Phase Diagrams
MT 2020 – Metals and Alloys
Introduction
• Many material properties are microstructure-sensitive
• Phase diagrams are an important tool in studying how microstructure
is developed
• Phase diagrams can accurately predict the microstructures of metal
alloys.
Processing
Structure
Applications and
Performance
Properties
Important definitions
A phase is a specific arrangement of atoms in a regular repeating array, with
a defined range of atomic compositions on each symmetrically unique site in
the array. It is a chemically and structurally homogeneous portion of the
microstructure.
A component is a distinct chemical substance from which the phase is
formed
AluminumCopper
Alloy
Adapted from chapteropening photograph,
Chapter 9, Callister,
Materials Science &
Engineering: An
Introduction, 3e.
b (lighter
phase)
a (darker
phase)
Single phase microstructure
• A single-phase microstructure can be
polycrystalline
• However, each crystal grain differs only
in crystalline orientation.
• Each crystal has the same chemical
composition.
Single phase microstructure
of pure molybdenum.
Single phase microstructure
Two phase microstructure
• Solid solubility is limited for many
material systems.
• For certain compositions, the result is
two phases, each richer in a different
component.
• A classic example is the pearlite structure
in carbon steel.
• The structure has alternating layers of
ferrite and cementite.
Two-phase microstructure of
pearlite found in a steel with 0.8
wt.% C.
Single Component Phase Diagram
• The simplest chemical compound to consider is H2O. This has three
common phases; vapour or steam, liquid water and solid ice.
Single component phase diagram
Single component phase diagram
Phase and component
• Phase must be distinguished from component.
• A component is a distinct chemical substance from which the phase is
formed.
• For example two components Cu and Ni are components in the Cu
and Ni continuous system where the elements are soluble in all
proportions.
• MgO and NiO form solid solutions in a way similar to that for Cu and
Ni. Here, MgO and NiO are considered components.
Degrees of Freedom
• Degrees of freedom are the number of independent variables available to
the system.
• For example, a pure metal at precisely its melting point has no degrees of
freedom.
• At this condition, or state, the metal exists in two phases in equilibrium in
solid and liquid phases simultaneously.
• Any increase in temperature will change the state of the microstructure.
• All of the solid phase will melt and become part of the liquid phase.
• Similarly, even a slight reduction in temperature will completely solidify the
material.
Phase Rule
• The phase rule is an important tool used for the quantitative treartment
of systems in equilibrium.
• It enables us to predict the conditions that must be specified for a system
to exhibit equilibrium.
• J. Willard Gibbs enunciated the phase rule in 1876 on the basis of
Thermodynamic principles
• This rule predicts qualitatively the effect of temperature, pressure and
concentration on a heterogenous equilibrium.
Phase Rule
• Gibbs phase rule: In a heterogeneous system in equilibrium is not
affected by gravity or by electrical and magnetic forces, the number
of degrees of freedom(F) of the system is related to the number of
component(C) and the number of phases(P) existing at equilibrium.
• It is expressed mathematically as,
F=C–P+2
where,
F - number of degrees of freedom
C - number of components
P - number of phases
2 - additional variables of temperature and pressure
Phase rule
• For most materials involving condensed systems, the effect of pressure is
slight, and we can consider pressure to be fixed at 1 atm.
• In this case, the phase rule can be rewritten to reflect one less degree of
freedom:
F=C–P+1
where,
F - number of degrees of freedom
C - number of components
P - number of phases
1 - additional variable of temperature
Phase Rule
Phase:
• A gaseous mixture constitutes a single phase since gases are
completely miscible.
• Example : Air
• Two or more liquids which are miscible with one another constitute a
single phase as there is no bounding surfaces separating the different
liquids.
• Example : water and alcohol, chloroform and benzene constitute one phase
system.
• A system consisting of a liquid in equilibrium with its vapour
constitute a two phase system
• Example : H2O(l)
H2O(g)
Phase Rule
Examples
• Sulphur system
• (a)monoclinic sulphur, (b)rhombic sulphur (c)liquid sulphur (d) sulphur
vapour.
(C = 1; P=4)
• Water system
• solid, liquid and vapour (C=1 ; P = 3)
.
• Salt + water system
• Certain salts are capable of existing as hydrates with different number of
water molecules of crystallization. The system is a two component.(C=2 , P =
1)
• The composition of each phase of the hydrates is described in terms of the
anhydrous salt and water. e.g., Na2SO4 + water
Phase diagram of complete solid solution
• The simplest phase diagram we can consider is that of a complete solid solution
• In this case, we have two metals of similar size and crystal structure that form a
single continuous phase in both liquid and solid states but have different melting
points
Tm(A)
Tm(B)
• Therefore there are only two phases – the Liquid and the Solid phase. A pure solution
of either A or B would have a single melting point, Tm(A) or Tm(B)
• For in-between compositions, like C(x), on cooling, the liquid phase will first
cool with a single composition, till the liquidus line is reached. At this point it
will split into 2 phases, the solid S which is relatively pure in A, and liquid of
composition C(x)
• As the alloy cooled down in the two-phase field, the alloy would solidify, with both the
solid and liquid phases increasing in B, but the fractions of phases would change with more
solid being formed, so that the overall composition is the same.
• The solid phase would follow the limit of solubility of S with temperature - the solidus,
while the liquid phase L would follow the liquidus.
All Liquid
Crystallites of
Solid in a matrix
of Liquid
Polycrystalline
Solid
Degrees of Freedom: F = C – P + 1
F=2–1+1=2
F=2–2+1=1
F=1–2+1=0
F=2–1+1=2
Cooling curve of A-B alloy
• From the cooling curves of an alloy, such as seen above, the liquidus
and solidus temperatures can be identified, which allows us to
determine the phase diagram experimentally
Criteria for Solid Solubility
Simple system (e.g., Ni-Cu solution)
Crystal
Structure
electroneg
r (nm)
Ni
FCC
1.9
0.1246
Cu
FCC
1.8
0.1278
• Both have the same crystal structure (FCC) and have
similar electronegativities and atomic radii (W. Hume –
Rothery rules) suggesting high mutual solubility.
• Ni and Cu are totally soluble in one another for all proportions.
Cu-Ni Phase Diagram
• Phase diagram:
Cu-Ni system.
• System is:
T(ºC)
1600
1500
L (liquid)
-- binary
i.e., 2 components:
Cu and Ni.
-- isomorphous
i.e., complete
solubility of one
component in
another; a phase
field extends from
0 to 100 wt% Ni.
Cu-Ni
phase
diagram
1400
1300
a
(FCC solid
solution)
1200
1100
1000
0
20
40
60
80
100
wt% Ni
Cu-Ni Phase Diagrams:
Determination of phase(s) present
• Rule 1: If we know T and Co, then we know:
-- which phase(s) is (are) present.
A(1100ºC, 60 wt% Ni):
1 phase: a
B(1250ºC, 35 wt% Ni):
2 phases: L + a
1600
L (liquid)
B (1250ºC,35)
• Examples:
T(ºC)
1500
1400
1300
A(1100ºC,60)
1100
1000
a
(FCC solid
solution)
1200
Adapted from Fig. 9.3(a), Callister &
Rethwisch 8e. (Fig. 9.3(a) is adapted from
Phase Diagrams of Binary Nickel Alloys,
P. Nash (Ed.), ASM International,
Materials Park, OH (1991).
Cu-Ni
phase
diagram
0
20
40
60
80
100
wt% Ni
The phase diagram shows the phases that will form at equilibrium, that
is, at the lowest energy state the system can be in. If the atoms are
sufficiently mobile, given enough time equilibrium will always be
obtained. Therefore phase diagrams are the most important tool we
have for understanding how microstructures form in materials.
However, care should be taken when using equilibrium phase diagrams
as they tell us only what is favourable to occur; we require an
understanding of kinetics (diffusion) to understand what happens and
how fast.
Microstructure development during cooling
of a solid solution alloy.
Eutectic Phase diagrams
Eutectic phase diagrams are used when
the alloying elements are not completely
soluble with each other, but can only take
a limited amount of each other. In this
situation you have Metals A and B again,
but then you have the A atoms preferring
an α phase, and the B atoms preferring a β
phase.
You can therefore get α phase solids, β
phase solids and two phase α + β solids.
You also have a eutectic point where the
liquid solidifies into the two solid phases
(α + β) immediately.
Solidification of Single phase alloys
In this diagram, you have
liquid solidifying into a
an α phase solid.
Solidification and solid-state precipitation in a
two-phase alloy.
Here you have a liquid
solidifying to an α phase
solid, but as it is cooled
further, it enters the α + β
phase, so β starts forming
around the grain boundaries
of the α crystals.
Solidification of the Eutectic Alloy
At the Eutectic point, the
liquid solidifies straight into
a α + β phase. The structure
consists of α and β phase as
lamellae (plate like
structures)
Solidification Sequence in a near eutectic
alloy
Close to the Eutectic point, the liquid
solidifies straight into a liquid + α phase.
Then past the eutectic temperature, the
liquid around the crystals solidifies into
a eutectic solid with α and β phase as
lamellae
Pb – Sn Phase Diagram
An example of a eutectic phase
diagram showing the Pb – Sn
system
• (a) A Hypoeutectic alloy (40wt.%
Sn), showing dendrites of primary
Pb in a Pb-Sn eutectic,
• (b) a eutectic Pb-Sn alloy,
• (c) a hypereutectic alloy (80wt.%
Sn) with dendrites of primary Sn
in a Pb-Sn eutectic,
• (d) the Pb-Sn binary eutectic
phase diagram