G. Selvaduray - SJSU BINARY PHASE DIAGRAMS Dr. Guna Selvaduray Materials Engineering Program San Jose State University San Jose, CA 95192-0086
G. Selvaduray - SJSU
BINARY PHASE DIAGRAMS
Dr. Guna SelvadurayMaterials Engineering Program
San Jose State UniversitySan Jose, CA 95192-0086
G. Selvaduray - SJSU
Utility of Phase Diagrams
Soldering Brazing Electromigration Diffusion Problems Kirkendahl Voiding Corrosion Electrical Resistivity
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Limitations to use of Phase Diagrams
Phase Diagrams are also known as Equilibrium Diagrams
Rate of Transformation is missing TTT (Time-Temperature-
Transformation) diagrams are a complement to Phase Diagrams
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Approach
Approach taken during this course will be phenomenological
No chemical thermodynamics will be used for derivations
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Useful References1. M. Hansen & K. Anderko, Constitution of Binary Alloys, McGraw-
Hill, 19582. R.P. Elliot, Constitution of Binary Alloys, First Supplement,
McGraw-Hill, 19653. F.A. Shunk, Constitution of Binary Alloys, Second Supplement,
McGraw-Hill,19694. ASM International, ASM Handbook Volume 3: Alloy Phase
Diagrams, 19925. 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 (contd)6. E.M. Levine, C.R. Robbins & H.F. McMurdie, Phase Diagrams for
Ceramists, The American Ceramic Society, 19647. A. Reisman, Phase Equilibria-Basic Principles, Applications,
Experimental Techniques, Academic Press, 19708. A. Findlay, The Phase Rule and its Applications, Dover
Publications, 19519. G. Humpston & D.M. Jacobson, Principles of Soldering and Brazing,
ASM International, 1993
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What is a Phase?
Sand and Salt Coffee and Sugar Oil and Vinegar
How many phases in each?
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What is a Phase? (contd)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-WaterAlso known as a P-T diagramSign of [dP/dT] for:
Solid-LiquidLiquid-GasGas-Solid
equilibria
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P-T Diagram for Water
Source: Barret, Nix & Tetelman, The Principles of EngineeringMaterials, 1973. p 118
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One Component Phase DiagramRegion Number of Phases Degrees of Freedom
The Gibbs Phase Rule
P + F = C + 2
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The Quasi-Chemical ApproachUnderstanding interactions on bond energies
Interaction between 2 species: A and BA-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 BTAlloy = TA + x ( TB - TA)
Examples:Copper NickelSilicon Germanium
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Nickel-Copper Phase Diagram
Source: ??
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Germanium-Silicon Phase Diagram
Source: Barret, Nix & Tetelman, The Principles of EngineeringMaterials, 1973. p 125
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Hume Rothery Rules
1. Relative Size Ratio 15%2. Crystal Structure-must be the same3. 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 - TinGold - Silicon
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Tin-Lead Phase Diagram
Source: Barret, Nix & Tetelman, The Principles of EngineeringMaterials, 1973. p 128
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Gold-Silicon Phase Diagram
Hansen & Anderko, Constitution of BinaryAlloys, 1958. p. 232
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Gold-Germanium Phase Diagram
Hansen & Anderko, Constitution of BinaryAlloys, 1958. p. 206
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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
Hansen & Anderko, Constitution of BinaryAlloys, 1958. p. 165
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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 Chemical Activity
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Copper-Silver Phase Diagram
Source: Callister, Materials Science and Engineering:An Introduction, 2000. p. 256
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Solidus and LiquidusSolidusTemperature at which alloy is completely
solid Temperature at which liquefaction beginsLiquidusTemperature at which alloy is completely
liquidTemperature at which solidification begins
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Overall Composition
Concentration: Relative amounts of each constituentIt 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 systemIn 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 compositionNot to be confused with overall composition
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Solid SolutionsWhat 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
G. Selvaduray - SJSUSource: Barret, Nix & Tetelman, The Principles of EngineeringMaterials, 1973. p 72
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Types of Solid SolubilityUnlimited Solid Solubility: Solute and solvent are mutually soluble at all concentrations, e.g., Cu-Ni systemMeets 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
Source: Smith, Principles of Materials ScienceAnd Engineering, 1996, p.440
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Cu-Ni Phase Diagram
Source: Callister, Materials Science and Engineering:An Introduction, 2000. p. 247
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Example Problem 1One kilogram of an alloy of 70% Pb and 30% Sn is
slowly cooled from 300C. Calculate the following:
a) Weight % of liquid and at 250Cb) Chemical composition of the liquid and at 250Cc) Weight % of the liquid and just above the eutectic
temperatured) Chemical composition of the liquid and at just above
the eutectic temperature
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Pb-Sn Phase Diagram
Source: Callister, Materials Science and Engineering:An Introduction, 2000. p. 258
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Invariant Reactions
Eutectic: L = (s) + (s); e.g., Pb-Sn
Peritectic: (s) + L = (s); e.g., Pb-In
Monotectic: L1 = (s) + L2; e.g., Cu-Pb
Syntectic: L1 + L2 = (s); e.g., Na-Zn
Metatectic: (s) + (s) = L1 e.g., U-Mn
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Pb-In Phase Diagram
Hansen & Anderko, Constitution of BinaryAlloys, 1958. p. 855
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Cu-Pb Phase Diagram
Hansen & Anderko, Constitution of BinaryAlloys, 1958. p. 610
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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 & EngineeringOf Materials, 1984, p 246
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Composition dependence of microstructure
Source: Askeland, The Science & EngineeringOf Materials, 1984, p 249
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Composition dependence of microstructure
Source: Askeland, The Science & EngineeringOf Materials, 1984, p 248
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Composition dependence of microstructure
Source: Askeland, The Science & EngineeringOf Materials, 1984, p 248
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Example Problem 2For the 70% Pb and 30% Sn alloy, calculate:(a) The weight percent of alpha and beta phases
at 100C(b) The chemical composition of the and
phases at 100C(c) Amount of primary and secondary (d) Amount of formed during the eutectic reaction
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Chemical ActivityWhat is activity?A measure of the escaping tendencyActivity = 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 DeterminationsIDEAL CASE: Activity Coefficient = 1Therefore: 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
G. Selvaduray - SJSUSource: Gaskell, Introduction to ThermodynamicsOf Materials, 1973
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Example Problem 3Draw an activity-composition diagram for the Cu-Ni system at 1200C
Draw an activity-composition diagram for the Ga-As system at 400C
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Intermetallic Compounds
Line compounds Stoichiometric Ratio Stoichiometric Range
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Au-Sn Phase Diagram
Hansen & Anderko, Constitution of BinaryAlloys, 1958. p. 233
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Ag-Sn Phase Diagram
Hansen & Anderko, Constitution of BinaryAlloys, 1958. p. 52
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Using Phase Diagrams to determine Heat Treatability
Heat Treatment is based on controlling the solid state transformation rate 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
The eutectoid reaction Martensite Austenite Pearlite TTT diagrams
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Fe-C Phase Diagram
Source: Barret, Nix & Tetelman, The Principles of EngineeringMaterials, 1973. p 1305
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TTT Diagram
Source: Flinn & Trojan, Engineering Materialsand their Applications, 1986, p 239
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Age Hardening/Precipitation Strengthening
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
Source: Askeland, The Science & EngineeringOf Materials, 1984, p 281
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Al-Cu Phase Diagram
Source: Hansen & Anderko, Constitutionof Binary Alloys, 1958. p. 85
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Heat Treatment vs Strength
Source: ??
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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 densitymatrixIf densityppt > densitymatrix
Region of compression is created around the ppt
Driving force is for migration of matrix atoms awayfrom ppt
If densityppt < densitymatrixRegion of tension is created around the ppt
Driving force of for migration of matrix atomstowards the ppt
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Lead Frame Alloys
Alloy 42Copper alloy lead framesKovar
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Lead Frame Alloy Compositions
Source: Electronic Materials Handbook Volume 1: Packaging, ASM International, 1989, p. 490
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Fe-NiPhaseDiagram
Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 85
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Fe-CuPhaseDiagram
Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 581
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Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 634
Cu-SnPhaseDiagram
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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
Ficks First Law: J = -D [dc/dx][dc/dx] is the concentration gradient and
driving force for diffusionIt this were true, multiphase alloys such
as Pb-Sn alloys must self-homogenizeover 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 differenceIn the case of Pb-Sn alloys, the phases are: (Pb rich) and (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 VoidingIf 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
Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 69
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Effect of composition on properties
Mechanical Properties Electrical Resistivity
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Composition vs Strength
Source: ??
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Composition vs Resistivity
Source: Askeland, The Science & EngineeringOf Materials, 1984, p 563
G. Selvaduray - SJSUSource: Askeland, The Science & EngineeringOf Materials, 1984, p 565
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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
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Cooling Curves
Source: Smith, Principles of Materials ScienceAnd Engineering, 1996, p.441
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Experimental measurement of Hm from DSC
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Mg-SiPhaseDiagram
Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 917
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Al-SiPhaseDiagram
Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 133
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Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 106
Al-MgPhaseDiagram
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Cr-Mo Phase Diagram
Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 538
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Cr-Ni Phase Diagram
Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 542
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Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 968
Mo-NiPhaseDiagram
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Au-Si Phase Diagram
Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 232
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Source: Hansen & Anderko,Constitution of BinaryAlloys, 1958. p. 233
Au-SnPhaseDiagram
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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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