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Crystallography Lecture Notes: Introduction to Crystal Structures, Symmetry, and Transformations

Explore crystallography fundamentals like point groups, space groups, deformation, texture, interfaces, and martensitic transformations. Learn about lattice structures, symmetry elements, lattice types, and crystal structures in detail.

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Crystallography Lecture Notes: Introduction to Crystal Structures, Symmetry, and Transformations

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  1. www.msm.cam.ac.uk/phase-trans/teaching.html Crystallography Lecture notes Many other things

  2. 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

  3. Introduction

  4. Liquid Crystals (Z. Barber)

  5. Form

  6. Anisotropy(elastic modulus, MPa) Ag Mo

  7. Polycrystals

  8. The Lattice

  9. Centre of symmetry and inversion

  10. Bravais Lattices • Triclinic P • Monoclinic P & C • Orthorhombic P, C, I & F • Tetragonal P & I • Hexagonal • Trigonal P • Cubic P, F & I

  11. Bravais Lattices

  12. body-centred cubic (ferrite) face-centred cubic (austenite)

  13. Bundy (1965)

  14. Fe Ru 6d 2s Os Hs

  15. -35 -45 -55 -65 Cubic-P Diamond cubic Cohesive energy (eV/atom) 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)

  16. 2D lattices

  17. Graphene, nanotubes

  18. 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

  19. 1/2 1/2 1/2 1/2 Crystal Structure

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

  21. 1/4 1/4 1/4 1/4 1/4 3/4 3/4 3/4 3/4 Lattice: face-centred cubic Motif: C at 0,0,0 C at 1/4,1/4,1/4

  22. 1/4 1/4 3/4 3/4

  23. 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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