engr 151: materials of engineering final review · pdf filefracture stable crack: resists...
TRANSCRIPT
FINAL REVIEW MATERIAL
ENGR 151: Materials of Engineering
Miller indices - A shorthand notation to describe certain crystallographic directions and planes in a material. Denoted by [ ], <>, ( ) brackets. A negative number is represented by a bar over the number.
Points, Directions and Planes in the Unit Cell
• Coordinates of selected points in the unit cell.
• The number refers to the distance from the origin in terms
of lattice parameters.
Point Coordinates
• Each unit cell is a reference or basis.
• The length of an edge is normalized as a unit of
measurement.
• E.g. if the length of the edge of the unit cell along the
X-axis is a, then ALL measurements in the X-direction
are referenced to a (e.g. a/2).
Point Coordinates – Contd.
Point coordinates for unit cell center are
a/2, b/2, c/2 ½ ½ ½
Point coordinates for unit cell corner are 111
Translation: integer multiple of lattice constants identical position in another unit cell
5
z
x
y a b
c
000
111
y
z
2c
b
b
Point Coordinates
Determine the Miller indices of directions A, B, and C.
Miller Indices, Directions
(c) 2003 Brooks/Cole Publishing /
Thomson Learning™
GENERAL APPROACH FOR MILLER INDICES
7
SOLUTION
Direction A
1. Two points are 1, 0, 0, and 0, 0, 0
2. 1, 0, 0, -0, 0, 0 = 1, 0, 0
3. No fractions to clear or integers to reduce
4. [100]
Direction B
1. Two points are 1, 1, 1 and 0, 0, 0
2. 1, 1, 1, -0, 0, 0 = 1, 1, 1
3. No fractions to clear or integers to reduce
4. [111]
Direction C
1. Two points are 0, 0, 1 and 1/2, 1, 0
2. 0, 0, 1 -1/2, 1, 0 = -1/2, -1, 1
3. 2(-1/2, -1, 1) = -1, -2, 2
2]21[ .4
(c) 2003 Brooks/Cole Publishing
/ Thomson Learning™
CRYSTALLOGRAPHIC DIRECTIONS
9
1. Vector repositioned (if necessary) to pass
through origin.
2. Read off projections in terms of
unit cell dimensions a, b, and c
3. Adjust to smallest integer values
4. Enclose in square brackets, no commas
[uvw]
ex: 1, 0, ½ => 2, 0, 1 => [ 201 ]
-1, 1, 1
z
x
Algorithm
where overbar represents a
negative index
[ 111 ] =>
y
Problem 3.6, pg. 58
10
HCP CRYSTALLOGRAPHIC DIRECTIONS
Hexagonal Crystals
4 parameter Miller-Bravais lattice coordinates are
related to the direction indices (i.e., u'v'w') as follows.
=
=
=
' w w
t
v
u
) v u ( + -
) ' u ' v 2 ( 3
1 -
) ' v ' u 2 ( 3
1 - =
] uvtw [ ] ' w ' v ' u [
Fig. 3.8(a), Callister & Rethwisch 8e.
- a3
a1
a2
z
11
HCP CRYSTALLOGRAPHIC DIRECTIONS
Fig. 3.8(a), Callister & Rethwisch 8e.
- a3
a1
a2
z
12
HCP CRYSTALLOGRAPHIC DIRECTIONS
1. Vector repositioned (if necessary) to pass
through origin.
2. Read off projections in terms of unit
cell dimensions a1, a2, a3, or c
3. Adjust to smallest integer values
4. Enclose in square brackets, no commas
[uvtw]
[ 1120 ] ex: ½, ½, -1, 0 =>
Adapted from Fig. 3.8(a),
Callister & Rethwisch 8e.
dashed red lines indicate
projections onto a1 and a2 axes a1
a2
a3
-a3
2
a 2
2
a 1
- a3
a1
a2
z
Algorithm
13
REDUCED-SCALE COORDINATE AXIS
14
PROBLEM 3.8
FAMILIES OF DIRECTIONS <UVW>
For some crystal structures, several
nonparallel directions with different
indices are crystallographically equivalent;
this means that atom spacing along each
direction is the same.
15
16
CRYSTALLOGRAPHIC PLANES
Adapted from Fig. 3.10,
Callister & Rethwisch 8e.
17
CRYSTALLOGRAPHIC PLANES
Miller Indices: Reciprocals of the (three) axial intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices.
Algorithm 1. Read off intercepts of plane with axes in terms of a, b, c 2. Take reciprocals of intercepts 3. Reduce to smallest integer values 4. Enclose in parentheses, no commas i.e., (hkl)
18
CRYSTALLOGRAPHIC PLANES z
x
y a b
c
4. Miller Indices (110)
example a b c z
x
y a b
c
4. Miller Indices (100)
1. Intercepts 1 1
2. Reciprocals 1/1 1/1 1/
1 1 0 3. Reduction 1 1 0
1. Intercepts 1/2
2. Reciprocals 1/½ 1/ 1/
2 0 0 3. Reduction 1 0 0
example a b c
19
CRYSTALLOGRAPHIC PLANES z
x
y a b
c
4. Miller Indices (634)
example 1. Intercepts 1/2 1 3/4
a b c
2. Reciprocals 1/½ 1/1 1/¾
2 1 4/3
3. Reduction 6 3 4
(001) (010),
Family of Planes {hkl}
(100), (010), (001), Ex: {100} = (100),
FAMILY OF PLANES
Planes that are crystallographically equivalent
have the same atomic packing.
Also, in cubic systems only, planes having the
same indices, regardless of order and sign,
are equivalent.
Ex: {111}
= (111), (111), (111), (111), (111), (111), (111), (111)
20
(001) (010), (100), (010), (001), Ex: {100} = (100),
_ _ _ _ _ _ _ _ _ _ _ _
MECHANICAL PROPERTIES OF METALS
TENSION TESTS
Specimen is deformed, to fracture, with load applied
uniaxially on long axis of specimen
Elongate specimen at a constant rate:
Measure the instantaneous applied load
Measure the resulting elongations
Destructive test: specimen is permanently deformed
and usually fractured
TENSION TESTS
Output is recorded as load or force versus
elongation
Engineering stress:
TENSION TESTS
Engineering Strain:
ELASTIC DEFORMATION
The degree to which a structure deforms or
strains depends on the magnitude of stress (in
proportion):
EXAMPLE PROBLEM 6.1
EXAMPLE PROBLEM 6.1 CONTD.
ELASTIC DEFORMATION
Deformation in which stress and
strain are proportional (plot of
stress v. strain is linear, slope is
modulus of elasticity)
The greater the modulus of
elasticity, the stiffer the material
(less strain resulting from stress)
Elastic Deformation is not
permanent (piece returns to
original shape after loads are
released)
ELASTIC DEFORMATION
Application of load corresponds to moving up
the graph, release of the load follows graph in
opposite direction
There are some materials in which the elastic
portion of curve is not linear (cannot find
modulus)
ELASTIC DEFORMATION
Take either the tangent
or secant modulus
Tangent is slope
(derivative) of stress-
strain curve at a
specified level of
stress
Secant is slope of
secant taken from
origin to a point on
the curve
ELASTIC DEFORMATION
At the atomic scale, strain is a result of small changes in interatomic spacing and stretching of atomic bonds.
Therefore, magnitude of modulus elasticity is a measure of the resistance to separation of bonded atoms (interatomic bonding)
Modulus is proportional to slope of interatomic force-separation curve
Increasing temperature, decreases modulus of elasticity
ELASTIC DEFORMATION
ELASTIC PROPERTIES OF MATERIALS
Strain exists along all three axes:
ELASTIC PROPERTIES OF MATERIALS
For uniaxial loads and isotropic materials
Poisson’s ratio:
Metals range from .25-.35
Maximum value is .5
ELASTIC PROPERTIES OF MATERIALS
Shear and Elastic moduli, and Poisson’s Ratio
are related:
For metals,
ELASTIC PROPERTIES OF MATERIALS
ELASTIC PROPERTIES OF MATERIALS
ELASTIC PROPERTIES OF MATERIALS
PLASTIC DEFORMATION
Most metals have elastic deformation only to
strains of about 0.005
After this amount of strain, plastic deformation
occurs (non-recoverable)
Curvature will occur at the onset of plastic
deformation
PLASTIC DEFORMATION
From atomic perspective, plastic deformation corresponds to the breaking of atomic bonds and the reforming of bonds with neighbors
Yielding: stress level at which plastic deformation occurs
Mark point P (proportional limit) at initial departure from linearity
Yield Strength:
0.002 offset intersection with curve (σy)
PLASTIC DEFORMATION
From atomic perspective, plastic deformation corresponds to the breaking of atomic bonds and the reforming of bonds with neighbors
Yielding: stress level at which
plastic deformation occurs
Mark point P (proportional limit) at initial departure from linearity
Yield Strength:
0.002 offset intersection with curve (σy)
PLASTIC DEFORMATION
Sometimes the plastic
transition occurs
abruptly
Upper yield point:
decrease in stress
Lower yield point: stress
rises with strain increase
Yield Strength: taken as
average of lower yield
point
TENSILE STRENGTH (FIGURE 6.11)
Tensile Strength (TS):
Point M, maximum stress
Prior to M, deformation
is uniform throughout
specimen
At M, neck begins to
form
After M, fracture occurs
For building purposes,
yield strength is used as
opposed to tensile
strength (Why?)
EXAMPLE PROBLEM 6.3
EXAMPLE PROBLEM 6.3 CONTD.
EXAMPLE PROBLEM 6.3 CONTD.
DUCTILITY
Measure of the
degree of plastic
deformation that has
been sustained at
fracture
Material with little or
no plastic deformation
at fracture is brittle
High degree of plastic
deformation at
fracture is ductile
DUCTILITY
Percent Elongation:
Percent Reduction:
COLD WORKING VS HEAT TREATMENT
Plastically deforming metal at low temperatures
affects physical properties of metal – cold
working
Elevated temperature treatment, e.g. annealing
Recovery
Recrystallization
RECOVERY, RECRYSTALLIZATION, AND GRAIN
GROWTH
Plastically deforming metal at low temperatures
affects physical properties of metal
Elevated temperature treatment
Recovery
Recrystallization
FAILURE
Simple fracture is the separation of a body into
two or more pieces in response to an imposed
static stress (constant or slowly changing with
time) and at temperatures relatively low as
compared to the material’s melting point
FRACTURE
Stress can be tensile, compressive, shear, or
torsional
For uniaxial tensile loads:
Ductile fracture mode (high plastic deformation)
Brittle fracture mode (little or no plastic
deformation)
FRACTURE
“Ductile” and “brittle” are relative (ductility is based on percent elongation and percent reduction in area)
Fracture process involves two steps:
Crack formation & propagation in response to applied stress
Ductile fracture characterized by extensive plastic deformation in the vicinity of an advancing crack
Process proceeds slowly as crack length is extended.
FRACTURE
Stable crack: resists further extension unless there is
increase in applied stress
Brittle fracture: cracks spread extremely rapidly with
little accompanying plastic deformation (unstable)
Ductile fracture preferred over brittle fracture
Brittle fracture occurs suddenly and catastrophically without
any warning
Ductile fracture gives preemptive “warning” that fracture is
imminent
Brittle (ceramics), ductile (metals)
DUCTILE FRACTURE
Figure 8.1 (differences between highly ductile,
moderately ductile, and brittle fracture)
DUCTILE FRACTURE
Common type of fracture
occurs after a moderate
amount of necking
After necking commences,
microvoids form
Crack forms perpendicular
to stress direction
Fracture ensues by rapid
propagation of crack
around the outer
perimeter of the neck (45°
angle)
Cup-and-cone fracture
DUCTILE VS. BRITTLE FRACTURE – EXAMPLE
BRITTLE FRACTURE
Takes place without much deformation (rapid crack
propagation)
Crack motion is nearly perpendicular to direction of tensile
stress
Fracture surfaces differ:
V-shaped “chevron” markings
Lines/ridges that radiate from origin in fan-like pattern
Ceramics: relatively shiny and smooth surface
BRITTLE FRACTURE
BRITTLE FRACTURE
Crack propagation corresponds to the successive and repeated breaking of atomic bonds along specific crystallographic planes (cleavage)
Transgranular: fracture cracks pass through grains
Intergranular: crack propagation is along grain boundaries (only for processed materials)
BINARY PHASE DIAGRAMS
Temperature and composition of mixture are
varied at constant pressure
Describe how the microstructure of an alloy vary
Ni-Cu system
This system is isomorphous because of the
complete liquid and solid solubility of the two
components
EXAMPLE – COPPER-NICKEL PHASE DIAGRAM
BINARY ISOMORPHOUS SYSTEMS
Metallic alloys are designated by lowercase
Greek letters (α, γ, β, etc.)
Liquidus line: line separating L and α+L regions
Solidus line: line separating α and α+L regions
L is a homogeneous liquid solution composed
of both Cu and Ni
The α phase is an substitutional solid solution
consisting of both Cu and Ni atoms – FCC
crystal structure
LIQUIDUS AND SOLIDUS LINES
Intersect at composition extremities (melting
temperatures)
On the left axis, pure copper remains solid until
melting point (α→L)
Alloys have an extended melting phenomenon
(α→α+L→L)
Occurs over range of temperatures between solidus
and liquidus lines
Both solid α and liquid phases will be in equilibrium
in the region between solidus and liquidus lines
INTERPRETING PHASE DIAGRAMS
Information we get:
Phases, compositions, percentages of the phases
Locate these points:
60 wt% Ni - 40 wt% Cu @ 1100°C
35 wt% Ni - 65 wt% Cu @ 1250°C
PHASE COMPOSITIONS
Locate temperature-composition point on the
phase diagram
Easy to figure for α, L phase
More complicated for α+L phase
Both α and L within α+L are composed of varying
compositions of alloy metals
PHASE COMPOSITIONS
Within two-phase region:
Draw tie line (horizontal) at alloy temperature
Note the phase boundaries
Record compositions at each intersection (CL, Cα =
phase composition)
PHASE COMPOSITIONS
Example:
35 wt% Ni - 65 wt% Cu @
1250°C
CL = 31.5% Ni, 68.5% Cu
Cα = 42.5% Ni, 57.5% Cu
PHASE AMOUNTS
Easy within single phase regions α and L
(100%)
Within α+L region, use lever rule:
Find your tie line
Fraction of one phase: length of tie line from point
to other phase boundary divided by total tie length
Length = wt% or at% composition
PHASE AMOUNTS
Mass fractions:
PHASE AMOUNTS
BINARY EUTECTIC SYSTEMS
BINARY EUTECTIC SYSTEMS
Example: Copper-silver system
Three single-phase regions (α,β,L)
Alpha(α): copper as solvent, FCC
Beta(β): silver as solvent, FCC
Pure copper and pure silver are considered to
be α and β phases respectively
BINARY EUTECTIC SYSTEMS
Below BEG line: only a limited amount of metal
will dissolve in other metal for α, β phases
Solubility limit for α phase corresponds to
boundary line CBA
Notice maximum amount of silver possible for
α phase.
Increases to a certain temperature, then decreases
to zero at the melting point of pure copper
BINARY EUTECTIC SYSTEMS
Solubility limit line separating α and α+β
phases is solvus line
Solubility limit line separating α and α+L
phases is solidus line
Solubility limit line separating β and α+β
phases is solvus line
Solubility limit line separating β and β+L
phases is solidus line
BINARY EUTECTIC SYSTEMS
Horizontal line BEG can also be considered a
solidus line (lowest temperature at which liquid
exists for alloy at equilibrium)
BINARY EUTECTIC SYSTEMS
Three two-phase regions: α+L, β+L, α+β
Tie-lines and lever rule stills apply to these
regions
COPPER-SILVER PHASE DIAGRAM
As silver is added to copper, temperature decreases at which alloy becomes liquid (melting point lowered by addition of silver)
Also works the other way around (liquidus lines meet at point E)
Invariant point: associated with composition (CE) and temperature (TE),
71.9 wt% Ag and 779°C
BINARY EUTECTIC SYSTEMS
As temperature passes through invariant point (TE),
reaction occurs:
Liquid is transformed into two solid phases at TE
(opposite reaction upon heating)
Eutectic reaction (easily melted)
CαE, CβE are compositions of α and β phases at TE (tie-
line)
( ) ( ) ( )cooling
E E Eheating
L C C C
(71.9 % ) (8.0 % ) (91.2 % )cooling
heatingL wt Ag wt Ag wt Ag
BINARY EUTECTIC SYSTEMS
General rules:
At most two phases may be in equilibrium within a
phase field (no α+β+L, only at equilibrium line)
Single phase regions are separated by two-phase
regions
Horizontal solidus line BEG at TE is called a
eutectic isotherm
BINARY EUTECTIC SYSTEMS
If a binary eutectic solution is cooled through
the invariant point, direct solidification occurs
No intermediate “L” phase
For binary phase system, no more than two
phases may be in equilibrium within a phase
field
At points along a eutectic isotherm, three phases
may be in equilibrium (e.g. point B)
BINARY EUTECTIC SYSTEMS
BINARY EUTECTIC SYSTEMS
Lead-Tin (Pb-Sn) system:
Notice that 60-40 Sn-Pb melts at 185°C (365°F),
attractive for soldering.
BINARY EUTECTIC SYSTEMS
BINARY EUTECTIC SYSTEMS
BINARY EUTECTIC SYSTEMS
BINARY EUTECTIC SYSTEMS
BINARY EUTECTIC SYSTEMS
BINARY EUTECTIC SYSTEMS
These values add
up to 1.0
BINARY EUTECTIC SYSTEMS
BINARY EUTECTIC SYSTEMS
BINARY EUTECTIC SYSTEMS
These values add
up to 1.0
EUTECTIC ALLOY DEVELOPMENT
For Lead-Tin alloy at 1
wt% Sn decreasing in
temperature from L
phase:
Remains liquid until
crossing of liquidus
line at 330°C
Continued cooling
creates more α
Solidification is
completed at solidus
line
EUTECTIC ALLOY DEVELOPMENT
For Lead-Tin alloy at
15 wt% Sn
decreasing in
temperature from L
phase:
Past the solidus
line, small β-phase
particles form
Continued cooling
slightly increases
the presence of β
EUTECTIC MICROSTRUCTURE
For Lead-Tin alloy at 61.9 wt% Sn decreasing in
temperature from L phase (invariant point, CE):
No change until TE is reached
Liquid transforms into two phases α, β
(61.9 % Sn) (18.3 % Sn) (97.8 % Sn)cooling
heatingL wt wt wt
EUTECTIC MICROSTRUCTURE
EUTECTIC MICROSTRUCTURE
For Lead-Tin alloy at 61.9
wt% Sn:
Distribution of α & β phases
are accomplished by atomic
diffusion (alternating layers
of α & β, lamellae)
Eutectic Structure
Lead atoms diffuse towards
α-phase
Tin diffuses towards β-phase
EUTECTIC MICROSTRUCTURE
EUTECTIC MICROSTRUCTURE
For Lead-Tin alloy at 40 wt% Sn decreasing in
temperature from L phase:
α-phase is present both in a eutectic structure and
α+L region
α-phase in eutectic structure is called eutectic α
α-phase primary to eutectic isotherm is called
primary α
EUTECTIC MICROSTRUCTURE
Microconstituent: an element of the
microstructure having an identifiable and
characteristic structure
In 40 wt% Sn, there exist two microconstituents in
the α+β phase (primary α and eutectic structure)
EUTECTIC MICROSTRUCTURE
Computing the amounts of eutectic and primary α microconstituents:
Use lever rule from solvus line to eutectic composition
We, fraction of eutectic microconstituent is equal to fraction of liquid WL from which it transforms
Wα, fraction of primary α is equal to fraction of α phase in existence prior to transformation
EUTECTIC MICROSTRUCTURE
EUTECTIC MICROSTRUCTURE
Eutectic α Primary α
Total α (w.r.t entire solution)
EUTECTIC MICROSTRUCTURE
Total β (w.r.t entire solution)
Total α (w.r.t entire solution)
INTERMEDIATE PHASES
EUTECTOID REACTIONS
Other invariant points exist involving three phases (Cu-
Zn system, 74 wt% Zn-26 wt% Cu)
Eutectoid (eutectic-like) reaction
One solid phase forms into two other solid phases
Point E is the eutectoid point, the corresponding tie line is the
eutectoid isotherm
cooling
heating
EUTECTOID REACTIONS
PERITECTIC REACTIONS
Upon heating, one solid phase transforms into a liquid
phase and another solid phase:
78.6 wt% Zn-21.4 wt% Cu
cooling
heatingL
CONGRUENT PHASE TRANSFORMATIONS
Congruent transformation: when there is no
change in the composition for phases involved
(Mg2Pb melts congruently)
Incongruent transformation: change occurs in
phase composition during transformation
(peritectic reaction)
CONGRUENT PHASE TRANSFORMATIONS
PHASE TRANSFORMATIONS
Alteration of microstructure
Three classifications:
Diffusion-dependent transformations (no change in
either number or composition of the phases
present)
Some alteration in phase compositions and number
of phases present
Diffusionless
KINETICS OF SOLID-STATE REACTIONS
At least one new phase is formed
Different physical/chemical properties and/or
different structure than parent phase
Transformations do not occur instantaneously
(obstacles impede course of reaction)
Diffusion is a time-dependent phenomenon
Increase in energy associated with phase
boundaries created between parent and
product phases
PHASE TRANSFORMATION
Stage 1, Nucleation: formation of very small
particles of new phase (capable of growing)
Likely to grow in imperfection sites
Stage 2, Growth: particles increase in size
(volume of parent phase disappears)
KINETICS OF SOLID-STATE REACTIONS
Time dependence of transformation rate
(kinetics)
Important for heat treatment of materials
Investigation of kinetics:
Temperature maintained as constant
Fraction of reaction is measured as function of time
KINETICS OF PHASE TRANSFORMATION
S-shaped curve (Avrami equation): Y = 1 – exp(-ktn)
k, n = time-independent constants for the reaction
Heating time (t) vs. Fraction of transformation (y)
Rate of transformation r = 1/t0.5
Reciprocal of time required for the transformation to proceed halfway to
completion
HARDENABILITY (HEAT TREATMENT OF STEELS)
Hardenability: Term used to describe the ability of an alloy to be hardened by the formation of martensite as a result of a given heat treatment
Hardenability is NOT “hardness,” rather it is the qualitative measure of the rate at which hardness drops off with distance into the interior of the material due to decreased martensite content
HARDENABILITY (HEAT TREATMENT OF STEELS)
Jominy end-quench test:
Determines hardenability
Cylindrical specimen austenized at specified temp and time
Remove from furnace and mount on fixture
Lower end is quenched by jet of water to room temp
Rockwell Hardness test (hardness v. position)
HARDENABILITY CURVES
Quenched end exhibits
maximum hardness
(100% martensite)
Cooling rates and
hardness decrease with
distance away from
quenched end
Hardness persists much
longer for 4340, 4140,
8640, 5140 steels than
for 1040 steel
RADIAL HARDNESS PROFILE
Water Oil
WHAT IS A POLYMER?
Poly mer many repeat unit
Adapted from Fig. 14.2, Callister & Rethwisch 9e.
C C C C C C
H H H H H H
H H H H H H
Polyethylene (PE)
Cl Cl Cl
C C C C C C
H H H
H H H H H H
Poly(vinyl chloride) (PVC)
H H
H H H H
Polypropylene (PP)
C C C C C C
CH3
H H
CH3 CH3 H
repeat
unit
repeat
unit
repeat
unit
ISOMERISM
Recall: different atomic configuration for same composition (butane/isobutane)
Stereoisomerism
Geometrical isomerism
STEREOISOMERISM
Isotactic (® groups on same side) Syndiotactic (® alternates sides)
Atactic (random)
ROTATION NOT ALLOWED! (must sever first)
Polymer can exhibit more than one configuration
3-D image
STEREOISOMERISM – ISOTACTIC
Isotactic – R groups on same side of the polymer chain
STEREOISOMERISM – SYNDIOTACTIC
Syndiotactic – R groups on alternate sides of the polymer chain
STEREOISOMERISM – ATACTIC
Atactic – R groups randomly positioned along the polymer chain
ISOMERISM
Geometrical Isomerism
Double bonds between C atoms
C atoms bonded to other atom or radical (side group)
Cis structure (same side, cis-polyisoprene)
Natural rubber
Trans structure (opposite sides, trans-polyisoprene)
Conversion from cis to trans not possible as bond rotation is not allowed – double bond is rigid
Cis Trans
POLYMER STRUCTURE CLASSIFICATION
Chemistry
Molecular size
Molecular weight
Molecular shape
Degree of twisting, coiling, bending
Molecular structure
The way units (mers) are joined together
POLYMER STRUCTURE CLASSIFICATION
ISOMERISM
Molecules having different atomic
arrangements
Example: Butane
Normal butane boils at -0.5°C
Isobutane boils at -12.3°C
Butane Isobutane
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
POLYMER MOLECULES
Polymer molecules are relatively large in size
(macromolecules) compared to hydrocarbon
molecules
Backbone of carbon chain polymer molecules
are carbon strings (long and flexible)
Side bonding allowed
Radical positioning
OTHER ORGANIC GROUPS
Contain radicals (groups of atoms that remain
intact during chemical reactions)
Alcohols (radical connected to OH)
Ethers (2 radical connected to O)
Acids (radical, OH, C/O double bond)
Aldehyde (radical, H, C/O double bond)
MER UNITS
Mer: successively repeated units along chain
Polymer: many mers
Monomer: stable molecule – small molecule from
which polymer is synthesized
MOLECULAR WEIGHT
• Molecular weight, M: Mass of a mole of chains.
Low M
high M
Not all chains in a polymer are of the same length
— i.e., there is a distribution of molecular weights
MOLECULAR WEIGHT
Large chains = large molecular weight
Average molecular weight:
Number-average molecular weight ( ):
Divide chains into different size ranges
Determine number of fraction chains within each size
range
Mi = mean molecular weight of size range i
xi = fraction of number of chains within size range
nM
n i iM x M=
MOLECULAR WEIGHT
Weight-average molecular weight ( ):
Mi = mean molecular weight of size range i
wi = weight fraction of molecules within
same size interval
wM
w i iM w M=
DEGREE OF POLYMERIZATION
n = average number of mer units in a chain
Number-average degree of polymerization (nn):
Weight-average degree of polymerization (nw):
m = mer molecular weight
ww
Mn
m=
nn
Mn
m=
EXAMPLE PROBLEM 14.1 (PG 542)
EXAMPLE PROBLEM 14.1 (PG 542)
EXAMPLE PROBLEM 14.1 (PG 542)
EXAMPLE PROBLEM 14.1 (PG 542)
MOLECULAR WEIGHT
Melting temperature increases with increased
molecular weight (up to 100,000 g/mol)
Polymers with short chains (100 g/mol) are
liquids/gases at room temp
1000 g/mol (paraffin wax, soft resin)
10,000-several million g/mol (solid polymers)
ISOMERISM
Recall: different atomic configuration for same composition (butane/isobutane)
Stereoisomerism
Geometrical isomerism
STEREOISOMERISM
Isotactic (® groups on same side) Syndiotactic (® alternates sides)
Atactic (random)
ROTATION NOT ALLOWED! (must sever first)
Polymer can exhibit more than one configuration
3-D image
STEREOISOMERISM – ISOTACTIC
Isotactic – R groups on same side of the polymer chain
STEREOISOMERISM – SYNDIOTACTIC
Syndiotactic – R groups on alternate sides of the polymer chain
STEREOISOMERISM – ATACTIC
Atactic – R groups randomly positioned along the polymer chain
ISOMERISM
Geometrical Isomerism
Double bonds between C atoms
C atoms bonded to other atom or radical (side group)
Cis structure (same side, cis-polyisoprene)
Natural rubber
Trans structure (opposite sides, trans-polyisoprene)
Conversion from cis to trans not possible as bond rotation is not allowed – double bond is rigid
Cis Trans
POLYMER STRUCTURE CLASSIFICATION
Chemistry
Molecular size
Molecular weight
Molecular shape
Degree of twisting, coiling, bending
Molecular structure
The way units (mers) are joined together
POLYMER STRUCTURE CLASSIFICATION
151
THERMOPLASTICS AND THERMOSETS
Thermoplastic
can be reversibly cooled & reheated, i.e. recycled
heat until soft, shape as desired, then cool
ex: polyethylene, polypropylene, polystyrene.
• Thermoset
– when heated forms a molecular network (chemical reaction)
– degrades (doesn’t melt) when heated
– a prepolymer molded into desired shape, then
chemical reaction occurs
– ex: urethane, epoxy
ELECTRICAL CONDUCTION
153
ELECTRICAL CONDUCTION
• Ohm's Law: V = I R voltage drop (volts = J/C)
C = Coulomb
resistance (Ohms) current (amps = C/s)
• Conductivity, σ
• Resistivity, ρ:
-- a material property that is independent of sample size and
geometry cross-sectional area
of current flow
current flow
path length
154
ELECTRICAL PROPERTIES
Which will have the greater resistance?
Analogous to flow of water in a pipe
Resistance depends on sample geometry and
size.
D
2D
2
155
DEFINITIONS
Further definitions
J = σ E <= another way to state Ohm’s law
J current density
E electric field potential = V/
=current
surface area=
IA
like a flux
Electron flux conductivity voltage gradient
J = (V/ )
156
• Room temperature values (Ohm-m)-1 = (Ω - m)-1
Selected values from Tables 18.1, 18.3, and 18.4, Callister & Rethwisch 9e.
CONDUCTIVITY: COMPARISON
Silver 6.8 x 10 7
Copper 6.0 x 10 7
Iron 1.0 x 10 7
METALS conductors
Silicon 4 x 10 -4
Germanium 2 x 10 0
GaAs 10 -6
SEMICONDUCTORS
semiconductors
Polystyrene <10 -14
Polyethylene 10 -15 -10 -17
Soda-lime glass 10
Concrete 10 -9
Aluminum oxide <10 -13
CERAMICS
POLYMERS
insulators
-10 -10 -11
157
What is the minimum diameter (D) of the wire so that V < 1.5 V?
EXAMPLE: CONDUCTIVITY PROBLEM
Cu wire I = 2.5 A - +
V
Solve to get D > 1.87 mm
< 1.5 V
2.5 A
6.07 x 107 (Ohm-m)-1
100 m
4
2Dp
=100 m