Pend Fisika Zat Padat (3) close packing

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  • 1. Pertemuan 3CLOSE PACKING STRUCTURE
    IwanSugihartono, M.Si
    JurusanFisika, FMIPA
    UniversitasNegeri Jakarta
    1
  • 2. Crystals
    06/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    2
    • Crystal 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. ferroelectricity
  • Objectives
    By 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 cell
    06/01/2011
    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
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 30. 06/01/2011
    18
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 31. 06/01/2011
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 32. MencariFraksi Packing
    Jumlah atom efektifdalam unit cell = 12(1/6)+2(1/2)+3=6
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 33. Primitive
    06/01/2011
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    © 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 |
  • 36. Summary
    • By understanding the basic geometry of a cube and use of Pythagoras’ theorem, we can calculate the bond lengths in a fcc structure
    • 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 schemes
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    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
  • 40. THANK YOU
    06/01/2011
    © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
    25