The document discusses close packing structures in crystals. It defines hexagonal close packing and cubic close packing, which differ based on how successive layers are stacked. Cubic close packing is shown to be equivalent to a face-centered cubic unit cell. Close packing yields a packing fraction of 0.74, maximizing the efficient use of space, while primitive unit cells have significantly lower packing fractions with more empty space. The key differences between close packing structures and their implications are summarized.

1. Pertemuan 3CLOSE PACKING STRUCTURE IwanSugihartono, M.Si JurusanFisika, FMIPA UniversitasNegeri Jakarta 1

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

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 cell06/01/2011 3 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

16. Packing Can pack with irregular shapes 06/01/2011 4 © 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) : 06/01/2011 5 © 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) : 06/01/2011 6 © 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) 06/01/2011 7 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

20. Hexagonal close packed Cubic close packed 06/01/2011 8 © 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 12 We will see that other coordination numbers are possible for non-equal size spheres 06/01/2011 9 © 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 understood 06/01/2011 10 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

23. ccp = fcc ? Build up ccp layers (ABC… packing) Add construction lines - can see fcc unit cell c.p layers are oriented perpendicular to the body diagonal of the cube 06/01/2011 11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

24. Hexagonal close packed structures (hcp) hcp bcc  06/01/2011 12 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

25. Recurring themes... Foot and mouth virus Body centred cubic 06/01/2011 13 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

26. Packing Fraction We (briefly) mentioned energy considerations in relation to close packing (low energy configuration) Rough estimate - C, N, O occupy 20Å3 Can use this value to estimate unit cell contents Useful to examine the efficiency of packing - take c.c.p. (f.c.c.) as example 06/01/2011 14 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

27. So the face of the unit cell looks like: Calculate unit cell side in terms of r: 2a2 = (4r)2 a = 2r 2 Volume = (162) r3 Face centred cubic - so number of atoms per unit cell =corners + face centres = (8  1/8) + (6  1/2) = 4 06/01/2011 15 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

28. Packing fraction The fraction of space which is occupied by atoms is called the “packing fraction”, , for the structure For cubic close packing: The spheres have been packed together as closely as possible, resulting in a packing fraction of 0.74 06/01/2011 16 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

29. Group exercise: Calculate the packing fraction for a primitive unit cell A = 2 r 06/01/2011 17 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

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32. MencariFraksi Packing Jumlah atom efektifdalam unit cell = 12(1/6)+2(1/2)+3=6 06/01/2011 20 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

33. Primitive 06/01/2011 21 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

34. Close packing Cubic close packing = f.c.c. has =0.74 Calculation (not done here) shows h.c.p. also has =0.74 - equally efficient close packing Primitive is much lower: Lots of space left over! A calculation (try for next time) shows that body centred cubic is in between the two values. THINK ABOUT THIS! Look at the pictures - the above values should make some physical sense! 06/01/2011 22 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

35. Hitunglahefisiensi packing dankerapatandariNaClbiladiberikan data sebagaiberikut: Jari-jari ion Na = 0,98 A Jari-jari ion Cl = 1,81 A Massa atom Na = 22,99 amu Massa atom Cl = 35,45 amu ? Solusinya: Parameter kisi, a = 2 (Jari-jari ion (Na + Cl)) = 5.58 A Fraksi Packing: = Volume ion yang adadalamsebuah unit cell Volume unit cellnya = 4 (4/3) phi (r3Na + r3Cl) / a3 = 66,3 % Density: = Massa unit cell / Volumenya = 2234 kg m-3 1 amu = 1,66 x 10-27 kg 06/01/2011 23 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

37. As a consequence, we can calculate the radius of the interstitial sites

38. we can calculate the packing efficiency for different packed structures

39. h.c.p and c.c.p are equally efficient packing schemes06/01/2011 24 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

40. THANK YOU 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 25