Lecture 5 - Crystal Systems and Polymers
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Transcript of Lecture 5 - Crystal Systems and Polymers
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Chapter 3CRYSTAL SYSTEMS
Cont
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Linear Density (LD)
Related to directional equivalency eg. Linear Density (LD) defined as number of atoms
per unit length whose centers lie on thedirection vector for a specific crystallographicdirection
Number of atoms centered on direction vector
Length of the direction vector
LD
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LD for FCC Unit Cell
x
y
z
Radius of the
atoms: R
Number of atoms centered on direction vector
Length of the direction vector
LD
110
2 1
4R 2LD
R
[110] Direction
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Planar Density (PD)
Related to planar equivalency eg. {111} PD is defined as the number of atoms per unit
area that are centered on a particularcrystallographic plane
Number of atoms centered on a plane
Area of the plane
PD
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Planar Density for FCC Unit Cell
x
y
z
(110) plane
2R2
4R
Number of atoms centered on a plane
Area of the planePD
2
2 1
4 *2 2 4 2PD
R R R
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rys a ne an on- rys a neMaterials
Crystalline SiO2
Amorphous or Non-Crystalline SiO2
atoms pack in periodic, 3D arrays typical of: -metals
-many ceramics-some polymers
atoms have no periodic packing occurs for: -complex structures
-rapidly cooledstructures
Si O
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Single Crystals and Poly Crystals
Single Crystals Properties vary with directionAnisotropic
E for BCC iron
Ediagonal
= 273 GPa
E edge = 125 GPa
Polycrystals (collection of many grains) Properties may / may not vary
with direction If grains are randomly oriented,
ISOTROPIC
If grains are textured,ANISOTROPIC
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Isotropy and Anisotropy
Isotropy: Measured properties (elasticmodulus, conductivity, refractive index)independent of direction of measurement
Structurally symmetric crystals display isotropic
behavior (cubic) Anisotropy: Directionality of properties
change with direction of measurement
Changes in atomic or ionic spacing withcrystallographic direction (Refer Table 3.7)
Increases with decreasing symmetry
Triclinic structures very anisotropic
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Determining Crystal Structures
Sir William Bragg
Lawrence Bragg Father-son shared Nobel
prize in Physics in 1915
Analysis of crystalstructures using X-rays
William Bragg in chargeof research on the
detection andmeasurement ofunderwater sounds inconnection with the
location of submarines
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- ay rac on or crys astructure
Diffraction A wave encounters
regular spaced objectsthat scatter it
Obstacle spacing is similarin length to thewavelength
Sca
ttering
Event
Scattering
Eve
nt
2 waves that mutually reinforce
One another Waves in phase
2 waves that cancel One anotherWaves out of phase
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-crystal structures
Path length difference between 2 waves = SQ + QT
Braggs law says thatthe path difference = order of reflection (n) * wavelength ()
n needs to be a whole no.
Hence, SQ + QT =n= 2 d
hkl
sin
dhkl(interplanar spacing)
Q
S T
P
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Braggs law
Applicable when waves interfere constructively When Braggs law not satisfied, waves interfere
destructively, resulting in a low intensity diffractedbeam
Interplaner spacing for cubic structures,
a is the lattice parameter (unit cell edge length)
h, k, lare Miller indices
Similar complex relations exist for other six crystal
systems
222lkh
ad
hkl
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X-Ray Diffraction Measurements
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POLYMERSTRUCTURES
Chapter 4
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Polymers
Naturally occurring Wood, rubber, cotton, wool, leather
Proteins, enzymes, starches, cellulose
Synthetic (from organic molecules) Plastics, synthetic rubbers, Fibers
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16
ISSUES TO ADDRESS...
What are the general structural and chemicalcharacteristics of polymer molecules?
What are some of the common polymericmaterials, and how do they differ chemically?
How is the crystalline state in polymers different
from that in metals and ceramics ?
Polymer Structures
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Hydrocarbon molecules
Most polymers are organicin origin
Many organic materials are
hydrocarbons Covalent bonds
Each C has 4 electrons thatmay participate in covalent
bonding
Single electron pair sharing single bond
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Unsaturated Hydrocarbons
Double & triple bonds somewhat unstablecan form new bonds Double bond found in ethylene or ethene - C2H4
Triple bond found in acetylene or ethyne - C2H2
C C
H
H
H
H
C C HH
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Isomerism
Isomerism two compounds with same chemical formula can have
quite different structures
for example: C8H18
normal-octane
2,4-dimethylhexane
C C C C C C C CH
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H H3C CH2 CH2 CH2 CH2 CH2 CH2 CH3=
H3C CH
CH3
CH2 CH
CH2
CH3
CH3
H3C CH2 CH3( )6
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Polymer Molecules
Much larger in comparison to the hydrocarbonmolecules Macromolecules
A chain of carbon atoms is the backbone
Mer
The repeating unit in a polymer chain Monomer a stable unit from which the
polymer is synthesized
l i i d
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Polymerization andPolymer Chemistry
Free radical polymerization
Initiator: example - benzoyl peroxide
C
H
H
O O C
H
H
C
H
H
O2 R= 2
C C
H H
HH
monomer(ethylene)
R +
free radical
R C C
H
H
H
H
initiation
R C C
H
H
H
H
C C
H H
HH
+ R C C
H
H
H
H
C C
H H
H H
propagation
dimer
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Chemistry of Polymer molecules
C C
H H
HH
Monomer
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Types of Polymers
HomopolymerAll repeating units along a chain are of the
same type; polymer formed from a singlemonomer
Eg. polyethylene, formed by polymerization ofethylene
Copolymer
2 or more different mer units involved
PMMA
http://en.wikipedia.org/wiki/Image:Ethylene-2D.png -
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Polymer Chains
Fiber of Kevlar
Polyglycolic acid and Poly Lacticacid
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Bulk or Commodity Polymers
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Bulk or Commodity Polymers (cont)
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Bulk or Commodity Polymers (cont)
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VMSE: Polymer Repeat Unit Structures
29
Manipulate and rotate polymer structures in 3-dimensions