This document discusses close packing structures in crystals. It explains that there are two main types of close packing: hexagonal close packing (hcp) and cubic close packing (ccp). Ccp packing is equivalent to a face-centered cubic unit cell. Both hcp and ccp structures make efficient use of space with a packing fraction of 0.74, while other structures like primitive unit cells have lower packing fractions with more empty space. The document provides examples of calculating packing fractions and analyzing the geometry of close packed structures.

1. Pertemuan 3CLOSE PACKING STRUCTUREIwanSugihartono, M.SiJurusanFisika, FMIPAUniversitasNegeri Jakarta1

2. Crystals07/03/2011© 2010 Universitas Negeri Jakarta | www.unj.ac.id |2Crystal structure basics

3. unit cells

4. symmetry

5. lattices

6. Diffraction

7. how and why - derivation

8. Some important crystal structures and properties

9. close packed structures

10. octahedral and tetrahedral holes

11. basic structures

12. ferroelectricityObjectivesBy the end of this section you should:understand the concept of close packing

13. know the difference between hexagonal and cubic close packing

14. know the different types of interstitial sites in a close packed structure

15. recognise and demonstrate that cubic close packing is equivalent to a face centred cubic unit cell07/03/20113© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

16. PackingCan pack with irregular shapes07/03/20114© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

17. Two main stacking sequences:If we start with one cp layer, two possible ways of adding a second layer (can have one or other, but not a mixture) :07/03/20115© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

18. Two main stacking sequences:If we start with one cp layer, two possible ways of adding a second layer (can have one or other, but not a mixture) :07/03/20116© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

19. Let’s assume the second layer is B (red). What about the third layer?Two possibilities:(1) Can have A position again (blue). This leads to the regular sequence …ABABABA…..Hexagonal close packing (hcp)(2) Can have layer in C position, followed by the same repeat, to give …ABCABCABC…Cubic close packing (ccp)07/03/20117© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

20. Hexagonal close packedCubic close packed07/03/20118© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

21. No matter what type of packing, the coordination number of each equal size sphere is always 12We will see that other coordination numbers are possible for non-equal size spheres07/03/20119© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

22. Metals usually have one of three structure types:ccp (=fcc, see next slide), hcp or bcc (body centred cubic)The reasons why a particular metal prefers a particular structure are still not well understood07/03/201110© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

23. ccp = fcc ?Build up ccp layers (ABC… packing)Add construction lines - can see fcc unit cellc.p layers are oriented perpendicular to the body diagonal of the cube07/03/201111© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

24. Hexagonal close packed structures (hcp)hcpbcc07/03/201112© 2010 Universitas Negeri Jakarta | www.unj.ac.id |

25. Recurring themes...Foot and mouth virusBody centred cubic07/03/201113© 2010 Universitas Negeri Jakarta | www.unj.ac.id |