More Related Content
Similar to Pertemuan 3 close packing (20)
More from jayamartha (20)
Pertemuan 3 close packing
- 7. how and why - derivation
- 10. octahedral and tetrahedral holes
- 15. recognise and demonstrate that cubic close packing is equivalent to a face centred cubic unit cell07/03/2011 3 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
- 16. Packing Can pack with irregular shapes 07/03/2011 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) : 07/03/2011 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) : 07/03/2011 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) 07/03/2011 7 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
- 20. Hexagonal close packed Cubic close packed 07/03/2011 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 07/03/2011 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 07/03/2011 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 07/03/2011 11 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
- 24. Hexagonal close packed structures (hcp) hcp bcc 07/03/2011 12 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
- 25. Recurring themes... Foot and mouth virus Body centred cubic 07/03/2011 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 07/03/2011 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 = (162) r3 Face centred cubic - so number of atoms per unit cell =corners + face centres = (8 1/8) + (6 1/2) = 4 07/03/2011 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 07/03/2011 16 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
- 29. Group exercise: Calculate the packing fraction for a primitive unit cell A = 2 r 07/03/2011 17 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
- 32. MencariFraksi Packing Jumlah atom efektifdalam unit cell = 12(1/6)+2(1/2)+3=6 07/03/2011 20 © 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! 07/03/2011 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 07/03/2011 23 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
- 37. As a consequence, we can calculate the radius of the interstitial sites
- 39. h.c.p and c.c.p are equally efficient packing schemes07/03/2011 24 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |