# Phase Diagrams a Review by cometjunkie44

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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: Lα+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
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
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: LL+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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