chapter 5 structure of solids
DESCRIPTION
Chapter 5 Structure of Solids. 6 Lectures. Solids. Crystalline. Noncrystalline. Long-range periodicity. No long-range periodicity. Gives sharp diffraction patterns. Does not give sharp diffraction patterns. Does not have a sharp meliing point. Has sharp melting point. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/1.jpg)
1
Chapter 5
Structure of Solids
6 Lectures
![Page 2: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/2.jpg)
2
Solids
Crystalline Noncrystalline
Gives sharp diffraction patterns
Does not give sharp diffraction patterns
Long-range periodicity No long-range periodicity
Has sharp melting point
Does not have a sharp meliing point
Has higher density Has a lower density
![Page 3: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/3.jpg)
3
![Page 4: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/4.jpg)
4
Factors promoting the formation of noncrystalline structures
1. Primary bonds do not extend in all three directions and the secondary bonds are not strong enough.
2. The difference in the free energy of the crystalline and non crystalline phases is small.
3. The rate of cooling from the liquid state is higher than a critical cooling rate.
Metallic Glass: 106 K s-1
![Page 5: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/5.jpg)
5
Inorganic SolidsCovalent SolidsMetals and AlloysIonic SolidsSilica: crystalline and amorphous
PolymersClassification StructureCrystallinityMechanical Behaviour
![Page 6: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/6.jpg)
6
7th. Group (Halogens): single covalent bondsDiatomic molecules Weak van der Waals bond between
moleculesF2, Cl2: Gas; Br2: Liquid; I2: orthorhombic xl
![Page 7: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/7.jpg)
7
6th. Group: two covalent bonds: long zig-zag chains
Weak van der Waals bonds between chainsmostly noncrystalline
![Page 8: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/8.jpg)
8
5th. Group: Three covalent bonds: Puckered sheets Weak van der Waals bond between sheetsMostly noncrystalline
![Page 9: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/9.jpg)
9
4th. Group: Carbon
![Page 10: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/10.jpg)
10
Graphite Diamond
Buckminster Fullerene1985
Carbon Nanotubes1991
Graphene2004
Allotropes of C
![Page 11: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/11.jpg)
11
GraphiteSp2 hybridization 3 covalent bonds
Hexagonal sheets
x ya b=a=120
a = 2 d cos 30°
= √3 dd = 1.42 Åa = 2.46 Å
![Page 12: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/12.jpg)
12
Graphite
x y
a = 2.46 Å c = 6.70 Å
B
A
A
www.scifun.ed.ac.uk/
c
Lattice: Simple HexagonalMotif: 4 carbon atoms
![Page 13: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/13.jpg)
13
Graphite Highly Anisotropic:
Properties are very different in the a and c directions
www.sciencemuseum.org.uk/
Uses:Solid lubricantPencils (clay + graphite, hardness
depends on fraction of clay)carbon fibre
![Page 14: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/14.jpg)
14
DiamondSp3 hybridization 4 covalent bonds
Location of atoms:8 Corners6 face centres4 one on each of the 4 body diagonals
Tetrahedral bonding
![Page 15: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/15.jpg)
15
Diamond Cubic Crystal: Lattice & motif?
AA BB
C
CD
D
x
y
P
P
RR
S
S
T
T
KK
L
L
MM
N
N
0,1
0,1
0,1
0,1
0,1
41
41
43
43
Diamond Cubic Crystal= FCC lattice + motif:
x
y
21
21
21
21
Projection of the unit cell on the bottom face of the cube
000; ¼¼¼
![Page 16: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/16.jpg)
16
Crystal Structure = Lattice + Motif
Diamond Cubic Crystal Structure
FCCLattice
2 atomMotif
41
41
41
000= +
There are only three Bravais Lattices: SC, BCC, FCC.
Diamond Cubic Lattice
![Page 17: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/17.jpg)
17
There is no diamond cubic lattice.
![Page 18: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/18.jpg)
18
Diamond Cubic
Structure
Effective number of atoms in the unit cell = 881
Corners
Relaton between lattice parameter and atomic radius
ra 243
38ra
Packing efficiency
34.01633
483
3
a
r
Coordination number 4
8621
41
InsideFace
![Page 19: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/19.jpg)
19
Diamond Cubic Crystal StructuresC Si Ge Gray Sn
a (Å) 3.57 5.43 5.65 6.46
![Page 20: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/20.jpg)
200,1 0,1
21
IV-IV compound: SiCIII-V compound:
AlP, AlAs, AlSb, GaP, GaAs, GaSb,
InP, InAs, InSbII-VI compound:
ZnO, ZnS,CdS, CdSe, CdTe
I-VII compound:CuCl, AgI
y
S
0,1 0,1
0,1
41
41
43
43
21
21
21
Equiatomic binary AB compounds having diamond cubic like structure
![Page 21: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/21.jpg)
21
USES:
DiamondAbrasive in polishing and grindingwire drawing dies
Si, Ge, compounds: semiconducting devices
SiCabrasives, heating elements of furnaces
![Page 22: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/22.jpg)
22
Inorganic SolidsCovalent SolidsMetals and AlloysIonic SolidsSilica: crystalline and amorphous
PolymersClassification StructureCrystallinityMechanical Behaviour
![Page 23: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/23.jpg)
23
Metals and Alloys
As many bonds as geometrically possible (to lower the energy)
2. Atoms as hard sphere (Assumption)
1, 2 & 3 Elemental metal crystals: close packing of equal hard spheres
1. Metallic bond: Nondrectional (Fact)
Close packing
3. Elements (identical atoms)
![Page 24: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/24.jpg)
24
Close packing of equal hard spheresArrangement of equal nonoverlapping
spheres to fill space as densely as possibleSphere packing problem: What is the densest packing of spheres in 3D?
Kissing Number Problem
Kepler’s conjecture, 1611 74.023
. EP
What is the maximum number of spheres that can touch a given sphere?
Coding TheoryInternet data transmission
![Page 25: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/25.jpg)
25
Close packing of equal hard spheres
1-D packing
A chain of spheres
P.E.=
Kissing Number=
Close-packed direction of atoms
=1 2lengthtotallengthoccupied
![Page 26: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/26.jpg)
26
Close packing of equal hard spheres
2-D packing
A hexagonal layer of atoms
P.E.= Kissing Number=6
Close-packed plane of atoms
Close-packed directions?
3
areatotalareaoccupied 907.
32
1940 L. Fejes Toth : Densest packing of circles in plane
![Page 27: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/27.jpg)
27
Close packing of equal hard spheres
3-D packing
A A A
AA AA
AA
A
A
A AA
A
A
B BB
B B B
B B B
C C C
C
C
C C
C C
First layer A
Second layer B
Third layer A or C
Close packed crystals:…ABABAB… Hexagonal close packed (HCP)…ABCABC… Cubic close packed (CCP)
![Page 28: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/28.jpg)
28
Geometrical properties of ABAB stacking
A A A
AA AA
AA
A
A
A AA
A
A
BB
B B B
B B B
C C C
C
C
C C
C C
B
A and B do not have identical neighboursEither A or B as lattice points, not both
a
b = a=120
Unit cell: a rhombus based prism with a=bc; ==90, =120
A
AB
Bc
The unit cell contains only one lattice point (simple) but two atoms (motif)ABAB stacking = HCP crystal = Hexagonal P lattice + 2 atom motif000
2/3 1/3 1/2
![Page 29: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/29.jpg)
29
c/a ratio of an ideal HCP crystal
A A A
AA AA
AA
A
A
A AA
A
A
BB
B B B
B B B
C C C
C
C
C C
C C
B
A single B atom sitting on a base of three A atoms forms a regular tetrahedron with edge length a = 2RThe same B atom also forms an inverted tetrahedron with three A atoms sitting above it
A
AB
Bc
c = 2 height of a tetrahedron of edge length a
ac322
![Page 30: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/30.jpg)
30
Geometrical properties of ABCABC stacking
A A A
AA AA
AA
A
A
A AA
A
A
B BB
B B B
B B B
C C C
C
C
C C
C C
B
A
CB
A
C
All atoms are equivalent and their centres form a latticeMotif: single atom 000
ABCABC stacking = CCP crystal
= FCC lattice + single atom motif 000
3 a
![Page 31: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/31.jpg)
31
Geometrical properties of ABCABC stacking B
A
CB
A
C
All atoms are equivalent and their centres form a latticeMotif: single atom 000
ABCABC stacking = CCP crystal
= FCC lattice + single atom motif 000
3 a
![Page 32: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/32.jpg)
32
Geometrical properties of ABCABC stacking B
A
CB
A
C
All atoms are equivalent and their centres form a latticeMotif: single atom 000
A A A
AA AA
AA
A
A
A AA
A
A
B BB
B B B
B B B
C C C
C
C
C C
C C
ABCABC stacking = CCP crystal
= FCC lattice + single atom motif 000
3 a
A
A
A
A AA
![Page 33: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/33.jpg)
33
A
C
A
Body diagonal
B
Close packed planes in the FCC unit cell of cubic close packed crystal
Close packed planes: {1 1 1}
B
![Page 34: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/34.jpg)
34
Stacking sequence?
ABA: HCP
![Page 35: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/35.jpg)
35
![Page 36: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/36.jpg)
36
http://www.tiem.utk.edu/~gross/bioed/webmodules/spherefig1.gif
Find the mistake in the following picture:
![Page 37: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/37.jpg)
37
CrystalStructure
Coordinationnumber
Packingefficiency
Table 5.1Coordination Number and Packing Efficiency
Diamond cubic (DC) 4 0.34
Simple cubic (SC) 6 0.52
Body-centred cubic 8 0.68
Face-centred cubic 12 0.74
![Page 38: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/38.jpg)
38
Voids in Close-Packed Crystals
A
AAB
A
AAA
A
B
B B
C
TETRAHEDRAL VOID OCTAHEDRAL VOID
A
No. of atoms defining 4 6the void
No. of voids per atom 2 1
Edge length of void 2 R 2 R
Size of the void 0.225 R 0.414 R
Experiment 2
HW
![Page 39: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/39.jpg)
39
Location of Voids in FCC Unit cell
![Page 40: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/40.jpg)
40
Solid Solution
A single crystalline phase consisting of two or more elements is called a solid solution.
Substitutional Solid solution of Cu and Zn (FCC)
Interstitial solid solution of C in Fe (BCC)
![Page 41: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/41.jpg)
41
Hume-Rothery Rules for Extensive Solid Solution (Unlimited solubility)
Interstitial solid solution Substitutional solid solution
1. Structure factor
Crystal structure of the two elements should be the same
2. Size factor:
Size of the two elements should not differ by more than 15%
3. Electronegativity factor:
Electronegativity difference between the elements should be small
4. Valency factor:
Valency of the two elements should be the same
![Page 42: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/42.jpg)
42
TABLE 5.2
System Crystal Radius of Valency Electro-structure atoms, Ǻ negativity
Ag-Cu Ag FCC 1.44 1 1.9Au FCC 1.44 1 1.9
Cu-Ni Cu FCC 1.28 1 1.9Ni FCC 1.25 2 1.8
Ge-Si Ge DC 1.22 4 1.8Si DC 1.18 4 1.8
All three systems exhibit complete solid solubility.
![Page 43: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/43.jpg)
43
BRASSCu + Zn
FCC HCP
Limited Solubility:
Max solubility of Cu in Zn: 1 wt% Cu
Max Solubility of Zn in Cu: 35 wt% Zn
Unfavourable structure factor
![Page 44: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/44.jpg)
44
Ordered and RandomSubstitutional solid solution
Random Solid Solution
Ordered Solid Solution
![Page 45: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/45.jpg)
45
Disordered solid solution of β-Brass:
Corner and centre both have 50% probability of being
occupied by Cu or ZnOrdered solid solution of β-Brass:
Corners are always occupied by Cu, centres always by Zn
470˚C
Above 470˚C
Below 470˚C
Ordered and random substitutional solid solution
β-Brass: (50 at% Zn, 50 at% Cu)
![Page 46: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/46.jpg)
46
Intermediate Structures
Crystal structure of Cu:
FCCCrystal structure of Zn:
HCP
Crystal structure of random β-brass: BCC
Such phases that have a crystal structure different from either of the two components are called INTERMEDIATE STRUCURESIf an intermediate structure occurs only at a fixed composition it is called an INTERMETALLIC COMPOUND, e.g. Fe3C in steels.
![Page 47: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/47.jpg)
47
IONIC SOLIDS
Cation radius: R+ Anion radius: R-
1. Cation and anion attract each other.
Usually
RR
2. Cation and anion spheres touch each other
1, 2, 3 => Close packing of unequal spheres
3. Ionic bonds are non-directional
![Page 48: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/48.jpg)
48
IONIC SOLIDS
Local packing geometry
1. Anions and cations considered as hard spheres always touch each other.
2. Anions generally will not touch, but may be close enough to be in contact with each other in
a limiting situation.3. As many anions as possible surround a central
cation for the maximum reduction in electrostatic energy.
![Page 49: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/49.jpg)
49
Anions not touching the central cation, Anions touching each other
Anions touching the central cationAnions touching
Anions touching central cationAnions not touching each other
155.0a
c
RR 155.0
a
c
RR 155.0
a
c
RR
unstable Critically stable stable
Effect of radius ratio
2155.0 LigancyRR
a
c
3155.0 LigancyRR
a
c
![Page 50: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/50.jpg)
50
3155.0 LigancyRR
a
c
However, when tetrahedral coordinationwith ligancy 4 becomes stable
225.0a
c
RR
Recall tetrahedral void in close-packed structure.
Thus
3225.0155.0 LigancyRR
a
c
![Page 51: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/51.jpg)
51
Table 5.3Ligancy as a Function of Radius Ration
Ligancy Range of radius ratioConfiguration2 0.0 ― 0.155 Linear
3 0.155 ― 0.225 Triangular
4 0.225 ― 0.414 Tetrahedral
6 0.414 ― 0.732 Octahedral
8 0.732 ― 1.0 Cubic
12 1.0 FCC or HCP
![Page 52: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/52.jpg)
52
Example 1: NaCl
cae2k.com
onCoordinatiOctahedralLigancy
RR
Cl
Na
6732.054.0414.0
54.0
NaCl structure =FCC lattice + 2 atom motif: Cl- 0 0 0
Na ½ 0 0
![Page 53: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/53.jpg)
53
aRRClNa
22 "
NaCl structure continued
CCP of Cl─ with Na+ in ALL octahedral voids
![Page 54: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/54.jpg)
54
seas.upenn.edu
Example 2 : CsCl Structure
191.0732.0
91.0Cl
Cs
RR
Ligancy 8Cubic coordination of Cl- around Cs+
CsCl structure = SC lattice + 2 atom motif: Cl 000
Cs ½ ½ ½ aRR
ClCs322 BCC
![Page 55: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/55.jpg)
55
Example 3: CaF2 (Fluorite or fluorospar)
732.073.0
73.02
F
Ca
RR
Octahedral or cubic coordination
Actually cubic coordination of F─ around Ca2+
But the ratio of number of F─ to Ca2+ is 2:1
So only alternate cubes of F─ are filled with Ca2+
![Page 56: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/56.jpg)
56
Simple cubic crystal of F─ with Ca2+ in alternate cube centres
Alternately, Ca2+ at FCC sites with F─ in ALL tetrahedral voids
CaF structure= FCC lattice + 3 atom motif
Ca2+ 000F─ ¼ ¼ ¼F─ -¼ -¼ -¼
![Page 57: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/57.jpg)
57
Example 4: ZnS (Zinc blende or sphalerite)
onCoordinatiOctahedralLigancy
RR
S
Zn
6732.048.0414.0
48.02
2
However, actual ligancy is 4 (TETRAHEDRAL COORDINATION)
Explanation: nature of bond is more covalent than ionic
wikipedia
![Page 58: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/58.jpg)
58
seas.upenn.edu
ZnS structure
CCP of S2─ with Zn2+ in alternate tetrahedral voids
ZnS structure = FCC lattice + 2 atom motif S2─ 0 0 0 Zn2+ ¼ ¼ ¼
![Page 59: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/59.jpg)
59
pixdaus.com
![Page 60: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/60.jpg)
60
theoasisxpress.com
![Page 61: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/61.jpg)
61
![Page 62: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/62.jpg)
62
pixdaus.com
What is common to 1, glass of the window2. sand of the beach, and 3. quartz of the watch?
![Page 63: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/63.jpg)
63
Structure of SiO2
414.29.0225.0
29.02
4
O
Si
RR
Bond is 50% ionic and 50 % covalent
Tetrahedral coordination of O2─ around Si4+
Silicate tetrahedron
![Page 64: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/64.jpg)
64
4+
2─
2─
2─
2─
4─
Silicate tetrahedron electrically unbalanced
O2─ need to be shared between two tetrahedra
![Page 65: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/65.jpg)
65
1. O2─ need to be shared between two tetrahedra.2. Si need to be as far apart as possible
Face sharing Edge sharing Corner sharing
Silicate tetrahedra share corners
![Page 66: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/66.jpg)
66
2D representation of 3D periodically repeating pattern of tetrahedra in crystalline SiO2. Note that alternate tetrahedra are inverted
![Page 67: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/67.jpg)
672 D representation of 3D random network of silicate tetrahedra in the fused silica glass
![Page 68: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/68.jpg)
68
Modification leads to breaking of primary bonds between silicate tetrahedra.
+ Na2O =Na
Na
Network Modification by addition of Soda
![Page 69: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/69.jpg)
692 D representation of 3D random network of silicate tetrahedra in the fused silica glass
![Page 70: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/70.jpg)
70
5.7 Structure of Long Chain Polymers
Degree of Polymerization:No. of repeating monomers in a
chain
109.5
A
C
C
C
H
H
![Page 71: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/71.jpg)
71
Freedom of rotation about each bond in space leads to different conformations of C-C backbone
109.5
![Page 72: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/72.jpg)
72
![Page 73: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/73.jpg)
73
5.8 Crystallinity in long chain polymers
Fig. 5.17: semicrystalline polymer
![Page 74: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/74.jpg)
74
Factors affecting crystallinity of a long chain polymer
1. Higher the degree of polymerization lower is the degree of crystallization.
Longer chains get easily entagled
![Page 75: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/75.jpg)
75
Branching
2. More is the branching less is the tendency to crystallize
![Page 76: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/76.jpg)
76
Tacticity
3. Isotactic and syndiotactic polymers can crystallize but atactic cannot.
![Page 77: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/77.jpg)
77
Copoymers: polymeric analog of solid solutions
4. Block and random copolymers promote non crystallinity.
![Page 78: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/78.jpg)
78
Plasticizers
Low molecular weight additives
Impedes chains coming together
Reduces crystallization
![Page 79: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/79.jpg)
79
ElastomerPolymers with very extensive elastic deformation
Stress-strain relationship is non-linearExample: Rubber
![Page 80: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/80.jpg)
80
Liquid natural rubber (latex) being collected from the rubber tree
![Page 81: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/81.jpg)
81
Isoprene molecule
commons.wikimedia.org
C=C-C=CH H
HH
H
H3C
![Page 82: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/82.jpg)
82
C C C CH H
HH
H
CH3
Isoprene molecule
Polyisoprene mer
C C C C H H
HH H CH3
Polymerization
Liquid(Latex)
![Page 83: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/83.jpg)
83
C C C C H H
HH H CH3
C C C C H H
HH
H CH3
+ 2S
Vulcanisation
Weak van der
Waals bond
![Page 84: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/84.jpg)
84
C C C C H H
HH H CH3
C C C C H H
HH
H CH3
S
Vulcanisation
S
Cross-links
![Page 85: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/85.jpg)
85
Natural rubber Elastomer Ebonite
liquid Elastic solid
Hard & brittle
not x-linked
lightly x-linked
heavilyx-linked
Effect of cross-linking on polyisoprene
![Page 86: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/86.jpg)
86
Charles GoodyearDecember 29, 1800-July 1,
1860Debt at the time of
death $200,000Life should not be estimated
exclusively by the standard of dollars and cents. I am not
disposed to complain that I have planted and others have gathered the fruits. One has cause to regret
only when he sows and no one reaps.
![Page 87: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/87.jpg)
87
Another interesting property of elastomers
Thermal behaviour
![Page 88: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/88.jpg)
88
Tensile force
F
Elastomer sample
Elastomer sample
under tension
Coiled chains
straight
chains
heat
Higher entropy
Lower entropy Still
lower entropy
Contracts on heating
![Page 89: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/89.jpg)
89
Elastomers have ve thermal expansion coefficient, i.e., they
CONTRACT on heating!!
EXPERIMENT 4
Section 10.3 of the textbook
![Page 90: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/90.jpg)
90
20
00
0
LL
LL
LkTNF
F applied tensile forceN0 number of cross-linksk Boltzmann constantT absolute temperatureL0 initial length (without F)L final length (with F)
![Page 91: Chapter 5 Structure of Solids](https://reader035.vdocuments.mx/reader035/viewer/2022081502/568166f7550346895ddb555d/html5/thumbnails/91.jpg)
91
Experimental
Theory: Chain uncoiling
20
00
0
LL
LL
LkTNF
Bond stretching in straightened out molecules