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
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: 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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