Phase Equilibrium and Diagrams

1
Phase Equilibrium and Diagrams

• Phenomenon
• Ice melts into water at 0C and evaporates into
  gas at 100C
• Al becomes liquid at 660C
• Fe is BCC-structured (a-Fe) below 912C, but
  FCC-structured (g-Fe) between 912 and 1394C
• Al-Cu alloys can be strengthened by precipitation
• Fe can be hardened by quenching
• Terminology
• phase e.g. liquid, solid, gas, a, g, etc. (i.e.
  the structure)
• microstructure what can be seen using a
  microscope

• Quantitative description
• equilibrium phase diagrams
• what phases are present and how much of each
  phase at a certain temperature and alloying
  composition
• Equilibrium microstructures
• prediction from phase diagrams
• in typical systems

Reading 9.1-9.9 (5th ed) 9.1-9.13 (6th ed)
more descriptions will be given later
2
Phase Equilibrium and Diagrams

• Concepts and Definitions
• Alloy not pure metal
• Al-4 wt Cu alloy
• Fe- 0.1 wt C alloy (a carbon steel)
• Component elementary constituent of an alloy
• Al and Cu
• Fe and C
• System alloys of the same components with
  various compositions
• Al-Cu system (a series of alloys containing Al
  and Cu)
• Fe-C system

• Phase a homogeneous portion of a system that has
  uniform physical and/or chemical characteristics
  (i.e. you cannot tell any one part from any other
  part)
• chocolate bar with nuts (chocolate nut)
• ice water ice water
• oil in water oil water
• too much sugar in coffee (solid sugar sweet
  liquid coffee)
• Pearlite steel a-Fe Fe3C
• precipitation strengthened Al-Cu alloy Al fine
  particles of CuAl2

A system may contain only one phase or multiple
phases depending on the composition, temperature,
pressure and other conditions
3
Phase Equilibrium and Diagrams

• Phase equilibrium
• a system is at equilibrium if the number of
  phases and their amounts do not change with time
• e.g. ice in water at 0C
• if no heat exchange with the environment
• dynamic any ice melting will absorb heat and
  cause freezing of water at the same time, i.e.
  although the total amount of ice does not change,
  the melting and freezing processes proceed at the
  same rate to keep the equilibrium

• when a system is at equilibrium, it attains a
  minimum energy state (with minimum free energy)
  and is said to be stable
• when a system at equilibrium contains multiple
  phases, the phases are at equilibrium with each
  other or phase equilibrium is reached
• Phase equilibrium may be destroyed if conditions
  are changed, most notibly by temperature changes
• liquid water changes into vapor if T is raised to
  100C
• Fe changes from BCC to FCC when T is raised to
  912C

Concept of free energy will be taught in
thermo-dynamics
4
Phase Equilibrium and Diagrams

• Metastable state
• an observed state of a system does not
  necessarily indicate that the system has attained
  the lowest energy possible, e.g. diamond (C) has
  higher free energy than graphite (C) at ambient
  conditions, but do not loose your sleep as your
  precious diamond is not going to become cheap
  pencil lead overnight (the energy barrier is too
  high for the change to take place at any
  detectable rate)!

• Microstructure
• in addition to the number of phases and the
  amount of each phase, microstructure tells the
  shape and size of each phase and their
  distribution in space
• microstructure is important as it often
  determines the properties of materials (e.g.
  nominally same materials with same compositions
  and phases may have very different strengths)

A host B dissolved in A
A host B fine particles
A host B lamellae
We will discuss the topic of phase transformation
in more details later
5
Phase Equilibrium and Diagrams

• Equilibrium Phase Diagrams
• What phases are there under a certain conditions
  ( e.g. T) for a given alloy (i.e. composition)
  and what changes will occur if T is altered
  (phase transformation)?
• For pure metals (i.e. one component system)
• Al (melting T 660C)
• solid (FCC) lt660C
• liquid gt 660C
• Fe (melting T 1538C)
• solid a (BCC) lt 912C
• solid g (FCC) 912-1394C
• solid d (BCC) 1394-1538C
• liquid gt 1538C

• Binary isomorphous systems
• involving two components
• at ambient atmosphere (P 1 atm)
• two axes are needed T and C

pure Cu
pure Ni
Other conditions such as pressure are usually
constant
Tm of pure Ni
liquid field
a L two phase field
lower limit of the liquid field
upper limit of the solid field
alpha field
a solid solution of Cu and Ni (FCC)
Tm of pure Cu
A diagram is necessary if a system consists of 2
or more components
6
Phase Equilibrium and Diagrams

• Phase present
• A Cu-60Ni at 1100C
• B Cu-35Ni at 1250C

• Compositions of phases present
• A a 40 wt Cu-60 wtNi (same as the alloy
  composition)
• B
• L 68.5 wt Cu-31.5 wtNi
• a 57.5 wt Cu-42.5 wtNi

The T and composition define the point in the
diagram
CL
Ca
CL and Ca are different from the alloy
composition Co
a mixture of a and L
100 a phase
IMSE Phase Diagrams
7
Phase Equilibrium and Diagrams

• Amounts of phasees present
• A 100 a (single phase)
• B using the lever law

mass fraction of liquid
mass fraction of a
If there are 100 g of alloy B, the amount of
liquid phase at 1250C is 68 g and that of a is
32 g. Total amount of Cu in liquid CLCu x 68 g
68.5 x 68 g 46.6 g Total amount of Cu in a
CaCu x 32 g 57.5 x 32 g 18.4 g Total amount
of Cu in alloy B is 46.6 18.4 65 g This is
the same if we calculate the total amount of Cu
using 100 g x 65 65 g
Referring to example 9.1
8
Phase Equilibrium and Diagrams
very slow cooling, i.e. the system is given as
much time as needed to reach equilibrium at each
temperature

• Microstructures
• following equilibrium cooling of Cu-35Ni from
  1300C
• To to T1 cooling of liquid (35Ni)
• just under T1 a (46Ni) nucleation starts (L
  35Ni)
• at T2
• L 32Ni
• a 43Ni
• WL 27.3
• Wa 72.7
• at T3 solidification finishes (100 a 35Ni)
• T3 to T4 cooling of a

Diffusion is necessary which is a slow process
To
starting temperature
How can such a change of composition be realised
in a?
T1
T2
T3
T4
using lever law
alloy
9
Phase Equilibrium and Diagrams
cooling is fast to allow little diffusion in a
(diffusion in liquid is taken to be still fast
enough to allow equilibrium to be reached)

• Microstructures
• following nonequilibrium cooling
• To to T1 cooling of liquid (35Ni)
• just under T1 a (46Ni) nucleation starts (L
  35Ni)
• at T2 L (29Ni) and a 40Ni
• at T3 L (24Ni) and a 35Ni
• at T4 L (21Ni) and a 31Ni
• T4 to T5 cooling of a with an average 35Ni
  (consisting of layers of different compositions)

To
The core with 46Ni
average composition of a
T1
The solidifying layer with 40Ni
a average 46Ni
T2
T3
a average 42Ni
The solidifying layer with 35Ni
T4
a average 38Ni
T5
The solidifying layer with 31Ni
a average 35Ni
solidification finishes at T4, not T3 !
Segregation/coring
alloy
Can the extent of segregation be reduced?
10
Phase Equilibrium and Diagrams

• Binary eutectic systems

Eutectic isotherm
b solid solution based on Ag with dissolved Cu
a solid solution based on Cu with dissolved Ag
Eutectic or invariant point
solubility limit (how much solute can be
dissolved in the host). e.g. at 600C, Cu can
dissolve a maximum of 3 wt Ag
3
11
Phase Equilibrium and Diagrams
Eutectic or invariant point
Eutectic isotherm
L (CE) a (Ca E) b (Cb E)
Eutectic reaction
The eutectic reaction takes place at a constant
temperature (TE 779C). At the end of the
reaction, all liquid has become a and b and their
relative amounts can be calculated by using the
lever law (Wa  19.3/83.2 23.2 and Wb 76.8).
Alloy Cu-71.9Ag
12
Phase Equilibrium and Diagrams

• Examples 9.2 and 9.3
• Pb-40Sn alloy at 150C
• a b two phases
• Ca Pb-10Sn
• Cb Pb-98Sn
• Wa 58/88 66
• Wb 30/88 34

Homework do the same for alloy A (20Sn) at
250C, alloy D (90Sn) at 200C, and alloy X
(50Sn) at TE just before the eutectic reaction
and just after the completion of the eutectic
reaction, respectively.
A
D
TE 183C
X
18.3
61.9
97.8
Hint just before the eutectic reaction there are
two phases, L a just after the reaction there
are two phases, a b.
13
Phase Equilibrium and Diagrams

• Microstructures following equilibrium cooling
• alloy C1
• T gt T1 100 L
• at T1 solidification of a starts
• at T2 solidification of a finishes
• lt T2 100 a

T1
T2
14
Phase Equilibrium and Diagrams

• alloy C2
• T gt T1 100 L
• at T1 solidification of a starts
• at T2 solidification of a finishes
• at T3 precipitation of b starts (in the a
  matrix)
• lt T3 Wb ? as T ? (using the lever law)
• lt T4 no more change

Composition of L
T1
T2
T3
Composition of a
Compositions of b are out of range
T4
15
Phase Equilibrium and Diagrams

• alloy C3
• T gt TE 100 L
• just reach TE co-solidification of a b starts
• at TE eutectic reaction continues until all L
  has become the eutectic structure
• lt TE Ca and Cb change along the respective
  solvus lines

The relative amount of each phase at a particular
temperature can be calculated by using the lever
law
TE
alternating a and b lamellae
16
Phase Equilibrium and Diagrams

• alloy C4

HW do the same analysis for alloy Pb-90Sn
Just before TE a L Wa 21.9/43.6 50.2 WL
21.7/43.6 49.8
At T1, a solidification starts
T1
TE
at TE L (61.9) a (18.3) b (97.8) eutectic
structure
18.3
61.9
97.8
Just after TE a b Wa 57.8/79.5 72.7 Wb
21.7/79.5 27.3
This microstructure consists of primary a and a
eutectic a b (lamellar) structure
HW what happens during cooling from TE to room
temperature?
HW how much of the eutectic structure in the
final material?
17
Phase Equilibrium and Diagrams

• Binary systems with intermediate intermetallic
  compounds

Intermetallic compound
18
Phase Equilibrium and Diagrams

• Binary systems with intermediate phases and
  reactions

Read 9.8 9.9 (5th ed), 9.12 9.13 (6th ed)
Intermediate solid solution
Peritectic reaction d L e
Terminal solid solution
Eutectoid reaction d g e
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Phase Equilibrium and Diagrams - Summary

• Terminology
• system
• component
• phase
• microstructure
• equilibrium
• Equilibrium phase diagram (binary)
• fields single phase, two phase
• tie lines
• phases present
• composition of each phase
• amount of each phase - the lever law
• eutectic reaction
• segregation due to nonequilibrium cooling

• Microstructure
• upon cooling from liquid to room temperature
• process
• change of composition during cooling
• change of amount of each phase during cooling
• change of microstructure during cooling and the
  final microstructure