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Phase Diagrams
a Review
Topic 2
Review of
Phase Transformation
Diagrams
Solution and Solubility
Example: Solubility of salt in water
There exists a maximum amount of salt that can be
completely dissolved in water; excess of salt stays as solid.
This maximum amount is the solubility of salt in water.
The solution containing the maximum concentration of salt
is a saturated solution.
Cooling of saturated solution results in the formation of
solid salt from the solution, indicating that solubility
decreases with decreasing T. This process is called
precipitation and the solid formed is a precipitate.
Heating the solution will lead to the dissolving of the Solid salt – the Salty water –
precipitate back into solution. precipitate the solution
In this example there exist two phases in the system and the two phases stay in
equilibrium: dissolving
Solution Solid
precipitation
The same concepts apply to solids: solid solution, saturation, solubility, precipitation
Phase Diagrams
phase diagram of water
Phase diagrams are used to map out
the existence and conditions of
Super-critical
Liquid
various phases of a give system.
fluid
The phase diagram of water is a Solid
common example. Water may stay Critical
point
in liquid, solid or gaseous states in
Pressure
221 bar
different pressure-temperature
regions. Boundaries of the regions 1 bar
express the equilibrium conditions in
terms of P and T. Water is a 0 bar Gas
monolithic system. For binary Triple
systems, which contains two point
constituents, such as binary alloys,
phase diagrams are often expressed 0°C 100°C 374°C
in the temperature-composition Temperature
plane.
Binary Phase Diagrams
liquid phase - 1455°C
The simplest type of binary phase Solution of
diagrams is the isomorphous system, in Cu and Ni
which the two constituents form a
continuous solid solution over the T1 Co
Temperature
entire composition range. An example CS
is the Ni-Cu system. T2 CL
CS 1
T3 CL 2
Solidification of alloy Co starts on Co 2
3
cooing at T1. The first solid formed has
α phase (fcc) -
a composition of Cs1 and the liquid Solid solution
Co. On further cooling the solid 1085°C of Cu and Ni
particles grow larger in size and change
their composition to Cs2 and then Co,
following the solidus whereas the liquid Cu Composition Ni
decrease in volume and changes its
composition from Co to CL3 following L
the liquidus. The solidification α
completes at T3.
Binary Phase Diagrams
The simplest type of binary phase liquid phase - 1455°C
diagrams is the isomorphous system, in Solution of
Temperature
which the two constituents form a Cu and Ni Co
continuous solid solution over the
entire composition range. An example
is the Ni-Cu system.
T* CL
Compositions of phases is determined CS
by the tie line
The relative fractions of the phases are
determined by the lever rule α phase (fcc) -
1085°C Solid solution
of Cu and Ni
W1 W2
L1 L2
Cu Composition Ni
Lever Rule
W1 W2
L1 L2
Weight fractions:
Example
At temperature T1, alloy Co is in the dual phase region,
CL CS
comprising the liquid phase and the α-phase.
Co
(i) Determine the compositions of the two phases;
(ii) Determine the weight fractions of the two phases
Read from the tie line: 1455°C
Liquid phase:Cu-30%Ni
α-phase: Cu-55%Ni C0
Cs − Co 55 − 50 T1 CL
WL = = = 0.2 = 20%
Cs − CL 55 − 30 CS
Co − CL 50 − 30
Wα = = = 0.8 = 80% 1085°C
Cs − CL 55 − 30
or 30%Ni 55%Ni
Wα = 1 − WL = 1 − 0.2 = 0.8 = 80% Cu 50%Ni Ni
Cooling Curves
determination of Phase diagrams
II
1455°C
1085°C
T Liquidus
(thermal arrest)
T1
Solidus
T
T2
I
T1 1085°C
T II I III
T2
Cu % Ni
t
Eutectic Systems
Pb-Sn phase diagram
350
The Pb-Sn system is
characteristic of a valley in the Liquid
300
middle. Such system is known as
Liquidus
the Eutectic system. The
250
Temperature
central point is the Eutectic Eutectic
point and the transformation point
α+L
though this point is called 200
L+β
Eutectic reaction: Lα+β
150 solidus
β phase: solid
Pb has a fcc structure and Sn has
α phase: solid solution of Pb in
a tetragonal structure. The 100 solution of Sn tetragonal Sn
system has three phases: L, α and in fcc Pb
β. solvus
50 α+β
solvus
0
0 10 20 30 40 50 60 70 80 90 100
Pb Sn
(Fcc) Wt% (Tetra)
Solidification of Eutectic Systems
Pb-Sn phase diagram
Alloy I: 350 II
I III
At point 1: Liquid
Solidification starts at liquidus 1 Liquid
At point 2: L+α 300
2
The amount α ↑ with ↓ T
Solidification finishes at solidus 250
Temperature
At point 3: α 3
Precipitation starts at solvus α
200
At point 4: α+β β
Further cooling leads to formation
and growth of more β precipitates 150
whereas Sn% in α decreases
following the solvus. 100 4
The cooling curve of this alloy is 50
similar to cooling curve I shown in
slide 9.
0
0 10 20 30 40 50 60 70 80 90 100
Pb Sn
(Fcc) Wt% (Tetra)
(a)
(1) L (2)
L
L
α
Precipitates in a Al-Si alloy;
(a) optical microscopy,
(b) scanning electron
microscopy of fracture surface
(3) (4)
α β
α
(b)
Solidification of Eutectic Systems
Alloy II: Pb-Sn phase diagram
At point 1: Liquid
Solidification starts at eutectic 350
point (where liquidus and solidus I III II
Liquid
join) 300
At point 2: L(α+β) (eutectic
reaction)
250 1
Temperature
The amounts of α and β increase
in proportion with time.
α
Solidification finishes at the same 200
β
temperature. 2
At point 3: α+β 150
Further cooling leads to the
depletion of Sn in α and the
100
depletion of Pb in β. 3
The cooling curve of this alloy is 50
similar to cooling curve II shown
in slide 9. 0
0 10 20 30 40 50 60 70 80 90 100
Pb Sn
(Fcc) Wt% (Tetra)
(1) L (2)
L
L
(3) Nucleation of colonies
of α and β laminates
Eutectic structure of
intimate mix of α and β to
Pb-Sn eutectic minimise diffusion path
Solidification of Eutectic Systems
Pb-Sn phase diagram
Alloy III:
At point 1: Liquid 350
Solidification starts at liquidus I III II
Liquid
At point 2: LL+α (pre-eutectic α) 300
The amount α ↑ with ↓T 1
At point 3: L (α+β) (eutectic
250
Temperature
reaction)
Solidification finishes at the eutectic
α 2
temperature 200
β
At point 4: α+β (pre-eutectic α +
3
(α+β) eutectic mixture) 150
Further cooling leads to the depletion
of Sn in α and the depletion of Pb in 4
100
β.
The cooling curve of this alloy is a 50
combination of the two cooling curves
shown in slide 9. 0
0 10 20 30 40 50 60 70 80 90 100
Pb Sn
(Fcc) Wt% (Tetra)
(1) L (2) Cooling curve
L
L
α
(3) (3)
Pr Cu-Ag alloy
e-
eu
tec
tic
L Eut α
α α
Eutectic laminate
of α and β
Solidification of Eutectic Systems
350
I III II IV
300 Liquid
Can you describe the
250
solidification process of alloy IV,
including microstructure
evolution, morphology of phases 200 α β
and cooling curve?
150
100
50
α+β
0
Pb Sn
Hypoeutectic Hypereutectic
Gibbs Phase Rule
Gibbs phase rule F =C+N-P
F: degree of freedom
C: number of chemical variables
N: number of non-chemical variables
P: number of phases
L one-phase region
Application of Gibbs phase rule:
For a binary system at ambient pressure: two-phase
C=2 (2 elements) equilibrium (line)
N=1 (temperature, no pressure)
For single phase: F=2: % and T α
(a region) β
For a 2-phase equilibrium: F=1:
% or T (a line)
For a 3-phase equilibrium: F=0, (invariant three-phase
point) equilibrium (point)
May we have a 4-phase equilibrium, in a
binary system, or in any system? α+β
Pb Sn
Non-Equilibrium Solidification
Some transformations do not cause changes in composition, such as the
solidification of a pure metal, whereas some other do, such as the
solidification of an alloy into a solid solution. The former is known as
congruent transformation and the latter incongruent
transformations. Congruent transformations are cooling rate insensitive
and incongruent transformations are cooling rate sensitive – they rely on
interdiffusion to proceed. Solidification under a fast cooling rate, where
diffusion is insufficient to homogenise the composition simultaneously
during the process is known as the non-equilibrium solidification.
A common consequence of non-equilibrium solidification is coring.
Coring
Alloy Co starts solidification at T1. The first Equilibrium
solid formed has composition Cs1. On solidus
Co
further cooling to T2, an outer shell of
composition Cs2 is formed surrounding T1 (start of solidification)
Cs1
Cs1. Due to inadequate diffusion on fast
Cs
cooling, a composition difference is created. T2
The average composition of the solid 2
composite at T2 is, thus, somewhere Cs T3 (end of solidification
under equilibrium)
between Cs1 and Cs2: Cs2*. The same 2
*
situation continues throughout the process. Cs
Under equilibrium condition solidification T4 (actual end of
* solidification)
completes at T3. However, under non- 3
equilibrium condition, the average Effective
composition of solid at T3 is Cs3* <Co, solidus
indicating that solidification is not completed A %B
yet. Solidification actually ends when the
average composition of solid equals Co, i.e., Non-equilibrium solidification lowers
at T4. effective melting temperature.
Coring
T1
L
T2 Equilibrium
Cs1
Cs1 solidus
Co
T1 (start of solidification)
Cs2 Cs1
Average solid
composition: Cs2* Cs T2
T3 2
Cs T3 (end of solidification
under equilibrium)
*
2
Average solid Cs T4 (actual end of
* solidification)
composition: Cs3* 3
T4 Effective
solidus
A %B
The cored structure: composition segregation,
Average solid enrichment of high-Tm constituent in the core
composition:
Co
Coring in Eutectic Systems
According to the lever rule, the co L
weight fraction of the eutectic
products can be computed as:
Under equilibrium condition:
α β
c−b a b c d
Weut =
d −b
Under non-equilibrium condition:
c−a α+β
*
W eut =
d −a
* A B
Weut > Weut
Coring leads to increase of weight fraction
of eutectic products
Constitutional Supercooling
Co
S L
CS
C CL
CL
Co
CS
x
T Tm A %B
T
S L
Supercooling window caused by x
rising Tm, resulting in unstable
interface
Dendrite Structure of Metals
A consequence of constitutional supercooling and destabilisation of solid-liquid interface is
the formation of dendritic structure, as commonly found in alloy castings. In such structure,
gaps between dendrites and between dentitic fingers are regions rich of low-melting
temperature phases and impurities. Dendritic branches themselves are often cored, too.
This often require post-casting heat treatment to homogenise the structure.
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