Thuc tap ve phan tich TEM

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Thuc tap ve phan tich TEM

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Thuc tap ve phan tich TEM

  1. 1. Exercise: Indexing of the electron diffraction patterns Louisa Meshi
  2. 2. Formation of electron diffraction and HRTEM image
  3. 3. Ewald sphere construction: <ul><li>Bragg’s conditions are satisfied when the Ewald sphere cuts a reciprocal lattice point specified by the indices of the reflecting plane. </li></ul>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. 4. For diffraction in electron microscope: <ul><li>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 . </li></ul>specimen Ewald sphere (1/  >>g) 1/  Camera Length (L) r L r = 1  g ; rd hkl =L  , L  - camera constant r
  5. 5. Types of electron diffraction patterns: <ul><li>Ring pattern – from polysrystalline specimen. Major use: </li></ul><ul><ul><ul><li>Identification of the phases; </li></ul></ul></ul><ul><ul><ul><li>Analysis of texture; </li></ul></ul></ul><ul><ul><ul><li>Determination of the camera constant L  . </li></ul></ul></ul><ul><li>Spot pattern – from single-crystal region of the specimen. Major use: </li></ul><ul><ul><ul><li>The foil orientation can be determined; </li></ul></ul></ul><ul><ul><ul><li>Identification of phases; </li></ul></ul></ul><ul><ul><ul><li>The orientation relationship between structures can be determined. </li></ul></ul></ul>
  6. 6. Ring pattern: <ul><li>The reciprocal lattice becomes a series of sphere concentric with the origin of the reciprocal lattice. </li></ul><ul><li>The main steps of indexing ring patterns: </li></ul><ul><li>Measuring ring diameters D 1 , D 2 , D 3 ……. </li></ul><ul><li>Calculation of the d hkl (using the expression: rd hkl =L  ) </li></ul><ul><li>Use some structure database to index each ring. </li></ul>beam O hkl sphere D
  7. 7. Spot pattern <ul><li>All diffraction spots are obtained from planes belonging to one zone . </li></ul>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. 8. Indexing the SAED pattern (spot pattern): <ul><li>Choose a parallelogram with smallest R 1 , R 2 , R 3 . </li></ul><ul><li>Measure distances R 1 , R 2 , R 3 and angles  1 ,  2 . </li></ul><ul><li>Calculate d 1 ,d 2 ,d 3 (using the rule rd=L  ). </li></ul><ul><li>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. </li></ul><ul><li>Check the condition that h 1 +h 2 =h 3 ; k 1 +k 2 =k 3 ; l 1 +l 2 =l 3 . </li></ul><ul><li>Compare the measured angles (both  1 and  2 ) with the calculated angles. </li></ul>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. 9. Practice time: <ul><li>In the tutorial of the school you will find three electron diffraction patterns. </li></ul><ul><li>These patterns are taken from Cu and Al. (Crystallographic data and L  of the microscope - are given). </li></ul><ul><li>Index the SAED patterns and calculate the Zone Axis (ZA). </li></ul>

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