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LECTURE #15: PHASE DIAGRAMS
ENGR 151: Materials of Engineering
TENSILE TESTING VIDEO
https://www.youtube.com/watch?v=-qukVZo2JSE
PROPERTIES OF ISOMORPHOUS ALLOYS
Solid solution strengthening
For Ni-Cu alloy
tensile strength increases with increasing Ni wt%
However, ductility decreases
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
HOMEWORK
HW (Due Monday, April 17th)
9.5, 9.6, 9.10, 9.13, 9.14
HOMEWORK
HW (Due Monday, April 24th)
9.21, 9.27, 9.34, 9.37, 9.44
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)