TEM workshop 2013: Electron diffraction

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This is a tutorial on indexing diffraction patterns, deriving reflection conditions from SAED, derving point groups from CBED and combining both to find the space group. The slides contain exercises, the page to work on is at the end of the presentation and should be printed first to be able to measure on that page.

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  • Light and its nature have caused a lot of ink to flow during these last decades. Its dual behavior is partly explained by (1)Double-slit experiment of Thomas Young - who represents the photon’s motion as a wave - and also by (2)the Photoelectric effect in which the photon is considered as a particle. A Revolution: SALEH THEORY solves this ambiguity and this difficulty presenting a three-dimensional trajectory for the photon's motion and a new formula to calculate its energy. More information on : https://youtu.be/mLtpARXuMbM https://www.slideshare.net/SalehTheory/saleh-theory?qid=e7da2b84-6d5e-409d-8b12-cae0f58a825b&v=&b=&from_search=1
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TEM workshop 2013: Electron diffraction

  1. 1. Electron Diffraction
  2. 2. At the end of this lecture you should be able to(1) index SAED patterns in case the cell parametersare already known(2) determine the possible space groups from SAEDpatterns(3) determine possible point groups from CBEDpatternsCombine (2) and (3) to find the space group.
  3. 3. Reflections: what do they represent?What is their origin? What informationcan they give us?
  4. 4. Constructive vs. destructive interferencereflection – no reflectionposition  distances between the planes (d-values)intensity  occupation in the planesboth symmetry of the structure
  5. 5. Singlephase?Crystalline oramorphous?Orientationcrystals/film?Targetedphase?Domainformation?Crystalparameters?
  6. 6. Selected Area ElectronDiffractionSAED
  7. 7. One atom type Aabb>aa=3 Åb=5 Å
  8. 8. One atom type Aabb>a(100)100000a=3 Åb=5 Å
  9. 9. One atom type Aabb>a(100)1000001/3Åa=3 Åb=5 Å
  10. 10. One atom type Aabb>a(100)100a*a=3 Åb=5 Å
  11. 11. One atom type Aabb>a(010)a=3 Åb=5 Å
  12. 12. One atom type Aabb>a(010)010a=3 Åb=5 Å
  13. 13. One atom type Aabb>a(010)010a=3 Åb=5 Å1/5Å
  14. 14. One atom type Aabb>a(010)010b*a=3 Åb=5 Å
  15. 15. One atom type A010100ab[001]b>a a*>b*a*b*a=3 Åb=5 Å
  16. 16. One atom type A010100ab[001]b>a a*>b*a*b*Central reflectionis always 000.000a=3 Åb=5 Å
  17. 17. One atom type A010100ab[001]a=3 Åb=5 Å
  18. 18. One atom type A010100ab[001]1/3Å1/5Åa=3 Åb=5 Å
  19. 19. 010100[001]Indices all other reflections:vector addition110020200 210120
  20. 20. 1/3Å1/5ÅExperimentally: the other way around:010100[001]*
  21. 21. *How?Make a list of all reflections with hkl and their d-values.• use Excel to make the list yourself• use free software like Powdercell• ...d hkl7.68 0015.64 0105.46 1004.55 0114.45 1013.92 110... ...
  22. 22. 010100Zone-index: [001]obtained by vector multiplication.Circle ACW around 000.1 0 0 1 0 00 1 0 0 1 00*0-0*1 0*0-1*0 1*1-0*0[ 0 0 1 ]0 01 00 10 01 00 1
  23. 23. (010)(100)(110)[001]010100 110[001]110-(110)-
  24. 24. Exercise:index the given patterns takenfrom a CaF2 mineral
  25. 25. abcbacCaF2cubica=5.46 ÅFm3m-
  26. 26. h k l d I F1 1 1 3.15349 83.73 61.892 0 0 2.731 0.11 3.072 2 0 1.93111 100 96.553 1 1 1.64685 31.44 46.492 2 2 1.57674 0.2 6.814 0 0 1.3655 12.69 74.253 3 1 1.25307 11.35 38.654 2 0 1.22134 0.54 8.674 2 2 1.11493 23.75 61.875 1 1 1.05116 6.88 34.23 3 3 1.05116 2.29 34.2You need this table made for CaF2
  27. 27. We are going to index these patterns.They are obtained by tilting around the diagonal row.(Online version:working page canbe found at theend.)
  28. 28. We are going to index these patterns.They are obtained by tilting around the diagonal row.(Online version:workpage can befound at the end.)
  29. 29. Start with easiest:highest symmetry or smallest interreflection distances= usually lower zone indices (“main zones”)(Online version:workpage can befound at the end.)
  30. 30. h k l d I F1 1 1 3.15349 83.73 61.892 0 0 2.731 0.11 3.072 2 0 1.93111 100 96.553 1 1 1.64685 31.44 46.492 2 2 1.57674 0.2 6.814 0 0 1.3655 12.69 74.253 3 1 1.25307 11.35 38.654 2 0 1.22134 0.54 8.674 2 2 1.11493 23.75 61.875 1 1 1.05116 6.88 34.23 3 3 1.05116 2.29 34.2Why go for smaller interreflection distances?=higher d = less choices
  31. 31. First pattern:Apparent symmetry: 4-foldGo for highest symmetry
  32. 32. abcAlong which direction does the 4-fold axis lie in a cubicsystem? <001><011><111>bacCaF2
  33. 33. abcAlong which direction does the 4-old axis lie in a cubicsystem? <001><011><111>bacCaF2
  34. 34. probably this is <001>(Cubic: [100], [010], [001] equivalent = <001>)
  35. 35. To do: measure the distances, compare to list d-hkl, indexconsistently.Scalebar = R (in mm)Step 1: Use the scalebar for the conversionfactor to 1/d-values.equal to 1/0.08 nmR.d=LL42434434.4 mmÅ53.8 mmÅ0.02 mmÅ
  36. 36. To do: measure the distances, compare to list d-hkl, indexconsistently.Scalebar = R (in mm)Step 1: Use the scalebar for the conversionfactor to 1/d-values.equal to 1/0.08 nmR.d=LL42434434.4 mmÅ53.8 mmÅ0.02 mmÅ
  37. 37. To do: measure the distances, compare to list d-hkl, indexconsistently.Scalebar = R (in mm)Step 1: Use the scalebar for the conversionfactor to 1/d-values.equal to 1/0.08 nmR.d=LL42434434.4 mmÅ53.8 mmÅ0.02 mmÅ
  38. 38. Step 2: measure the distance of two reflections,not on the same line, calculate the correspondingd-valuePoint 1d5.46 Å3.15 Å2.73 ÅPoint 2d5.46 Å3.15 Å2.73 Å12
  39. 39. Step 2: measure the distance of two reflections,not on the same line, calculate the correspondingd-valuePoint 1d5.46 Å3.15 Å2.73 ÅPoint 2d5.46 Å3.15 Å2.73 Å12
  40. 40. Step 2: measure the distance of two reflections,not on the same line, calculate the correspondingd-valuePoint 1d5.46 Å3.15 Å2.73 ÅPoint 2d5.46 Å3.15 Å2.73 Å12
  41. 41. To do: measure the distances, compare to list d-hkl, index.Step 3: look up in the table to whichreflection this corresponds100110200Point 1dPoint 2dPoint 1hklPoint 2hkl125.46 Å3.15 Å2.73 Å5.46 Å3.15 Å2.73 Å100110200
  42. 42. To do: measure the distances, compare to list d-hkl, index.Step 3: look up in the table to whichreflection this corresponds100110200Point 1dPoint 2dPoint 1hklPoint 2hkl125.46 Å3.15 Å2.73 Å5.46 Å3.15 Å2.73 Å100110200
  43. 43. To do: measure the distances, compare to list d-hkl, index.Step 3: look up in the table to whichreflection this corresponds100110200Point 1dPoint 2dPoint 1hklPoint 2hkl125.46 Å3.15 Å2.73 Å5.46 Å3.15 Å2.73 Å100110200
  44. 44. Keep in mind: d-values valid for all equivalent {hkl}!Step 4: make the indexation consistent10001012If point 1 is 200 then point 2 is 020 or 002.Choose and stick with your choice.
  45. 45. 100010200020
  46. 46. Step 5: calculate the zone-index[100][010][001]010200020
  47. 47. Step 5: calculate the zone-index[100][010][001]200020
  48. 48. Next zoneWhich one would be easiest next?234
  49. 49. Next zoneWhich one would be easiest next?234
  50. 50. Next zone: with reflections closest to the central beam.Reflections closer to the central beam:higher d-valuessmaller amount of possible matches of hkl to this d135
  51. 51. Measure the distance of two reflections, not on thesame line, calculate the corresponding d-valuePoint 1d2.57 Å2.75 Å3.15 ÅPoint 2d1 22.57 Å2.73 Å3.15 Å
  52. 52. Measure the distance of two reflections, not on thesame line, calculate the corresponding d-valuePoint 1d2.57 Å2.75 Å3.15 ÅPoint 2d1 22.57 Å2.73 Å3.15 Å
  53. 53. Measure the distance of two reflections, not on thesame line, calculate the corresponding d-valuePoint 1d2.57 Å2.75 Å3.15 ÅPoint 2d1 22.57 Å2.73 Å3.15 Å
  54. 54. Look up in the table to which reflectionthis corresponds110200111110200111Point 1d = 3.15 ÅPoint 2d = 2.73 Åhkl hkl1 2
  55. 55. Look up in the table to which reflectionthis corresponds110200111110200111Point 1d = 3.15 ÅPoint 2d = 2.73 Åhkl hkl1 2
  56. 56. Look up in the table to which reflectionthis corresponds110200111110200111Point 1d = 3.15 ÅPoint 2d = 2.73 Åhkl hkl1 2
  57. 57. Make the indexation in a consistent manner.1 2Point 2 should be indexed as200020200all are correct-
  58. 58. Make the indexation in a consistent manner.1 2Point 2 should be indexed as200020200all are correct-
  59. 59. Consistency:This is a tilt series......so the common row needs to have thesame indices in all patterns200 200200 200
  60. 60. Consistency:1352001Point 1 should be indexed as111111111all of the above are allowed---
  61. 61. Consistency:1352001Point 1 should be indexed as111111111all of the above are allowed---
  62. 62. Consistency:200111111-If 111 for point 1-311-Point 3 is311111
  63. 63. Consistency:If 111 for point 1-311-Point 3 is3111112001
  64. 64. Consistency:200111111-12003If 111 for point 1-point 3 = 311-
  65. 65. Consistency:200111111-12003If 111 for point 1-point 3 = 311-d311 ≠ dpoint3-but
  66. 66. Consistency:200111111-12003If 111 for point 1-point 3 = 311-d311 ≠ dpoint3-but
  67. 67. Consistency:200111111- 120031 and 3 have the same d-value+relation between 1 and 3 = vector 200you need two indices such thath3+2 = h1k3+0 = k1l3+0 = l1(also possible 111 and 111, make a choice and stick to it for the following patterns)- - -= h1 k1 l1
  68. 68. Consistency:200111111-Sum = 022.Indeed consistent: if 𝑔 perpendicular to 𝑔200then type of reflection needs to be 0kl.022 200022
  69. 69. Calculate the zone-indexThe zone-index is: [011][011]200111111-022-
  70. 70. Calculate the zone-indexThe zone-index is: [011][011]200111111-022-
  71. 71. ...this helps to index the two remaining patterns!!!Consistency:This is a tilt series...
  72. 72. abcThe crystallite is threedimensional.
  73. 73. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0] So, the reciprocal lattice is threedimensional.
  74. 74. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0]ED patterns are sections of reciprocal space.[001]This section is the [001] zone.
  75. 75. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0][011]-This section is the [011] zone:-
  76. 76. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0][001][011]-We tilt from [001] to [011]:-
  77. 77. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0][001][011]-So the tilt series gives pattern of consecutive sectionsbetween these two end zonesClosest is 020.
  78. 78. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0][001][015]-[011]-x051Closest is 151.
  79. 79. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0][011][001][013]-x031Closest is 131.
  80. 80. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0][011][001]x021[012]-042Closest is 042.
  81. 81. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0][011][001][035]-x053Closest is 153.
  82. 82. 0,4,00,4,21,5,10,4,41,5,30,2,00,2,21,3,10,2,42,4,01,3,32,4,23,5,10,0,22,4,41,1,13,5,30,0,42,2,01,1,32,2,23,3,12,2,44,4,03,3,32,0,04,4,25,5,12,0,24,4,43,1,15,5,32,0,44,2,03,1,34,2,25,3,14,2,45,3,34,0,04,0,25,1,14,0,45,1,3Zone axis : [0,0,0][001][011]-Closest is 111. Perpendicular is 022.
  83. 83. 0,4,00,4,20,4,40,2,01,5,10,2,21,5,30,2,41,3,10,0,21,3,30,0,42,4,01,1,12,4,21,1,32,4,42,2,03,5,12,2,23,5,32,2,42,0,03,3,12,0,23,3,32,0,44,4,03,1,14,4,23,1,34,4,44,2,05,5,14,2,25,5,34,2,44,0,05,3,14,0,25,3,34,0,45,1,15,1,3We can also see this in projection
  84. 84. 0,4,40,4,20,4,01,5,31,5,10,2,40,2,20,2,01,3,31,3,10,0,40,0,22,4,42,4,22,4,01,1,31,1,13,5,33,5,12,2,42,2,22,2,03,3,33,3,12,0,42,0,22,0,04,4,44,4,24,4,03,1,33,1,15,5,35,5,14,2,44,2,24,2,05,3,35,3,14,0,44,0,24,0,05,1,35,1,1We can also see this in projection
  85. 85. 0,4,40,4,20,4,00,2,40,2,20,2,00,0,40,0,21,5,31,5,11,3,31,3,11,1,31,1,12,4,42,4,22,4,02,2,42,2,22,2,02,0,42,0,22,0,03,5,33,5,13,3,33,3,13,1,33,1,14,4,44,4,24,4,04,2,44,2,24,2,04,0,44,0,24,0,05,5,35,5,15,3,35,3,15,1,35,1,1Zone axis : [0,0,0]We can also see this in projection
  86. 86. 0,0,40,0,20,2,40,2,20,4,40,2,00,4,20,4,01,1,31,1,11,3,31,3,11,5,31,5,12,0,42,0,22,2,42,0,02,2,22,4,42,2,02,4,22,4,03,1,33,1,13,3,33,3,13,5,33,5,14,0,44,0,24,2,44,0,04,2,24,4,44,2,04,4,24,4,05,1,35,1,15,3,35,3,15,5,35,5,1xis : [0,0,0]We can also see this in projectionwhich is easier to draw manually...
  87. 87. 0,0,40,0,20,2,40,2,20,4,40,2,00,4,20,4,01,1,31,1,11,3,31,3,11,5,31,5,12,0,42,0,22,2,42,0,02,2,22,4,42,2,02,4,22,4,03,1,33,1,13,3,33,3,13,5,33,5,14,0,44,0,24,2,44,0,04,2,24,4,44,2,04,4,24,4,05,1,35,1,15,3,35,3,15,5,35,5,1xis : [0,0,0][001]
  88. 88. 0,0,40,0,20,2,40,2,20,4,40,2,00,4,20,4,01,1,31,1,11,3,31,3,11,5,31,5,12,0,42,0,22,2,42,0,02,2,22,4,42,2,02,4,22,4,03,1,33,1,13,3,33,3,13,5,33,5,14,0,44,0,24,2,44,0,04,2,24,4,44,2,04,4,24,4,05,1,35,1,15,3,35,3,15,5,35,5,1xis : [0,0,0][001][015]-
  89. 89. 0,0,40,0,20,2,40,2,20,4,40,2,00,4,20,4,01,1,31,1,11,3,31,3,11,5,31,5,12,0,42,0,22,2,42,0,02,2,22,4,42,2,02,4,22,4,03,1,33,1,13,3,33,3,13,5,33,5,14,0,44,0,24,2,44,0,04,2,24,4,44,2,04,4,24,4,05,1,35,1,15,3,35,3,15,5,35,5,1xis : [0,0,0][001][015]-[013]-
  90. 90. 0,0,40,0,20,2,40,2,20,4,40,2,00,4,20,4,01,1,31,1,11,3,31,3,11,5,31,5,12,0,42,0,22,2,42,0,02,2,22,4,42,2,02,4,22,4,03,1,33,1,13,3,33,3,13,5,33,5,14,0,44,0,24,2,44,0,04,2,24,4,44,2,04,4,24,4,05,1,35,1,15,3,35,3,15,5,35,5,1xis : [0,0,0][001][015]-[013]-[012]-
  91. 91. 0,0,40,0,20,2,40,2,20,4,40,2,00,4,20,4,01,1,31,1,11,3,31,3,11,5,31,5,12,0,42,0,22,2,42,0,02,2,22,4,42,2,02,4,22,4,03,1,33,1,13,3,33,3,13,5,33,5,14,0,44,0,24,2,44,0,04,2,24,4,44,2,04,4,24,4,05,1,35,1,15,3,35,3,15,5,35,5,1xis : [0,0,0][001][015]-[013]-[012]-[035]-
  92. 92. 0,0,40,0,20,2,40,2,20,4,40,2,00,4,20,4,01,1,31,1,11,3,31,3,11,5,31,5,12,0,42,0,22,2,42,0,02,2,22,4,42,2,02,4,22,4,03,1,33,1,13,3,33,3,13,5,33,5,14,0,44,0,24,2,44,0,04,2,24,4,44,2,04,4,24,4,05,1,35,1,15,3,35,3,15,5,35,5,1xis : [0,0,0][001][015]-[013]-[012]-[035]-[011]-
  93. 93. Right upper zone:Point 2d1.22 Å1.11 Å1.05 ÅMeasure the distance of two reflections, not on thesame line, calculate the corresponding d-valueWe already know thefirst point: 200.2002
  94. 94. Right upper zone:Point 2d1.22 Å1.11 Å1.05 ÅMeasure the distance of two reflections, not on thesame line, calculate the corresponding d-valueWe already know thefirst point: 200.2002
  95. 95. Look up in the table to which reflection this corresponds:We know already it is either 151 or 131 or 042 or 1531.05 Å 151131042Point 2dPoint 2hkl2002
  96. 96. Look up in the table to which reflection this corresponds:We know already it is either 151 or 131 or 042 or 1531.05 Å 151131042Point 2dPoint 2hkl2002
  97. 97. If this were not a tilt series...Point 2 could have been at first sightboth 115 and 333...In this case:Can compare the experimental angles between reflectionsto the theoretical angles-either formulas from any standard crystallography work-or simply simulate the different zones calculated for thedifferent options (JEMS, CrystalKit, Carine,...) to check thisOr in this particular case of 333: you would need to see 111 and 222 at 1/3 and 2/3 of the distance.
  98. 98. Calculate the zone-indexThe zone-index is:[0 2 10][0 1 5][0 1 5]200151-
  99. 99. Calculate the zone-indexThe zone-index is:[0 2 10][0 1 5][0 1 5]200151-
  100. 100. [001][015]-[013]-[012]-[035]-[011]-010031 051053What if you didn’t know the material?You would just need to checkmore possibilities:043032041021[025]-052 [014]-[023]-[034]-When indexed correctly, the patterns in betweenhave to give you one of these as zone-index.011
  101. 101. Pattern bottom left:Point 2dMeasure the distance of two reflections, not on thesame line, calculate the corresponding d-value20021.65 Å1.58 Å1.37 Å
  102. 102. Pattern bottom left:Point 2dMeasure the distance of two reflections, not on thesame line, calculate the corresponding d-value20021.65 Å1.58 Å1.37 Å
  103. 103. Look up in the table to which reflection this corresponds.We know already it is either: 151 or 131 or 042 or 1531.65 Å 042131153Point 2dPoint 2hkl2002
  104. 104. Look up in the table to which reflection this corresponds.We know already it is either: 151 or 131 or 042 or 1531.65 ÅPoint 2dPoint 2hkl2002042131153
  105. 105. The indexation is indeed consistent.200131062131-
  106. 106. 200131062131-[013]-
  107. 107. Make your analysis easier by not takingED patterns from separate crystals, buttaking different ED patterns from thesame crystallite, if possible.=“Tilt series”
  108. 108. So now you have indexed these four patterns.200131200151200111200020[001] [015]-[013]-[011]-
  109. 109. ...indexed patterns give you info on fase,orientation, cell parameters,...200131200151200111200020[001] [015]-[013]-[011]-
  110. 110. What if you do not have any priorknowledge when you have toindex?Analyse the patterns  try to propose basis vectors(For example reflections closest to the central beam)Same system as previous slides:can you index all reflections?If not, adapt your choice ofbasis vectors and try again.
  111. 111. If we do not know the space group, the next step wouldbe to determine it!(maybe you started from 0 or you had only cell parameters from XRD or...)200131200151200111200020[001] [015]-[013]-[011]-
  112. 112. Reflection conditions(SAED)Space group?P no reflection conditionsF h+k=2n, k+l=2n, h+l=2nI h+k+l=2nA/B/C k+l=2n/h+k=2n/h+k=2nPoint Group (CBED)glide planes conditions on hk0/h0l/0klscrew axes conditions on h00/0k0/00lmirror planes, inversioncentre, rotation axesno extra conditionsCBEDSAED+
  113. 113. Reflection conditions can be looked up in tables inInternational Tables for Crystallography Vol. AOr using freeware such as Space Group Explorer
  114. 114. Be careful: forbidden reflections can occur because ofdynamical diffractionIncident electron wave
  115. 115. When reflectionconditions say this:For example possible020100Can see this:010100
  116. 116. 020100F(100)≠0F(110) ≠0F(010)=0Need to tilt to remove these paths...
  117. 117. Destroy double diffraction paths by tilting.If becomesIf staysthen extinct, was due to DDthen not extinct.
  118. 118. You will need this table (from IT volume A)Figure out reflectionconditions for thesesets.
  119. 119. hkl:h+k+l=2nh+k, k+l, h+l=2nh+k=2nStep 1: determine the reflection conditions from the patterns.200131200151200111200020[001] [015]-[013]-[011]-
  120. 120. hkl:h+k+l=2nh+k, k+l, h+l=2nh+k=2nStep 1: determine the reflection conditions from the patterns.200131200151200111200020[001] [015]-[013]-[011]-For these patternsboth would begood....!?
  121. 121. This means we do not have sufficient information.we missed [012], which will make the difference.-By coincidence200042
  122. 122. 0,0,40,0,20,2,40,2,20,4,40,2,00,4,20,4,01,1,31,1,11,3,31,3,11,5,31,5,12,0,42,0,22,2,42,0,02,2,22,4,42,2,02,4,22,4,03,1,33,1,13,3,33,3,13,5,33,5,14,0,44,0,24,2,44,0,04,2,24,4,44,2,04,4,24,4,05,1,35,1,15,3,35,3,15,5,35,5,1xis : [0,0,0][001][015]-[013]-[012]-[035]-[011]-
  123. 123. This means we do not have sufficient information.we missed [012], which will make the difference.-By coincidence200042 hkl:h+k+l=2nh+k, k+l, h+l=2nh+k=2n
  124. 124. This means we do not have sufficient information.we miss [012], which will make the difference.-By coincidence200042 hkl:h+k+l=2nh+k, k+l, h+l=2nh+k=2nFor only h+k=2n there is no reason why021 would be absent.
  125. 125. It is possible to draw the wrongconclusions if you do not haveenough zones!
  126. 126. 0kl:k=2nk,l=2nk+l=2nStep 1: determine the reflection conditions from the patterns.200131200151200111200020[001] [015]-[013]-[011]-200042
  127. 127. 0kl:k=2nk,l=2nk+l=2nStep 1: determine the reflection conditions from the patterns.200131200151200111200020[001] [015]-[013]-[011]-200042
  128. 128. hhl:h=2nh,l=2nh+l=2nStep 1: determine the reflection conditions from the patterns.200131200151200111200020[001] [015]-[013]-[011]-200042
  129. 129. hhl:h=2nh,l=2nh+l=2nStep 1: determine the reflection conditions from the patterns.200131200151200111200020[001] [015]-[013]-[011]-200042
  130. 130. 00l:no conditionl=2nl=4nStep 1: determine the reflection conditions from the patterns.200131200151200111200020[001] [015]-[013]-[011]-200042
  131. 131. 00l:no conditionl=2nl=4nStep 1: determine the reflection conditions from the patterns.200131200151200111200020[001] [015]-[013]-[011]-200042
  132. 132. Step 2: look up the matching extinctionsymbol in the International Tables ofCrystallography.??
  133. 133. 200 and 020 could be due to doublediffraction...200131200151200111200020[001] [015]-[013]-[011]-
  134. 134. 200 and 020 could be due to doublediffraction... Tilt around 200 until all otherreflections gone except h00 axis:200131200151200111200020[001] [015]-[013]-[011]-
  135. 135. 200 and 020 could be due to doublediffraction...Tilt around 200 until all other reflectionsgone except h00 axis:200 does not disappear It is not double diffraction 00l: l=2nnot 00l: l=4n
  136. 136. Step 2: look up the matching extinction symbol inthe International Tables of Crystallography.
  137. 137. From the reflection conditions you getthe extinction symbol:F - - -
  138. 138. From the reflection conditions you getthe extinction symbol:F - - -This still leaves 5 possible space groupsF23 Fm3 F432 F43m Fm3m-- -
  139. 139. From the reflection conditions you getthe extinction symbol:F - - -This still leaves 5 possible space groupsF23 Fm3 F432 F43m Fm3mOnly difference: rotation axes and mirror planescannot be derived from reflection conditions need CBED- -
  140. 140. Convergent Beam Electron DiffractionCBED
  141. 141. 6mm1R3m1R6mm6mRmR61R31R66RmmR3m3mR6R34mm1R4RmmR4mm4mRmR41R4R42mm1R2RmmR2mm2mRmRm1RmmR21R2R21R1-112m2/m222mm2mmm4-44/m4224mm-42m4/mmm3-3323m-3m6-66/m6226mm-6m26/mmm23m3432-43mm3mTable redrawnfrom B.F. Buxton,J.A. Eades, J.W.Steeds, G.M.Rackham: Phil.Trans. R. Soc.London, 281(1976) 171Diffraction groups vs. Point groups
  142. 142. 6mm1R3m1R6mm6mRmR61R31R66RmmR3m3mR6R34mm1R4RmmR4mm4mRmR41R4R42mm1R2RmmR2mm2mRmRm1RmmR21R2R21R1-112m2/m222mm2mmm4-44/m4224mm-42m4/mmm3-3323m-3m6-66/m6226mm-6m26/mmm23m3432-43mm3mTable redrawnfrom B.F. Buxton,J.A. Eades, J.W.Steeds, G.M.Rackham: Phil.Trans. R. Soc.London, 281(1976) 171Diffraction groups vs. Point groups
  143. 143. For CBED you need sufficiently thick crystals:10 nm 20 nm 30 nm40 nm 50 nm
  144. 144. Table from: J.A. Eades,Convergent beam diffraction, in:Electron Diffraction Techniques,volume 1, ed. J. Cowley, OxfordUniversity Press, 1992
  145. 145. Symmetry is 4mm.Whole pattern projection symmetry
  146. 146. Table from: J.A. Eades,Convergent beam diffraction, in:Electron Diffraction Techniques,volume 1, ed. J. Cowley, OxfordUniversity Press, 1992
  147. 147. Table from: J.A. Eades,Convergent beam diffraction, in:Electron Diffraction Techniques,volume 1, ed. J. Cowley, OxfordUniversity Press, 1992
  148. 148. 6mm1R3m1R6mm6mRmR61R31R66RmmR3m3mR6R34mm1R4RmmR4mm4mRmR41R4R42mm1R2RmmR2mm2mRmRm1RmmR21R2R21R1-112m2/m222mm2mmm4-44/m4224mm-42m4/mmm3-3323m-3m6-66/m6226mm-6m26/mmm23m3432-43mm3mTable redrawnfrom B.F. Buxton,J.A. Eades, J.W.Steeds, G.M.Rackham: Phil.Trans. R. Soc.London, 281(1976) 171Diffraction groups vs. Point groups
  149. 149. [111]
  150. 150. 6mm[111]
  151. 151. Table from: J.A. Eades,Convergent beam diffraction, in:Electron Diffraction Techniques,volume 1, ed. J. Cowley, OxfordUniversity Press, 1992
  152. 152. 6mm1R3m1R6mm6mRmR61R31R66RmmR3m3mR6R34mm1R4RmmR4mm4mRmR41R4R42mm1R2RmmR2mm2mRmRm1RmmR21R2R21R1-112m2/m222mm2mmm4-44/m4224mm-42m4/mmm3-3323m-3m6-66/m6226mm-6m26/mmm23m3432-43mm3mTable redrawnfrom B.F. Buxton,J.A. Eades, J.W.Steeds, G.M.Rackham: Phil.Trans. R. Soc.London, 281(1976) 171Diffraction groups vs. Point groups
  153. 153. 6mm1R3m1R6mm6mRmR61R31R66RmmR3m3mR6R34mm1R4RmmR4mm4mRmR41R4R42mm1R2RmmR2mm2mRmRm1RmmR21R2R21R1-112m2/m222mm2mmm4-44/m4224mm-42m4/mmm3-3323m-3m6-66/m6226mm-6m26/mmm23m3432-43mm3mTable redrawnfrom B.F. Buxton,J.A. Eades, J.W.Steeds, G.M.Rackham: Phil.Trans. R. Soc.London, 281(1976) 171Diffraction groups vs. Point groups
  154. 154. 6mm1R3m1R6mm6mRmR61R31R66RmmR3m3mR6R34mm1R4RmmR4mm4mRmR41R4R42mm1R2RmmR2mm2mRmRm1RmmR21R2R21R1-112m2/m222mm2mmm4-44/m4224mm-42m4/mmm3-3323m-3m6-66/m6226mm-6m26/mmm23m3432-43mm3mTable redrawnfrom B.F. Buxton,J.A. Eades, J.W.Steeds, G.M.Rackham: Phil.Trans. R. Soc.London, 281(1976) 171Diffraction groups vs. Point groups
  155. 155. CBEDSAED
  156. 156. So, sometimes just whole pattern projectionsymmetry is enough if you combine it with thereflection conditions from SAED.
  157. 157. Try it yourself on example SnO2
  158. 158. SAED CBEDExample: rutile-type SnO2
  159. 159. Projection whole pattern symmetry [001]44mm2mm
  160. 160. Projection whole pattern symmetry [001]44mm2mm
  161. 161. Table from: J.A. Eades,Convergent beam diffraction, in:Electron Diffraction Techniques,volume 1, ed. J. Cowley, OxfordUniversity Press, 1992Projection WP: 4mmProjection diffraction group:Table Eades44RmmR4mm1R
  162. 162. Table from: J.A. Eades,Convergent beam diffraction, in:Electron Diffraction Techniques,volume 1, ed. J. Cowley, OxfordUniversity Press, 1992Projection WP: 4mmProjection diffraction group:Table Eades44RmmR4mm1R
  163. 163. Projection diffraction group:4mm1RPossible diffraction groups:4mRmR4mm4RmmR4mm1RTable from: J.A. Eades,Convergent beam diffraction, in:Electron Diffraction Techniques,volume 1, ed. J. Cowley, OxfordUniversity Press, 1992
  164. 164. 6mm1R3m1R6mm6mRmR61R31R66RmmR3m3mR6R34mm1R4RmmR4mm4mRmR41R4R42mm1R2RmmR2mm2mRmRm1RmmR21R2R21R1-112m2/m222mm2mmm4-44/m4224mm-42m4/mmm3-3323m-3m6-66/m6226mm-6m26/mmm23m3432-43mm3mTable redrawnfrom B.F. Buxton,J.A. Eades, J.W.Steeds, G.M.Rackham: Phil.Trans. R. Soc.London, 281(1976) 171
  165. 165. What will be useful to narrow it down further?look at the bright field symmetrylook at the whole pattern symmetry[...] [...]
  166. 166. What will be useful to narrow it down further?look at the bright field symmetrylook at the whole pattern symmetry[...] [...]
  167. 167. WholePatternprojectionsymmetryWholepatternsymmetry
  168. 168. WP symmetry44mm2mm
  169. 169. WP symmetry44mm2mm
  170. 170. [...] [...]
  171. 171. 6mm1R3m1R6mm6mRmR61R31R66RmmR3m3mR6R34mm1R4RmmR4mm4mRmR41R4R42mm1R2RmmR2mm2mRmRm1RmmR21R2R21R1-112m2/m222mm2mmm4-44/m4224mm-42m4/mmm3-3323m-3m6-66/m6226mm-6m26/mmm23m3432-43mm3m
  172. 172. Projection whole pattern [101]2m2mm(smaller cond.ap.)
  173. 173. Projection whole pattern [101]2m2mm(smaller cond.ap.)
  174. 174. Possible projectiondiffraction group:21Rm1R2mm1RProjectionwhole pattern:2mm
  175. 175. Possible projectiondiffraction group:21Rm1R2mm1RProjectionwhole pattern:2mm
  176. 176. Possible projectiondiffraction group:21Rm1R2mm1RProjectionwhole pattern:2mm
  177. 177. Whole pattern [101]2m2mm(smaller cond.ap.)
  178. 178. Whole pattern [101]2m2mm(smaller cond.ap.)
  179. 179. Diffraction group:2mm2RmmR2mm1RWhole patternm
  180. 180. Diffraction group:2mm2RmmR2mm1RWhole patternm
  181. 181. 6mm1R3m1R6mm6mRmR61R31R66RmmR3m3mR6R34mm1R4RmmR4mm4mRmR41R4R42mm1R2RmmR2mm2mRmRm1RmmR21R2R21R1-112m2/m222mm2mmm4-44/m4224mm-42m4/mmm3-3323m-3m6-66/m6226mm-6m26/mmm23m3432-43mm3m
  182. 182. Possible point groups4/mmmm3m
  183. 183. What would make a difference further?For example:-cell parameters-look for a third zone etc.-SAED for reflection conditions
  184. 184. For example, if you needcell parameters a=b= 4.72 Å, c=3.16 Åto be able to index all patterns,the point group is4/mmmm3m
  185. 185. For example, if you needcell parameters a=b= 4.72 Å, c=3.16 Åto be able to index all patterns,the point group is4/mmmm3m
  186. 186. CBEDSAEDSpace Group P42/mnmThen you would combine this again with reflectionconditions (not derived in this exercise) to get thespace group.
  187. 187. At the end of this lecture you should be able to(1) index SAED patterns in case the cell parametersare already known(2) determine the possible space groups from SAEDpatterns(3) determine possible point groups from CBEDpatternsCombine (2) and (3) to find the space group.
  188. 188. Working page for indexing

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