L 1

phase – a region in a material that differs in
structure and function from other regions
phase diagrams – graphical representations of
what phases are present in a materials system
at different conditions (temperature, pressure
and composition)
(1) phase diagrams of pure substances
pure substance exist as solid, liquid and
vapor phases depending on the conditions of
temperature and pressure
pressure-temperature (PT) phase diagram
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5. phase diagrams
phase – a region in a material that differs in
structure and function from other regions
phase diagrams – graphical representations of
what phases are present in a materials system
at different conditions (temperature, pressure
and composition)
(1) phase diagrams of pure substances
pure substance exist as solid, liquid and
vapor phases depending on the conditions of
temperature and pressure
pressure-temperature (PT) phase diagram
• water
two-phase equilibrium line
triple point
4.579 torr
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• iron
three distinct solid phases: ? Fe, ? Fe, ? Fe
three triple points
(2) Gibbs phase rule
P + F = C + 2
P: number of phases that coexist in a system
C: number of components
F: degrees of freedom
ex. water
triple point 3 + F = 1 + 2 F = 0
L-S freezing curve 2 + F = 1 + 2 F = 1
degrees of freedom indicate number of
variables that can be changed without
changing number of phases
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(3) cooling curves
used to determine phase transition temperature
temperature vs. time data of cooling molten
material is recorded and plotted
BC – plateaue or region of thermal arrest
• cooling curve for pure Fe
undercooling
freezing
polymorphic
transformation
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(4) binary isomorphous alloy systems
binary alloy – a mixture of two metals
isomorphous system – two elements completely
soluble in each other in liquid and solid state
usually satisfy one or more Hume-Rothery solid
solubility rules
• copper-nickel system
liquidus
solidus
composition of liquid + solid phases at any
temperature can be determined by drawing a
tie line
ex. at 1300oC an alloy of 53% Ni + 47% Cu
in liquid + solid phase
composition of liquid phase: 45% Ni
composition of solid phase: 58% Ni
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binary equilibrium phase diagram
cooling curves equilibrium phase diagram
points of change of slope of cooling curves
(thermal arrests) are noted
for metal alloys, solidification begins at a
specific temperature (L) and ends at a lower
temperature (S)
the freezing temperature of a metal alloy is
the temperature at which the solidification
process is complete
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(5) lever rule
the lever rule gives the weight % of phases in
any two phase regions
Xs + Xl = 1 Xs = 1 - Xl
consider 1 g of alloy, weight balance of B:
(1 g)(%w0) = (1g)(Xl)(%wl) + (1g)(Xs)(%ws)
w0 = Xlwl + Xsws w0 = Xlwl + (1 - Xl)ws
w0 = (1 - Xs)wl + Xsws
w0 = wl - Xswl + Xsws
w0 – w1 Wt fraction of solid phase = Xs = ————
ws – w1
w0 = Xlwl + ws - Xlws
ws – w0 Wt fraction of liquid phase = Xl = ————
ws – w1
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the weight fraction of liquid phase is the ratio
of OS/LS
the weight fraction of solid phase is the ratio
of LO/LS
ex. Cu-Ni alloy contains 47 wt% Cu and 53
wt% Ni at 1300oC
a. what is the wt% of Cu in liquid and in
solid phases?
b. what wt% of this alloy is liquid?
a. from the phase diagram,
wt% of Ni in liquid is 45% and in solid is 58%
wt% of Cu in liquid is 55% and in solid is 42%
b. ws – w0 58 - 53
Xl = ———— = ———— = 5/13 = 0.38 38%
ws – w1 58 - 45
w0 – wl 53 - 45
Xs = ———— = ———— = 8/13 = 0.62 62%
ws – w1 58 - 45
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ex. calculate the wt% liquid and solid for
Ag-Pd phase diagram shown below at
1200oC and 70 wt% Ag.
ws – w0 64 - 70
Xl = ———— = ———— = 6/10 = 0.6 60%
ws – w1 64 - 74
w0 – wl 70 - 74
Xs = ———— = ———— = 4/10 = 0.4 40%
ws – w1 64 - 74
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(6) nonequilibrium solidification of alloys
slowly solidified alloys usually
have a cored structure
70% Cu-30% Ni alloy
rapid cooling (nonequilibrium) delays
solidification
homogenization: as-cast ingots are heated to
elevated temperature to accelerate solid-state
diffusion and to eliminate the cored structure
temperature of homogenization must be lower
than lowest melting point of any of the alloy
components
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(7) binary eutectic alloy systems
in some binary alloy systems, components have
limited solid solubility – eutectic system
ex. Pb-Sn system
• terminal solid solutions with restricted solid
solubility ? (Pb-rich) and ? (Sn-rich) phases
• eutectic composition freezes at lower
temperature than all other compositions, this
lowest temperature is called eutectic
temperature
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eutectic reaction
eutectic temperature
liquid ? solid solution + ? solid solution
cooling
eutectic reaction is an invariant reaction –
degree of freedom F = 0
• slow cooling of a Pb-Sn alloy of eutectic
composition
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• slow cooling of 60% Pb – 40% Sn alloy
a. liquid at 300oC
b. at about 245oC first solid solution ? (12%
Sn) forms – primary or proeutectic ?
c. slightly above 183oC composition of alpha
follows solidus and composition of Sn
varies from 12% to 19.2%, composition of
liquid phase varies from 40% to 61.9%
d. at eutectic temperature, all the remaining
liquid solidifies
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ex. make phase analysis at the following
points in Pb-Sn phase diagram:
(a) at eutectic composition just below 183oC
(b) point c at 40% Sn and 230oC
(c) point d at 40% Sn and 183oC + ?T
(d) point e at 40% Sn and 183oC - ?T
(a) ? phase (19.2% Sn) + ? phase (97.5% Sn)
97.5 – 61.9 61.9 – 19.2
wt% (?) = ————— wt% (?) = —————
97.5 – 19.2 97.5 – 19.2
= 45.5% = 54.5%
(b) ? phase (15% Sn) + liquid (48% Sn)
48 – 40 40 – 15
wt% (?) = ———— wt% (L) = ————
48 – 15 48 – 15
= 24% = 76%
(c) ? phase (19.2% Sn) + liquid (61.9% Sn)
61.9 – 40 40 – 19.2
wt% (?) = ————— wt% (L) = —————
61.9 – 19.2 61.9 – 19.2
= 51% = 49%
(d) ? phase (19.2% Sn) + ? phase (97.5% Sn)
97.5 – 40 40 – 19.2
wt% (?) = ————— wt% (?) = —————
97.5 – 19.2 97.5 – 19.2
= 73% = 27%
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ex. an alloy of 70% Pb + 30% Sn is slowly
cooled from 300oC, calculate the following:
(a) wt% of the liquid and proeutectic ? form
at 250oC
(b) wt% of the liquid + proeutectic ? form
just above eutectic temperature (183oC)
(c) wt% of the ? and ? phases formed by the
eutectic reaction
(a) ? phase (12% Sn) + liquid(40% Sn)
40 – 30 30 – 12
wt% (?) = ———— wt% (L) = ————
40 – 12 40 – 12
= 36% = 64%
(b) ? phase (19.2% Sn) + liquid (61.9% Sn)
61.9 – 30 30 – 19.2
wt% (?) = ————— wt% (L) = —————
61.9 – 19.2 61.9 – 19.2
= 74.7% = 25.3%
(c) ? phase (19.2% Sn) + ? phase (97.5% Sn)
97.5 – 30 30 – 19.2
wt% (?) = ————— wt% (?) = —————
97.5 – 19.2 97.5 – 19.2
= 86.2% = 13.8%
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ex. a Pb-Sn alloy contains 64 wt% proeutectic
? and 36 wt% eutectic ? + ? at 183oC - ?T
calculate the average composition of this
alloy
assume x wt% Sn in this alloy
since 64 wt% proeutectic ? exists, the alloy
must be hypoeutectic and 19.2 < x < 61.9
61.9 – x
wt% = ————— = 64%
61.9 – 19.2
x = 34.6
this alloy consists of 34.6 wt% Sn and 65.4 wt% Pb
• in a binary eutectic reaction two solid phases
(? and ?) can have various morphologies
• structure depends on factors like minimization
of free energy at ? /? interface
• manner in which two phases nucleate and
grow also affects structures
ex. lamellar eutectic
structure of Pb-Sn alloy
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(8) binary peritectic alloy system
peritectic reaction – liquid phase reacts with a
solid phase to form a new and different solid
phase
liquid + ? ?
cooling
peritectic reaction occurs when a slowly cooled
alloy
ex. Fe-Ni phase diagram
? phase – Ni in BCC-Fe
? phase – Ni in FCC-Fe
Fe-4.3 wt% Ni passes through peritectic
temperature of 1517oC
1517oC
liquid (5.4 wt% Ni) + ? (4.0 wt% Ni) ? (4.3 wt% Ni)
cooling
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ex. Pt-Ag phase diagram
the peritectic reaction occurs at 42.4 wt% Ag
and 1186oC
ex. make phase analysis at the following:
a. at 42.4% Ag and 14000C
b. at 42.4% Ag and 11860C + ?T
c. at 42.4% Ag and 11860C ? ?T
d. at 60% Ag and 1150oC
a. phases present liquid ?
composition 55% Ag 7%Ag
amount of phases 42.4 –7 55-42.4
???? ????
55 – 7 55 - 7
= 74% = 26%
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b. phases present liquid ?
composition 66.3% Ag 10.5%Ag
amount of phases 42.4 – 10.5 66.3 – 42.4
????? ?????
66.3 – 10.5 66.3 – 10.5
= 57% =43%
c. phase present ? only
composition 42.4% Ag
amount of phase 100%
d. phases present liquid ?
composition 77% Ag 48%Ag
amount of phases 60 – 48 77-60
??? ?????
77 - 48 77 – 48
= 41% = 59%
very slow cooling of an alloy of peritectic
composition through the peritectic temperature
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surrounding or encasement – during rapid
solidification of alloy through peritectic
reaction, the ? phase created surrounds
primary ?
? creates diffusion barrier resulting in coring
cast 60% Ag-40% Pt hyperperitctic alloy
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(9) binary monotectic systems
monotectic reaction – liquid phase transforms
into solid phase and another liquid
cooling
L1 ? + L2
two liquids are immiscible
ex. Cu-Pb system at 955oC and 36% Pb
Cu-rich portion
Pb-rich portion
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(10) invariant reactions
zero degree of freedom at the reaction points
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(11) phase diagrams with intermediate phases
and compounds
terminal phases – phases occur at the end of
phase diagrams
intermediate phases – phases occur in a
composition range inside phase diagram.
ex. Cu-Zn diagram has both terminal and
intermediate phases.
• ? and ? –
terminal phases
• ?, ?, ?, ? –
intermediate phases
• five invariant
peritectic points +
one eutectic point
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ex. Al2O2 – SiO2 system
an intermediate phase called mullite is
formed, which includes the compound
3Al2O3.2SiO2
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in some phase diagrams, intermediate
compound are formed – stoichiometric
percent ionic/covalent bond depends on
electronegativeness
ex. Mg-Ni phase diagram contains two
intermetallic compounds:
MgNi2 - congruently melting compound
Mg2Ni - incongruently melting compound
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(12) ternary phase diagrams
three components phase diagrams constructed by
using a equilateral triangle as base
• pure components at each end of triangle binary
alloy composition represented on edges
• temperature can be represented as uniform
throughout the whole diagram – isothermal
section
to determine the composition of a ternary
alloy:
• draw a perpendicular line from a pure metal
corner to the side of the triangle opposite
that corner
• measure the distance from the side to the
corner along the perpendicular line
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ex. determine the wt% of metals A, B, C for
ternary alloy at points x and yon the
following phase diagram
draw three perpendicular lines AD, BE, CF
for point x
(i) on AD line 40% A
(ii) on BE line 40% B
(iii) on CF line 20% C
for point y
(i) on AD line 20% A
(ii) on BE line 30% B
(iii) on CF line 50% C
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ex. Fe-Cr-Ni phase diagrams.
• isothermal reaction at 650oC for this system
• the most important stainless steel has a
composition essentially of 74% Fe, 18%
Cr, and 8% Ni