www msm cam ac ukphasetransteaching html Crystallography Lecture
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www. msm. cam. ac. uk/phase-trans/teaching. html 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 6 d 2 s
Cohesive energy (e. V/atom) -35 Cubic-P Diamond cubic Pure iron -45 Hexagonal-P -55 -65 b. c. c. p h. c. p 0. 8 1. 0 1. 2 1. 4 1. 6 Normalised volume Paxton et al. (1990)
2 D lattices
Graphene, nanotubes
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
1/2 1/2 Crystal Structure
lattice + motif = structure primitive cubic lattice motif = Cu at 0, 0, 0 Zn at 1/2, 1/2
1/4 3/4 1/4 Lattice: face-centred cubic Motif: C at 0, 0, 0 C at 1/4, 1/4
3/4 1/4 3/4
3/4 1/4 3/4 Lattice: face-centred cubic Motif: Zn at 0, 0, 0 S at 1/4, 1/4
fluorite
Rotation axes 2 diad 3 triad 4 tetrad 6 hexad
Point groups 2 m
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 [uv w] uh+vk+wl = 0 (hkl)
z ) (110 y x [11 0] z y x
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