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972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
972 B3102005 Xray3
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972 B3102005 Xray3

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  • 1. Diffraction theory: diffraction by crystals
  • 2. Fig. 3.1 Diffraction of a parallel primary beam by a small crystal.
  • 3. (3.1) … .structure factor (3.2) After summation over all atoms:
  • 4. (3.3)
  • 5. (3.4)
  • 6. Let
  • 7. (3.6) (3.5)
  • 8. Maximum I p happens only when h’, k’ and l’ are integers.
  • 9. Fig. 3.2 The function (sin 2 Nx)/sin 2 x for N=20. The function peaks at values of x which are integral multiples of π, and it is essentially zero everywhere else.
  • 10.  
  • 11.  
  • 12.  
  • 13. (3.10) Fig. 3.3 Representation of the basis vector r n in terms of the fractional coordinates x n , y n , and z n . Structure factor =
  • 14. For face-centered crystals: (3.11) hkl unmixed : hkl mixed :
  • 15. For body-centered crystals: h+k+l = even : h+k+l = odd :
  • 16. For rock salt, NaCl hkl unmixed : hkl mixed : hkl all even : hkl all odd : hkl mixed :
  • 17. In the Zinc blende form of ZnS hkl unmixed : h+k+l = 4n : h+k+l =(2n+1)2 : hkl all odd : hkl mixed :
  • 18. For copper hkl unmixed : hkl mixed : For Tungsten h+k+l = even : h+k+l = odd :
  • 19. For Zn (hcp): For hexagonal close-packed structure h+2k =3n , l =even : h+2k =3n  1 , l =odd : h+2k =3n  1 , l =even : h+2k =3n , l =odd :
  • 20. Hexagonal close-packed Zn, Mg, Be,  -Ti
  • 21. Thermal diffuse scattering: Let
  • 22.  
  • 23.  
  • 24. For single kind of atom: Thermal diffuse scattering: Debye-Waller factor:
  • 25.  = Debye Temperature  Appendix 13 h = Planck’s constant k = Boltzmann’s constant m = mass of the vibration atom x =  /T  (x)  Appendix 13 For Cubic element:
  • 26. For iron at 20  C
  • 27. Diffraction method variable fixed powder variable (in part) fixed Rotating- crystal fixed variable Laue   method
  • 28. -S 0 /  S/  [hkl]* (hkl)   P Ewald sphere construction for a crystal
  • 29. For powder sample: Each reciprocal lattice point circulates around the origin to form a sphere, which intersects the Ewald sphere in a Debye ring, see next page.
  • 30. A Debye ring of a powder sample
  • 31. Debye ring of a powder sample: intersection of two spheres
  • 32.  
  • 33.  
  • 34.  
  • 35.  
  • 36.  
  • 37.  
  • 38. Diffractometer
  • 39. * Detector travels along the measuring circle * Detector intersects each Debye ring in one arc
  • 40. [2h 2k 2l]* Increasing  Increasing  A crystal in a diffractometer
  • 41. A powder sample in a diffractometer
  • 42.  
  • 43. Pinhole camera
  • 44.  
  • 45. Laue camera
  • 46.  
  • 47. (a) Transmission (b) back-reflection Laue W radiation, 30kV, 19mA
  • 48.  
  • 49. Rotating crystal method
  • 50.  
  • 51. Rotating crystal method
  • 52. Peak broadening
    • Instrument broadening
    • Sample broadening
    § Particle-size broadening § Non-uniform strain § Stacking fault Scherrer’s formula B = grain size
  • 53. Origin of particle-size broadening   (radians, Debye-Scherrer formulae)
  • 54.  
  • 55.  
  • 56. A single (analyzing) crystal with a specific (hkl) plane//sample surface
  • 57. ∑ A =sum of atomic weights of all atoms in a unit cell X-ray density   in g/cm 3 , A in grams, V’ in Å 3
  • 58. Homework assignment
    • Cullity 3-1
    • Cullity 3-3
    • Cullity 4-3
    • Cullity 4-4
  • 59. (3.7)
  • 60. (3.8) (3.9)

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