Transcript L-5: Thermodynamics of Mixtures (Chapter 7)

FE-2: Continuation of part 1
Polymers, phase diagrams, steel
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•
•
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Carbon-based of concern here.
One or more monomers joined to form giant molecules.
The bonding within a molecule is primarily covalent.
Polymer solids held together by:
– Entanglement of the polymer chains.
– Van der Waals forces.
– Cross linking between polymer chains by chemical reactions, often at elevated
temperature (thermoset). For rubber, called vulcanization, typically by sulfur.
Cross-linked polymers can't be heated and reshaped as can thermoplastics.
• May have partial crystallization, with molecule chains folded within small
crystals and going between crystals. Crystals have higher density (g/cc)
– Crystallization favored by polymer molecules having the same shape, and
without cross linking. For example, polyethylene.
– Another example: isotactic polyvinyl chloride rather than
syndiotactic or atactic chains.
Last revised January 11, 2014 by W.R.Wilcox at Clarkson University.
Mechanical behavior of polymers
• Plastic deformation of polymers usually involves the movement of polymer
molecules past one another.
• In addition to brittle and plastic
brittle
behavior, can also be highly
elastic (elastomeric).
• An amorphous polymer may
behave like a brittle glass

below a glass transition
temperature and a rubbery
ductile
solid at intermediate
temperatures.
• For small deformations,
elastomeric
the behavior depends on
how quickly the stress is
applied and released.

If this is fast, the material behaves elastically. If very slow, it flows and takes
a new permanent shape. (Think silly putty.)
• For intermediate rates, the deformation is viscoelastic, so that only part of
the strain is recovered when the stress is removed.
From the FE exam handbook
• Tg is the glass-transition T,
below which it's brittle.
• Tm is the melting T, above
which it flows when stressed
and can be formed into
shapes. (But it's not a usual
liquid.)
• Notice that these are not
sharp transitions like the
melting point of nonpolymers.
Conditions favoring solubility in solid metals
Interstitial impurities
• Atomic radius of impurity must be much smaller than host, e.g. C (0.071nm)
in Fe (0.1241nm).
Substitutional impurities: Hume-Rothery rules
1) Atomic size: The closer the atomic radii the greater the solubility.
2) Electronegativity: The closer the electronegativities, the greater the
solubility. True when metals are near one another in the periodic table. If
not near, formation of an intermetallic compound is favored.
• For complete solid solubility, the pure components must have the same
crystal structure, i.e. "isomorphous." Uncommon.
• The electronegativities must be near and the atomic radii close.
• Most often get limited solubility with formation of other phase(s). The
solubility usually depends strongly on temperature.
• Example of complete
electroneg
Crystal
r (nm)
solid solubility: Ni-Cu
Structure
Ni
FCC
1.9
0.1246
Cu
FCC
1.8
0.1278
Nickel-copper binary phase diagram at 1 atm
• Only melt
above the
liquidus.
• Only solid 
below the
solidus.
• Both in between
• Isotherm shows
composition of
the liquid and
solid in equil.
• Called a tie line
At B: T = __oC?
Solid = __%Ni?
Liquid = __%Cu?
1
Liquid
T
1.
2.
3.
4.
5.
2
Melting point pure B
Solubility of B
Melting point pure A
Solubility of A
Eutectic point
3
Solution 2
and solid B
4
A+4
When two phases are
in equilibrium with one
another they are at the
same temperature.
5
Find compositions in
equilibrium with one
another by drawing
an isotherm, called a
“tie line.”
For example:
Solid A and solid B in equilibrium with one another
A
Fraction of B
B
Binary phase diagram with no solid solubility – simple eutectic
Eutectic
with some
solubility,
e.g.
Pb-Sn
Greek
letters 
and  used
for solid
solutions.
Metallurgists
call eutectic
liquid going
to solid
the “eutectic
reaction”
L  +
Compound formation, e.g. Mg-Pb
Two
eutectics
Intermetallic
compound
Mg2Pb
shown at
exact
comp’n, but
would exist
over small
comp’n
range.
Some
compounds
decompose
before
melting
Peritectic
• At the peritectic point, when heated a solid goes to
another solid and a melt. Vice versa when cooled.
• Metallurgists call this the “peritectic reaction” and
write it:
S1 + L
heat
S2
• At 184oC,
27wt%Bi
goes from 
to  + L.
• Where’s the
eutectic
point?
• What
phases can
be in
equilibrium
at the
peritectic
point?
• At A?
A
Pb
cool
Bi
Eutectoid points
• A eutectoid point is where a solid dissociates to two solids when cooled.
Analogous to a eutectic point, at which a liquid dissociates to two solids
when cooled. For example, V-Zr phase diagram:
• Eutectoid
point:
A
• Zr 
V2Zr + Zr
• What is
sequence of
phases as A
is cooled ?
•L
• L + Zr
• Zr
• Zr + Zr
• V2Zr + Zr
Liquid immiscibility and monotectic points
• Sometimes melts separate into two
liquids below a certain temperature,
e.g. Pb & Zn:
• At the monotectic point, a liquid
separates into a solid and the other
liquid.
• Here liquid A  Zn + liquid B
• What happens as we cool from the
blue dot?
• What do we have at the red oval?
Zn
Pb
Another viewpoint
For example:
simple eutectic with no
solid solubility.
Fraction of A equals
the distance from the mixture
composition to the opposite
phase (B)
divided by
the total distance between
phases A & B
Cmix
Distance to opposite phase
Check: the closer the mixture composition
is to a phase the more of that phase must
be present, in the limit 100%!
Total distance
Fraction of grains with eutectic structure
Liquid
T
B+L
A+L
opposite
total
A
Weight fraction of B
• Consider the red point.
• Rather than asking how
much of A and B are present,
we can ask what weight
fraction of the grains is
eutectic and what fraction is
primary B.
• To do this, treat the eutectic
as a compound.
• Then use the lever rule in the
usual way to calculate the
weight fraction of grains that
have the eutectic
B microstructure.
• The fraction of eutectic is
opposite/total.
Fe – Fe3C (cementite): C steels and cast iron
Eutectoid reaction to form pearlite
• When slowly cool eutectic or eutectoid compositions get a lamellar structure.
• For example, 0.76 wt% C austenite gives pearlite, which consists of
alternating layers of
ferrite and cementite.
To left of eutectoid, get pearlite + ferrite steel. To right, brittle pearlite+Fe3C.