The document discusses techniques for indexing electron diffraction patterns obtained from transmission electron microscopy. It describes how Bragg's law is used to index both ring patterns from polycrystalline samples and spot patterns from single crystal regions. Indexing ring patterns involves measuring ring diameters and calculating interplanar spacings, while indexing spot patterns requires measuring spot distances and angles to determine indices based on known crystal structures. Practice problems are provided to have students index selected electron diffraction patterns from copper and aluminum samples.

1. Exercise: Indexing of the electron diffraction patterns Louisa Meshi

2. Formation of electron diffraction and HRTEM image

3. Ewald sphere construction: Bragg’s conditions are satisfied when the Ewald sphere cuts a reciprocal lattice point specified by the indices of the reflecting plane. sin  = = = g/2 1/  1/  1/d hkl * 1/2 =  /2d hkl Bragg’s law g hkl O P hkl Origin of the reciprocal lattice 2  specimen 1/  Points of reciprocal lattice (hkl) plane

4. For diffraction in electron microscope: The single crystal electron diffraction pattern is a series of spots equivalent to a magnified view of a planar section through the reciprocal lattice normal to the incident beam . specimen Ewald sphere (1/  >>g) 1/  Camera Length (L) r L r = 1\  g ; rd hkl =L  , L  - camera constant r

5. Types of electron diffraction patterns: Ring pattern – from polysrystalline specimen. Major use: Identification of the phases; Analysis of texture; Determination of the camera constant L  . Spot pattern – from single-crystal region of the specimen. Major use: The foil orientation can be determined; Identification of phases; The orientation relationship between structures can be determined.

6. Ring pattern: The reciprocal lattice becomes a series of sphere concentric with the origin of the reciprocal lattice. The main steps of indexing ring patterns: Measuring ring diameters D 1 , D 2 , D 3 ……. Calculation of the d hkl (using the expression: rd hkl =L  ) Use some structure database to index each ring. beam O hkl sphere D

7. Spot pattern All diffraction spots are obtained from planes belonging to one zone . O g 1 g 2 g 3 Crystal beam Ewald sphere Reciprocal lattice plane h 1 k 1 l 1 h 2 k 2 l 2 beam Zone of reflecting planes B – is a zone axis B Schematic representation of diffraction pattern: Real diffraction pattern: h 1 k 1 l 1 h 2 k 2 l 2

8. Indexing the SAED pattern (spot pattern): Choose a parallelogram with smallest R 1 , R 2 , R 3 . Measure distances R 1 , R 2 , R 3 and angles  1 ,  2 . Calculate d 1 ,d 2 ,d 3 (using the rule rd=L  ). Correlate the measured d-values with d hkl taken from the list of standard interplanar distances for the given structure and ascribe h 1 k 1 l 1 and h 2 k 2 l 2 and h 3 k 3 l 3 indices for the chosen three spots. Check the condition that h 1 +h 2 =h 3 ; k 1 +k 2 =k 3 ; l 1 +l 2 =l 3 . Compare the measured angles (both  1 and  2 ) with the calculated angles. h 1 k 1 l 1 h 2 k 2 l 2 h 3 k 3 l 3  1  2 R 3 R 1 R 2 Zone axis of the ED pattern = (h 1 k 1 l 1 ) (h 2 k 2 l 2 )

9. Practice time: In the tutorial of the school you will find three electron diffraction patterns. These patterns are taken from Cu and Al. (Crystallographic data and L  of the microscope - are given). Index the SAED patterns and calculate the Zone Axis (ZA).