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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
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https://edge.edx.org/courses/MSM/C6/2013_Winter/about
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Introduction
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Liquid Crystals (Z. Barber)
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Form
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Anisotropy (elastic modulus, MPa)
Ag Mo
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Polycrystals
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2D lattices
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The Lattice
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Graphene, nanotubes
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Centre of symmetry and inversion
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Bravais Lattices Triclinic P Monoclinic P & C Orthorhombic P, C, I & F
Tetragonal P & I Hexagonal Trigonal P Cubic P, F & I
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Bravais Lattices
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body-centred cubic (ferrite)
face-centred cubic (austenite)
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Bundy (1965)
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Fe Ru 6d 2s Os Hs
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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)
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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 Weiss zone rule Symmetry Crystal structure Point group symmetry Point group symbols Examples
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Crystal Structure 1/2 1/2 1/2 1/2
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lattice + motif = structure
primitive cubic lattice motif = Cu at 0,0,0 Zn at 1/2, 1/2, 1/2
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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
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3/4 1/4 1/4 3/4
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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
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fluorite
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2 diad 3 triad 4 tetrad 6 hexad
Rotation axes 2 diad 3 triad 4 tetrad 6 hexad
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Point groups 2m
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Water and sulphur tetrafluoride have same point symmetry and hence same number of vibration modes - similar spectra
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Sulphur tetraflouride
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Gypsum 2/m
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Epsomite 222
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without high order axes
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without order axes
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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)
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[110] (110) x y z y x z
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