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Crystallography H. K. D. H. Bhadeshia Introduction and point groups

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1 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

2 https://edge.edx.org/courses/MSM/C6/2013_Winter/about

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7 Introduction

8 Liquid Crystals (Z. Barber)

9 Form

10 Anisotropy (elastic modulus, MPa)
Ag Mo

11 Polycrystals

12 2D lattices

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17 The Lattice

18 Graphene, nanotubes

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36 Centre of symmetry and inversion

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

40 Bravais Lattices

41 body-centred cubic (ferrite)
face-centred cubic (austenite)

42 Bundy (1965)

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44 Fe Ru 6d 2s Os Hs

45 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)

46 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

47 Crystal Structure 1/2 1/2 1/2 1/2

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

50 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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52 3/4 1/4 1/4 3/4

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54 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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57 fluorite

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60 2 diad 3 triad 4 tetrad 6 hexad
Rotation axes 2 diad 3 triad 4 tetrad 6 hexad

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62 Point groups 2m

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

64 Sulphur tetraflouride

65 Gypsum 2/m

66 Epsomite 222

67 without high order axes

68 without order axes

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70 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)

71 [110] (110) x y z y x z

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