binary phase diagrams

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G. Selvaduray - SJSU

BINARY PHASE DIAGRAMS

Dr. Guna Selvaduray

Materials Engineering ProgramSan Jose State University

San Jose, CA 95192-0086




Utility of Phase Diagrams

Soldering Brazing

Electromigration Diffusion Problems

Kirkendahl Voiding

Corrosion Electrical Resistivity




Limitations to use of PhaseDiagrams

Phase Diagrams are also known asEquilibrium Diagrams

Rate of Transformation is missing

TTT (Time-Temperature-Transformation) diagrams are a

complement to Phase Diagrams




Approach

Approach taken during this course willbe phenomenological

No chemical thermodynamics will beused for derivations




Useful References

1. M. Hansen & K. Anderko, Constitution of Binary Alloys, McGraw-Hill, 1958

2. R.P. Elliot, Constitution of Binary Alloys, First Supplement,McGraw-Hill, 1965

3. F.A. Shunk, Constitution of Binary Alloys, Second Supplement,McGraw-Hill,1969

4. ASM International, ASM Handbook Volume 3: Alloy PhaseDiagrams, 1992

5. R. Hultgren, P.D. Desai, et al, Selected Values of theThermodynamic Properties of Binary Alloys, ASM International,1973




Useful References (cont’d)

6. E.M. Levine, C.R. Robbins & H.F. McMurdie, Phase Diagrams forCeramists, The American Ceramic Society, 1964

7. A. Reisman, Phase Equilibria-Basic Principles, Applications,Experimental Techniques, Academic Press, 1970

8. A. Findlay, The Phase Rule and its Applications, DoverPublications, 1951

9. G. Humpston & D.M. Jacobson, Principles of Soldering and Brazing,ASM International, 1993




What is a “Phase”?

Sand and Salt Coffee and Sugar

Oil and Vinegar

How many phases in each?




What is a “Phase”? (cont’d)

A phase is a homogenous, physically distinct andmechanically separable portion of the material with agiven chemical composition and structure.

For solids: Chemically and structurally distinct

For liquids: Miscibility

For gases: Always 1 phase




One Component Phase Diagram

The simplest case-WaterAlso known as a P-T diagram

Sign of [dP/dT] for:

Solid-Liquid

Liquid-Gas

Gas-Solidequilibria




P-T Diagram for Water

Source: Barret, Nix & Tetelman, The Principles of Engineering Materials, 1973. p 118




One Component Phase Diagram

Region Number of Phases Degrees of Freedom

The Gibbs Phase Rule

P + F = C + 2




The Quasi-Chemical Approach

Understanding interactions on bond energiesInteraction between 2 species: A and B

A-A and B-B bonds

Thermodynamic Parameter: Melting Point (T)

How does mixing of A-A and B-B bonds affect T?




The Ideal Case

(A-B) = x(A-A) + (1-x) (B-B)

Where x is the mole fraction of A in B

T Alloy = T A + x ( T B - T A)

Examples:

Copper – NickelSilicon – Germanium




Nickel-Copper Phase Diagram

Source: ??




Germanium-Silicon PhaseDiagram





Hume Rothery Rules

1. Relative Size Ratio ±15%2. Crystal Structure-must be the same

3. Electronegativity Difference – within

± 0.4 e.u.

4. Valence must be the same




Eutectic Behavior

A-B < 0.5 (A-A + B-B)

T Alloy

< T A

, T B

Examples:

Lead - TinGold - Silicon




Tin-Lead Phase Diagram





Gold-Silicon Phase Diagram

Hansen & Anderko, Constitution of Binary Alloys, 1958. p. 232




Gold-Germanium Phase Diagram





Intermetallic CompoundFormation

A-B > 0.5 (A-A + B-B)

T Alloy

> T A

, T B

Example:

Gallium -Arsenic




Arsenic-Gallium Phase Diagram





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 Chemical Activity




Copper-Silver Phase Diagram

Source: Callister, Materials Science and Engineering: An Introduction, 2000. p. 256




Solidus and Liquidus

SolidusTemperature at which alloy is completelysolid

Temperature at which liquefaction beginsLiquidusTemperature at which alloy is completely

liquidTemperature at which solidification begins




Overall Composition

Concentration: Relative amounts of eachconstituent

It is the horizontal axis in all binary

phase diagramsThe scale can be in weight %, atomic %or mole %




Chemical Composition of Phases

It is the chemical composition of eachphase in the system

In a system having more than one phase,

each phase will have a unique chemicalcomposition which will be different fromeach other, and will also be different from

the overall compositionNot to be confused with overallcomposition




Solid Solutions

What is a solid solution?

When foreign atoms are incorporated into a crystal structure,whether in substitutional or interstitial sites, the resultingphase is a solid solution of the matrix material (solvent) and

the foreign atoms (solute)Substitutional Solid Solution: Foreign (solute) atoms occupy

“normal” lattice sites occupied by matrix (solvent) atoms,e.g. Cu-Ni;Ge-Si

Interstitial Solid Solutions: Foreign (solute) atoms occupyinterstitial sites, e.g., Fe-C



G. Selvaduray - SJSU Source: Barret, Nix & Tetelman, The Principles of Engineering Materials, 1973. p 72




Types of Solid Solubility

Unlimited Solid Solubility: Solute and solvent are mutuallysoluble at all concentrations, e.g., Cu-Ni system

Meets the requirements of the Hume-Rothery Rules

Result is a “single phase alloy”

Limited or Partial Solid Solubility: There is a limit to how muchof the solute can dissolve in the solvent before “saturation” isreached, e.g., Pb-Sn and most other systems

Does not meet the requirements of the Hume-Rothery RulesResults in a “multi-phase alloy”




Amount of each phase

Dependent on the Overall Compositionand Temperature

The (Inverse) Lever Rule

Tie-Lines




Lever Rule - 1

Source: Smith, Principles of Materials Science And Engineering, 1996, p.440




Cu-Ni Phase Diagram





Example Problem 1

One kilogram of an alloy of 70% Pb and 30% Sn isslowly cooled from 300ºC. Calculate thefollowing:

a) Weight % of liquid and α at 250ºC

b) Chemical composition of the liquid and α at 250ºC

c) Weight % of the liquid and α just above the eutectictemperature

d) Chemical composition of the liquid and α at just abovethe eutectic temperature




Pb-Sn Phase Diagram





Invariant Reactions

Eutectic: L = α (s) + β (s); e.g., Pb-Sn

Peritectic: α (s) + L = β (s); e.g., Pb-In

Monotectic: L1 = α (s) + L2; e.g., Cu-Pb

Syntectic: L1 + L2 = α (s); e.g., Na-Zn

Metatectic: β (s) + α (s) = L1 e.g., U-Mn




Pb-In Phase Diagram





Cu-Pb Phase Diagram





Microstructure Development

The microstructure developed depends onthe overall composition and the cooling

rate




Composition dependence ofmicrostructure

Source: Askeland, The Science & Engineering Of Materials, 1984, p 246

d d f






C i i d d f




Example Problem 2

For the 70% Pb and 30% Sn alloy, calculate:(a) The weight percent of alpha and beta phasesat 100ºC

(b) The chemical composition of the α and βphases at 100ºC

(c) Amount of primary and secondary α

(d) Amount ofα

formed during the eutectic reaction




Chemical Activity

What is activity?

A measure of the “escaping tendency”

Activity = 1 if species is in its standard

state (pure, most stable form, attemperature of interest)

What is the activity of a species in a

solution?Activity (a) =Activity Coefficient x MoleFraction




Activity Determinations

IDEAL CASE: Activity Coefficient = 1

Therefore: Activity = Mole Fraction; e.g., Cu-Ni

NON-IDEAL CASE:

Positive Deviation: a>aid, i.e., activity coefficient>1e.g. Pb-Sn

Negative Deviation: a<aid, i.e., activity coefficient<1

e.g. Ga-As



G. Selvaduray - SJSU Source: Gaskell, Introduction to Thermodynamics Of Materials, 1973




Example Problem 3

Draw an activity-composition diagram forthe Cu-Ni system at 1200ºC

Draw an activity-composition diagram forthe Ga-As system at 400ºC

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Intermetallic Compounds

Line compounds Stoichiometric Ratio

Stoichiometric Range

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Au-Sn Phase Diagram





Ag-Sn Phase Diagram


U i Ph Di t




Using Phase Diagrams todetermine Heat Treatability

Heat Treatment is based on“controlling” the solid statetransformation rate Heat treatment of steels: control of the

eutectoid reaction Age hardening (precipitation strengthening)

of aluminum alloys: control of precipitation

reaction




Heat Treatment of Steels

The eutectoid reaction Martensite

Austenite

Pearlite TTT diagrams




Fe-C Phase Diagram

Source: Barret, Nix & Tetelman, The Principles of Engineering

Materials, 1973. p 1305




TTT Diagram

Source: Flinn & Trojan, Engineering Materials and their Applications, 1986, p 239

Age Hardening/Precipitation




Age Hardening/PrecipitationStrengthening

Particularly relevant for aluminum alloys,e.g., aluminum lines on ICs

Phase diagrams tell us if an alloy system

is age-hardenable, and the compositionrange over which the alloy system isage-hardenable

Al-Cu system




Age Hardening Al Alloys

Source: Askeland, The Science & Engineering

Of Materials, 1984, p 281




Al-Cu Phase Diagram

Source: Hansen & Anderko, Constitution of Binary Alloys, 1958. p. 85




Heat Treatment vs Strength

Source: ??




Heat Treatment vs Ductility

Source: ??

Coherent & Incoherent




Coherent & Incoherent

Precipitates

Source: ??

Effect of aging on




Effect of aging onElectromigration

Critical parameter: densityppt vs densitymatrix

If densityppt > densitymatrix

Region of compression is created around the ppt

Driving force is for migration of matrix atoms awayfrom ppt

If densityppt < densitymatrix

Region of tension is created around the ppt

Driving force of for migration of matrix atomstowards the ppt




Lead Frame Alloys

Alloy 42Copper alloy lead frames

Kovar

Lead Frame Alloy




L a Fram y

Compositions

Source: Electronic Materials Handbook Volume 1: Packaging, ASM International, 1989, p. 490




Fe-NiPhaseDiagram

Source: Hansen & Anderko,Constitution of Binary Alloys, 1958. p. 85




Fe-CuPhaseDiagram






Cu-SnPhase

Diagram




Example Problem 4

Will the age hardening processcharacteristics affect the electricalresistivity (or conductivity) of lead

frames?Will the conductivity increase or decreasewith overaging?

Application of Phase Diagrams




pp g

to Diffusion

Fick’s First Law: J = -D [dc/dx]

[dc/dx] is the concentration gradient anddriving force for diffusion

It this were true, multiphase alloys suchas Pb-Sn alloys must “self-homogenize”over time and transform into a single

phase alloy

Activity: Driving Force for




y g

DiffusionThe driving force for diffusion to occur isthe activity difference

In the case of Pb-Sn alloys, the phases are:

α (Pb rich) and β (Sn rich)Diffusion of a species from one phase intoanother will not occur if:

aSn (beta) = aSn (alpha)aPb (beta) = aPb (alpha)




Relevance of solid solubility limits

Phase diagrams also tell us the maximumextent to which one species can diffuseinto another

This is given by the solid solubility limitsat the temperature of interest

The Cu-Ni example in standardtextbooks is most often not applicable




Kirkendahl Voiding

If there is a major difference in solidsolubility limits, voiding can be expected tooccur in the phase that permits less solidsolubility

e.g., the Al-Au system

Interdiffusion does not necessarily occur atthe same rate




Al-Au Phase Diagram

Source: Hansen & Anderko,Constitution of Binary

Alloys, 1958. p. 69

Effect of composition on




p

properties

Mechanical Properties

Electrical Resistivity




Composition vs Strength

Source: ??




Composition vs Resistivity








Determination of 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 Microscopy




Cooling Curves

Source: Smith, Principles of Materials Science

And Engineering, 1996, p.441

Experimental measurement of




∆Hm from DSC




Mg-SiPhaseDiagram





Al-SiPhaseDiagram






Al-MgPhaseDiagram




Cr-Mo Phase Diagram

Source: Hansen & Anderko,Constitution of Binary

Alloys, 1958. p. 538




Cr-Ni Phase Diagram






Mo-NiPhaseDiagram




Au-Si Phase Diagram






Au-SnPhase

Diagram

T Ph D




Ternary Phase Diagrams

Three components

Overall composition

Number of phases

Chemical composition of each phase Amount of each phase

Solidification sequence

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E l P bl 5




Example Problem 5

What is the maximum number of phasesthat can exist in a ternary system?

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binary phase diagrams

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