Ch 11 – Phase diagram and alloy formation...
Ch 11 – Phase diagram and alloy formation
11.1-Introduction;
11.2-Alloy systems;
11.3-Total solid solubility;
11.4-Interpretation of phase diagram;
11.5-Solid solubility;
11.6-Phase diagram for total solid solubility;
11.7-Partial solid solubility;
11.10-Effect of alloy type on properties in metallic system;
Text Book: V. B. John. Introduction to Engineering Materials. 4th Ed. Palgrave Macmillan; 2003
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Ch 11 – Phase diagram and alloy formation...
11.1-Introduction: Let us start with some definitions and explanations of the
terms which are going to be used throughout this chapter:
Phase: a portion of a matter (one component or more) which is homogeneous
(uniform), having same structure and same physical properties. It can be a
solution, metal or chemical compound. For example; NaCl is a solid phase, water
is a phase, a solution of salt dissolved in water gives a homogenous solution,
termed as a single phase
Phase diagrams (Equilibrium diagram): A graphical representation shows
conditions at which distinct phases can occur at equilibrium. Thus it gives the
amount of phases present in equilibrium w.r.t certain variables.
One-component.
Two -component (binary systems).
Three-component (ternary system).
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The Phase Rule: The phases represented in the phase diagram are related by
the phase rule, Which states that:
P + F = C + 2 (Gas, Liquid and solid)
P = number of phases that can coexist in equilibrium; statistics
C = number of components making up the phases;
F = degrees of freedom, describes the minimum number of variables
(Temperature, Pressure, Chemical Composition...etc.) that must be fixed in
order to define a particular condition of the system..
Condensed systems have no gas phase and are insensitive to changes in
pressure, so that one fewer variable needs to be specified, which results in the
condensed phase rule:
P + F = C + 1 (Liquid and solid only)
Reading Materials...
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P+F=C+2
P+F= 1+2
At a triple point (C), a condition in
which three stability fields intersect.
The phase rule (3 + F = 1 + 2)
indicates that the variance is 0. Point
C is therefore an invariant point; a
change in either pressure or
temperature results in the loss of one
or more phases
At point (a) a single solid phase exists
1 + F = 1 + 2, so F = 2. For point A (or any point
in which only a single phase is stable), two
degrees of freedom exist. Thus, the two
variables (pressure and temperature) can be
changed independently, and the same phase
exist in equilibrium.
a
Reading Materials...
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Ch 11 – Phase diagram and alloy formation...
Condensed systems have no gas phase and are insensitive to changes in
pressure, so that one fewer variable needs to be specified, which results in the
condensed phase rule:
P+F=C+1
P = number of phases that can coexist in equilibrium;
C = number of components (alloying elements) that making up the phases;
F = degrees of freedom (Temperature and Chemical Composition)
At constant temperature and constant composition F = 0;
P+0=C+1
For two component system C = 2 ... P = 3
For three component system C = 3 ...P = 4
The maximum number of phases can coexist in equilibrium is C (number
of alloying compounds +1)
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Phase diagram and cooling curves:
Phase diagram can be constructed from information obtained from cooling curves
which can be experimentally done. Several cooling curves for pure metals involved
in the alloy construction as well as a mixed of different compositions cooling curves
are used.
Cooling curve for a pure metal
Cooling curve for alloy system
A cooling curve for each mixture is constructed and the initial and final phase
change temperatures are determined. Then these temperatures are used for the
construction of the phase diagrams.
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Ch 11 – Phase diagram and alloy formation...
80% A
20% B
(Volume fraction – Percent weight)
Temperature-composition phase diagrams.
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Crystal growth:
For pure metals; Slower rates of cooling will create larger crystals. Rapid cooling
allows little time for element accumulation in the crystal, therefore, the crystals
created will be smaller.
As the rate of cooling increase, the number of nuclei (centre of crystallization)
produced per unit volume increase. As a consequence of that, the number of
crystals will increase...smaller size grains.
The crystals of pure metal grow in a tree like crystal called “dendritic structure”.
Many metals solidify from liquid in a dendritic manner...to form a skeleton type
crystal.
The outward growth ceases when the advancing dendrite arms meet an adjacent
crystal. Then the dendrite arms thicken.
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Ch 11 – Phase diagram and alloy formation...
11.2-Alloy systems.
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11.3-Total solid insolubility.
Equilibrium diagram of binary alloys made up of two components which are soluble
In the liquid state and insoluble in the solid state.
Temperature-composition phase diagrams.
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I
Total solid insolubility.
III
Eutectic...point
II
IV
Line AEB is called the liquidus curves; and Line CED as solidus line.
I : Liquid from A+B. One phase (homogenous)
II and III : Solid + liquid. Two phase
II : Solid (A) + Liquid (A+B); Crystals of solid pure A , and liquid (A+B) enriched with B.
III : Solid (B) + Liquid (A+B); Crystals of solid pure B , and liquid (A+B) enriched with A.
IV : Solid A + solid B; Two phase.
After solidifications we have an alloy of two metals, in which each metal kept its original
structure.
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Eutectic...point...mixture...alloy...reaction...temperature...etc.
Eutectic mixture is a mixture at such proportions that the melting point is as low as
possible. Furthermore all the constituents crystallize and separated simultaneously
at this temperature from molten liquid solution. The cooling curve of such mixture is
the same as the cooling curve of pure metal.
Such a simultaneous crystallization of a eutectic mixture is known as a eutectic
reaction. The temperature at which it takes place is the eutectic temperature, and
the
. composition and temperature at which it takes place is called the eutectic point.
At point E: Solid (A) + Solid (B) + Liquid (A+B) co-exist at the same time.
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L+A
L+A+B
The Phase Rule: P + F = C + 1
P+0=2+1
P = 3 (Three phases coexist in equilibrium)
At the point (E), T is constant and
composition is constant; F = 0
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The primary crystal (A)could be “Dendritic” in form,
and the remaining will be eutectic alloy (A + B)
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11.4-Interpretation of phase diagram.
I think we interpret the phase diagram more than enough...for further reading refer to your text book...
Section 11.4; Page 162.
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In the above solution the relative quantities were calculated?
Percentage of (A) at point (U) = Uy/xy %
Percentage of (L) at point (U) = Ux/xy %
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11.5-Solid solubility:
Solid solution (SS): A two component system, form a single solid phase with one
crystal structure.
The atoms of both metals share the same crystal lattice...one component retained
its structure after solidification and the other component give up its atoms. The
component which retained its structure called “ Solvent”, and the one gives its
atoms called “Solute”.
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Restrictions to solid solution formation
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Solid solutions can be classified as:
• Complete solid solubility:
At any conditions or concentration the two metals form a SS.
An example Gold-Copper alloy; both have FCC; same melting temperature.
• Limited solid solubility. Has a limited a mount of concentration.
For complete solid solubility. The following factors must be satisfied:
1. The components must have the same crystal structures. i.e.
FCC...FCC, and BCC...BCC...etc.
2. The size of the atoms and the lattice parameters must not vary by 7% for
complete solid solubility.
3. The elements should belong to the same group in the periodic table; have
the same electron configurations i.e. Same valency.
For interstitial solid solubility. The conditions that must be satisfied:
1. The solute atoms must be small compared with the solvent atoms.
Ex. (C), (H2), (N2)...
2. The inter atomic distance between the solvent atoms must be large..
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Ch 11 – Phase diagram and alloy formation...
11.6-Phase diagram for total solid solubility.
Copper-Nickel phase diagram.
An example of complete
solubility in solid state: Both
component have the same
crystal structure FCC; similar
valances; very close atomic
radii and electro-negativities.
Note that the solid solutions
are commonly represented by
lower case Greek letters.
To find phase composition; for
single phase point (A) has a
composition as the overall
composition of the alloy (40%
Cu – 60% Ni). For two phase
region see next slide:
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Ch 11 – Phase diagram and alloy formation...
Point (B) located in two phase region; first
we draw a Tie line connecting the phase
boundaries.
CL, Co and C represent the composition.
To find the phases amount in two phase
region as mass fraction or percentage, we
apply the lever principle “inverse lever
rule”:
At point B (alloy Cu%-Ni%)
Amount of liquid with CL composition = S/(R+S)
Amount of  with C composition= R/(R+S)
For calculation we use one component %, or we
measure the distance.
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Coring: In-homogenous crystal structure called dendritic
segregation, since the composition of the branches
(dendrites) is varying from one arm to another. The centre
of the crystal will be rich in Ni (high melting temperature
element); the outer edges will be rich in copper.
This structure is unwanted in fabrication processes, and
leads to cracking and failure of the alloy during machining
and manufacturing processes. So it must be eliminated.
Heat and hold at annealing temperature for long time...How long is long?
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11.7-Partial solid solubility.
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For an alloy with composition C1:
Solidification will take place as complete
solid solution.
(a) The alloy is totally liquid, of composition C1
(b) Crossing the liquidus line, solid  phase
begins to form; with continued cooling
more solid  forms.
(c) When solidification is complete, the
structure will be one of cored  (lead-rich)
solid solution; with a uniform composition
of C1.
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Ch 11 – Phase diagram and alloy formation...
For an alloy with composition C2:
(d), (e) and (f) changes for the alloy with
composition C2 will be similar to the changes for
the alloy C1, discussed previously.
(f) Just above the solvus line the micro structure
consists of  grains of composition C2.
(g) Crossing the solvus line the  solid solubility
limit is exceeded, which results in the formation
of small ? (tin-rich/not pure tin) phase particles
rejected from  solid solution as precipitate. 
may be precipitated either at the  grain
boundaries; or within the  crystals; or at both
sites.
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Ch 11 – Phase diagram and alloy formation...
2
1
3
L
L
L
L+
L+
L+
L++

+E

+E
At (s): The structure is composed of crystals of  of composition q; and
 particles of composition r:
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11.10-Effect of alloy type on properties in metallic system.
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End of chapter-11
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11.9-Compound formation:
It frequently occurs in phase diagrams of metals and ceramics that an A-B binary
phase diagram will reveal one or more compounds formed from A and B. In that
case, we divide the overall phase diagram into “panels”, each of which can be
interpreted as a phase diagram between each pair of pure substances present in
the system.
() is a chemical compound of single phase (SS) with variable composition of
limited solubility.
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The number of “repeats” of the basic phase diagram tells how many such
compounds there are. The “dividing lines” between the individual phase diagrams
are intended to indicate compound formation, rather than an actual phase boundary.
An example of compound forming
in ceramic alloy system
Four different compounds formed
in this system.
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Ch 11 – Phase diagram and alloy formation...
Intermetallic compounds:
Mg2 Sn
Fe3C
Fe
C
Fe3C
1538
3525
1148
BCC
Cubic (diamond); Hexagon (graphite)
very complex
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11.12-Ternary diagrams.
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Note: In normal solidification rates, the
rate is too fast for full equilibrium to be
attained and the crystal will be “cored”
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