This document discusses the basics of crystal structures, including unit cells, symmetry, and lattices. It defines a unit cell as the smallest repeating unit that shows the full symmetry of a crystal structure. There are seven possible shapes for unit cells: cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, and rhombohedral. Examples of identifying unit cells in 2D patterns are provided.

1. Peretemuan 1 PENDAHULUAN FISIKA ZAT PADAT 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. Why Solids? most elements solid at room temperature  atoms in ~fixed position “simple” case - crystalline solid  Crystal Structure Why study crystal structures? description of solid  comparison with other similar materials - classification  correlation with physical properties 4 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

14. Crystals are everywhere! 5 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

15. More crystals 6 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

16. Early ideas Crystals are solid - but solids are not necessarily crystalline Crystals have symmetry (Kepler) and long range order Spheres and small shapes can be packed to produces regular shapes (Hooke, Hauy) 7 ? 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

17. Group discussion 8 Kepler wondered why snowflakes have 6 corners, never 5 or 7. By considering the packing of polygons in 2 dimensions, demonstrate why pentagons and heptagons shouldn’t occur. 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

19. 3 angles - , , 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

21. Tetragonal a=bc===90°

22. Orthorhombicabc===90°

23. Monoclinic abc==90°,   90°

24. Triclinic abc    90°

25. Hexagonala=bc==90°, =120°

26. Rhombohedrala=b=c ==90°Think about the shapes that these define - look at the models provided. 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 10

27. 2D example - rocksalt(sodium chloride, NaCl) 11 We define lattice points ; these are points with identical environments 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

28. Choice of origin is arbitrary - lattice points need not be atoms - but unit cell size should always be the same. 12 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

29. This is also a unit cell - it doesn’t matter if you start from Na or Cl 13 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

30. - or if you don’t start from an atom 14 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

31. This is NOT a unit cell even though they are all the same - empty space is not allowed! 15 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

32. In 2D, this IS a unit cellIn 3D, it is NOT 16 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

33. All M.C. Escher works (c) Cordon Art-Baarn-the Netherlands.All rights reserved. 17 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

34. Examples 18 The sheets at the end of handout 1 show examples of periodic patterns. On each, mark on a unit cell. [remembering that there are a number of different (correct) answers!] 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

36. All unit cells must be identical

37. Unit cells must show the full symmetry of the structure  next section06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |

38. THANK YOU 06/01/2011 © 2010 Universitas Negeri Jakarta | www.unj.ac.id | 20