phase behavior - university of cincinnatibeaucag/classes/properties of materials...1 phase behavior...
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Phase Behavior
Callister P. 252Chapter 9
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Chalcolithic Era (7000 BC)(Copper Working)
Bronze AgeCopper and Arsenic (3000 BC)
Ores from same site
or Copper and Tin “Alloys” (2000 BC times vary around world)Coincident Ores in Thailand others involve trade
(UK source of Tin)
Iron AgeCast Iron
Steel (Iron & Carbon and Chromium Alloys) & Brass (Copper and Zinc Alloy) came later
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Difference between enthalpic interactions of A and B chain units alone and in blend
per kT ~ 1/Temperature.
There are 3 regimes for this equation: Single Phase,
Critical Condition, 2 Phase
Flory-Huggins Equation for Polymer Blends
Ideal gas mixing
Can be derived from the Boltzman Equation Ω is the number of arrangements
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
Two Phase Regime
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
Two Phase Regime
Miscibility gap is defined bydG/dΦ = μA = μB
Between circles and squaresPhase Separation is an
Uphill Battle
Need a Nucleus
Nucleation and Growth
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
Two Phase Regime
Miscibility gap is defined bydG/dΦ = μA = μB
Between circles and squaresPhase Separation is an
Uphill Battle
Need a Nucleus
Nucleation and Growth
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
Two Phase Regime
Between squaresPhase Separation is a
Down Hill Battle
Spontaneous Phase Separation
Spinodal Decomposition
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
Two Phase Regime
Between squaresPhase Separation is a
Down Hill Battle
Spontaneous Phase Separation
Spinodal Decomposition
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
Equilibrium Phase DiagramχAB
(1/T)
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
Single Phase to Critical
to Two Phase Regimeas Temperature Drops
(chi increases)
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
Tie Line
χAB
(1/T)
A B
Equilibrium Composition Determined by Binodal
Amount of Phase Determined by Lever Rule (a with A; b with B)
PVME PS
ab
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
For Single Phase Every Attempt to Separate is Up Hill on Average
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ΔG Free energy difference in going from separate polymers to mixed polymersΦA Volume Fraction of polymer ANA Degree of polymerization (molecular weight/monomer molecular weight) of polymer AχAB Average interaction between A and B chain units ~ 1/Temperature.
Flor Huggins Equation for Polymer Blends
Phase Diagram
χAB
(1/T)Spinodal Decomposition
Nucleation and Growth
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Degrees of Freedom = Components - Phases + 2 or 1 (T & P)Gibbs Phase Rule
2 2 11
Isomorphous Phase Diagram
For Metals/CeramicsWe do not Usually Consider Liquid/Liquid Phase Separation
Consider Crystallization From a Liquid Phase
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Degrees of Freedom = Components - Phases + 2 or 1 (T & P)Gibbs Phase Rule
2 2 11
For Metals/CeramicsWe do not Usually Consider Liquid/Liquid Phase Separation
Consider Crystallization From a Liquid Phase
Liquidus
and
Solidus
Lines
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Degrees of Freedom = Components - Phases + 2 or 1 (T & P)Gibbs Phase Rule
2 2 11
For Metals/CeramicsWe do not Usually Consider Liquid/Liquid Phase Separation
Consider Crystallization From a Liquid Phase
In the two phase regime if you pick temperature
The composition of the liquid and soid phases are fixed
by the tie line
If you pick the composition of the liquid or solid phase the temperature is fixed
by the tie line
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Substitutional Solid Solution
Solid solution strengthening
Disclinations are trapped by lattice strain near larger or smaller substitutional atoms
Hummel
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ThermodynamicEquilibrium
Kinetics
Hummel
Hummel
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Dendritic Growth
Crystalline growth occurs at different rates for different crystallographic directions so there is a preferred direction of growth
Growth can involve exclusion of impurities and transport of impurities from a “clean” crystal to the “dirty” melt
Crystallization releases energy so the temperature near a growth front can be too high for crystallization to occur. The melt can be colder and more likely to crystallize
Temperature differentials and the “kinetic” phase diagram can lead to segregation or coring as described by Hummel
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Callister p. 294
Equilibrium Non-Equilibrium
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Mechanical Properties of Isomorphous Binary Alloy
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Types of Phase Diagrams
2 PhasesIsomorphous
3 PhasesEutectic
Eutectoid
Peritectic
Peritectoid
Monotectic
Monotectoid
Degrees of Freedom = Components - Phases + 1
1 phase => 2 DOF (T & Comp)2 phase => 1 DOF3 phase => 0 DOF
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Eutectic Phase Diagram
Degrees of Freedom = Components - Phases + 1
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Eutectic Phase Diagram
Degrees of Freedom = Components - Phases + 1
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Hyper and Hypo Eutectic
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δ=>γ+ε
Eutectoid
Eutectic L => α+β
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β+L=>γ
γ+L=>δ
δ+L=>ε
ε+L=>η
Peritectic
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Monotectic L1 => L2 + α
Monotectoid α1 => α2+γ
Peritectoid β+γ=> εPeritectic β+L => γ
Eutectic L => α+β
Eutectoid β=>γ+ε
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Intermetallic
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FCC
Martensite (non equilibrium BCT phase from quench of γ)
BCC
Orthorhombic
Iron/Carbon Phase Diagram