Download presentation
Published byClara Owen Modified over 9 years ago
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
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.