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Pertemuan 3 close packing
1.
Pertemuan 3CLOSE PACKING
STRUCTURE IwanSugihartono, M.Si JurusanFisika, FMIPA UniversitasNegeri Jakarta 1
2.
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.
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 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 |
30.
07/03/2011 18 ©
2010 Universitas Negeri Jakarta | www.unj.ac.id |
31.
07/03/2011 19 ©
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 |
33.
Primitive 07/03/2011 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! 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 |
36.
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 schemes07/03/2011 24 © 2010 Universitas Negeri Jakarta | www.unj.ac.id |
40.
THANK YOU 07/03/2011
© 2010 Universitas Negeri Jakarta | www.unj.ac.id | 25
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