lecture 5 - crystal systems and polymers

7/27/2019 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

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Manipulate and rotate polymer structures in 3-dimensions

lecture 5 - crystal systems and polymers

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