MSE 260 PHASE TRANSFORMATIONS Dr. Emmanuel Gikunoo Department of - - PowerPoint PPT Presentation

MSE 260 PHASE TRANSFORMATIONS

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• Dr. Emmanuel Gikunoo

Department of Materials Engineering

Second Semester 2019/2020 Mondays and Fridays 08:00 – 09:55

COURSE INFORMATION

• Lecturer: Dr. Emmanuel Gikunoo

 Office : 321 New Block  Email: egikunoo.soe@knust.edu.gh  Lecture Hours: Mondays 08:00 – 09:55 (Metallurgical) Fridays 08:00 – 09:55 (Materials)

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• Website: https://egikunoo.wordpress.com
• T

.A: Miss Stefania Akromah

 Email: stefania.akromah@yahoo.com

COURSE OBJECTIVES

• Develop an understanding of why materials and

microstructures undergo changes

• Provide an understanding of how diffusion enables

changes in the chemical distribution and microstructure of materials

• Formulate and discuss a variety of phase

transformations

• Discuss the effects of temperature and driving force
• n the nature of the transformation and its impact
• n the resulting microstructure

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Why Study Phase Transformation

• A phase refers to a physically homogeneous state of matter where

the phase has a certain chemical composition, and a distinct type

• f atomic bonding and arrangement of elements.
• Phases are distinct materials that are composed of the elements in

an alloy.

• Forming one or more phases from a different phase is called a

phase transformation.

• Phase transformation is a change from one state (solid, liquid, gas,
• r plasma) to another without a change in chemical composition.
• It therefore takes place by one of the three routes: diffusion,

interface-controlled, and diffusionless.

• Phase transformation have a major impact on vital engineering

aspects of the material behaviour such as ductility, strength, and formability.

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Why Study Phase Transformation

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Solid Liquid Gas Plasma Solid Melting Sublimation Liquid Freezing Vaporization Gas Deposition Condensation Ionisation Plasma Recombination

Phase transitions of matter

Why Study Phase Transformation

• The development of a set of desirable mechanical properties for

a material often results from a phase transformation which is a wrought by a heat treatment.

• The time and temperature dependencies of some phase

transformations are conveniently represented on modified phase diagrams.

• This shows that the desirable mechanical properties of a material

can be obtained as a result of phase transformations using heat treatment processes.

• It is important to know how to use these phase diagrams in
• rder to design a heat treatment procedure for some alloys that

will yield the desired room-temperature mechanical properties.

• T

ensile strength of iron-carbon alloy of eutectoid composition can be varied between 700 MPa and 2000 MPa depending on heat treatment employed.

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Phase Diagram for Water Three Phases

• 1. Solid
• 2. Liquid
• 3. Vapour

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Classifications of Phase Diagram

1) Diffusion-dependent transformation (Simple)  No change in number of composition of the phases present  Solidification of a pure metal  Allotropic transformations  Recrystallisation and grain growth 2) Diffusion-dependent transformation  Some alternation in phase compositions  Often alternation in the number of phases present  Final microstructure ordinarily consists of 2 phases  Eutectoid and other three phase reactions 3) Diffusionless transformation  Metastable phase is produced  Martensitic transformation in some steel alloys

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Polymorphism of Allotropy

• Metals exist in more than one crystalline form
• Change of these forms is called Allotropic T

ransformation

• Iron exists in both BCC and FCC form depending on the

temperature

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Allotropy of Iron

Phase diagram of pure Fe

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Cooling curve of pure Fe

Crystal Structures

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Atomic Packing Factors

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MSE 260 Phase Transformations (2, 0, 2)

• Fundamentals of phase changes: definitions,

thermodynamics of phase changes, Gibbs phase rule, free energy and stability of phase changes

• Phase diagrams of pure substances, binary

isomorphous systems with special emphasis on the Fe – C system. Introduction to ceramic and ternary phase diagrams.

• Phase transformations: Kinds, kinetic and

thermodynamic aspects of phase transformations, thermodynamic classification, structural classification, and phase transformation in different crystal structures

Course Content

• William D. Callister, Jr., Materials Science and Engineering – An

Introduction, Ninth John Wiley And Sons, USA (2015).

• Donald R. Askeland And Pradeep P

. Phule, The Science and Engineering of Materials, Nelson Education, USA (2015).

• David A. Porter, Kenneth E. Easterling, And Mohamed Y

. Sherif, Phase Transformations in Metals and Alloys, 3rd Edition, CRC Press, (2009).

• Class Presentations
• Related Online Materials

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Suggested Reading

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HOMEWORK

• Homework will be assigned roughly once a week.
• You may discuss homework with fellow classmates and

this is encouraged. However, you are expected to individually write up your solutions.

• No LATE homework will be accepted.
• Look over the marked homework as soon as it is
• returned. If you detect mistakes in the marking, notify

your lecturer or sometimes the T .A. Immediately. Homework scores will only be changed during the first two weeks after they have been returned!!!

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• ATTENDANCE IS COMPULSORY and you are required to sign

at each class section.

• Only those with tangible permission will be allowed to miss a
• class. Permissions will only be granted BEFORE the class.
• Classwork/homework submitted after the deadline will not be

accepted.

• Students are not allowed to leave the room after lectures

have commenced. Where it is VERY necessary you leave, permission needs to be granted by the lecturer.

• All ELECTRONIC APPLIANCES must be turned off and stored

away (should not be seen) during all lectures. Failure will lead to CONFISCATION. They will only be released at the end of the semester. NO excuses will be allowed.

Class Policy

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Quizzes 10 Assignments 5 MidSem Exam 15 Final Exam 70 Total 100

Grading

DEFINITIONS AND BASIC CONCEPTS

• Homogeneous System – a system in which every property of

the system is constant irrespective of the coordinates of the system.

• Phase – a portion of a system that has uniform physical and

chemical characteristics

• A single phase system is called homogenous system
• Systems with two or more phases are called mixtures or

heterogeneous systems. At least one property is a discontinuous function with the coordinates

• Solvent and Solute – a solvent is the host or major component

in solution and the solute is the minor component.

• A phase of a thermodynamic system and the states of matter

have uniform physical properties.

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DEFINITIONS AND BASIC CONCEPTS

• System – some portion of the universe that you wish to study
• Surroundings – the adjacent part of the universe outside the

system

• Closed system – only exchange of mechanical and thermal

energy, no mass exchange.

• Open system – exchange of energies and mass
• Degrees of freedom – the number of variables to define a

system in a phase diagram

• Intensive properties – P, T, pH, Eh (materials variables)
• Extensive properties – V, m, partial pressure

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DEFINITIONS AND BASIC CONCEPTS

• A eutectic transformation, is one in which a two component

single phase liquid is cooled and transforms into two solid

• phases. The same process, but beginning with a solid instead of

a liquid is called a eutectoid transformation.

• Liquid crystals (LCs) are a state of matter which has properties

between those of conventional liquids and those of solid crystals

• A diffusionless transformation is a phase change that occurs

without the long-range diffusion of atoms but rather by some form of cooperative, homogeneous movement of many atoms that results in a change in crystal structure.

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• Component: The elements or compounds which are present in the

alloy (e.g., Al and Cu)

• Solubility limit of a component in a phase is the maximum amount
• f the component that can be dissolved in it. Example, alcohol has

unlimited solubility in water, sugar has limited solubility, and oil is insoluble

• Phase

 The physically and chemically distinct material regions that form (e.g.  and )  A material may undergo various phase changes during processing.  A phase change may include melting, vaporization, sublimation, transformation, crystallization, or the chemical formation of a compound

COMPONENTS AND PHASES

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 (darker phase)  (lighter phase)

Figure 1. Aluminum – copper alloy

• When a system is in equilibrium, its free energy is at a minimum

under some specified conditions of temperature, pressure, and composition.

• Hence a system in equilibrium has uniform temperature and

pressure throughout. The chemical potential or vapour pressure

• f each constituent should also be the same in every phase
• For a one component system involving two phases (, ),

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THERMODYNAMICS OF PHASE CHANGES

For equilibrium to be achieved,

 (T, p, )  (T, p, ) T = T; p = p; and  = ,

• Chemical potential plays a vital role in phase and chemical

equilibrium considerations. It is defined as the free energy per mole of a pure substance  = f (T, p, phase)

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THERMODYNAMICS OF PHASE CHANGES

From definition,  = G, where g is the molar free energy of the  phase Similarly,  = G At equilibrium and from the expression, dG = – sdT + vdP dG = – sdT + vdP = dG = – sdT + vdP Or, (v – v)dP = (s – s)dT

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THERMODYNAMICS OF PHASE CHANGES

For isothermal transformations and at equilibrium, g = h – Ts = 0 where h mostly represents the latent heat of transformation Hence, This is known as the Clausius–Clayperon equation The equation shows the relationship between pressure and temperature at which phases  and  exist in equilibrium. It also shows the enthalpy and volume changes that accompany such changes

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HEAT EFFECTS ACCOMPANYING PHASE CHANGES OF PURE SUBSTANCES

Clausius–Clayperon equation But Hence approximate relation (Clausius – Clapeyron equation)

𝑤 𝑤 2 𝑤

where the

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Gibb’s Phase Rule

• Gibb’s phase rule describes the thermodynamic state of a material.
• It also states the degree of freedom available to describe a

particular system with various phases and substances

F = C – P + v

F = number of degrees of freedom

The number of variables to define a system in a phase diagram

P = number of phases Phases are mechanically separable constituents C = minimum number of components chemical constituents that must be specified in order to define all phases

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Gibb’s Phase Rule

F = C – P + v F = number of degrees of freedom The number of variables to define a system in a phase diagram P = number of phases Phases are mechanically separable constituents C = minimum number of components chemical constituents that must be specified in order to define all phases v = intensive properties or materials variables P/T and pH/Eh diagrams = 2

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Gibb’s Phase Rule

• Gibbs phase rule works best in (constructing) a phase diagram.

And those are usually 2-dimensional - with pressure along one axis and temperature the other. So the "2" simply reflects that 2 dimensionality.

• At 2 degrees of freedom, there are no constraints and the system

can change either pressure or temperature and be stable without a phase transition.

• If you have 1 degree of freedom, then you likely to have a

constraint

• These are not really constants, but if the degrees of freedom is

0, then they are ... "fixed‘' – or better yet "constrained".

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1. It is applicable to both physical and chemical equilibria. 2. It requires no information regarding molecular/microstructure, since it is applicable to macroscopic systems. 3. It is a convenient method of classifying equilibrium states in terms of phases, components and degrees of freedom. 4. It helps us to predict the behaviour of a system, under different sets of variables. 5. It indicates that different systems with same degree of freedom behave similarly. 6. It helps in deciding whether under a given set of conditions: a) various substances would exist together in equilibrium, or b) some of the substances present would be interconverted,

• r

c) some of the substances present would be eliminated.

Merits of the Phase Rule

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1. It can be only be applied to systems in equilibrium. Consequently, it is of little value in case of very slow equilibrium state attaining system. 2. It applies only to a single equilibrium system; and provide no information regarding any other possible equilibria in the system. 3. Phases existing in the equilibrium state must be carefully stated, since it considers only the number of phases, rather than their

• amounts. Thus even if a trace of phase is present, it accounts

towards the total number of phases. 4. All phases of the system must be present simultaneously under the identical conditions of temperature and pressure. 5. Solid and liquid phases must not be in finely-divided state;

• therwise deviations will occur.

Limitations of Phase Rule

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Phase Diagrams

• A phase is a state of matter with the following characteristics:

 It has the same structure or atomic arrangement throughout  It has roughly the same composition and properties throughout  There exists a definite interface between it and its surroundings or adjoining phases

• A phase diagram is a graphical representation of the phases that

are present in a material at various temperatures, pressures and compositions

 It usually describes the equilibrium conditions  Sometimes non-equilibrium conditions are also shown when well known.  It indicates the melting/solidification temperatures of the constituents  It indicates the compositions of alloys where solidification begins and the temperature range over which it occurs

• Phase transformation – is an alteration in the number and/or

character of the phases in the system

Phase Diagrams: The diagram representing conditions of temperature, pressure and composition at which one or more phases exit together. Phase Diagram of Water System:

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Phase Diagrams

Pressure Pc Temperature Tc Liquid (1 phase) Vapor (1 phase) Solid (1 phase) Sublimation Curve (2 phases) Triple Point (3 phases) Vapor Pressure Curve (2 phases) Critical Point Fusion Curve 2 phases

Phase Diagram of Water System:

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Phase Diagrams

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Phase Diagrams

• Some important features of Water System:

 Possible phases : Ice (s), Water(l), Vapour (g)  Curves: three stable curves throughout

• OA ( Vapour pressure curve, Water 

Vapour)

• OB ( Sublimation Curve, Ice 

Vapour)

• OC ( Melting point curve, Ice 

Water)  One metastable curve OA'

• (Vapour pressure curve of super cooled water)

 Areas : Three areas representing ice, water and vapour.  Triple point (O): Where all the three phases are in equilibrium (0.0098 oC and 4.58 mm pressure).

• The melting point curve OC has a negative slope, showing that

the melting point of ice decreases with increase of pressure

Phase Diagram of Sulphur System:

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Phase Diagrams

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Phase Diagrams

• Some important features of Sulphur System:

 Possible phases : Rhombic sulphur (SR), monoclinic sulphur (SR), sulphur vapour (SV) and sulphur liquid (SL).  Maximum phases: If P = 4, then F = C – P + 2 = 1 – 4 + 2 = –1 Which is meaningless. Hence all the four phases cannot coexist.  Areas : Four areas containing one phase each  Curves: there are six stable curves

• Sublimation curve of SR
• Sublimation curve of SM
• Vapour pressure curve of SL
• T

ransition curve of SR

• Melting curve of SM
• Melting curve of SR

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Phase Diagrams

• Some important features of Sulphur System:

 Metastable curves : There are four metastable curves

• Sublimation curve of SR
• Sublimation curve of SM
• Vapour pressure curve of SL
• Melting curve of SR

 Triple point (O): There are three stable triple points SR-SM-SV, SM-SL-SV, SR-SM-SL and one metastable triple point SR-SL-SV.

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Phase Diagrams

The system SiO2

T wo variables: P and T One component : SiO2 7 different phases

Point A: F = C – P + 2 F = 1 – 1 + 2 F = 2 Divariant area = T wo variables to define a position in the coesite stability field A

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Phase Diagrams

The system SiO2

T wo variables: P and T One component : SiO2 7 different phases

Point B: F = C – P + 2 F = 1 – 2 + 2 F = 1 Univariant area = One variable to define a position on the coesite – α-quartz phase boundary B

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Phase Diagrams

The system SiO2

T wo variables: P and T One component : SiO2 7 different phases

Point C: F = C – P + 2 F = 1 – 3 + 2 F = 0 Invariant area = T riple point do not need any variable to define equilibrium between coesite – α- and β-quartz C

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General Types of Alloys

• There are two general types of alloys having phase diagrams.

 Substitutional alloys  Interstitial alloys

• Subtitutional alloys have elements, which are incorporated into

regular lattice positions within the unit cell  An example is Sn and Zn alloying additions to Cu to form bronze and brass, respectively  Hume Rothery rules of solid solubility

• Interstitial alloys have elements, which are incorporated into the

interstitial sites of the unit cell  An example is carbon in iron to form steel

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Two Components Phase Diagrams

• Application of Phase Rule to two component systems:

As C = 2, minimum P = 1 and hence minimum F = C – P + 2 =

• 3. Thus the three variables (pressure, temperature and

composition) should be plotted. But for convenience, two dimension diagrams are plotted by keeping the third variable

• constant. Hence we have P – T

, C – P , or T – C diagrams. Generally pressure is kept constant at atmospheric pressure and we have T – C diagrams.

• Reduced phase rule:

If pressure is kept constant then the degree of freedom is reduced by one and hence the phase rule equation becomes C – P + 1

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Two Components Phase Diagrams

T ypes of T wo Component Systems:

• T

ype 1: T wo metals completely soluble in both liquid and solid states – Isomorphous

• T

wo metals completely soluble in the solid state, type of solid phase formed will be the substitution solid solution.

• The diagram shows the series
• f cooling curves for

different alloys in a completely soluble system. The dotted lines form the phase diagram

• The diagram plots

temperature vs. composition.

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Two Components Phase Diagrams

T ypes of T wo Component Systems:

• T

ype 2: T wo metals completely soluble in the liquid state and completely insoluble in the solid state

• One liquid solution.
• Solids A and B mix to

form a two phase solid

• The point at which the

liquidus lines intersect the minimum point E, is known as the eutectic point.

• TE is called the eutectic

temperature.

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Two Components Phase Diagrams

T ypes of T wo Component Systems:

• T

ype 3: T wo metals completely soluble in the liquid state but only partly soluble in the solid state

• One liquid solution.
• Solids α and β mix to

form a two phase solid

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Working with Phase Diagrams

• Overall composition
• Solidus
• Liquidus
• Limits of solid solubility
• Chemical composition of phases at any temperature
• Amount of phases at any temperature
• Invariant reactions
• Development of microstructure

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Working with Phase Diagrams

• Cooling curves
• Differential scanning calorimetry
• Thermomechanical analysis
• Differential thermal analysis
• Metallography/petrography
• Energy dispersive X-ray spectroscopy
• Electron microprobe analyzer
• X-ray diffraction
• Transmission electron microscope

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Cooling Curves

• The liquidus temperature is the temperature above which a

material is completely liquid

• The solidus temperature is the temperature below which the

alloy is 100 % solid

• The freezing range of the alloy is the temperature difference

between the liquidus and solidus where the two phases exists, i.e., the liquid and solid

Cooling curve for an isomorphous alloy during

• solidification. The

changes in slope

• f the cooling

curve indicate the liquidus and solidus temperatures.

Phase Diagrams - Two Component

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Cooling Curves

• Series of cooling curves at different metal compositions are first

constructed

• Points of change of slope of cooling curves (thermal arrests)

are noted and used in the construction of phase diagram

• Pure metals solidifies at a constant temperature which is known

as the melting temperature

• Binary alloys solidify over a range of temperatures

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Isomorphous Phase Diagrams

• When only two elements or two compounds are present in a

material a “binary phase diagram” can be constructed.

• In isomorphous binary phase diagrams, only one solid phase

forms as the two components in the system display complete solid solubility.

• Examples include the Cu-Ni and NiO-MgO systems.

Note that the concentrations can be expressed in wt.% or mole %.

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Isomorphous Systems

Systems With Complete Solid Solution

Plagioclase (Ab-An, NaAlSiO8 - CaAl2Si2O8)

Liquidus = a curve or a surface along which compositions of a melt are in equilibrium with a crystalline phase. Solidus = a curve or a surface along which compositions of a crystalline phase are in equilibrium with a melt.

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Amount of Phases in Binary Alloys

• When an alloy is present in a

two phase region, a tie line at the temperature of interest fixes the composition of the two phases.

• This is a consequence of the

Gibbs phase rule, which provides for only one degree of freedom.

• The Lever Rule is used to calculate the

weight % of the phase in any two- phase region of the phase diagram (and

• nly the two phase region!)
• In general:
• Example, for the liquid – solid (CL – CS)

region, the weight fractions of

• where CL = the liquid composition,

CS = the solid composition, and CO = the bulk composition

Co

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Determination of Phase(s) Present

Cu-Ni system

• Rule 1: If we know T and Co, then we must know:

 how many phases and which phases are present.

wt% Ni

20 40 60 80 100 1000 1100 1200 1300 1400 1500 1600

T(°C)

L (liquid)



(FCC solid solution)

L + 

liquidus s

• l

i d u s A(1100,60) B(1250,35)

• Example:

Melting points: Cu = 1085 °C Ni = 1453 °C

A (1100 C, 60 wt.% Ni): 1 phase: α B (1250 C, 35 wt.% Ni): 2 phases: L + α

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Composition of Phase(s)

Cu-Ni system

• Rule 2: If we know T and Co, then we must know:

 the composition of each phase

• Example:

At TA = 1320 C Only liquid (L) present

CL = C0 (35 wt.% Ni)

At TD = 1190 C

Only solid (α) present Cα = C0 (35 wt.% Ni)

At TB = 1250 C

Both α and L present CL = Cliquidus (32 wt.% Ni) Cα = Csolidus (43 wt.% Ni)

wt% Ni

20 1200 1300

T(°C) L (liquid)  (solid) L + 

l i q u i d u s solidus 30 40 50

TA A D TD TB B

tie line

L +  43 35 32 Co CL C

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Weight Fraction of Phase(s)

Cu-Ni system

• Rule 3: If we know T and Co, then we must know:

 the amount of each phase (given in wt.%)

• Example:

Co = 35 wt.% Ni At TA = Only liquid (L)

WL = 100 wt.%, Wα = 0

At TD = Only solid (α)

WL = 0, Wα = 100 wt.%

At TB = Both α and L

WL = Wα =

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Solidification of a Solid-Solution Alloy

• Change in structure and

composition of a Cu – 40 % Ni alloy during equilibrium solidification

• Liquid contains 40 % Ni

and the first solid contains Cu – 52 % Ni.

• At 1250 C, solidification

has advanced and the phase diagram of the liquid contains 32 % Ni and the solid 45 % Ni, which continues until just below the solidus.

• Solid contains 40 % Ni,

which is achieved through diffusion.

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Solidification of a Solid-Solution Alloy

• When cooling is too fast

for atoms to diffuse and produce equilibrium conditions, nonequilibrium concentrations are produced.

• The first solid formed

contains 52 % Ni and the last solid only 25 % Ni with the last liquid containing only 17 % Ni. The average composition

• f Ni is 40 % but it is not

uniform.

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Cored vs Equilimbrium Phases

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Microsegregation and Homogenization

• The nonuniform composition produced by nonequilibrium

solidification is known as segregation

• Microsegregation, also known as interdendritic segregation and

coring, occurs over short distances on the micron length scale

• Microsegregation can cause hot shortness which is the melting of the

material below the melting point of the equilibrium solidus

• Homogenization, which involves heating the material just below

the non-equilibrium solidus and holding it there for a few hours, reduces the microsegregation by enabling diffusion to bring the composition back to equilibrium

• Macrosegregation can also exist where there exist a large

composition difference between the surface and the center of a casting, which cannot be affected by diffusion as the distance is too large

• Hot working breaks down the cast macrostructure enabling the

composition to be evened out

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Rapidly Solidified Powders

• Many complex metal alloys are made by rapidly solidifying a

spray of fine droplets of material, usually consisting of complex compositions, in a quenching gas such as argon, nitrogen or water.

• Examples are nickel- and cobalt-based super alloys and some

stainless steels.

• This process minimizes microsegregation, macrosegregation and

porosity since the process happens so rapidly that there is no time for segregation or diffusion.

• The fine particles are then processed into shapes using

sintering, hot pressing and hot isostatic pressing (HIP).

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Mechanical Properties: Cu – Ni System

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Binary Phase Diagrams – Limited Solubility

• Not all metals are completely soluble in each other.

Distinctions can be made between two types solid solutions with limited solubility – (i) Eutectic and (ii) Peritectic.

• When the melting points of two metals are comparable, a

eutectic system forms while a peritectic results when melting points are significantly different.

• A eutectic reaction is defined as the one which generates two

solids from the liquid at a given temperature and composition, L → α + β

• Peritectic is Liquid + Solid 1 → Solid 2 (L + α → β)
• In both cases three phases (two solids and a liquid) coexist and

the degrees of freedom F = 2 – 3 + 1 = 0. This is known as invariant (F = 0) reaction or transformation.

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• Many alloy systems are based on only two elements.
• A good example is the lead – tin system, which is used for

soldering but because of the toxicity of Pb, it is now being replaced with other Sn alloys. Solid Solution Alloys

• A single phase solid solution forms during solidification.
• Examples include Pb – 2 wt.% Sn.
• These alloys strengthen by solid-solution strengthening, by strain

hardening and by controlling the solidification process to refine the grain structure.

Eutectic Phase Diagrams

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• In the eutectic system

between two metals A and B, two solid solutions, one rich in A (α) and another rich in B (β) form.

• In addition to

liquidus and solidus lines there are two more lines on A and B rich ends which define the solubility limits B in A and A in B respectively. These are called solvus lines.

Eutectic Phase Diagrams

Partially Soluble in the Solid Phase

Eutectic isoterm

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Eutectic Phase Diagrams

Completely Insoluble in the Solid Phase

• In this eutectic

system, two compounds are completely soluble in each other in the liquid phase but insoluble in each

• ther in the solid
• phase. i.e. they exists

as independent crystals in the solid phase.

• There are the liquidus

and solidus lines but no solvus lines.

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Eutectic Phase Diagrams

• Three phases (L + α + β) coexist at point E. This point is called

eutectic point or composition. Left of E is called hypoeutectic whereas right of E is called hypereutectic.

• A eutectic composition solidifies as a eutectic mixture of α and β
• phases. The microstructure at room temperature (RT) may consist
• f alternate layers or lamellae of α and β.
• In hypoeutectic alloys the α phase solidifies first and the

microstructure at RT consists of this α phase (called proeutectic α) and the eutectic (α + β) mixture. Similarly hypereutectic alloys consist of proeutectic β and the eutectic mixture.

• The melting point at the eutectic point is minimum. Other

eutectic systems are Ag-Cu, Al-Si, Al-Cu.

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Eutectic Cooling Curves

• While cooling a hypoeutectic alloy from the liquid state, the

temperature drops continuously till liquidus point, a, at which crystals of proeutectic α begins to form.

• On further cooling the fraction of α increases. At a point, b, in

the two-phase region the α fraction is given by the lever rule as bn/mn.

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Eutectic Cooling Curves

• Solidification of proeutectic α continues till the eutectic

temperature is reached. The inflection in the cooling curve between points a and e is due to evolution of the latent heat.

• At the eutectic point (e) the solidification of eutectic mixture (α

+ β) begins through the eutectic reaction and proceeds at a constant temperature as F = 0 (2 – 3 + 1).

• The cooling behavior in hypereutectic alloy is similar except that

proeutectic β forms below the liquidus.

• For a eutectic composition, the proeutectic portion is absent and

the cooling curve appears like that of a pure metal.

• Any composition left of point c or right of point d (α and β

single phase region respectively) will cool and solidify like an isomorphous system.

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Peritectic Cooling Curves

• L + α → β. An alloy cooling slowly through the peritectic point,

P, the α phase will crystallize first just below the liquidus line. At the peritectic temperature, TP all of the liquid and α will convert to β.

• Any composition

left of P will generate excess α and similarly compositions right

• f P will give rise to

an excess of liquid.

• Peritectic systems –

Pt - Ag, Ni - Re, Fe - Ge, Sn - Sb (Babbitt)

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Monotectic Cooling Curves

• Another three phase invariant reaction that occurs in some binary

system is monotectic reaction in which a liquid transforms to another liquid and a solid. L1 → L2 + α.

• T

wo liquids are immiscible like water and oil over certain range

• f compositions. Cu–Pb system has a monotectic at 36 % Pb and

955 C.

71

Phase Diagrams with Intermediate Phases

• Binary systems can have two types of solid solutions/phases

– terminal phases and intermediate phases.

• T

erminal phases occur near the pure metal ends, e.g. α and β phases in the eutectic system.

• Intermediate phases occur inside the phase diagram and are

separated by two-phase regions.

• The Cu-Zn system contains both types of phases. α and  are

terminal phases and β, , , and  are intermediate phases.

• Intermediate phases form in ceramic phase diagrams also. For

example, in the Al2O3 – SiO2 system an intermediate phase called mullite (3Al2O3.2SiO2) is formed.

72

Phase Diagrams with Compounds

• Sometimes a crystalline compound called intermetallic

compound may form between two metals.

• Such compounds generally have a distinct chemical formula or

stoichiometry.

• Example – Mg2Pb in the Mg-Pb system (appear as a vertical line

at 81 wt.% Pb ), Mg2Ni, Mg2Si, Fe3C. Mg - Pb phase diagram

73

Phase Diagrams with Compounds

Properties and Applications of Intermetallics

• Intermetallics such as Ti3Al and Ni3Al have an ordered crystal structure where

the Ti and Al atoms occupy specific locations in the crystal rather than random locations as in most solid solutions.

• In TiAl the Ti atoms are located at the corner and the top and bottom faces of

the unit cell whereas Al atoms are only at the other four faces of the unit cell.

• This ordered structure makes it difficult for dislocations to move, which results

in poor ductility at low temperatures, which increases at high temperatures.

• TiAl also has a high activation energy for diffusion, giving good creep

resistance at elevated temperatures. The unit cell of two intermetallic compounds: a) TiAl has an ordered tetragonal structure and b) Ni3Al has an ordered cubic structure.

74

Example

Point C has a composition 60 wt.% Pb alloy and at 150 C. a) What are the phases present? b) What are the compositions

• f the phases present?

c) Mass fraction? d) Volume fraction? Knowing that the densities of Pb and Sn are 11.23 and 7.24 g/cm3, respectively

75

Example

76

Phase Diagrams Containing Three-Phase Reactions

• In the more complex binary phase diagrams, the type of melting

is sometimes used to describe the type of intermediate that

• ccurs along with a particular type of solid state reaction
• Congruently melting compounds are those that maintain their

specific composition right up to the melting point. This appears as a localized “dome” in the liquidus region of the phase diagram

• Incongruent melting compounds do not occur directly from the

liquidus, but are formed by some form of solid-state reaction

• The five most common three-phase reactions that occur in phase

diagrams are:

 Eutectic – a liquid transforming into two new solids on cooling  Peritectic – a liquid plus a solid transforms into a new solid  Monotectic – a liquid transforms into a new liquid and a solid  Eutectoid – a solid transforms into two new solids  Peritectoid – two solids transforms into a new solid

77

Phase Diagrams Containing Three-Phase Reactions

Three phase reaction type, reaction equation and appearance on a phase diagram

78

Phase Diagrams Containing Three-Phase Reactions

Three phase reaction types and reaction equations

Above Below T ype Homotectic Monotectic Eutectic Catatectic L L L S1 L' + L “ L' + S S1 + S2 S2 + L Eutectic Monotectoid Eutectoid S1 S1 S'1 + S2 S2 + S3 Eutectoid Syntectic Peritectic L + L ‘ L + S1 S S2 Peritectic Peritectoid S1 + S2 S3 Peritectoid

79

• Locate a horizontal line (isotherm)
• n the phase diagram. The

horizontal line, which indicates the presence of a three-phase reaction, represents the temperature at which the reaction occurs under equilibrium conditions

• Locate three distinct points on the

horizontal line: the two end points plus a third point. The center point represents the composition at which the three-phase reaction occurs

• Write in reaction form the phase(s)

above the center point transforming to the phase(s) below the point. In most cases the reaction will be a eutectic, eutectoid, peritectic, etc.

RULES OF THREE PHASE REACTIONS

80

Development of Microstructure in Eutectic Alloys

• Cooling of

liquid lead/tin system at different compositions.

• Several types of

microstructures forms during slow cooling at different compositions.

81

Development of Microstructure in Eutectic Alloys

• Co less than 2 wt.% Sn
• In this case of lead – rich

alloy (0 – 2 wt.% of tin) solidification proceeds in the same manner as for isomorphous alloys (e.g. Cu – Ni) that was discussed earlier.

• Result
• at extreme ends
• polycrystals of α grains

i.e. only one solid phase

82

Alloys that exceed the solubility limit

• Pb – Sn alloys between

2 – 19 wt.% Sn also solidify to produce a single solid solution, however, as the solid- state reaction continues, a second solid phase, β, precipitates from the α phase.

Development of Microstructure in Eutectic Alloys

• The solubility of Sn in solid Pb at any temperature is given by the

solvus curve.

• Any alloy containing between 2% – 19 % Sn that cools past the solvus

exceeds the solubility resulting in the precipitation of the β phase.

83

Development of Microstructure in Eutectic Alloys

• 2 wt.% Sn < Co <

19 wt.% Sn

• Result
• initially liquid + α
• then α alone
• finally two phases

 α polycrystals  fine β phase inclusions

84

Development of Microstructure in Eutectic Alloys

Alloys that exceed the solubility limit

• The Pb – 61.9

wt.% Sn alloy has the eutectic composition.

• The eutectic

composition has the lowest melting temperature.

• The eutectic composition has no freezing range as solidification occurs at
• ne temperature (183 C in the Pb - Sn alloy).
• The Pb - Sn eutectic reaction forms two solid solutions and is given by:

L61.9 % Sn → α19 % Sn + β 97.5% Sn

• The compositions are given by the ends of the eutectic line.

85

Development of Microstructure in Eutectic Alloys

• The Pb - Sn eutectic reaction :

L61.9 % Sn → α19 % Sn + β 97.5% Sn

• Co = CE
• Result
• eutectic

microstructure (lamellar structure) i.e. alternating layers (lamellar) of α and β phases

86

Development of Microstructure in Eutectic Alloys

Cooling curve for a eutectic alloy is a simple thermal arrest, since eutectics freeze or melt at a single temperature. a) Atom redistribution during lamellar growth of a Pb-Sn

• eutectic. Sn atoms from the

liquid preferentially diffuse to the  plates, and Pb atoms diffuse to the  plates. b) Photograph of the Pb-Sn eutectic.

87

Development of Microstructure in Eutectic Alloys

Hypoeutectic Alloy

• This is an alloy whose composition will be between the left-

hand-side of the end of the tie line and the eutectic composition.

• For the Pb-Sn alloy, it

is between 19 wt.% and 61.9 wt.% Sn.

• In the hypoeutectic

alloy, the liquid solidifies at the liquidus temperature producing solid, α and is completed by going through the eutectic reaction.

• 19 wt.% Sn < Co < 61.9 wt.% Sn
• Result
• initially liquid + α
• then α and eutectic

microstructure

• Just above TE:

Cα = 19 wt.% Sn and Cβ = 61.9 wt.% Sn

• Just below TE:

Cα = 19 wt.% Sn and Cβ = 97.5 wt.% Sn

• 88

Development of Microstructure in Eutectic Alloys

Hypoeutectic Alloy

a) A hypereutectic alloy of Pb-Sn and b) a hypoeutectic alloy of Pb-Sn where the dark constituent is the Pb-rich α phase and the light constituent is the Sn-rich β phase and the fine plate structure is the eutectic. 89

Development of Microstructure in Eutectic Alloys

Hypereutectic Alloy

• This is an alloy whose composition will be between the right-

hand-side of the end of the tie line and the eutectic composition.

• For the Pb-Sn alloy, it is

between 61.9 % and 97.5 % Sn.

• The primary or

proeutectic solid that forms before the eutectic phase is the  phase which is different from the eutectic solid and leads to a variation in microstructure.

90

Hypoeutectic and Hypereutectic

91

Strength of Eutectic Alloys

• Some eutectics can be strengthened by cold working.
• Adding grain refiners, or inoculants, during solidification can

decrease grain size.

• The amount and microstructure of the eutectic can also be

controlled.

• Each eutectic colony can nucleate and grow independently

having the orientation of the lamellae being identical.

Colonies in the Pb-Sn eutectic and the effect of growth rate, R, on the interlamellar spacing, l, in the eutectic, which follows the relationship:

2 / 1 

 cR l

92

Strength of Eutectic Alloys

• The lamellae orientation changes on crossing from one colony

boundary to another.

• By refining the colony size by inoculation, the strength can be

improved.

• The eutectic is strengthened by decreasing the interlamellar

spacing.

The interlamellar spacing in a eutectic microstructure.

Interlamellar spacing

• This is the distance between the center
• f one α lamella to the center of the

next α lamella.

• A small interlamellar spacing indicates

that the amount of  → β interface area is large.

• A small interlamellar spacing therefore

increases the strength of the eutectic.

93

Microstructure of Eutectic Alloys

• Not all eutectics give a lamellar structure.
• The morphology of the two phases depends on the cooling rate,

presence of impurities, and the nature of the alloy.

• An example is a Al-Si alloy where the Si portion of the eutectic grows

as thin platelets (much have a high surface interface energy) growing as thin, flat platelets, which concentrate stresses leading to reduced ductility and toughness.

• Modification causes the Si phase to grow as thin, interconnected rods

between dendrites of Al, which increases strength and elongation.

T ypical eutectic microstructures of Al-Si where a) shows needle-like plates and b) shows a modified structure of rounded rods

94

Microstructure of Eutectic Alloys

• If the alloys cools too quickly, a non-equilibrium solidus curve is produced.
• Example, for a Pb-15 wt.% Sn alloy, the  phase should freeze at 230 C,

which is well above the eutectic temperature of 183 C.

• As the α phase continues to grow until, just above 183 C, the remaining

non-equilibrium liquid contains 61.9 wt.% Sn, the eutectic composition.

• This liquid then transforms to the eutectic microconstituent, surrounding the

primary α phase. For the conditions shown in the figure below, the amount

• f eutectic is:

At near equilibrium conditions, 100 % α phase should form. For non-equilibrium solidification a microstructure of α phase and a eutectic microconstituent form if the solidification is too rapid.

% 6 . 9 100 10 9 . 61 10 15 eutectic %     

95

Peritectic Cooling Curves

• L + β → α. An alloy cooling slowly through the peritectic point,

P, the β phase will crystallize first just below the liquidus line. At the peritectic temperature, TP all of the liquid and β will convert to α.

• Any composition

left of P will generate excess β and similarly compositions right

• f P will give rise to

an excess of liquid.

• Peritectic systems –

Pt - Ag, Ni - Re, Fe - Ge, Sn - Sb (Babbitt)

The Iron – iron Carbide (Fe-Fe3C) Phase Diagram

In their simplest form, steels are alloys of Fe and

• C. The Fe-C

phase diagram is a fairly complex one, but we will consider the steel and cast iron part of the diagram, up to around 6.70 wt% C.

96

97

Phases in Fe-Fe3C Phase Diagram

• 1. α-ferrite – solid solution of C in BCC Fe
• Stable form of iron at room temperature
• The maximum solubility of C is 0.022 wt.%
• T

ransforms to FCC γ-austenite at 912 oC

• 2. γ-austenite – solid solution of C in FCC Fe
• The maximum solubility of C is 2.14 wt.%
• T

ransforms to BCC δ-ferrite at 1395 oC

• Is not stable below the eutectoid temperature (727 oC) unless

cooled rapidly

• 3. δ-ferrite – solid solution of C in BCC Fe
• The same structure as α-ferrite
• Stable only at high T

, above 1394 oC

• Melts at 1538 oC
• 4. Fe3C (iron carbide or cementite)
• This intermetallic compound is metastable, it remains as a

compound indefinitely at room T , but decomposes (very slowly, within several years) into α-Fe and C (graphite) at 650-700oC

• 5. Fe-C liquid solution

98

Phases in Fe-Fe3C Phase Diagram

The following phases are involved in the transformation, occurring with iron-carbon alloys:

• L – Liquid solution of carbon in iron
• δ-ferrite – Solid solution of carbon in iron. Maximum

concentration of carbon in δ-ferrite is 0.09 wt.% C at 1493 C – temperature of the peritectic transformation. The crystal structure of δ-ferrite is BCC.

• Austenite –interstitial solid solution of carbon in in -iron.

Austenite has FCC crytal structure, permitting high solubility of carbon – up to 2.06 wt.% C at 1147 C and maximum carbon concentration at this temperature is 0.83 wt.% C.

• α-ferrite – solid solution of carbon in α-iron. Α-ferrite has BCC

crystal structure and low solubility of carbon – up to 0.25 wt.% C at 723 C. α-ferrite exists at room temperature.

• Cementite – iron carbide, intermetallic compound, having fixed

composition Fe3C.

99

Iron – Iron Carbide (Fe-Fe3C) Phase Diagram

Phase Compositions at Room T emperature

• Hypoeutectoid steels (carbon content from 0.025 to 0.83 wt.%

C) consist of primary (proeutectoid) ferrite and pearlite

• Eutectoid steel (carbon content of 0.83 wt.% C) consists of

pearlite

• Hypereutectoid steels (carbon content from 0.83 wt.% C to 2.14

wt.% C) consist of primary (proeutectoid) cementite and pearlite

• Cast iron (carbon content from 2.14 wt.% C) consist of

proeutectoid cementite ejected from austenite according to the curve ACM, pearlite and transformed ledeburite (ledeburite in which austenite transformed to pearlite).

100

A Few Comments On Fe-Fe3C System

• 1. Carbon is an interstitial impurity in Fe. It forms a solid solution

with α, γ, δ phases of iron.

• 2. Maximum solubility in BCC α-ferrite is limited (max. 0.022 wt%

at 727 oC) – BCC has relatively small interstitial positions.

• 3. Maximum solubility in FCC austenite is 2.14 wt.% at 1147 oC –

FCC has larger interstitial positions.

• 4. Mechanical properties: Cementite is very hard and brittle – can

strengthen steels. Mechanical properties also depend on the microstructure, that is, how ferrite and cementite are mixed.

• 5. Magnetic properties: α-ferrite is magnetic below 768 oC, austenite

is non-magnetic.

• 6. Classification: Three types of ferrous alloys:
• Iron: less than 0.008 wt.% C in α-ferrite at room temperature
• Steels: 0.008-2.14 wt.% C (usually < 1 wt.%) – α-ferrite + Fe3C at RT
• Cast iron: 2.14 – 6.7 wt.% C (usually < 4.5 wt.%)

101

A Few Comments On Fe-Fe3C System

Invariant Reactions

• Peritectic reaction at 1495 C

L0.53 wt.% C + δ0.09 wt.% C → 0.17 wt.% C

• Eutectic reaction at 1147 C

L4.3 wt.% C → 2.11 wt.% C + Fe3C6.67 wt.% C

• Eutectoid reaction at 727 C

0.77 wt.% C → α0.02 wt.% Sn + Fe3C6.67 wt.% C

102

Microstructure of Hypoeutectoid and Hypereutectoid Steels

103

104

Critical Temperatures in Fe – Fe3C Phase Diagrams

• Upper critical temperature (point) A3 is the temperature, below

which ferrite starts to form as a result of ejection from austenite in the hypoeutectoid alloys.

• Upper critical temperature (point) Acm is the temperature, below

which cementite starts to form as a result of ejection from austenite in the hypereutectoid alloys.

• Lower critical temperature (point) A1 is the temperature of the

austenite-to-pearlite eutectoid transformation. Below this temperature austenite does not exist.

• Magnetic transformation temperature A2 is the temperature

below which α-ferrite is ferromagnetic.

• Curie temperature A0 – it is the point at which magnetic to non-

magnetic change on heating of cementite takes place.