C O U R S E I N S T R U C T O R : TA U H E E D

MM 231 Phase Equilibria and

Microstructures

MM 231 Phase Equilibria & Microstructures

C O U R S E I N S T R U C T O R : TA U H E E D

Learning Outcomes  Development of new alloys for specific applications.

Fabrication of these alloys into useful configurations.

Design and control of heat treatment procedures for specific alloys that will produce the required mechanical, physical, and chemical properties.

Solving problems that arise with specific alloys in their performance in commercial applications, thus improving product predictability.

Basic knowledge on thermodynamics and kinetic factors controlling solid state phase transformations in metals and alloys. Diffusional and diffusionless solid state phase transformations.

Understand the processes by which solid state phase transformations occur including both diffusion controlled and diffusionless transformations.

Porter, D. A and Easterling, K.E, ”Phase Transformations in Metals and Alloys”, Chapman & Hall, 2001.

Physical Metallurgy Principles: Reza Abbaschian,Robert E.Reed –Hill, Fourth Edition

Honeycombe, R. W. K., and Bhadeshia, H. K. D. H., “Steels, Microstructures and Properties”, Edward Arnold, 2005

Cahn and Haasen, “Physical Metallurgy” 2001 .

William F. Hosford, University of Michigan, Ann Arbor, USA, “Physical Metallurgy, Second Edition”, 2010

Martin, Doherty and Canter, “Stability of Microstructures in Metallic Systems” Cambridge University Press, 1997

Text and Reference Books

Grading Policy:

Assignment (min 4) 5%,

Quizzes (min 6)15%,

Presentations /Class Projects 10%,

Mid term Exam 30 %

&

Final Exam 40%Teaching Methodology : 45 Lectures [03 lectures/week]

Attendance: 100%, (min 80% to sit in the final exam)

Solid Solutions and Hume Rothery Rules

LECTURE 1:

Solid Solutions

Solute + Solvent = Solution

Solution???????

Alloy?????????

Mixing of atleast two metals

Solid Solution:

A solid solution is formed when two metals are completely soluble in liquid state and also completely soluble in solid state. ORwhen homogeneous mixtures of two or more kinds of atoms (of metals) occur in the solid state, they are known as solid solutions.

Solid Solutions

Question is …………………….

How Solid Solution Forms

Solid Solutions

Solid Solution occurs in two distinct Types:

• Substitutional Solid Solution

• Interstitial Solid Solution

Solid Solutions

Substitutional Solid Solution:

If the atoms of the solvent or parent metal are replaced in the crystal lattice by atoms of the solute metal then the solid solution is known as substitutional solid solution.

For example, copper atoms may substitute for nickel atoms without disturbing the FCC. Similarly Ag-Au FCC binary systems and the Mo-W BCC binary system.

Solvent

Solute

Solid Solutions

In the substitutional solid solutions, the substitution can be either disordered or ordered.

In disordered substitutional solid solution, the solute atoms have substituted disorderly for the solvent atoms on their lattice site. In ordered substitutional solid solution, the solute atoms have substituted in an orderly manner for the solvent atoms on their lattice site.

Solvent

Solute

Ordering in Substitutional Solid solutions

As stated before substitutional solid solutions can be either ordered or random. This depends on a thermodynamic parameter called enthalpy of mixing,ΔHmix

Δ Gmix = Δ Hmix - T ΔSmix

ΔGmix is the Gibbs free energy change and ΔSmix entropy of mixing.

For an ideal solution ΔHmix = 0.

•If ΔHmix> 0, formation of like bonds (A-A or B-B) is preferred in a solid solution between metals A and B. This is known as clustering.

•If ΔHmix< 0, unlike bonds (A-B) are preferred. This leads to ordering which may exist over short range or long range

Solid Solutions

Solid Solutions

Interstitial Solid Solution:

In interstitial solid solutions, the solute atom does not displace a solvent atom, but rather it enters one of the holes or interstices between the solvent atoms.

The atoms crowd into the interstitial sites, causing the bonds of the solvent atoms to compress and thus deform. Elements commonly used to form interstitial solid solutions include H, Li, Na, N, C, and O. Normally, atoms which have atomic radii less than one angstrom are likely to form interstitial solid solutions. Examples are atoms of carbon (0.77 A°), nitrogen (0.71 A°), hydrogen (0.46 A°), Oxygen (0.60 A°) etc.

Carbon in iron (steel) is one example of interstitial solid solution.Solvent

Solute

Several factors determine the limits of solubility. These factors are

defined by Hume Rothery Rules

Hume Rothery Rules

1. Atomic Size Factor

2. Crystal Structure

3. Valancy

4. Electronegativity

Hume Rothery Rules

Atomic Size Factor (the 15%) Rule:

Extensive substitutional solid solution occurs only if the

relative difference between the atomic diameters (radii)

of the two species is less than 15%. 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:

Hume Rothery Rules

Crystal structure Rule :

For appreciable solid solubility, the two elements should have the same type of crystal structure i.e., both elements should have

either F.C.C. or B.C.C. or H.C.P. structure.

Valency Rule :

A metal will dissolve a metal of higher valency to a greater extent than one of lower valency. The solute and solvent atoms should typically have the same valence in order to achieve maximum solubility.For example in aluminium-nickel alloy system, nickel (lower valance) dissolves 5 percent aluminium but aluminium (higher valence) dissolves only 0.04 percent nickel.

The Electronegativity Rule :

Electronegativity difference close to 0 gives maximum solubility.

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. The solute and the solvent should lie relatively

close in the electrochemical series.

Hume Rothery Rules

Interstitial solid solution

Hume-Rothery rules can be applied for interstitial solid solutions:

Interstitial solid solutions are formed if:

1. a solute is smaller than pores in the lattice of a solvent;

2. a solute has approximately the same Electronegativity as a solvent.

There are very few elements that create ions, small enough to fit in

interstitial positions, therefore, appreciable solubility is rare for

interstitial solid solutions.

Ions that often may be a solute in solid solutions are: H, Li, Na, B.

Hume Rothery Rules

Gibbs Phase Rule and one components Phase Diagram

LECTURE 2:

Useful Terminology

• Phase

• Component

• System

• Solubility Limit

• Phase Equilibrium

• Variables of system

Useful Terminology

??????? Phase – a portion of a system that has uniform physical

and chemical characteristics. Two distinct phases in a

system have distinct physical and/or chemical

characteristics (e.g. water and ice, water and oil) and are

separated from each other by definite phase boundaries. A

phase may contain one or more components.

A single-phase system is called homogeneous systems

Homogeneous system:

The one whose chemical composition and physical properties are the

same in all parts of the system, or change continuously from one point to

another.

A homogeneous system can be exemplified by

imagining a column of atmospheric air, which is a

mixture of a number of gases, mainly nitrogen and

oxygen. In a system of this kind, acted upon by the

force of gravity, both the composition of the system

and its physical properties will continuously change

from one point to another.

Useful Terminology

Heterogeneous system:

One consisting of two or more homogeneous bodies. The homogeneous bodies of a heterogeneous system are referred to as phases. Each phase is separated from other phases by interfaces, or boundaries, and in passing over such a boundary the chemical composition of the substance or its physical properties abruptly change.

An example of a heterogeneous system is water with ice floating in it. This system has two homogeneous bodies, water and ice. The chemical composition of the two phases is the same, but their physical properties differ drastically.

Useful Terminology

Useful Terminology

Solubility limit:For almost all alloy systems, at a specific temperature, a maximum of solute

atoms can dissolve in solvent phase to form a solid solution. The limit is known

as solubility limit. In general, solubility limit changes with temperature.

The same concepts apply to solid phases: Cu and Ni are mutually soluble in any

amount (unlimited solid solubility), while C has a limited solubility in Fe.

If solute available is more than the

solubility limit that may lead to

formation of different phase, either

a solid solution or compound.

Mole Fractions

where XA is called the “mole fraction” of component A in some phase.

If the same component is used in more than one phase, Then we can define the mole fraction of component A in phase i as X i

A

For a simple binary system, XA + XB = 1

Useful Terminology

Component:is either pure metal and/or compounds of which an alloy is composed. The components of a system may be elements, ions or compounds. They refer to the independent chemical species that comprise the system.

System :It can either refer to a specific body of material under consideration or it may relate to the series of possible alloys consisting of the same components but without regard to alloy composition. Degree of freedom (or variance) F :It is the number of variables (T, p, and composition) that can be changed independently without changing the phases of the system

Equilibrium in terms of free energy

Free energy is a function of internal energy and randomness /disorder (entropy) of a atoms or molecules of a system.

Equilibrium

Consider a map of the ‘potential energy’ (vertical axis) of a system in four different states:

State (a) is an equilibrium position, which is stable to small perturbations. It does not, however represent the lowest energy stateof the system and we refer to it as a metastable equilibrium.

State (b) is an equilibrium position, but is not stable to any small perturbations. This is an unstable equilibrium position.

State (c) is not an equilibrium position. There is a driving force to the right.

State (d) is the position of stable equilibrium: it occupies the lowest energy state, and is stable to perturbations.

Phase Diagrams

Equilibrium Diagrams

Represents phase relationships as a function of temperature, pressure and composition (equilibrium phases and microstructure)

A phase diagram is a type of graph used to show the equilibrium conditions between the thermodynamically-distinct phases; or to show what phases are present in the material system at various T, p, and compositions

But many useful diagrams are constructed for constant pressure of 1 atmosphere, so only composition and temperature are variables

Phase diagrams provides us with information needed for the control of phase and microstructure in the materials we make

Gibbs Phase Rule

Variables of a system:These include two external variables namely temperature and pressure along with internal variable such as composition (C) and number of phases (P). Number of independent variables among these gives the degrees of freedom (F) or variance. All these are related for a chosen system as follows: P + F = C + N

which is known as Gibbs Phase rule.

N = number of non-compositional variablesN = 1 or 2 for T (temperature) and P (pressure)N = 1 If P=const or T=constP is usually constant so N is usually 1)

P + F = C + 1

Gibbs Phase Rule Significance for Phase Diagrams

For Two Dimensional Phase Diagrams:

Stability fields:

Area (T-P,T-X,P-X space) where a phase or phase assemblage (more than one phase ) is stable.

Equilibrium boundary lines:

These define the limits of stability fields. These represents values of parameter where phases in adjacent fields coexist.

Triple point:

Points where equilibrium boundary lines meet. All phases in the adjacent stability fields must coexist.

Silica Phase Diagram and Phase Rule

Point

Number of Component

s (C)

Number of

Phases (P)

Degree of

Freedom(F)

a 1 1 2 (T,P)

a’ 1 1 2 (T,P)

b 1 2 1 (T or P)

b’ 1 2 1 (T or P)

One Component Phase Diagram

One Component Phase Diagram

Application of Gibbs Phase Rule

Introduction to Binary Phase Diagram

Isomorphous systems contain metals which are completely soluble in

each other and have a single type of crystal structure.

Phase diagrams, also called equilibrium diagrams or constitution

diagrams, are a very important tool in the study of alloys. They

define the regions of stability of the phases that can occur in an

alloy system under the condition of constant pressure

(atmospheric).

Cooling Curve

The melting temperature of any pure material (a one-component system) at constant pressure is a single unique temperature.

The liquid and solid phases exist together in equilibrium only at this temperature. When cooled, the temperature of the molten material will steadily decrease until the melting point is reached.

At this point the material will start to crystallise, leading to the evolution of latent heat at the solid liquid interface, maintaining a constant temperature across the material.

Once solidification is complete, steady cooling resumes. The arrest in cooling during solidification allows the melting point of the material to be identified on a time-temperature curve.

Cooling Curve

Simplified Cooling Curve of Pure Copper

Construction of Binary Phase Diagram

Most systems consisting of two or more components

exhibit a temperature range over which the solid and

liquid phases are in equilibrium. Instead of a single

melting temperature, the system now has two different

temperatures, the liquidus temperature and the solidus

temperature which are needed to describe the change

from liquid to solid.The liquidus temperature is the temperature above which the system is entirely liquid, and

the solidus is the temperature below which the system is completely solid. Between these

two points the liquid and solid phases are in equilibrium. When the liquidus temperature is

reached, solidification begins and there is a reduction in cooling rate caused by latent heat

evolution and a consequent reduction in the gradient of the cooling curve.

By taking a series of cooling curves for the same

system over a range of compositions the liquidus and

solidus temperatures for each composition can be

determined allowing the solidus and liquidus to be

mapped to determine the phase diagram.

Cooling curves for the same system recorded for different compositions and then

displaced along the time axis. The red regions indicate where the material is liquid, the

blue regions indicate where the material is solid and the green regions indicate where the

solid and liquid phases are in equilibrium.

Construction of Binary Phase Diagram

By removing the time axis from the curves and replacing it with composition, the cooling curves indicate the temperatures of the solidus and liquidus for a given composition.

Construction of Binary Phase Diagram

This allows the solidus and liquidus to be plotted to produce the phase diagram

Construction of Isomorphous phase Diagram

Phase Diagram

Phase Diagram of Cu –Ni System

Phase Diagram of Cu –Ni System

Binary Phase Diagram

There are three main types of binary phase diagrams :

Complete solid and liquid solution diagram

Eutectic diagram (including Eutectic diagram with partial solubility of the components in solid state and Eutectic diagram with intermetallic compound)

Peritectic diagram

Binary Phase Diagram(Eutectic System)

Eutectic means EASILY MELTED

In most alloy systems, components are only partially miscible in the solid state. In other words, solid solution only exist over a limited range of compositions and temperatures.

Example: Cu and Ag are both FCC, but their lattice parameters and atomic radii are very different, so they have limited solubility in the solid state.

This kind of system is called Eutectic System

Construction of Phase Diagram (Eutectic Alloy)

Cooling Curves (Temp Vs. Time ) with addition of 2nd element

Cooling Curves (Temp Vs. composition)

Construction of Phase Diagram (Eutectic Alloy)

Construction of Phase Diagram (Eutectic Alloy)

Eutectic Alloy

In Eutectic System, the two elements are completely soluble in all proportions in the liquid state. On cooling two possibilities may arise

i-The two elements are completely insoluble in solid state ii-The two elements are partly soluble in the solid state

Liquid (L) A+B (Possibility (i)

Where A and B are metals, and

Liquid (L) α+β (Possibility (ii)

Where α is A rich solid solution and β is B rich solid solution

Cooling

Heating

Cooling

Heating

Eutectic Alloy

These reactions takes place at fixed temperature, called eutectic temperature, and the composition of participating phases is also fixed.

Gibbs phase rule can be applied to this equilibrium system.

All three phases coexist at a single temperature. This temperature is the melting point of the eutectic alloy

The characteristic feature of eutectic alloy is,

It melts at fixed temperature just like a pure metal.

It have a good casting characteristics such as fluidity and minimum porosity.

Eutectic Alloy

Fig:Partial Phase diagram for the Pb-Sn system, showing the limiting behavior at high and low temperatures

The lower part replicates the sugar water behavior ; the solubility of Pb in Sn (and Sn in Pb) increases with temperature.Note: Solubilities of these elements in one another is low, especially Pb in Sn on right of the diagram.The upper part of the diagram shows the partition behavior from the melting points of both pure elements.

Eutectic Alloy

To complete the diagram, consider where the falling solidus boundaries meet the rising solvus boundaries.The point where they intersect represent the points of maximum solubility in the single phase solids.

Fig: Completed solid phase and two phase solids

Eutectic Alloy

Thermodynamics dictates that liquid boundaries meet the horizontal line at a single point, and the liquid field closes in a shallow “V”. At this special composition, two solid phases and liquid of that composition can co-exist. This point on the diagram is very important , and is known as a eutectic point.

Fig: The completed phase diagram for the Pb-Sn system, showing the eutectic point

Interpretation of Eutectic Phase Diagram

Limited Solid Solubilityα is solid A with small amount of solid B dissolved in itβ is solid B with small amount of solid A dissolved in itComponents have different solid solubilities

Interpretation of Eutectic Phase Diagram

Applications of Eutectic Alloys

Eutectic alloys for soldering, composed of tin (Sn), lead (Pb) and sometimes silver (Ag) or gold (Au) — especially Sn63Pb37 alloy formula for electronics

Casting alloys, such as aluminium-silicon and cast iron (at the composition of 4.3% carbon in iron producing an austenite-cementite eutectic)

Silicon chips are bonded to gold-plated substrates through a silicon-gold eutectic by the application of ultrasonic energy to the chip.

Brazing, where diffusion can remove alloying elements from the joint, so that eutectic melting is only possible early in the brazing process.

Experimental glassy metals, with extremely high strength and corrosion resistance.

Eutectic alloys of sodium and potassium (NaK) that are liquid at room temperature and used as coolant in experimental fast neutron nuclear reactors.

Construction of Phase Diagram (Eutectic Alloy)

Interpretation of Phase Diagrams

A binary phase diagram can be used to determine three important

types of information:

(1) The phases, that are present

(2) The composition of the phases

(3) The percentages or fractions of the phases.

The phases that are present can be determined by locating the temperature-composition point on the diagram and noting the phase(s) present in the corresponding phase field.

30wt%Ni-70wt%Cu at 1315 °C (2400 °F)

Point lies totally within the liquid field, the alloy would be a liquid.

The same alloy at 1095 °C (2000 °F), designated point cwithin the solid solution, α, field, only the single α phasewould be present.

At alloy at 1190 °C (2170 °F)(point b) would consist of a two-phase mixture of Solid solution, α, and liquid, L.

Prediction of Phases

Prediction of Chemical Compositions of Phases

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.

To compute the equilibrium concentrations/Chemical Composition of the two phases, the following procedure is used:

Prediction of Chemical Compositions of Phases

Locate the point on the phase diagram. If only one phase is present, the composition of the phase is the overall composition of the alloy.

At Point (A), at corresponding T, only Liquid is present , so composition will be 30wt%Ni-70wt%Cu.

At Point (C) only the α phase is present, so the composition is 30wt%Ni-70wt%Cu.

Prediction of Chemical Compositions of Phases

At Point (B) considering the 30wt%Ni-70wt%Cu alloy at 1190 °C (2170 °F) with the two-

phase, α + L, field.

The perpendicular line from the liquidus boundary

to the composition axis is 20wt%Ni-80wt%Cu,

which is the composition, CL, of the liquid phase.

The composition of the solid-solution phase, Cα,

is read from the perpendicular line from the

solidus line down to the composition axis, in

this case 35wt%Ni-65wt%Cu.

Prediction of Amounts of Phases

The single and two-phase situations must be

treated separately.

In the single phase region: Since only one phase is

present, the alloy is composed entirely of that

phase; i.e. the phase fraction is 1.0 or 100%.

At 60 wt% Ni–40 wt% Cu alloy at 1100oC(point A),

Only α is present alloy is completely or 100%

α

The relative amounts (fraction/%) computed with phase diagrams.

Prediction of Amounts of Phases

If the composition and temperature position is located within a two-phase region, things are more complex. The tie line must be utilized in conjunction with a procedure that is often called the lever rule (or the inverse lever rule)

Steps to determine Phase Amount using Lever Rule

1. The tie line is constructed across the two-phase region at the temperature of the alloy.

2. The overall alloy composition is located on the tie line.

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

tie line length.

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.

.