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# Pend Fisika Zat Padat (3) close packing

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• 1. Pertemuan 3CLOSE PACKING STRUCTURE
IwanSugihartono, M.Si
JurusanFisika, FMIPA
UniversitasNegeri Jakarta
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• 2. Crystals
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© 2010 Universitas Negeri Jakarta | www.unj.ac.id |
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• 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
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© 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• 16. Packing
Can pack with irregular shapes
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© 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) :
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© 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) :
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© 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)
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© 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• 20. Hexagonal close packed
Cubic close packed
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• 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
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© 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
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© 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
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© 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• 24. Hexagonal close packed structures (hcp)
hcp
bcc

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© 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• 25. Recurring themes...
Foot and mouth virus
Body centred cubic
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© 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
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© 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
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© 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
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© 2010 Universitas Negeri Jakarta | www.unj.ac.id |
• 29. Group exercise:
Calculate the packing fraction for a primitive unit cell
A = 2 r
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© 2010 Universitas Negeri Jakarta | www.unj.ac.id |
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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
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• 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.
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© 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:
= 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
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© 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
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