then one or more rings may be absent, or the intensity in any particular ring may vary along the ring. From an analysis of these intensity distributions, one can, in principal, derive information about the thin foil texture.
- 13. Analysis of polycrystalline diffraction pattern • Step 1) measure the scale bar and set scale using imageJ • Step 2) Measuring the radii of the rings r1, r2, r3, … etc. • Step 3) Calculating the d-spacings d1, d2, d3, … etc. of the planes giving rise to these rings using equation rd=Lλ • Step 4) Having obtained the d-spacings of the rings, then an unknown material can often be identified with the help of a reference source such as ASTM handbook or ICDD PDF card, which lists the d-spacings of the thousands of materials • Step 5) Index the ring pattern Ring diameter (nm) Ratios of diameter R1 16.5 1 R2 19.1 1.15757 R3 26.9 1.63030 R4 31.5 1.9090 Allowed hkl Sqrt h2+k2+l2 Ratios 111 1.7320 1 200 2 1.1570 220 2.8284 1.6324 311 3.31662 1.9148
- 14. analysis of single crystal pattern • Step 1) measure the scale bar and set scale using imageJ • Step 2) Any 2-D section of a reciprocal lattice can be defined by two vectors so we only need to index 2 spots. All others can be deduced by vector addition • Step 3) Choose one spot to be the origin, Measure the spacing of one prominent spot, r1 and Measure the spacing of a second spot, r2. • Step 4) Measure the angle between the spots, φ. • Step 5) Prepare a table giving the ratios of the spacings of permitted diffraction planes in the known structure • Step 6) Take the measured ratio r1/r2 and locate a value close to this in the table • Step 7) Calculate the angle between pair of planes of the type you have indexed. If the experimental angle agrees with one of the possible values - accept the indexing. If not, revisit the table and select another possible pair of planes. • Step 8) Finish indexing the pattern by vector addition
- 15. Example: A fcc structure diffraction patterns The ratio of interplanar spacings between two different planes, d1 and d2 is • Choose two spots, spot 1 and 2, in x and y direction. Or we can choose two spots along any direction • By measurement, we know r1=1.10cm, r2=0.65 cm, and Φ =90 °, calculate 𝑟1 𝑟2 = 𝑑2 𝑑1 = 1.10 0.65 = 1.69 • List the ratios of d from the allowed (hkl) according to the structure factor rule. Put these ratios into a table. For fcc, the allowed diffraction planes are (111), (200), (220), (311), (222), (400). Start from the low order planes
- 16. Indexing the zone axis