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Solidification of Pure Metal and Alloys
¾ Solidification is the most important phase transformation, because most of
metals/alloys undergo this transformation before becoming useful objects.
¾ Solidification involve liquid-solid phase transformation, e.g: casting process.
Phase Diagrams
¾ The solidification process differs depending on whether the metal is a pure
element or an alloy
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
PHASE DIAGRAMS
¾ These laws give information of the movements of the atoms during the
rearrangement.
dXNXURYD8QLYHUVLW\
Mechanical Engineering Department
2022
¾ In most cases, a driving force is involved that makes it possible to derive the rate
of the solidification process.
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The definition of Material Equilibrium is that in each phase of the closed
system, the numbers of moles of each substance in that phase remains
constant in time.
¾ Thermal equilibrium
¾ Reaction Equilibrium
¾ Phase Equilibrium
Material Equilibrium
¾ When conditions of reaction and phase equilibrium are satisfied,
we have material equilibrium.
¾ The term thermodynamic equilibrium implies that, we have
thermal, mechanical and chemical equilibrium.
The fraction of reactants and products remains constant
Reaction equilibrium with time
Phase Diagrams
¾ Mechanical equilibrium
Note: Nothing happens/changes in a
system under equilibrium
macroscopically
ME 208 Materials Science II
Kinds of Equilibrium
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Material Equilibrium
‰ Equilibrium refers to a state o wherein there is a balance of
¶IRUFHV·.
Phase Diagrams
¾ Solidification or crystallization is a process where the atoms are transferred
from the disordered liquid state to the more ordered solid state. The rate of the
crystallization process is described and controlled by kinetic laws.
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Stability and Equilibrium
ME 208 Materials Science II
¾ In metals and alloys, solidification involves the formation of crystals, a crystalise
solid exhibiting regularity in atomic spacing over a considerable distance.
Material equilibrium
Number of moles of each
substance remains
constant with time
Phase equilibrium The fraction of various phases remains constant with time
¾ Reaction Equilibrium is the equilibrium where the conversion of
quantity stops between two sets of chemicals.
¾ Phase Equilibrium is where the transport of matter reaches a balance
point without conversion of one species to another.
Equilibrium
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Why study Phase Diagrams?
¾ A system is said to be in equilibrium if no macroscopic changes take
place with time.
Reasons for studying phase diagrams are as follows:
¾ Equilibrium phase diagram indicates the temperatures that must be
attained to achieve desired structure and the change that will occur on
subsequent cooling.
¾ Phase diagram is used to design and control the heat treatment
procedures for specific alloys that will produce specific
mechanical, physical and chemical properties.
Phase Diagrams
¾ The resulting structures can be predicted by the use of equilibrium
phase diagrams.
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾ Most processing heat treatments involve rather slow cooling or
extended times at elevated temperatures, thus tending to approximate
equilibrium conditions.
¾ Phase diagrams provide valuable information about melting,
casting, solidification, crystallization and other phenomena.
¾ Phase diagrams are helpful in predicting phase transformations
and the resulting microstructures.
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¾ Terms like Phase and Microstructure are key to understanding phase diagrams.
¾ Phase diagrams in conjunction with TTT/CCT diagrams can be used to ¶HQJLQHHU
PLFURVWUXFWXUHV· and hence ¶WDLORU· the properties of a material.
¾ Two kinds of phase diagrams can be differentiated;
9 those involving time and
9 those which do not involve time.
¾ Temperature-Composition (TC) diagrams (i.e. axes are T and
composition) are extensively used in materials science and will be
considered in detail in this lecture.
¾ Time-Temperature-Transformations (TTT) diagrams and ContinuousCooling-Transformation (CCT) diagrams involve time. These diagrams
are usually designed to have an cover of microstructural information
including microstructural evolution.
Phase Diagrams
9 Those without composition as a variable (e.g. P vs T).
Crystal
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾ Phase diagrams not involving time can be further sub-classified into:
9 Those with composition as a variable (e.g. T vs %Cu)
9 Casting
9 Metal Forming
9 Welding
9 Powder Processing
9 Machining
Thermo-mechanical
Treatments
Atom
Structure
Electromagnetic
Microstructure
Phases
Processing determines shape and microstructure
of a component
+
Component
Defects + Residual Stress
¾ Vacancies
¾ Dislocations
¾ Twins
¾ Stacking Faults
¾ Grain Boundaries
¾ Voids
¾ Cracks
& their distributions
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Phase
¾ Gases
Physically distinct, chemically homogenous and mechanically separable
region of a system (e.g. gas, crystal, amorphous...).
Gaseous state always a single phase
ĺ mixed at atomic or molecular level.
¾ Liquids
¾ Based on Band structure o Insulating, Semi-conducting, Semi-metallic,
Metallic.
¾ Based on Property o 3DUDHOHFWULF)HUURPDJQHWLF6XSHUFRQGXFWLQJ«
ŹLiquid solution is a single phase
ĺ e.g. alcohol in water, NaCl in H2O.
Phase Diagrams
¾ Based on state o Gas, Liquid, Solid.
¾ Based on atomic order o Amorphous, Quasicrystalline, Crystalline.
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
What kinds of Phases exist?
¾ Based on Stability o Stable, Metastable, (also Neutral, unstable).
¾ Based on Size/geometry of an entity o Nanocrystalline, mesoporous,
OD\HUHG«
Phase transformation
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Microstructure
(Phases + defects + residual stress) & their distributions
Phase Diagrams
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Phase Diagrams
The single crystalline part of polycrystalline metal separated by similar
entities by a grain boundary.
¾ Solids
In general due to several compositions and crystal structures many phases
are possible.
x For the same composition different crystal structures represent different
phases. E.g. Fe (BCC) and Fe (FCC) are different phases.
x For the same crystal structure different compositions represent different
phases. E.g. in Au-Cu alloy 70%Au-30%Cu & 30%Au-70%Cu are different phases.
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¾ Components:
The elements or compounds which are present in the alloy
(e.g., Al and Cu)
¾ Phases:
The physically and chemically distinct material regions
that form (e.g., Į and ǀ).
Ź D- Fe (BCC) ĺ J- Fe (FCC)
¾ J- Fe (FCC) ĺ D- Fe (ferrite) + Cementite (change in composition)
Ź Ferromagnetic phase ĺ Paramagnetic phase (based on a property).
Grain
Ź Liquid mixture consists of two or more phases
ĺ e.g. Oil in water (no mixing at the atomic/molecular level).
Components and Phases
Phase Transformation is the change of one phase into another.
E.g.:
Ź Water ĺ Ice
ME 208 Materials Science II
Three immiscible liquids
Aluminum-Copper
Alloy
ǀ (lighter phase)
Į (darker phase)
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Definitions
An alloy phase may be in form of valence compound
(substance formed from two or more elements), with a fixed ratio
determining the composition) or in form of solid solution.
¾ The components are pure metals and/or compounds of which an alloy is
composed. For example, in a copper²zinc (brass), the components are Cu
and Zn.
Solid solution is a phase, where two or more elements are
completely soluble in each other.
(e.g., a ladle of molten steel), or it may relate to the series of possible
alloys consisting of the same components but without regard to alloy
composition (e.g., the iron²carbon system).
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Substitution solid solution
¾ If the atoms of the solvent metal and solute element are of similar sizes
(not more than 15% difference), they form substitution solid solution,
where part of the solvent atoms are substituted by atoms of the alloying
element
Interstitial solid solution
¾ If the atoms of the alloying elements are considerably smaller, than the
atoms of the matrix metal, interstitial solid solution forms, where the
matrix solute atoms are located in the spaces between large solvent atoms
9 When the solubility of a solute element in interstitial solution is exceeded,
a phase of intermediate compound forms. These compounds (TiN, WC, Fe3C
etc.) play important role in strengthening steels and other alloys.
9 Some substitution solid solutions may form ordered phase where ratio
between concentration of matrix atoms and concentration of alloying atoms
is close to simple numbers like AuCu3 and AuCu.
9 Solid solution formation usually causes increase of electrical resistance and
mechanical strength and decrease of plasticity of the alloy.
Phase Diagrams
¾ System may refer to a specific body of material under consideration
ME 208 Materials Science II
concentration.
Depending on the ratio of the solvent (matrix) metal atom
size and solute element atom size, two types of solid solutions may
be formed:
9 substitution or
9 interstitial.
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¾ In interstitial solid solutions; the solute atoms fit in to the spaces
between the solvent or parent atoms.
¾ Interstitial solid solutions can form when one atom is much larger than
another.
Phase Diagrams
¾ Solute is used to denote an element or compound present in a minor
ME 208 Materials Science II
Phase Diagrams
amount; on occasion, solvent atoms are also called host atoms.
Phase Diagrams
ME 208 Materials Science II
ME 208 Materials Science II
¾ Solvent is the element or compound that is present in the greatest
Figure: (a) Substitutional solid solution. The solute and solvent atoms must have similar bond
characteristics. (b) Interstitial solid solution of carbon in FCC iron (The radius of largest
interstitial hole in FCC iron is 0.53 mm. In BCC iron is only 0.036 mm.
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Phase Diagrams
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Phase Diagrams
ME 208 Materials Science II
Figure: Schematic structure of a complete solubility of
the two components in the solid state
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¾For many alloy systems at some specific temperature, there is a maximum
¾ Some alloy systems exhibit complete solid solubility (e.g. Cu-Ni, Cd-Mg),
others show only limited solubility at any temperature.
concentration of solute atoms that may dissolve in the solvent to form a solid
solution; this is called a solubility limit.
¾ Several factors determine the limits of solubility. These are expressed
as a series of rules called Hume-Rothery Rules. These are:
Sugar/Water Phase Diagram
L
40
(liquid solution
i.e., syrup)
20
Water
0
For 65 wt% sugar.
At 20ƒC, if C < 65 wt% sugar: syrup
At 20ƒC, if C > 65 wt% sugar: syrup + sugar
(liquid)
+
S
(solid
sugar)
20
40
60 65 80
C = Composition (wt% sugar)
100
9 Hume-Rothery Rule 1:Atomic Size Factor (The 15%) Rule
Phase Diagrams
60
L
ME 208 Materials Science II
Solubility
Limit
80
Sugar
What is the solubility limit for
sugar in water at 20ƒC?
Temperature (ƒC)
Phase Diagrams
ME 208 Materials Science II
10 0
¾ Solubility Limit:
Maximum concentration for which only
a single phase solution exists.
9 Hume-Rothery Rule 2:Crystal Structure Rule
9 Hume-Rothery Rule 3: Valency Rule
9 Hume-Rothery Rule 4: The Electronegativity Rule
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Hume-Rothery Rule 2:Crystal Structure Rule
¾ For appreciable solid solubility, the crystal structures of the two
elements must be identical.
Hume-Rothery Rule 1:Atomic Size Factor (The 15%) Rule
Hume-Rothery Rule 3: Valency Rule
Phase Diagrams
¾ A metal will dissolve a metal of higher valency to a greater extent than
one of lower valency.
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾ Extensive substitutional solid solution occurs only if the relative
difference between the atomic diameters (radii) of the two species is
less than 15%.
¾ If the difference > 15%, the solubility is limited. Comparing the atomic
radii of solids that form solid solutions, the empirical rule given by
Hume-Rothery is given as:
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¾ The solute and solvent atoms should typically have the same valence in
order to achieve maximum solubility.
Hume-Rothery Rule 4: The Electronegativity Rule
¾ Electronegativity difference close to 0 gives maximum solubility.
¾ The more electropositive one element and the more electronegative the
other, the greater is the likelihood that they will form an intermetallic
compound instead of a substitutional solid solution.
¾ The solute and the solvent should lie relatively close in the
electrochemical series.
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Criteria for Solid Solubility
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¾ Ag-Au, Cu-Ni and Ge-Si are the systems which satisfy Hume Rothery
conditions very well. These systems form complete solid solutions, i.e.
the elements mix in each other in all proportions.
Electroneg
r (nm)
Ni
FCC
1.9
0.1246
Cu
FCC
1.8
0.1278
¾
Both have the same crystal structure (FCC) and have
similar electronegativities and atomic radii (W. Hume ²
Rothery rules) suggesting high mutual solubility.
¾
Ni and Cu are totally soluble in one another for all proportions.
Phase Diagrams
Crystal
Structure
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
Simple system (e.g., Ni-Cu solution)
Microstructure
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¾ The term phase equilibrium, refers to equilibrium as it applies to
¾ Physical properties and the mechanical behavior of a material often
systems in which more than one phase may exist.
¾ In metal alloys, microstructure is characterized by the number of
¾ It can be best illustrates by a sugar²water
phases present, their proportions, and the manner in which they are
distributed or arranged.
syrup is contained in a closed vessel and the
solution is in contact with solid sugar at 20ΣC.
¾ If
the system is at equilibrium, the
composition of the syrup is 65 wt% C12H22O11²
35 wt% H2O, and the amounts and
compositions of the syrup and solid sugar will
remain constant with time.
Phase Diagrams
¾ The microstructure of an alloy depends on such variables as
9 the alloying elements present,
9 their concentrations, and
9 the heat treatment conditions of the alloy (i.e., the temperature,
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
depend on the microstructure.
the heating time at temperature, and the rate of cooling to room
temperature).
¾ If the temperature of the system is suddenly
65-35
80-20
raised; say to 100ΣC, this equilibrium or
balance is temporarily upset and the solubility
limit is increased to 80 wt% C12H22O11.
Figure. The solubility of sugar (C12H22O11) in
a sugar²water syrup.
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One-component (Or Unary) Phase Diagrams
One-component (Or Unary) Phase Diagrams
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¾Pressure²temperature phase diagrams for a number of substances have
¾Three externally controllable parameters affect phase structure;
been determined experimentally, which have solid, liquid, and vapor phase
regions.
temperature, pressure, and composition.
¾Phase diagrams are constructed when various combinations of these
¾This one-component phase diagram (or unary phase diagram, sometimes
also called a pressure² temperature (or P²T) diagram is represented as a
two-dimensional plot of pressure versus temperature. Most often, the
pressure axis is scaled logarithmically.
Phase Diagrams
for a one-component system, in which composition is held constant (i.e.,
the phase diagram is for a pure substance); this means that pressure and
temperature are the variables.
ME 208 Materials Science II
¾Perhaps the simplest and easiest type of phase diagram to understand
Phase Diagrams
ME 208 Materials Science II
parameters are plotted against one another.
Figure. Pressure²temperature phase diagram for H2O. Intersection of the dashed horizontal line at 1 atm pressure
with the solid liquid phase boundary (point 2) corresponds to the melting point at this pressure (T=0ƒC). Similarly,
point 3, the intersection with the liquid²vapor boundary, represents the boiling point (T=100ƒC).
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¾Regions for three different phases; solid,
liquid, and vapor are available.
¾The three curves labeled as aO, bO, and cO
boundary, curve bO, and the liquid²vapor boundary, curve cO.
¾Upon crossing a boundary as temperature and/or pressure is altered, one phase transforms
into another.
¾For example, at 1 atm pressure, during heating the solid phase transforms to the liquid
Phase Diagrams
¾Equilibrium between solid and vapor phases is along curve aO likewise for the solid²liquid
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
are phase boundaries; at any point on one of
these curves, the two phases on either side of
the curve are in equilibrium (or coexist) with
one another.
¾Solid ice sublimes or vaporizes upon crossing the curve labeled aO. All three of
the phase boundary curves intersect at a common point, which is labeled O (for
this H2O system, at a temperature of 273.16 K and a pressure of 6.04п10²3
atm). This means that at this point only, all of the solid, liquid, and vapor phases
are simultaneously in equilibrium with one another.
phase (i.e., melting occurs) at the point 2; this point corresponds to a temperature of 0ΣC.
The melting point at this pressure. The reverse transformation (liquid to solid, or
solidification) takes place at the same point upon cooling.
¾Similarly, at the liquid²vapor phase boundary (point 3, at 100ΣC) the liquid transforms into
the vapor phase (or vaporizes) upon heating; condensation occurs for cooling. The boiling
point at this pressure.
Binary Phase Diagrams
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Overview of Possible Binary Phase diagrams
¾ Phase diagrams involving solids and liquids only.
¾ For many of the phase reactions involving liquid phase only, there are solid state
analogues (i.e. involving only solids).
Solid State analogue ´-WRLGµ
´-WLFµ Liquid State
¾Another type of common phase diagram is one in which temperature
and composition are variable parameters and pressure is held constant,
normally 1 atm.
¾Binary phase diagrams are maps that represent the relationships
between temperature and the compositions and quantities of phases at
equilibrium, which influence the microstructure of an alloy.
Isomorphous
Phase Diagrams
extremely complicated and difficult to represent. Phase diagrams can be
demonstrated using binary alloys even though most alloys contain more
than two components.
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾If more than two components are present, phase diagrams become
Complete Solubility in both liquid &
solid states
Isomorphous with
phase separation
Complete Solubility in liquid state,
but limited solubility in the solid
state
¾Many
microstructures develop from phase transformations, the
changes occur when the temperature is altered (typically upon cooling).
This may involve the transition from one phase to another.
Isomorphous with
ordering
Eutectic
Eutectoid
Peritectic
Peritectoid
Monotectic
Limited Solubility in both liquid &
solid states
Solid state analogue
of Isomorphous
Monotectoid
Syntectic
Note: The ones ending with ´-WLFµimply the existence of a liquid in the
reaction, while those ending with ´-toidµimply a fully solid state reaction.
Binary Isomorphous Systems
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Solidification of Alloys
¾The
easiest type of binary phase
diagram to understand and interpret is
the type characterized by the copper²
nickel system.
¾ Most alloys freeze over a temperature
range and cooling curve for different alloy
systems.
¾ Characteristic grain structure in an alloy
(100 wt% Cu) on the far left horizontal
extreme to 100 wt% Ni (0 wt% Cu) on the
right.
Phase Diagrams
¾The composition ranges from 0 wt% Ni
casting, showing segregation of alloying
components in center of casting.
ME 208 Materials Science II
is plotted along the
ordinate, and the abscissa represents the
composition of the alloy, in weight
percent (bottom) and atom percent (top)
of nickel.
Phase Diagrams
ME 208 Materials Science II
¾Temperature
Figure. (a) The copper²nickel phase diagram.
¾Three different phase regions, or fields, appear on the diagram; an alpha (Į) field,
a liquid (L) field, and a two-phase Į+L field.
¾Each region is defined by the phase or phases that exist over the range of
Cooling curve for alloy solidification
temperatures and compositions delineated by the phase boundary lines.
Types of Cooling Curves
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Types of Cooling Curves
There are various types of cooling curves: Depending on
composition (characteristics)
1. Pure Element
4. Mixtures undergoing Phase Reactions
9 1. At the composition for phase reaction
9 2. Before the composition for phase reaction
Phase Diagrams
3. Mixture of Partially Soluble 2 elements
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
2. Mixture of soluble 2 elements
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Binary Isomorphous Systems
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¾The liquid L is a homogeneous liquid solution
composed of both copper and nickel.
consisting of both Cu and Ni atoms and has an
FCC crystal structure.
¾At temperatures below about 1085ΣC, copper
and nickel are mutually soluble in each other in
the solid state for all compositions. This
complete solubility is explained by the fact
that both Cu and Ni have the same crystal
structure (FCC), nearly identical atomic radii
and electronegativities, and similar valences.
Phase Diagrams
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Phase Diagrams
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¾The Į phase is a substitutional solid solution
¾The copper²nickel system is termed isomorphous because of complete liquid and
solid solubility of the two components.
¾The line separating the L and Į+L phase fields is termed the liquidus line; the
liquid phase is present at all temperatures and compositions above this line.
¾The solidus line is located between the Į and Į+L regions, below which only the
solid Į phase exists.
Binary Isomorphous Systems
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¾The solidus and liquidus lines intersect at the two
For a binary system of known composition and
temperature at equilibrium, at least three kinds of information
are available:
composition extremes; these correspond to the melting
temperatures of the pure components.
1280ΣC
the left-hand temperature axis. Copper remains solid
until its melting temperature is reached.
¾The solid-to-liquid transformation takes place at the
melting temperature, and no further heating is possible
until this transformation has been completed.
50 wt% Ni²50 wt% Cu
¾For any composition other than pure components, this melting phenomenon
occurs over the range of temperatures between the solidus and liquidus lines;
both solid Į and liquid phases are in equilibrium within this temperature range.
¾For example, upon heating of an alloy of composition 50 wt% Ni²50 wt% Cu,
melting begins at approximately 1280ΣC; the amount of liquid phase continuously
increases with temperature until about 1320ΣC, at which point the alloy is
completely liquid.
Phase Diagrams
and nickel are 1085ΣC and 1453ΣC, respectively.
¾Heating pure copper corresponds to moving vertically up
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾For example, the melting temperatures of pure copper
1320ΣC
¾ the phases that are present,
¾ the compositions of these phases, and
¾ the percentages or fractions of the phases.
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Determination of Phases Present
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Figure: Reading the phase diagram of an alloy
system with complete solubility of the
components (solid solution)
¾The establishment of what phases are present is
relatively simple.
wt% Cu at 1100ΣC would be located at point A;
because this is within the Į region, only the single Į
phase will be present.
Phase Diagrams
¾For example, an alloy of composition 60 wt% Ni²40
ME 208 Materials Science II
just locates the temperature²composition
point on the diagram and notes the phase(s) with
which the corresponding phase field is labeled.
Phase Diagrams
ME 208 Materials Science II
¾One
¾However, a 35 wt% Ni²65 wt% Cu alloy at 1250ΣC
(point B) consists of both Į and liquid phases at
equilibrium.
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Isomorphous Binary Phase Diagram
L (liquid)
Cu-Ni
phase
diagram
1400
1300
Į
1200
(FCC solid
1100
1000
solution)
0
20
40
60
80
100 wt% Ni
‡([DPSOHV
A(1100ƒC, 60 wt% Ni):
1 phase: Į
B (1250ƒC, 35 wt% Ni):
2 phases: L + Į
T(ƒC)
1600
L (liquid)
1500
B (1250ž&
Isomorphous i.e.,
complete solubility of one
component in another; Į
phase field extends from
0 to 100 wt% Ni.
1500
‡5XOH,IZHNQRZT and Co, then we know: which phase(s) is (are) present.
Phase Diagrams
Phase Diagrams
ME 208 Materials Science II
‡6\VWHPLV
Binary: i.e., 2
components: Cu and Ni.
T(ƒC)
1600
ME 208 Materials Science II
‡3KDVHGLDJUDP
Cu-Ni system.
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Phase Diagrams: Determination of phase(s) present
1400
1300
Į
(FCC solid
solution)
1200
A(1100ž&
1100
1000
0
Cu-Ni
phase
diagram
20
40
60
80
100 wt% Ni
Determination of Phase Compositions
Determination of Phase Compositions
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¾For
an alloy having composition and
temperature located in a two-phase region,
the situation is more complicated.
¾The first step in the determination of phase
compositions is to locate the temperature²
composition point on the phase diagram.
¾In all two-phase regions, one may imagine a
series of horizontal lines, one at every
temperature; each of these is known as a tie
line, or sometimes as an isotherm.
trivial: the composition of this phase is simply the
same as the overall composition of the alloy.
¾For example, consider the 60 wt% Ni²40 wt%
Cu alloy at 1100ΣC (point A). At this composition
and temperature, only the Į phase is present,
having a composition of 60 wt% Ni²40 wt% Cu.
Phase Diagrams
¾If only one phase is present, the procedure is
ME 208 Materials Science II
phase regions.
Phase Diagrams
ME 208 Materials Science II
¾Different methods are used for single and two
¾These tie lines extend across the two-phase
region and terminate at the phase boundary
lines on either side. To compute the
equilibrium concentrations of the two phases,
the following procedure is used:
1. A tie line is constructed across the two-phase region at the temperature of the alloy.
2. The intersections of the tie line and the phase boundaries on either side are noted.
3. Perpendiculars are dropped from these intersections to the horizontal composition
axis, from which the composition of each of the respective phases is read.
Determination of Phase Compositions
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Phase Diagrams: Determination of phase compositions
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¾For example, consider again 35 wt% Ni²
65 wt% Cu alloy at 1250ΣC, located at point
B and lying within the Į+L region.
‡5XOH,IZHNQRZT and C0, then we can determine: the composition of each
phase.
Cu-Ni
¾The
of the tie line with the liquidus boundary
meets the composition axis at 31.5 wt% Ni²
68.5 wt% Cu, which is the composition of
the liquid phase, CL.
C0 =35 wt% Ni²65 wt% Cu at 1250ΣC
CL =31.5 wt% Ni²68.5 wt% Cu
Cߙ=42.5 wt% Ni²57.5 wt% Cu.
¾Likewise,
for
the
solidus²tie
line
intersection, we find a composition for the
Į solid-solution phase, Cߙ, of 42.5 wt% Ni²
57.5 wt% Cu.
Consider C0 = 35 wt% Ni
At TA = 1320ƒC:
Phase Diagrams
phase region.
¾The perpendicular from the intersection
‡([DPSOHV
ME 208 Materials Science II
¾The tie line is constructed across the Į+L
Phase Diagrams
ME 208 Materials Science II
problem is to determine the
composition (in wt% Ni and Cu) for both the
Į and L phases.
Only Liquid (L) present
CL = C0 ( = 35 wt% Ni)
At TD = 1190ƒC:
Only Solid (Į) present
CĴ = C0 ( = 35 wt% Ni)
At TB = 1250ƒC:
Both Į and L present
CL = C liquidus ( = 32 wt% Ni)
CĮ = C solidus ( = 43 wt% Ni)
system
T(ƒC)
A
TA
1300 L (liquid)
TB
1200
TD
20
tie line
B
D
Į
(solid)
30 35 40
50
32 C0
43 wt% Ni
CL
CĮ
Determination of Phase Amounts
Determination of Phase Amounts
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¾If the composition and temperature position is
located within a two-phase region, The tie line
must be used in conjunction with a procedure
that is often called the lever rule, which is
applied as follows:
¾The relative amounts (as fractions or as
region. Because only one phase is present, the
alloy is composed entirely of that phase, that
is, the phase fraction is 1.0, or, alternatively,
the percentage is 100%.
¾For the 60 wt% Ni²40 wt% Cu alloy at 1100ΣC
2. The overall alloy composition is located on the
tie line.
Phase Diagrams
¾The solution is obvious in the single-phase
1. The tie line is constructed across the twophase region at the temperature of the alloy.
ME 208 Materials Science II
Phase Diagrams
percentages) of the phases present at
equilibrium may also be computed with the aid
of phase diagrams.
ME 208 Materials Science II
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3. The fraction of one phase is computed by
taking the length of tie line from the overall
alloy composition to the phase boundary for
the other phase and dividing by the total tieline length.
(point A), only the Į phase is present; hence,
the alloy is completely, or 100% Į.
4. The fraction of the other phase is determined
in the same manner.
5. If phase percentages are desired, each phase
fraction is multiplied by 100.
Determination of Phase Amounts
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Determination of Phase Amounts
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¾Consider the example, in which at 1250ΣC both Į and
L phases are present for a 35 wt% Ni²65 wt% Cu
alloy (Point B).
¾When the composition axis is scaled in weight
product of each phase fraction and the total
alloy mass.
¾In the use of the lever rule, tie-line segment
lengths may be determined either by direct
measurement from the phase diagram using a
linear scale, preferably in millimeters, or by
subtracting compositions as taken from the
composition axis.
the Į and Liquid phases.
¾The tie line is constructed that was used for the
determination of Į and L phase compositions.
Phase Diagrams
¾The mass of each phase is computed from the
¾The problem is to compute the fraction of each of
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
percent, the phase fractions computed using
the lever rule are mass fractions, the mass (or
weight) of a specific phase divided by the total
alloy mass.
¾The overall alloy composition be located along the
tie line and denoted as C0, and let the mass fractions
be represented by WL and Wߙ for the respective
phases.
¾From the lever rule, WL may be computed according
to
or, by subtracting compositions,
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Phase Diagrams: Determination of phase weight fractions
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Determination of Phase Amounts
WL =
WĮ =
S
R + S
R
R + S
42,5 35
42,5 31,5
0.68
20
30
31,535
CL C0
40
fractions of phases in any two-phase region for a binary alloy if the
temperature and composition are known and if equilibrium has been
established.
¾Compositions of phases are expressed in terms of weight percents of
the components (e.g., wt% Cu, wt% Ni).
Phase Diagrams
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾The lever rule may be employed to determine the relative amounts or
‡5XOH,IZHNQRZT and C0, then can determine: the weight fraction of each
phase.
Cu-Ni system
‡([DPSOHV
T(ƒC)
Consider C0 = 35 wt% Ni
A
TA
tie line
At TA : Only Liquid (L) present
L (liquid)
1300
WL = 1.00, WĮ = 0
B
TB
At TD : Only Solid ( Į ) present
R S
Į
WL = 0, W Į = 1.00
(solid)
1200
D
At TB : Both Į and L present
TD
50
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¾At the solidification temperature, atoms
from the liquid such as molten metal, begin
to bond together and start to form
crystals.
Equilibrium Cooling
¾It
Phase Diagrams
¾The moment a crystal begins to grow is
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
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Nucleation and Growth of Crystals
Development of Microstructure in Isomorphous Alloys
very slowly, in that phase equilibrium is continuously
maintained.
extremes of which determine the compositions of the respective
phases.
or liquid phase), when a single phase exists, the alloy is completely that
phase. For a two-phase alloy, the lever rule is used, in which a ratio of
tie-line segment lengths is taken.
= 32
¾Firstly, treat the situation in which the cooling occurs
phase is the same as the total alloy composition.
¾If two phases are present, the tie line must be employed, the
¾With regard to fractional phase amounts (e.g., mass fraction of the Į
42,5
&Į wt% Ni
is informative to examine the development of
microstructure that occurs for Isomorphous alloys during
solidification.
¾For any alloy consisting of a single phase, the composition of that
know as nucleus and the point where it
occurs is the nucleation point.
¾When a metal begins to solidify, multiple
crystals begin to grow in the liquid. The
final sizes of the individual crystals depend
on the number of nucleation points.
¾The crystals increase in size by the
progressive addition of atoms and grow
until they impinge upon adjacent growing
crystal.
Figure.
a)Nucleation of crystals,
b) crystal growth,
c) irregular grains form as crystals grow
together,
d) grain boundaries
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Nucleation and Growth Transformation
¾Nucleation: The physical process by which a new phase is
produced in a material. In the case of solidification, this refers
to the formation of tiny stable solid particles in the liquid.
Phase Diagrams
size. In the case of solidification, this refers to the formation
of a stable solid particle as the liquid freezes.
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾Growth: The physical process by which a new phase increases in
Figure: Microstructure of polycrystalline iron
Equilibrium Cooling
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Equilibrium Cooling
¾Consider the copper²nickel system, an
alloy of composition 35 wt% Ni²65 wt% Cu,
as it is cooled from 1300ΣC.
Phase Diagrams
liquid (of composition 35 wt% Ni² 65 wt%
Cu)
and
has
the
microstructure
represented by the circle inset in the
figure.
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾At 1300ΣC, point a, the alloy is completely
cooling begins, no microstructural or
compositional changes will be realized until
reaching the Liquidus line (point b, ~1260ΣC).
¾At this point, the first solid Į begins to form,
¾Cooling of an alloy of this composition
corresponds to moving down the vertical
dashed line.
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¾As
which has a composition dictated by the tie line
drawn at this temperature (i.e., 46 wt% Ni²54 wt%
Cu); the composition of liquid is still approximately
35 wt% Ni²65 wt% Cu, which is different from
that of the solid Į.
¾With continued cooling, both compositions and
relative amounts of each of the phases will change.
¾ The compositions of the Liquid and Į phases will
follow the Liquidus and solidus lines, respectively.
Furthermore, the fraction of the Į phase will
increase with continued cooling.
¾The overall alloy composition (35 wt% Ni²65 wt%
35 wt% Ni²65 wt% Cu
Figure. Schematic representation of the development
of microstructure during the equilibrium solidification
of a 35 wt% Ni²65 wt% Cu alloy.
Cu) remains unchanged during cooling even though
there is a redistribution of copper and nickel
between the phases.
Equilibrium Cooling
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Development of Microstructure in Isomorphous Alloys$VVLVW3URI'U'XUPX
¾At 1250ΣC, point c, the compositions of the Liquid
Nonequilibrium Cooling
and Į phases are 32 wt% Ni²68 wt% Cu and 43
wt% Ni²57 wt% Cu, respectively.
¾Conditions of equilibrium solidification and the development of microstructures are
realized only for extremely slow cooling rates.
liquid solidifies; the final product is a
polycrystalline Į-phase solid solution that has a
uniform 35 wt% Ni²65 wt% Cu composition (point
e).
compositions of the liquid and solid phases in accordance with the phase diagram (i.e., with
the liquidus and solidus lines).
Phase Diagrams
¾Upon crossing the solidus line, this remaining
¾The reason for this changes in temperature, there must be readjustments in the
ME 208 Materials Science II
about 1220ΣC, point d; the composition of the solid
Į is approximately 35 wt% Ni²65 wt% Cu (the
overall alloy composition), whereas that of the last
remaining liquid is 24 wt% Ni²76 wt% Cu.
Phase Diagrams
ME 208 Materials Science II
¾The solidification process is virtually complete at
these compositional readjustments and maintenance of equilibrium;
microstructures other than those previously described develop.
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Nonequilibrium Cooling
¾Cooling from a temperature of about 1300ΣC; this is
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¾At point cŁ, the average composition of the solid Į
grains that have formed would be some volumeweighted average composition lying between 46 and
40 wt% Ni. For the sake of argument, let us take this
average composition to be 42 wt% Ni²58 wt% Cu.
¾At point bŁ (approximately 1260ΣC), Į-phase particles
¾Furthermore,
¾Because diffusion in the solid Į phase is relatively
slow, the Į phase formed at point bŁ has not changed
composition appreciably, that is, it is still about 46
wt% Ni, and the composition of the Į grains has
continuously changed with radial position, from 46
wt% Ni at grain centers to 40 wt% Ni at the outer
grain perimeters.
Phase Diagrams
liquid composition has shifted to 29 wt% Ni²71 wt%
Cu; at this temperature the composition of the Į
phase that solidified is 40 wt% Ni²60 wt% Cu.
ME 208 Materials Science II
¾Upon further cooling to point cŁ (about 1240ΣC), the
Phase Diagrams
ME 208 Materials Science II
consequently,
indicated by point aŁ in the liquid region. This liquid
has a composition of 35 wt% Ni²65 wt% Cu, and no
changes occur while cooling through the liquid phase
region.
begin to form, which, from the tie line constructed,
have a composition of 46 wt% Ni²54 wt% Cu.
35 wt% Ni²65 wt% Cu
¾Diffusion rates are especially low for the solid phase and, for both phases, decrease with
¾In virtually all practical solidification situations, cooling rates are much too rapid to allow
or compositional alterations.
Figure. The development of microstructure
during the nonequilibrium solidification of a 35
wt% Ni²65 wt% Cu alloy.
and liquid phases and also across the solid²liquid interface. Because diffusion is a timedependent phenomenon to maintain equilibrium during cooling, sufficient time must be
allowed at each temperature for the appropriate compositional readjustments.
diminishing temperature.
¾Subsequent cooling produces no microstructural
Nonequilibrium Cooling
¾These readjustments are accomplished by diffusional processes, diffusion in both solid
on
the
basis
of
lever-rule
computations, a greater proportion of liquid is
present for these nonequilibrium conditions than for
equilibrium cooling.
¾The implication of this nonequilibrium solidification
phenomenon is that the solidus line on the phase
diagram has been shifted to higher Ni contents, to
the average compositions of the Į phase (e.g., 42 wt%
Ni at 1240ΣC), and is represented by the dashed line.
¾ There is no comparable alteration of the liquidus
line inasmuch as it is assumed that equilibrium is
maintained in the liquid phase during cooling because
of sufficiently rapid diffusion rates.
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Nonequilibrium Cooling
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¾The degree of displacement of the nonequilibrium solidus curve from the equilibrium
¾At point dŁ (‫׽‬1220ΣC) and for equilibrium cooling
one depends on the rate of cooling; the slower the cooling rate, the smaller this
displacement, the difference between the equilibrium solidus and average solid
composition is lower. Furthermore, if the diffusion rate in the solid phase increases,
this displacement decreases.
rates, solidification should be completed.
¾For this nonequilibrium situation, there is still an
finally
reaches
¾The composition of the last Į phase to solidify at
this point is about 31 wt% Ni; the average
composition of the Į phase at complete solidification
is 35 wt% Ni.
under nonequilibrium conditions.
Phase Diagrams
solidification
completion at point eŁ (‫׽‬1205ΣC).
¾There are some important consequences for isomorphous alloys that have solidified
ME 208 Materials Science II
¾Nonequilibrium
Phase Diagrams
ME 208 Materials Science II
appreciable proportion of liquid remaining, and the Į
phase that is forming has a composition of 35 wt%
Ni; also, the average Į-phase composition at this
point is 38 wt% Ni. (Average of 35 and 40)
¾The inset at point fŁ shows the microstructure of
¾The distribution of the two elements within the grains is nonuniform, a phenomenon
termed segregation, that is, concentration gradients are established across the grains.
¾The center of each grain, which is the first part to freeze, is rich in the high-melting
element (e.g., nickel for this Cu²Ni system), whereas the concentration of the lowmelting element increases with position from this region to the grain boundary. This is
termed a cored structure, which gives rise to less than the optimal properties.
¾As a casting having a cored structure is reheated, grain boundary regions will melt
the totally solid material.
first because they are richer in the low-melting component. This produces a sudden
loss in mechanical integrity due to the thin liquid film that separates the grains.
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Cored vs Equilibrium Structures
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‡&Į changes as we solidify.
‡&X-Ni case:
First Į to solidify has CĮ = 46 wt% Ni.
Last Į to solidify has CĮ = 35 wt% Ni.
¾The mechanical properties of solid isomorphous alloys are affected by
¾ Slow rate of cooling:
¾ Fast rate of cooling:
¾For all temperatures and compositions below the melting temperature of the
Cored structure
lowest melting component, only a single solid phase exists. Therefore, each
component experiences solid-solution strengthening or an increase in strength and
hardness by additions of the other component.
First Į to solidify:
46 wt% Ni
Last Į to solidify:
< 35 wt% Ni
Phase Diagrams
Phase Diagrams
Uniform CĮ:
35 wt% Ni
composition as other structural variables (e.g., grain size) are held constant.
ME 208 Materials Science II
Equilibrium structure
ME 208 Materials Science II
Mechanical Properties of Isomorphous Alloys
TS for pure Ni
TS for pure Cu
¾ Coring may be eliminated by a homogenization heat treatment carried out at a temperature
below the solidus point for the particular alloy composition.
¾ During this process, atomic diffusion occurs which produces compositionally homogeneous
grains.
Figure. For the copper²nickel system,
(a) tensile strength versus composition and
(b) ductility (%EL) versus composition at
room temperature.
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How to build a phase diagram
Binary Eutectic Systems
¾Binary: 2 component
¾They
make great solders. Tin-Lead
and
copper²silver system can be
example.
¾ The composition of an alloy is given in the form
A-x%B. For example, Cu-20%Al is 80% copper
and 20% aluminium.
Phase Diagrams
melting point of the alloy at the
eutectic point composition is lower
than the melting point of the individual
components.
ME 208 Materials Science II
Phase Diagrams
¾ A binary phase diagram shows the phases
formed in differing mixtures of two elements
over a range of temperatures.
¾ Compositions run from 100% Element A on the
left of the diagram, through all possible
mixtures, to 100% Element B on the right.
¾Eutectic-Easily Melted: The minimum
ME 208 Materials Science II
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¾ Weight percentages are often used to specify
the proportions of the alloying elements, but
atomic percent may be used. The type of
percentage is specified e.g.
¾ Cu-20wt%Al for weight percentages and
¾ Cu-20at%Al for atomic percentages.
How to build a phase diagram
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How to build a phase diagram
¾ Sometimes there is a mixture of the
constituent
elements
which
produces
solidification at a single temperature like a pure
element. This is called the eutectic point. The
eutectic point can be found experimentally by
plotting cooling rates over ranges of alloy
composition.
Phase Diagrams
¾ At each end of the phase diagram only one of
the elements is present (100% A or 100% B) and
therefore a specific melting point exists.
¾ By cooling alloys from the liquid state and
recording their cooling rates, the temperature
at which they start to solidify can be
determined and then plotted on the phase
diagram.
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾ Alloys tend to solidify over a temperature
range, rather than at a specific temperature
like pure elements.
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¾ If enough experiments are performed over a
range of compositions, a start of solidification
curve can be plotted onto the phase diagram.
¾ This curve will join the three single
solidification points and is called the liquidus
line.
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¾ At alloy compositions and temperatures
between the start of solidification and the
point at which it becomes fully solid (the
eutectic temperature) a mushy mix of either
alpha or beta will exist as solid lumps with a
liquid mixture of A and B. These partially solid
regions are marked on the phase diagram.
¾ The region below the eutectic line, and outside
the solid solution region will be a solid mixture
of alpha and beta.
¾ Some elements that are alloyed have zero solid
solubility; a good example is Al - Si alloys, where
aluminium has zero solid solubility in silicon.
Binary Eutectic Systems
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Binary Eutectic Systems
¾Common and relatively simple phase
¾Three single-phase regions are found
respectively.
¾The solubility in each of these solid phases is limited, at any temperature below
line BEG only a limited concentration of silver dissolves in copper (for the Į phase),
and similarly for copper in silver (for the ߚ phase).
Phase Diagrams
Figure. The copper²silver phase diagram.
¾The ߚ-phase solid solution has an FCC structure, but copper is the solute.
¾Pure copper and pure silver are also considered to be Į and ߚ phases,
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
on the diagram: Į ߚ, and liquid.
copper; it has silver as the solute
component and an FCC crystal structure.
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¾The solubility limit for the Į phase
corresponds to the boundary line,
labeled CBA, between the Į/(Įߚ) and
Į Į/) phase regions; it increases with
temperature to a maximum (8.0 wt% Ag
at 779ΣC) at point B and decreases back
to zero at the melting temperature of
pure copper, point A (1085ΣC).
diagram found for binary alloys for the
Copper²Silver system known as a binary
eutectic phase diagram.
¾The Į phase is a solid solution rich in
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¾ If an alloy's composition does not place within
the small solid solution regions at either side of
the phase diagram, the alloy will become fully
solid at the eutectic temperature.
Phase Diagrams
¾ The extent of the solid solubility region can be
plotted onto the phase diagram and labelled
appropriately. A solid solution of B in A (i.e.
mostly A) is called alpha and a solid solution of A
in B (i.e. mostly B) is called beta.
How to build a phase diagram
ME 208 Materials Science II
¾ In the same way, sugar dissolves into hot tea (a
liquid solution), it is possible for one element to
dissolve in another, both remain in the solid
state. This is called solid solubility and is
characteristically up to a few percent by
weight. This solubility limit will normally change
with temperature.
Phase Diagrams
ME 208 Materials Science II
How to build a phase diagram
¾At temperatures below 779ΣC, the
Figure. The copper²silver phase diagram.
solid solubility limit line separating the Į
and Įߚ phase regions is termed a solvus
line; the boundary AB between the Į and
Į/ fields is the solidus line.
¾For the ߚ phase, both solvus and solidus lines also exist, HG and GF, respectively.
¾The maximum solubility of copper in the ߚ phase, point G (8.8 wt% Cu), occurs at
779ΣC. This horizontal line BEG may also be considered a solidus line; it represents
the lowest temperature at which a liquid phase may exist for any copper²silver
alloy at equilibrium.
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Binary Eutectic Systems
Ex.: Cu-Ag system
‡VLQJOHSKDVHUHJLRQV
(L, Į, ǀ)
¾There
¾Compositions and relative amounts for
ǀ: mostly Ag
Phase Diagrams
Figure. The copper²silver phase diagram.
coexist for all compositions and
temperatures within the Įߚ phase
field; the ĮL and ߚ+L phases also
coexist in their respective phase
regions.
‡/LPLWHGVROXELOLW\
Į: mostly Cu
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
are also three two-phase
regions found for the copper²silver
system: Į/, ߚ+L, and Įߚ.
¾The Į and ߚ phase solid solutions
L+ Į
71.9 91.2
600
Į ȕ
400
200
0
20
¾Liquidus lines meet at the point E on
the phase diagram, which is designated
by composition CE and temperature TE;
the values for these two parameters are
71.9 wt% Ag and 779ΣC, respectively.
40
60 CE 80
100
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changes temperature in passing through TE;
¾ Upon cooling, a liquid phase is transformed into the two solid Į and ߚ
Phase Diagrams
introduction of copper reduces the
temperature of complete melting along
the other liquidus line, FE.
L+ȕ ȕ
779ƒC
8.0
¾ An important reaction occurs for an alloy of composition CE as it
ME 208 Materials Science II
¾The same may be said for silver: the
Phase Diagrams
Į
TE 800
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temperature at which the alloys become
totally liquid decreases along the
liquidus line, line AE; thus, the melting
temperature of copper is lowered by
silver additions.
ME 208 Materials Science II
‡CE : Composition at
temperature TE
L (liquid)
1000
¾ Solidus Line: Boundary between Į, /Į
¾ Liquidus Line: Boundary between L, /Į
¾ Solvus Line: Boundary between Į Į+ȕ
¾ Eutectic Isotherm Line: Boundary between Įȕ, L+Į and L+ȕ
¾As silver is added to copper, the
Figure. The copper²silver phase diagram.
‡TE : No liquid below TE
Cu-Ag system
T(ƒC)
1200
C, wt% Ag
the phases may be determined using
tie lines and the lever rule.
Binary Eutectic Systems
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Binary Eutectic Systems
phases at the temperature TE; the opposite reaction occurs upon
heating. This is called a eutectic reaction (eutectic means ´HDVLO\
PHOWHGµ and CE and TE represent the eutectic composition and
temperature; CߙE and CߚE are the respective compositions of the Į
and ߚ phases at TE.
¾ For the copper²silver system, the eutectic reaction may be written
as follows:
¾ The horizontal solidus line at TE is called the eutectic isotherm.
Development of Microstructure in Eutectic Alloys
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Development of Microstructure in Eutectic Alloys
¾Consider an alloy of composition C1 as it is slowly
¾ Depending on composition, several different
cooled from a temperature within the liquid-phase
region, say, 350ΣC; this corresponds to moving down the
line wwŁ.
types of microstructures are possible for
the slow cooling of alloys belonging to binary
eutectic systems.
¾The alloy remains totally liquid and of composition C1
alloys containing between 0 and about 2 wt% Sn
(for the Į-phase solid solution) and also between
approximately 99 wt% Sn and pure tin(for the ߚ
phase).
until we cross the liquidus line at approximately 330ΣC,
at which time the solid Į phase begins to form.
solidification proceeds with continued cooling, more of
the solid Į forms.
¾Furthermore, liquid and solid phase compositions are
different, which follow along the liquidus and solidus
phase boundaries.
¾Solidification reaches completion at the point where
Figure. The equilibrium microstructures for a
lead²tin alloy of composition C1, as it is cooled
from the liquid-phase region.
Development of Microstructure in Eutectic Alloys
¾While passing through this narrow Į/ phase region,
Phase Diagrams
¾For the lead²tin system, this includes lead-rich
ME 208 Materials Science II
between a pure component and the maximum
solid solubility for that component at room
temperature (20ΣC).
Phase Diagrams
ME 208 Materials Science II
¾The first case is for compositions ranging
Figure. The equilibrium microstructures for a
lead²tin alloy of composition C1, as it is cooled
from the liquid-phase region.
wwŁ crosses the solidus line. The resulting alloy is
polycrystalline with a uniform composition of C1, and no
subsequent changes occur upon cooling to room
temperature (point c).
Development of Microstructure in Eutectic Alloys
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¾The second case considered is for compositions that range
between the room temperature solubility limit and the
maximum solid solubility at the eutectic temperature.
¾The third case involves solidification of the
¾Let us examine an alloy of composition C2 as it is cooled along
eutectic composition, 61.9 wt% Sn (C3).
the vertical line xxŁ.
¾Consider an alloy having this composition that is
above the solvus intersection, (point f)
microstructure consists of Į grains of composition C2.
the
¾Upon crossing the solvus line, the Į solid solubility is
exceeded, which results in the formation of small ߚ-phase
particles; these are indicated in the microstructure (point g).
¾With continued cooling, these particles grow in size because
the mass fraction of the ߚ phase increases slightly with
decreasing temperature.
Figure. The equilibrium microstructures
for a lead²tin alloy of composition C2, as
it is cooled from the liquid-phase
region.
¾As the temperature is lowered, no changes occur
Phase Diagrams
¾Just
cooled from a temperature within the liquid-phase
region (e.g., 250ΣC) down the line yyŁ.
ME 208 Materials Science II
that occur are similar to the previous case as we pass through
the corresponding phase regions (at points d, e, and f ).
Phase Diagrams
ME 208 Materials Science II
¾Down to the intersection of xxŁ and the solvus line, changes
until we reach the eutectic temperature, 183ΣC.
¾Upon crossing the eutectic isotherm, the liquid
transforms into the two Į and ߚ phases.
¾This transformation may be represented by the
Figure. The equilibrium microstructures for a
lead²tin alloy of eutectic composition C3 above
and below the eutectic temperature.
reaction in which the Į and ߚ phase compositions
are dictated by the eutectic isotherm end points.
Development of Microstructure in Eutectic Alloys
Development of Microstructure in Eutectic Alloys
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¾During this transformation, there must be a
¾The
microstructural change that accompanies
eutectic transformation, which shows the Į±ߚ layered
eutectic growing into and replacing the liquid phase.
redistribution of the lead and tin components
because the Į and ߚ phases have different
compositions, neither of which is the same as
that of the liquid. This redistribution is
accomplished by atomic diffusion.
¾The process of the redistribution of lead and tin
occurs by diffusion in the liquid just ahead of the
eutectic²liquid interface.
called
a
eutectic
structure
characteristic of this reaction.
and
is
Phase Diagrams
¾This microstructure, represented at point i, is
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾The microstructure of the solid that results
from
this
transformation
consists
of
alternating layers (sometimes called lamellae)
of the Į and ߚ phases that form simultaneously
during the transformation.
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¾The arrows indicate the directions of diffusion of
Figure. The formation of the eutectic
structure for the lead²tin system.
Directions of diffusion of tin and lead
atoms are indicated by blue and red
arrows, respectively.
lead and tin atoms; lead atoms diffuse toward the Įphase layers because this Į phase is lead rich (18.3
wt% Sn²81.7 wt% Pb); conversely, the direction of
diffusion of tin is in the direction of the ߚ, tin-rich
(97.8 wt% Sn²2.2 wt% Pb) layers.
¾The eutectic structure forms in alternating layers
¾Subsequent cooling of the alloy from just
because, for this lamellar configuration, atomic
diffusion of lead and tin need occur over only
relatively short distances.
below the eutectic to room temperature
results
in
only
minor
microstructural
alterations.
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Development of Microstructure in Eutectic Alloys
¾Consider the composition C4, which lies to the
Development of Microstructure in Eutectic Alloys
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left of the eutectic; as the temperature is
lowered, the line zzŁ, beginning at point j.
Figure. The equilibrium microstructures for a
lead²tin alloy of composition C4 as it is cooled
from the liquid-phase region.
eutectic, the liquid phase transforms into the
eutectic structure (i.e., alternating Į and ߚ
lamellae); insignificant changes will occur with the
Į phase that formed during cooling through the
Į/ region.
eutectic structure and phase that formed
while cooling through the Į/ phase field.
Phase Diagrams
¾As the temperature is lowered to just below the
¾The Į phase is present both in the
ME 208 Materials Science II
j and l is similar to that for the second case, just
prior to crossing the eutectic isotherm (point l),
the Į and liquid phases are present with
compositions of approximately 18.3 and 61.9 wt%
Sn, respectively, as determined from the
appropriate tie line.
Phase Diagrams
ME 208 Materials Science II
¾The microstructural development between points
¾To distinguish one Į from the other, that
which resides in the eutectic structure is
called eutectic Į, whereas the other that
formed prior to crossing the eutectic
isotherm is termed primary Į.
Figure. The equilibrium microstructures for a
lead²tin alloy of composition C4 as it is cooled
from the liquid-phase region.
Development of Microstructure in Eutectic Alloys
Development of Microstructure in Eutectic Alloys
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sometimes convenient to use the term
microconstituent, an element of the
microstructure having an identifiable and
characteristic structure.
Phase Diagrams
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
¾In dealing with microstructures, it is
microconstituents, primary
eutectic structure.
(Pb-Sn System)
300
Į
200
¾Because the eutectic microconstituent always forms
L+ Į
L+ȕ ȕ
from the liquid having the eutectic composition, this
microconstituent may be assumed to have a
composition of 61.9 wt% Sn.
Į +ȕ
Hypoeutectic: C0 = 50 wt% Sn
Į
Į
Į
Į
60
80
Eutectic
61.9
100
Hypereutectic: C0 = 80 wt% Sn
Eutectic: C0 = 61.9 wt% Sn
ȕ
Į
ȕ
Į
175 ȝm
C, wt% Sn
ȕ
ȕ ȕ
ȕ
160 ȝm
Eutectic micro-constituent
¾The lever rule is applied using a tie line between the
Phase Diagrams
40
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
100
20
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both eutectic and primary Į microconstituents.
TE
0
the
¾It is possible to compute the relative amounts of
L
T(ƒC)
and
eutectic
structure
is
a
microconstituent even though it is a
mixture of two phases, because it has a
distinct lamellar structure with a fixed
ratio of the two phases.
Development of Microstructure in Eutectic Alloys
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Į
¾The
Figure. The equilibrium microstructures for a
lead²tin alloy of composition C4 as it is cooled
from the liquid-phase region.
Figure. The microstructure of a lead²tin alloy of composition 50 wt% Sn²50 wt% Pb. This
microstructure is composed of a primary lead-rich Į phase (large dark regions) within a lamellar
eutectic structure consisting of a tin-rich ߚ phase (light layers) and a lead-rich Į phase (dark layers).
400õ.
Hypoeutectic & Hypereutectic
¾For example, in the point m, there are two
Į± Įߚ) phase boundary (18.3 wt% Sn) and the
eutectic composition.
¾For example, consider the alloy of composition CŁ4.
Figure. The lead²tin phase diagram used in
computations for relative amounts of primary Į
and eutectic microconstituents for an alloy of
composition CŁ4.
The fraction of the eutectic microconstituent We is
just the same as the fraction of liquid WL from which
it transforms, or
Eutectoid Reactions
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¾The fractions of total Į, Wߙ (both eutectic and
primary), and also of total ߚ, Wߚ, are determined by
use of the lever rule and a tie line that extends
entirely across the Į+ߚ phase field. Again, for an alloy
having composition CŁ4,
Phase Diagrams
points involving three different phases are found
for some alloy systems.
¾One of these occurs for the copper²zinc system
at 560ΣC and 74 wt% Zn²26 wt% Cu.
¾Upon cooling, a solid ߜ phase transforms into
two other solid phases (Ȗ and İ) according to the
reaction
ME 208 Materials Science II
¾In addition to the eutectic, other invariant
of the Į phase that existed prior to the eutectic
transformation,
Peritectic Reactions
reaction, and the invariant point (point E) and the horizontal tie line at 560ΣC are termed
the eutectoid and eutectoid isotherm, respectively.
¾The feature distinguishing eutectoid from eutectic is that one solid phase instead of a
liquid transforms into two other solid phases at a single temperature.
¾A eutectoid reaction found in the iron²carbon system is very important in the heat
treating of steels.
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Eutectic, Eutectoid, & Peritectic
¾The peritectic reaction is another invariant
¾One of the latter peritectics exists at about 97 wt% Zn and 435ΣC, where the Ș phase,
when heated, transforms into İ and liquid phases.
¾Three other peritectics are found for the Cu²Zn system, the reactions of which involve ߚ
, ߜ, and Ȗ intermediate solid solutions as the low-temperature phases that transform upon
heating.
Phase Diagrams
Figure. A region of the copper²zinc phase diagram
Show eutectoid peritectic invariant points,
labeled P (598ƒC, 78.6 wt% Zn).
heat
ME 208 Materials Science II
phase transforms into a liquid phase and
another solid phase.
¾A peritectic exists for the copper²zinc
system (point P) at 598ΣC and 78.6 wt% Zn²
21.4 wt% Cu; this reaction is as follows:
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¾ Eutectic - liquid transforms to two solid phases
L cool Į + ȕ
(For Pb-Sn, 183㼻C, 61.9 wt% Sn)
reaction involving three phases at equilibrium.
¾With this reaction, upon heating, one solid
Phase Diagrams
Figure. A region of the copper²zinc phase diagram
Show eutectoid invariant points, labeled E (560ƒC,
74 wt% Zn).
¾The reverse reaction occurs upon heating. It is called a eutectoid (or eutectic-like)
and
ME 208 Materials Science II
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¾The fraction of primary Į, WߙŁ, is just the fraction
Phase Diagrams
ME 208 Materials Science II
Development of Microstructure in Eutectic Alloys
¾ Eutectoid ² one solid phase transforms to two other solid phases
cool
S1+S3
S2
intermetallic compound - cementite
Ȗ
heat
cool
heat
Į + Fe3C (For Fe-C, 727ƒC, 0.76 wt% C)
¾ Peritectic - liquid and one solid phase transform to a second solid phase
S1 + L cool S2
heat
į + L cool Ȗ
heat
(For Fe-C, 1493ƒC, 0.16 wt% C)
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Eutectoid & Peritectic
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Ternary Phase Diagrams
Peritectic transformation Ȗ + L
Peritectic transformation į + L
į
¾ Phase diagrams have also been determined for metallic (as well
İ
as ceramic) systems containing more than two components;
however, their representation and interpretation can be
exceedingly complex.
Eutectoid transformation
į
Ȗ+İ
¾A
Phase Diagrams
ME 208 Materials Science II
Phase Diagrams
ME 208 Materials Science II
Cu-Zn Phase diagram
ternary, or three-component, composition²temperature
phase diagram in its entirety is depicted by a threedimensional model.