Exercise: Indexing of the electron diffraction patterns

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Presentation transcript:

Exercise: Indexing of the electron diffraction patterns Louisa Meshi

Formation of electron diffraction and HRTEM image

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

For diffraction in electron microscope: specimen Ewald sphere (1/>>g) 1/ Camera Length (L) r 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. r L r = 1\ g ; rdhkl=L, L - camera constant

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.

Ring pattern: The reciprocal lattice becomes a series of sphere concentric with the origin of the reciprocal lattice. beam O hkl sphere D The main steps of indexing ring patterns: Measuring ring diameters D1, D2, D3 ……. Calculation of the dhkl (using the expression: rdhkl=L) Use some structure database to index each ring.

Spot pattern All diffraction spots are obtained from planes belonging to one zone. beam beam Schematic representation of diffraction pattern: Crystal h1k1l1 Ewald sphere h2k2l2 h1k1l1 h2k2l2 g1 g2 O g3 Reciprocal lattice plane Real diffraction pattern: B Zone of reflecting planes B – is a zone axis

Indexing the SAED pattern (spot pattern): Choose a parallelogram with smallest R1, R2, R3. Measure distances R1, R2, R3 and angles 1, 2. Calculate d1,d2,d3 (using the rule rd=L). Correlate the measured d-values with dhkl taken from the list of standard interplanar distances for the given structure and ascribe h1k1l1 and h2k2l2 and h3k3l3 indices for the chosen three spots. Check the condition that h1+h2=h3; k1+k2=k3; l1+l2=l3. Compare the measured angles (both 1 and 2) with the calculated angles. h1k1l1 h2k2l2 h3k3l3 R3 R1 R2 1 2 Zone axis of the ED pattern = (h1k1l1) (h2k2l2)

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).