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

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Presentation transcript:

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

Introduction

Form

Anisotropy 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

2D lattices

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

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

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

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 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

Point groups 2m

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

Gypsum 2/m

Epsomite 222

2/m

mm2

4/m mm or 4/mmm

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)

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