FE-2: Continuation of part 1 Polymers, phase diagrams, steel

FE-2: Continuation of part 1Polymers, phase diagrams, steel

• 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

behavior, can also be highly elastic (elastomeric).

brittle

elastomeric

ductile

• An amorphous polymer may behave like a brittle glass below a glass transition temperature and a rubbery solid at intermediate temperatures.

• For small deformations, 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.

• 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 non-polymers.

From the FE exam handbook

Conditions favoring solubility in solid metals

Substitutional impurities: Hume-Rothery rules1)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 solid solubility: Ni-Cu

Interstitial impurities• Atomic radius of impurity must be much smaller than host, e.g. C (0.071nm) in

Fe (0.1241nm).

CrystalStructure

electroneg r (nm)

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 lineAt B: T = __oC?Solid = __%Ni?Liquid = __%Cu?

1

1. Melting point pure B2. Solubility of B3. Melting point pure A4. Solubility of A5. Eutectic point

2

3

4

5

Solid A and solid B in equilibrium with one another

T

A BFraction of B

Binary phase diagram with no solid solubility – simple eutectic

Liquid

Solution 2 and solid B

A + 4

When two phases are in equilibrium with one another they are at the same temperature.

Find compositions in equilibrium with one another by drawing an isotherm, called a “tie line.” For example:

Eutectic with some solubility,

e.g.Pb-SnGreek

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

PeritecticS1 + L S2

coolheat

• 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:

• 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?

BiPb

A

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:

• Zr V2Zr + Zr

• What is sequence of phases as A is cooled ?

• L• L + Zr• Zr• Zr + Zr• V2Zr + Zr

A

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

Cmix

Distance to opposite phase

Total distance

For example: simple eutectic with no

solid solubility.

the total distance between phases A & B

Check: the closer the mixture composition is to a phase the more of that phase must be present, in the limit 100%!

Fraction of A equals the distance from the mixture composition to the opposite phase (B) divided by

Fraction of grains with eutectic structure

• 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 microstructure.

• The fraction of eutectic is opposite/total.

T

A BWeight fraction of B

Liquid

B + L

A + L

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.