Transcript Introduction

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Crystallography
Lecture notes
Many other things
Crystallography
Introduction and point groups
Stereographic projections
Low symmetry systems
Space groups
Deformation and texture
Interfaces, orientation relationships
Martensitic transformations
H. K. D. H. Bhadeshia
Introduction
Liquid Crystals
(Z. Barber)
Form
Anisotropy
(elastic modulus, MPa)
Ag
Mo
Polycrystals
The Lattice
Centre of symmetry
and inversion
Bravais Lattices
• Triclinic P
• Monoclinic P & C
• Orthorhombic P,
C, I & F
• Tetragonal P & I
• Hexagonal
• Trigonal P
• Cubic P, F & I
Bravais
Lattices
body-centred
cubic (ferrite)
face-centred
cubic
Bundy
(1965)
Fe
Ru
Os
Hs
6d 2s
-35
Cubic-P
Cohesive energy (eV/atom)
Diamond cubic
Pure iron
-45
Hexagonal-P
-55
-65
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)
2D lattices
Graphene, nanotubes
Amorphous - homogeneous, isotropic
Crystals - long range order, anisotropic
Crystals - solid or liquid
Crystals - arbitrary shapes
Weiss zone rule
Polycrystals
Symmetry
Lattice, lattice points
Crystal structure
Unit cell, space filling
Point group symmetry
Primitive cell, lattice vectors
Point group symbols
Bravais lattices
Examples
Directions, planes
1/2
1/2
1/2
1/2
Crystal
Structure
lattice + motif = structure
primitive cubic lattice
motif = Cu at 0,0,0
Zn at 1/2, 1/2, 1/2
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
3/4
1/4
1/4
3/4
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
fluorite
Rotation axes
2 diad
3 triad
4 tetrad
6 hexad
Point groups
2m
Water and sulphur tetrafluoride have
same point symmetry and hence same
number of vibration modes - similar
spectra
Sulphur tetraflouride
Gypsum
2/m
222
Epsomite
4/m mm or 4/mmm
first number c-axis
second number normal to c-axis
some exceptions
Weiss Law
If a direction [uvw] lies in a plane (hkl)
then
uh+vk+wl = 0
(hkl)
z
y
x
z
y
x