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face centered cubic, fcc

Institute of Solid State Physics. Technische Universit ät Graz. Crystal Structure . Atoms are arranged in a periodic pattern in a crystal. The atomic arrangement affects the macroscopic properties of a material. Crystals are relatively easy to model.

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face centered cubic, fcc

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  1. Institute of Solid State Physics Technische Universität Graz Crystal Structure Atoms are arranged in a periodic pattern in a crystal. The atomic arrangement affects the macroscopic properties of a material. Crystals are relatively easy to model. Many important materials (silicon, steel) are crystals face centered cubic, fcc simple cubic body centered cubic, bcc

  2. Crystals = unit cell Bravais lattice Crystal a3 a2 a1

  3. Example NaCl • Primitive Vectors: • Basis Vectors: http://cst-www.nrl.navy.mil/lattice/struk/b1.html

  4. 14 Bravais lattices Points of a Bravais lattice do not necessarily represent atoms. http://en.wikipedia.org/wiki/Bravais_lattice

  5. Unit Cell a3 a2 Choice of unit cell is not unique a1 volume of a unit cell = diamond

  6. Wigner-Seitz Cells fcc bcc Truncated octahedron Rhombic dodecahedron http://britneyspears.ac/physics/crystals/wcrystals.htm http://en.wikipedia.org/wiki/Rhombic_dodecahedron http://en.wikipedia.org/wiki/Truncated_octahedron

  7. Coordination number Number of atoms touching one atom in a crystal Diamond 4 Graphite 3 bcc 8 fcc 12 hcp 12 sc 6

  8. atomic packing density HCP FCC close packing density = 0.74 random close pack = 0.64 simple cubic = 0.52 diamond = 0.34

  9. Fcc Primitive unit cell Wigner-Seitz cell conventional unit cell showing close packed plane From: Hall, Solid State Physics

  10. bcc Wigner Seitz cell Crystal planes and directions: Miller indices [ ] specific direction < > family of equivalent directions ( ) specific plane { } family of equivalent planes KOH rapidly etches the Si <100> planes

  11. Cementite - Fe3C cell 5.09000 6.74800 4.52300 90.000 90.000 90.000 natom 3 Fe1 26 0.18600 0.06300 0.32800 Fe2 26 0.03600 0.25000 0.85200 C 6 0.89000 0.25000 0.45000 rgnr 62 Cohenite (Cementite) Fe3 C Unit cell Asymmetric unit Generated by PowderCell

  12. Groups Crystals can have symmetries: translation, rotation, reflection, inversion,... Symmetries can be represented by matrices. All such matrices that bring the crystal into itself form the group of the crystal. AB  G for A, B  G 32 point groups (one point remains fixed during transformation) 230 space groups

  13. Asymmetric Unit http://www.pdb.org/robohelp/data_download/biological_unit/asymmetric_unit.htm

  14. http://it.iucr.org/A/

  15. simple cubic Po Number: 221 Primitive Vectors: • Basis Vector: http://cst-www.nrl.navy.mil/lattice/

  16. fcc Al, Cu, Ni, Sr, Rh, Pd, Ag, Ce, Tb, Ir, Pt, Au, Pb, Th Number 225 Primitive Vectors: Basis Vector: http://cst-www.nrl.navy.mil/lattice/

  17. hcp Mg, Be, Sc, Ti, Co, Zn, Y, Zr, Tc, Ru, Cd, Gd, Tb, Dy, Ho, Er, Tm, Lu, Hf, Re, Os, Tl http://cst-www.nrl.navy.mil/lattice/

  18. bcc W Na K V Cr Fe Rb Nb Mo Cs Ba Eu Ta Primitive Vectors: Basis Vector: http://cst-www.nrl.navy.mil/lattice/

  19. NaCl http://cst-www.nrl.navy.mil/lattice/

  20. CsCl http://cst-www.nrl.navy.mil/lattice/

  21. perovskite http://cst-www.nrl.navy.mil/lattice/

  22. ybco http://cst-www.nrl.navy.mil/lattice/

  23. graphite http://cst-www.nrl.navy.mil/lattice/

  24. diamond C Si Ge Number: 227 • Primitive Vectors: • Basis Vectors: http://cst-www.nrl.navy.mil/lattice/

  25. zincblende ZnS GaAs InP http://cst-www.nrl.navy.mil/lattice/

  26. wurtzite ZnO CdS CdSe GaN AlN http://cst-www.nrl.navy.mil/lattice/

  27. Quartz http://cst-www.nrl.navy.mil/lattice/

  28. face centered cubic, fcc body centered cubic, bcc simple cubic

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