MM-231: Phase Equilibria & MicrostructureCourse Outline

Spring 2013 Course AimTo understand the basics of phase equilibria, Phase diagram and evolution of microstructure in different processing conditions. These are the bases for the development of advanced engineering materials.  Course Contents•Phase rule and Phase diagrams•Microstructures•Diffusion•Nucleation & growth•Solidification•Annealing•TransformationsNote: Contents of the course may change according to the circumstances.

Text Book•Physical Metallurgy Principles by Reza Abbaschian, Robert E. Reed-Hill, 4th edition, (2009).•Phase

MM-231: Phase Equilibria & MicrostructureCourse Outline

Spring 2013 Course AimTo understand the basics of phase equilibria, Phase diagram and evolution of microstructure in different processing conditions. These are the bases for the development of advanced engineering materials.  Course Contents•Phase rule and Phase diagrams•Microstructures•Diffusion•Nucleation & growth•Solidification•Annealing•TransformationsNote: Contents of the course may change according to the circumstances.

Text Book•Physical Metallurgy Principles by Reza Abbaschian, Robert E. Reed-Hill, 4th edition, (2009).•Phase Diagrams and Heterogeneous Equilibriua: A Practical Introduction by B. Predel, M. Hoch, (2004).

Reference Books

•An introduction to Materials Engineering and Science by Brian S. Mitchell, A John Wiley & Sons, Inc., (2004).•Essentials of Materials Science and Engineering, 2nd Edition, Donald R. Askeland, CL-Engineering, (2010).•Phase Diagrams in Metallurgy, Their Development and Application by Frederick N. Rhines, (1956).

Grading Policy

Quizzes (Un-announced): 20%, Assignments: 5%, Mid Term: 30%, Final Exam: 45%Attendance: Minimum 80% for appearing in the final exam.

PHASESA phase is a homogeneous portion of a system with uniform physical and chemical characteristics, in principle separable from the rest of the system

A difference in either physical or chemical properties constitutes a phase

gaseous state• seemingly only one phase occurs (gases always mix)

liquid state• often only one phase occurs (homogeneous solutions), e.g., salt water, molten Na2O-SiO2

• two immiscible liquids (or liquid mixtures) count as two phasessolid state• crystalline phases: e.g., ZnO and SiO2 = two phases• polymorphs: e.g., wurtzite and sphalerite ZnS are different phases• solid solutions = one phase (e.g., Al2O3-Cr2O3 mixtures)

Note: metastable phases do not appear on equilibrium phase diagrams.

First Assignment

Definitions and understanding of basic terms of thermodynamics

•Internal Energy•Entropy•Enthalpy •Laws of thermodynamics •Free energy•Gibbs Free energy•Helmholtz Free Energy

Note: Not only, you should make a written assignment but you must have a clear idea of these terms and all this will be asked and discussed in the class.

Reference book: Introduction to the thermodynamics of materials, 4th Edition by David R. Gaskell, Taylor & Francis group (2003)

DEFINITION

A Phase Diagram describes the state of a materials system in thermodynamic equilibrium as a function of temperature, pressure and composition.

Phase Diagrams are maps of the equilibrium phases associated with various combinations of temperature, pressure, and composition.

One-component (unary) phase diagram

Two-component (binary) phase diagram

Three-component (ternary) phase diagram (partial isothermal section)

Why Do We Need Phase Diagrams?

For example:

to understand solidification processes ( microstructure properties)

metallurgy, geology, …

to characterize compounds and phases“CrTe” (actually Cr1-xTe)“YbInCu4” (valence transition; transition temp. different due to nonstoichiometry)

to understand reactionsweldingsolderingcontacting of semiconductorssurface layers (hardening, e.g.)

First Fe-C Phase Diagram

(1897)

Sir William Chandler Roberts-Austen

Number of Metallic Phase Diagrams(Assumption: 80 metallic elements)

No. of componentsn

No. of possible systems

Approximate No. of investigated systems

1 80 80

2 3 160 2 500

3 82 160 3 000

4 1 581 580 200

5 24 141 016 20

6 300 500 200 -

7 3 176 716 400 -… … …

approximately 1023 40-component systems!

Phase DiagramsStructure of the Lecture

• Basics(Phase rule, lever rule, …)

• Unary (one-component) systems• Binary systems

types of phase diagrams-x diagramsinvariant reactionscomplex systemspossible errors

• Ternary systemstypes of phase diagramstypes of representations

(isotherms, isopleths, liquidus projections, Scheil

diagrams)invariant reactionscomplex systems

• Quaternary systems• p-T diagrams for higher-order systems

Books on Phase Equilibria• B. Predel: „Heterogene Gleichgewichte: Grundlagen und

Anwendungen“; Steinkopf (Darmstadt), 1982• B. Predel, M. Hoch, M. Pool: „Phase Diagrams and

Heterogeneous Equilibria“; Springer (Berlin), 2004• F.N. Rhines: „Phase Diagrams in Metallurgy: Their Development

and Application“; McGraw-Hill (New York), 1956• P. Gordon: „Principles of Phase Diagrams in Materials

Systems“; McGraw-Hill (New York), 1968• A. Prince: „Alloy Phase Equilibria“; Elsevier (Amsterdam), 1966• J. Zernike: „Chemical Phase Theory“; N.V. Uitgevers-

Maatschappij – Ae.E. Kluwer (Deventer), 1955

Collections of Phase Diagrams• T.B. Massalski et al. (Ed.): „Binary Alloy Phase Diagrams“

(3 Volumes); ASM International (Materials Park, OH), 1995.• P. Villars, A. Prince, H. Okamoto (Ed.): “Handbook of Ternary

Alloy Phase Diagrams” (10 Volumes) , ASM International (Materials Park, OH), 1995.

Journals on Phase Diagrams• Journal of Phase Equilibria and Diffusion; Springer• CALPHAD - Computer Coupling of Phase Diagrams and

Thermochemistry; Elsevier

GIBBS PHASE RULE

P + F = C + 2or

F = C + 2 – P

P = number of phasesC = number of componentsF = degrees of freedom

(number of variables that can be varied independently)

If the pressure is kept constant:

P + F‘ = C + 1or

F‘ = C + 1 – P

PHASE EQUILIBRIA IN UNARY SYSTEMS

221 bar

1.01325 bar

6.1 mbar

A

B

C

F = C - P + 2 A, B: C = 1, P = 1F = 1 – 1 + 2 = 2

C: C = 1, P = 2F = 1 – 2 + 2 = 1

Triple Pt.: C = 1, P = 3F = 1 – 3 + 2 = 0

Example: H2O

Example: H2O

1 MPa = 106 Pa = 10 bar

Example: CO2

ALLOTROPY• Elements can exist in more than one (crystalline) forms

POLYMORPHISM• A substance can exist in more than one crystalline

forms

TRANSFORMATIONS

(Principle)

• Enantiotropic transformation

Example: S S

H2O(s) H2O(l)• Monotropic transformation

Example: Pw Pr

x

Lmet

p

T

Gmet/G

1.01 bar

TmTm(met) Tb

Both stable forms

Only one stable form

TRANSFORMATIONSGibbs Energy vs. Temperature

(p = const.)

Phase ß stable(enantiotropic transformation)

Phase ß metastable(monotropic transformationpossible ß )

Metastable into stable phase, irreversible

Stable into stable phase, reversible

UNARY PHASE DIAGRAMS: EXAMPLES

Fe(enantiotropic transformations)

SiO2 (schematic)

(series of monotropic transformations)

[Pa]

TRIPLE POINTS OF METALS

Metall T (°C) p (atm) p (Pa)

Ag 960 0.000 1 1.01101

As 814 36 *) 3.65106

Ba 704 0.001 1.01102

Ca 850 0.000 1 1.01101

Cu 1083 0.000 000 78 7.910-2

Fe() 1535 0.000 05 5.1

Hg -39 0.000 000 001 3 1.3210-4

Mn 1240 0.001 1.01102

Ni 1455 0.000 1 1.01101

Pb 327 0.000 000 1 1.0110-2

Pt 1773 0.000 001 1.0110-1

Sr 770 0.000 1 1.01101

Zn 419 0.05 5.07103

*) As: 1 atm (sublimation) at 610°C

Isomorphous Systems

p-T-x Diagram

T-x diagram

p-x diagram

p-T diagram of pure B

p-T diagram of pure A

GGibbs Energy of Mixing

p = constant !

tie line(Konnode)

Basis of the CALPHAD-Methodto calculate phase diagrams

LEVER RULE

T

C

a b

N(1-y) Ny

N = total number of atomsy = fraction of atoms in phase ß(1-y) = fraction of atoms in phase L

y : (1-y) = a : b

xB xBßxB

L

a b(1-y) yC

Coring

Solidification

for case of coring

Frozen firstFrozen last

Dendritic solidification

Assumption:homogeneous equilibrium in the liquid phase is always retained

Minima and Maxima

xB xB

Error

P b-T l phase diagram .

Pb Tl xTlA ssessed A u-N i phase diagram .

Au Ni xNi

A ssessed A u-C u phase diagram .

Au Cu xCu

Miscibility Gap

Superstructures

Special Cases:

Eutectic Systems

Eutectic Line

e: Eutectic Point

Metastable extension into two-phase field!

A xBA xB

T

The Boundary Rule: Any p-phase region can be bounded only by regions containing p +/- 1 phases, where p denotes the number of phases.The Boundary Curvature Rule: Boundaries of one-phase regions must meet with curvatures such that the boundaries extrapolate into the adjacent two-phase regions.The Solubility Rule: All components aresoluble to some degree in all phases

Eutectic ReactionInvariant Reaction:

Often: lamellar microstructure of eutectic alloys

G-xbinary eutectic

Eutectic Systems: Examples

Al-Si

Pb-Bi

Ag-Cu

Al-Sn

Eutectic Systems:Primary Crystallization and Microstructure

Hypereutectic Al-Si 14% alloy: primary crystallization

Hypereutectic Al-Si 14% alloy: final microstructure

ß

Eutectic Systems:Solidification and Non-equilibrium

xB

No eutectic mixture should be detected in this case, however ...

xB

Eutectic Systems:Isothermal Diffusion / Diffusion Couples

700°C

900°C

Eutectic Systems:Limiting Cases

T

xB xB

degenerateeutectic

Eutectic Systems:Errors

(from a customer journal of the company METTLER)

Eutectoid Systems

Eutectoid Reaction: +

T

t

TL

TS

TßTe

cool

heat

Eutectoid

Fe – Fe3C(“Pearlite”)

+ Fe3C

: bcc (Ferrite): fcc (Austenite): bcc

Fe3C: cementite

hypoeutectoid: 0.3 % C

eutectoid: 0.8 % C

hypereutectoid: 1.2 % C

Eutectoid ReactionsExamples

A ssessed F e-T e phase diagram .

A ssessed N i-Z n phase diagram.

Fe-Te

Ni-Zn

Monotectic SystemsMonotectic Reaction: L1 L2 +

L2

... the phase field L1+L2 can be regarded as being made up of an infinite number of tie-lines ...

L2

L2

L2

Monotectic SystemsSolidification

Monotectic SystemsExamplesA ssessed C u-P b phase diagram .

A ssessed B i-F e phase diagram .

Cu Pb

Bi Fe

Cu-Pb

Bi-Fe

(limiting case with virtually no solubility in the solid and very limited solubility in the liquid state)

Monotectic SystemsExamplesA ssessed N i-A g phase diagram .

AgNi

upper critical solution temperature (UCST

Peritectic Reaction

A very rare example. Peritectic reactions are frequent components of complex phase diagrams with many phases, but they rarely occur as the only feature of a phase diagram.

Three stages of peritectic reaction in a directionally solidified high-speed steel. (a) First-stage structure. Dark gray is austenite; white is ferrite. The mottled structure is quenched liquid. (b) Subsequent peritectic transformation of (a). (c) Further peritectic transformation of (b). Dark gray in the middle of the white ferrite is newly formed liquid. Source: ASM Handbook, Vol. 9, Metallography and Microstructures, 2004, p 100

Peritectoid Systems

A ssessed A g-A l phase diagram .

Ag Al

+

http://www.docstoc.com/docs/62283223/monotectic-and-syntectic

http://www.docstoc.com/docs/62283223/monotectic-and-syntectic

Syntectic reaction

Complex Binary SystemsExamplesA ssessed A g-O s phase diagram .

A ssessed C u-Sn phase diagram . F rom [44R ay].

Ag Os

Cu Sn

Reaction e:L2 G + (Os)

Reaction r:G + (Os) L1

Reaction l(Metatectic or

Catatectic Reaction): + L

Complex Binary SystemsPossible Errors

Complex Binary SystemsTechnically Important SystemsA ssessed C u-Z n phase diagram .

Cu Zn

Cu-Zn = Brass

A ssessed F e-C phase diagram .

Fe

Martensite

Fe-C = Steel

Complex Binary Systems

Diffusion Couple