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Hexagonal system

Hexagonal system. c. Note: 3 axes in a plane and 1 axis perpendicular to the plane. a 3. a 2. 120º. a 1. Hexagonal close-packed structure. * Ideal packing ratio c/a=1.633. Miller-Bravais indices (hkil). Note: i=-(h+k). Components a 1 = a cos 90 = 0 a 2 = a cos 90 = 0

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Hexagonal system

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  1. Hexagonal system c • Note: 3 axes in a plane and 1 axis perpendicular to the plane a3 a2 120º a1

  2. Hexagonal close-packed structure * Ideal packing ratio c/a=1.633

  3. Miller-Bravais indices (hkil) Note: i=-(h+k) Components a1= a cos 90 = 0 a2= a cos 90 = 0 a3= a cos 90 = 0 c = a cos 0 = 1 [0 0 0 1] c Components a1= a cos 0 = 1 a2= a cos 120 = -1/2 a3= a cos 240 = -1/2 c = a cos90 = 0 [1 -1/2 -1/2 0] [2 1 1 0] Components a1= a cos240 =-1/2 a2= a cos 0 = 1 a3= a cos120 = -1/2 c = a cos90 = 0 [-1/2 1 -1/2 0] [1 2 1 0] a3 a2 a1

  4. Planes:Miller-Bravais indices Intersections , , , 1 Inverse 0 0 0 1 (0 0 0 1) Intersections 1, -1, ,  Inverse 1 -1 0 0 (1 1 0 0) c Intersections , , , 1/2 Inverse 0 0 0 2 (0 0 0 2) Intersections 1, 1, -1/2, 1 Inverse 1 1 -2 1 (1 1 2 1) a3 Intersections 1, 1, -1/2, 1/2 Inverse 1 1 -2 2 (1 1 2 2) a2 120º a1

  5. QUESTIONS

  6. Planar and linear atomic densities • Planar atomic density (PAD) • PAD = • Linear atomic density (LAD) • LAD = number of atoms on plane Area of plane number of atoms along line Length of line

  7. Example {100} SC

  8. Example {110} BCC

  9. Example {111} FCC

  10. Example c a3 a2 {0001} HCP 120º a1

  11. Example R R a <100> SC

  12. Example <110> BCC

  13. Example <110> FCC

  14. Example c a3 a2 <2110> HCP a1

  15. Stacking sequence of close-packed planesFCC {111} A A A A B B B C C C A C A A A A B B B B C A A C A C A

  16. Stacking sequence in fcc {111} B B B B B B C C C C B B B B B B B B C C C

  17. Stacking sequence in fcc {111} B B B C B B C B C C B B B B B B B C B C C ABCABCABCABCABC…

  18. Close-packing in fcc

  19. Stacking sequence of close-packed planesHCP {0001} A A A A B B B C C C A C A A A A B B B B C A A C A C A

  20. Stacking sequence in hcp B B B C C C C B B B B C C C ABABABABAB… Or ACACACACAC...

  21. Stacking sequence in hcp B B B C C C C B B B B C C C ABABABABAB… Or ACACACACAC...

  22. Close-packing in hcp

  23. Crystal structure identification techniques • X-ray diffraction • Electron diffraction

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