BINARY PHASE DIAGRAMS
Dr. Guna Selvaduray
Materials Engineering Program
San Jose State University
San Jose, CA 95192-0086
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Utility of Phase Diagrams
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Soldering
Brazing
Electromigration
Diffusion Problems
Kirkendahl Voiding
Corrosion
Electrical Resistivity
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Limitations to use of Phase
Diagrams
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Phase Diagrams are also known as
Equilibrium Diagrams
Rate of Transformation is missing
TTT (Time-TemperatureTransformation) diagrams are a
complement to Phase Diagrams
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Approach
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Approach taken during this course will
be phenomenological
No chemical thermodynamics will be
used for derivations
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Useful References
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M. Hansen & K. Anderko, Constitution of Binary Alloys, McGrawHill, 1958
R.P. Elliot, Constitution of Binary Alloys, First Supplement,
McGraw-Hill, 1965
F.A. Shunk, Constitution of Binary Alloys, Second Supplement,
McGraw-Hill,1969
ASM International, ASM Handbook Volume 3: Alloy Phase
Diagrams, 1992
R. Hultgren, P.D. Desai, et al, Selected Values of the
Thermodynamic Properties of Binary Alloys, ASM International,
1973
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Useful References (cont’d)
6. E.M. Levine, C.R. Robbins & H.F. McMurdie, Phase Diagrams for
Ceramists, 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, Dover
Publications, 1951
9. G. Humpston & D.M. Jacobson, Principles of Soldering and Brazing,
ASM International, 1993
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What is a “Phase”?
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Sand and Salt
Coffee and Sugar
Oil and Vinegar
How many phases in each?
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What is a “Phase”? (cont’d)
A phase is a homogenous, physically distinct and
mechanically separable portion of the material with a
given chemical composition and structure.
For solids: Chemically and structurally distinct
For liquids: Miscibility
For gases: Always 1 phase
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One Component Phase Diagram
The simplest case-Water
Also known as a P-T diagram
Sign of [dP/dT] for:
Solid-Liquid
Liquid-Gas
Gas-Solid
equilibria
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P-T Diagram for Water
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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
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The Quasi-Chemical Approach
Understanding interactions on bond energies
Interaction 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?
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The Ideal Case
(A-B) = x(A-A) + (1-x) (B-B)
Where x is the mole fraction of A in B
TAlloy = TA + x ( TB - TA)
Examples:
Copper – Nickel
Silicon – Germanium
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Nickel-Copper Phase Diagram
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Source: ??
Germanium-Silicon Phase
Diagram
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Source: Barret, Nix & Tetelman, The Principles of Engineering
Materials, 1973. p 125
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
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Eutectic Behavior
A-B < 0.5 (A-A + B-B)
TAlloy < TA , TB
Examples:
Lead - Tin
Gold - Silicon
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Tin-Lead Phase Diagram
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Source: Barret, Nix & Tetelman, The Principles of Engineering
Materials, 1973. p 128
Gold-Silicon Phase Diagram
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Hansen & Anderko, Constitution of Binary
Alloys, 1958. p. 232
Gold-Germanium Phase Diagram
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Hansen & Anderko, Constitution of Binary
Alloys, 1958. p. 206
Intermetallic Compound
Formation
A-B > 0.5 (A-A + B-B)
TAlloy > TA , TB
Example:
Gallium -Arsenic
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Arsenic-Gallium Phase Diagram
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Hansen & Anderko, Constitution of Binary
Alloys, 1958. p. 165
Working with Phase Diagrams
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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
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Copper-Silver Phase Diagram
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Source: Callister, Materials Science and Engineering:
An Introduction, 2000. p. 256
Solidus and Liquidus
Solidus
Temperature at which alloy is completely
solid
Temperature at which liquefaction begins
Liquidus
Temperature at which alloy is completely
liquid
Temperature at which solidification begins
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Overall Composition
Concentration: Relative amounts of each
constituent
It is the horizontal axis in all binary
phase diagrams
The scale can be in weight %, atomic %
or mole %
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Chemical Composition of Phases
It is the chemical composition of each
phase in the system
In a system having more than one phase,
each phase will have a unique chemical
composition which will be different from
each other, and will also be different from
the overall composition
Not to be confused with overall
composition
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Solid Solutions
What is a solid solution?
When foreign atoms are incorporated into a crystal structure,
whether in substitutional or interstitial sites, the resulting
phase 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 occupy
interstitial sites, e.g., Fe-C
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Source: Barret, Nix & Tetelman, The Principles of Engineering
Materials, 1973. p 72
Types of Solid Solubility
Unlimited Solid Solubility: Solute and solvent are mutually
soluble 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 much
of the solute can dissolve in the solvent before “saturation” is
reached, e.g., Pb-Sn and most other systems
Does not meet the requirements of the Hume-Rothery Rules
Results in a “multi-phase alloy”
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Amount of each phase
Dependent on the Overall Composition
and Temperature
The (Inverse) Lever Rule
Tie-Lines
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Lever Rule - 1
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Source: Smith, Principles of Materials Science
And Engineering, 1996, p.440
Cu-Ni Phase Diagram
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Source: Callister, Materials Science and Engineering:
An Introduction, 2000. p. 247
Example Problem 1
One kilogram of an alloy of 70% Pb and 30% Sn is
slowly cooled from 300ºC. Calculate the
following:
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 eutectic
temperature
d)
Chemical composition of the liquid and α at just above
the eutectic temperature
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Pb-Sn Phase Diagram
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Source: Callister, Materials Science and Engineering:
An Introduction, 2000. p. 258
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
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Pb-In Phase Diagram
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Hansen & Anderko, Constitution of Binary
Alloys, 1958. p. 855
Cu-Pb Phase Diagram
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Hansen & Anderko, Constitution of Binary
Alloys, 1958. p. 610
Microstructure Development
The microstructure developed depends on
the overall composition and the cooling
rate
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Composition dependence of
microstructure
Source: Askeland, The Science & Engineering
Of Materials, 1984, p 246
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Composition dependence of
microstructure
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Source: Askeland, The Science & Engineering
Of Materials, 1984, p 249
Composition dependence of
microstructure
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Source: Askeland, The Science & Engineering
Of Materials, 1984, p 248
Composition dependence of
microstructure
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Source: Askeland, The Science & Engineering
Of Materials, 1984, p 248
Example Problem 2
For the 70% Pb and 30% Sn alloy, calculate:
(a) The weight percent of alpha and beta phases
at 100ºC
(b) The chemical composition of the α and β
phases at 100ºC
(c) Amount of primary and secondary α
(d) Amount of α formed during the eutectic reaction
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Chemical Activity
What is activity?
A measure of the “escaping tendency”
Activity = 1 if species is in its standard
state (pure, most stable form, at
temperature of interest)
What is the activity of a species in a
solution?
Activity (a) =Activity Coefficient x Mole
Fraction
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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>1
e.g. Pb-Sn
Negative Deviation: a<aid, i.e., activity coefficient<1
e.g. Ga-As
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Source: Gaskell, Introduction to Thermodynamics
Of Materials, 1973
Example Problem 3
Draw an activity-composition diagram for
the Cu-Ni system at 1200ºC
Draw an activity-composition diagram for
the Ga-As system at 400ºC
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Intermetallic Compounds
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Line compounds
Stoichiometric Ratio
Stoichiometric Range
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Au-Sn Phase Diagram
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Hansen & Anderko, Constitution of Binary
Alloys, 1958. p. 233
Ag-Sn Phase Diagram
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Hansen & Anderko, Constitution of Binary
Alloys, 1958. p. 52
Using Phase Diagrams to
determine Heat Treatability
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Heat Treatment is based on
“controlling” the solid state
transformation rate
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Heat treatment of steels: control of the
eutectoid reaction
Age hardening (precipitation strengthening)
of aluminum alloys: control of precipitation
reaction
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Heat Treatment of Steels
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The eutectoid reaction
Martensite
Austenite
Pearlite
TTT diagrams
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Fe-C Phase Diagram
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Source: Barret, Nix & Tetelman, The Principles of Engineering
Materials, 1973. p 1305
TTT Diagram
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Source: Flinn & Trojan, Engineering Materials
and their Applications, 1986, p 239
Age Hardening/Precipitation
Strengthening
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Particularly relevant for aluminum alloys,
e.g., aluminum lines on ICs
Phase diagrams tell us if an alloy system
is age-hardenable, and the composition
range over which the alloy system is
age-hardenable
Al-Cu system
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Age Hardening Al Alloys
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Source: Askeland, The Science & Engineering
Of Materials, 1984, p 281
Al-Cu Phase Diagram
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Source: Hansen & Anderko, Constitution
of Binary Alloys, 1958. p. 85
Heat Treatment vs Strength
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Source: ??
Heat Treatment vs Ductility
Source: ??
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Coherent & Incoherent
Precipitates
Source: ??
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Effect of aging on
Electromigration
Critical parameter: densityppt vs densitymatrix
If densityppt > densitymatrix
Region of compression is created around the ppt
Driving force is for migration of matrix atoms away
from ppt
If densityppt < densitymatrix
Region of tension is created around the ppt
Driving force of for migration of matrix atoms
towards the ppt
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Lead Frame Alloys
Alloy 42
Copper alloy lead frames
Kovar
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Lead Frame Alloy
Compositions
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Source: Electronic Materials Handbook Volume 1:
Packaging, ASM International, 1989, p. 490
Fe-Ni
Phase
Diagram
Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 85
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Fe-Cu
Phase
Diagram
Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 581
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Cu-Sn
Phase
Diagram
Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 634
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Example Problem 4
Will the age hardening process
characteristics affect the electrical
resistivity (or conductivity) of lead
frames?
Will the conductivity increase or decrease
with overaging?
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Application of Phase Diagrams
to Diffusion
Fick’s First Law: J = -D [dc/dx]
[dc/dx] is the concentration gradient and
driving force for diffusion
It this were true, multiphase alloys such
as Pb-Sn alloys must “self-homogenize”
over time and transform into a single
phase alloy
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Activity: Driving Force for
Diffusion
The driving force for diffusion to occur is
the 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 into
another will not occur if:
aSn (beta) = aSn (alpha)
aPb (beta) = aPb (alpha)
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Relevance of solid solubility limits
Phase diagrams also tell us the maximum
extent to which one species can diffuse
into another
This is given by the solid solubility limits
at the temperature of interest
The Cu-Ni example in standard
textbooks is most often not applicable
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Kirkendahl Voiding
If there is a major difference in solid
solubility limits, voiding can be expected to
occur in the phase that permits less solid
solubility
e.g., the Al-Au system
Interdiffusion does not necessarily occur at
the same rate
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Al-Au Phase Diagram
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Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 69
Effect of composition on
properties
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Mechanical Properties
Electrical Resistivity
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Composition vs Strength
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Source: ??
Composition vs Resistivity
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Source: Askeland, The Science & Engineering
Of Materials, 1984, p 563
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Source: Askeland, The Science & Engineering
Of Materials, 1984, p 565
Determination of Phase
Diagrams
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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
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Cooling Curves
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Source: Smith, Principles of Materials Science
And Engineering, 1996, p.441
Experimental measurement of
∆Hm from DSC
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Mg-Si
Phase
Diagram
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Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 917
Al-Si
Phase
Diagram
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Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 133
Al-Mg
Phase
Diagram
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Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 106
Cr-Mo Phase Diagram
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Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 538
Cr-Ni Phase Diagram
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Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 542
Mo-Ni
Phase
Diagram
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Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 968
Au-Si Phase Diagram
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Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 232
Au-Sn
Phase
Diagram
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Source: Hansen & Anderko,
Constitution of Binary
Alloys, 1958. p. 233
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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Example Problem 5
What is the maximum number of phases
that can exist in a ternary system?
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