1.
Crystallography
Lecture notes
Many other things

2. Crystallography H. K. D. H. Bhadeshia Introduction and point groups
Stereographic projections
Low symmetry systems
Space groups
Deformation and texture
Interfaces, orientation relationships
Martensitic transformations

3. Introduction

4. Liquid Crystals
(Z. Barber)

5. Form

6. Anisotropy (elastic modulus, MPa)Ag Mo

7. Polycrystals

12. The Lattice

29. Centre of symmetry and inversion

32. Bravais Lattices Triclinic P Monoclinic P & C Orthorhombic P, C, I & F
Tetragonal P & I
Hexagonal
Trigonal P
Cubic P, F & I

33. Bravais Lattices

34. body-centred cubic (ferrite)
face-centred cubic (austenite)

35. Bundy (1965)

37. Fe Ru
6d 2s Os Hs

38. Cohesive energy (eV/atom) Pure iron
-65
-55
-45
-35
Cubic-P
Cohesive energy (eV/atom)
Diamond cubic
Pure iron
Hexagonal-P
b.c.c
c.c.p
h.c.p
0.8
1.0
1.2
1.4
1.6
Normalised volume
Paxton et al. (1990)

39. 2D lattices

40. Graphene, nanotubes

41. Amorphous - homogeneous, isotropic
Crystals - long range order, anisotropic
Crystals - solid or liquid
Crystals - arbitrary shapes
Polycrystals
Lattice, lattice points
Unit cell, space filling
Primitive cell, lattice vectors
Bravais lattices
Directions, planes
Weiss zone rule
Symmetry
Crystal structure
Point group symmetry
Point group symbols
Examples

42. Crystal Structure
1/2
1/2
1/2
1/2

44. lattice + motif = structure
primitive cubic lattice
motif = Cu at 0,0,0
Zn at 1/2, 1/2, 1/2

45. Lattice: face-centred cubic Motif: C at 0,0,0 C at 1/4,1/4,1/4
3/4
1/4
3/4
1/4
3/4
1/4
3/4
1/4
Lattice: face-centred cubic
Motif: C at 0,0,0 C at 1/4,1/4,1/4

47. 3/4
1/4
1/4
3/4

48. Lattice: face-centred cubic Motif: Zn at 0,0,0 S at 1/4,1/4,1/4
3/4
1/4
1/4
3/4
Lattice: face-centred cubic
Motif: Zn at 0,0,0 S at 1/4,1/4,1/4

51. fluorite

54. 2 diad 3 triad 4 tetrad 6 hexad
Rotation axes
2 diad
3 triad
4 tetrad
6 hexad

56. Point groups 2m

57. Water and sulphur tetrafluoride have same point symmetry and hence same number of vibration modes - similar spectra

58. Sulphur tetraflouride

59. Gypsum
2/m

60. Epsomite
222

61. 4/m mm or 4/mmm

62. first number c-axis
second number normal to c-axis
some exceptions

63. If a direction [uvw] lies in a plane (hkl) then uh+vk+wl = 0
Weiss Law
If a direction [uvw] lies in a plane (hkl) then
uh+vk+wl = 0
[uvw]
(hkl)

64. [110]
(110) x y z y x z