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.

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

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

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

43. Pinhole camera

45. Laue camera

47. (a) Transmission (b) back-reflection Laue W radiation, 30kV, 19mA

49. Rotating crystal method

51. Rotating crystal method

53. Origin of particle-size broadening   (radians, Debye-Scherrer formulae)

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

59. (3.7)

60. (3.8) (3.9)