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. MaximumI phappens
only whenh, kandlare integers. 9. Fig. 3.2 The function (sin 2
Nx)/sin 2 x for N=20. The function peaks at values of xwhich are
integral multiples of , and it is essentially zero everywhere else.
10. 11. 12. 13. (3.10) Fig. 3.3 Representation of the basis vectorr
n in terms of the fractional coordinatesx n ,y n , andz n .
Structure factor = 14. For face-centered crystals: (3.11)hklunmixed
hklmixed 15. For body-centered crystals: h+k+l= even h+k+l= odd 16.
For rock salt, NaCl hklunmixed hklmixed hklall even hklall odd
hklmixed 17. In the Zinc blende form ofZnS hklunmixed h+k+l= 4n
h+k+l=(2n+1)2 hklall odd hklmixed 18. For copperhklunmixed hklmixed
For Tungsten h+k+l= even h+k+l= odd 19. For Zn (hcp): For hexagonal
close-packed structureh+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 = Plancks constant k = Boltzmanns
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
fixedvariable 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
samplein 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
Scherrers formula B = grain size 53. Origin of particle-size
broadening (radians, Debye-Scherrer formulae) 54. 55. 56. A single
(analyzing) crystal witha 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 3 58. Homework assignment
