“phase equilibriain materials” · 2018. 1. 30. · source: reed-hill, abbaschian,physical...
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Advanced Physical MetallurgyAdvanced Physical Metallurgy
““Phase Phase EquilibriaEquilibria in Materialsin Materials””
EunEun SooSoo ParkPark
Office: 33-316 Telephone: 880-7221Email: [email protected] hours: by an appointment
2009 fall
10. 06. 2009
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Contents for previous class
- Gibbs Phase Rule
- Invariant reaction
- Peritectic reaction
F = C − P + 2 (from T, P)
- Congruent transformationa melting point minimum, a melting point maximum, and a critical temperature associated with a order-disorder transformation
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ΔΔHHmixmix = = --25 kJ/mol25 kJ/mol
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Peritectic solidification
Fe C
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Peritectic solidification
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Peritectic solidification
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Congruent vs IncongruentCongruent phase transformation: no compositional change associated with
transformation
Incongruent phase transformation:at least one phase will experience change in composition
Examples:
• Allotropic phase transformations• Melting points of pure metals• Congruent Melting Point
Examples:
• Melting in isomorphous alloys• Eutectic reactions• Pertectic Reactions• Eutectoid reactions
Ni Ti
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Cu-Ni: Binary Isomorphous Alloy Example
Isomorphous systems contain metals which are completely soluble in each other and have a single type of crystal structure.
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4.3.5. Non-stoichiometeric compounds
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4.3.5. Non-stoichiometeric compounds
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Contents for today’s class
- Monotectic reaction: Liquid1 ↔Liquid2+ solid
- Binary Phase Diagrams: Reactions in the Solid State
* Eutectoid reaction: α ↔ β + γ
* Monotectoid reaction: α1 ↔ β + α2
* Peritectoid reaction: α + β ↔ γ
- Synthetic reaction:
Liquid1+Liquid2 ↔ α
L1+L2
α
K-Zn, Na-Zn,K-Pb, Pb-U, Ca-Cd
- Allotropy of the Components
* SYSTEMS IN WHICH TWO PHASES ARE IN EQUILIBRIUM WITH THE LIQUID PHASE
* SYSTEMS IN WHICH ONE PHASE IS IN EQUILIBRIUM WITH THE LIQUID PHASE
Metatectic reaction: β ↔ L + α Ex. Co-Os, Co-Re and Co-Ru
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ΔGm=NCXA(1-XA)+NkT[XAlnXA + (1-XA)ln(1-XA)] where, C=Z[HAB-(HAA+HBB)/2.
Here, C is an energy term, and k is bolzmann’s constant (energy/temperature).
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Free energy and activity curves for (a) kT/C<0.5, (b) kT/C=0.5 (c) kT/C>0.5
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Effect of very large positive deviations from ideality in changing the phase diagram from a eutectic to a monotectic reaction
Eutectic reaction: Liquid ↔α+β
Monotectic reaction: Liquid1 ↔Liquid2+ solid
The reversible transition, on cooling, of a liquid to a mixture of a second liquid and a solid
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15G.A. Chadwick, Brit. J. App. Phys., 16 (1965) 1096
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Monotectic
Source: Reed-Hill, Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.
Monotectic Reaction: L L1 + Solid
Cu + L1
cool
heat
Pb and Zn do not mix in solid state:
• RT: Cu in Pb < 0.007%• RT: Pb in Cu ~ 0.002 – 0.005%
0.1281.9FCCCu
0.1751.8FCCPb
r (nm)electronegCrystalStructure
0.1281.9FCCCu
0.1751.8FCCPb
r (nm)electronegCrystalStructure
26.8%
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Morphology in monotectic solidification
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Case 1:22 11 llll γγγ αα −<
Hg-Te single crystal
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Case 2: θγγγ αα cos22 11 llll +=
5.0−∝ Vλ
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Case 3: 22 11 llll γγγ αα +>
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Synthetic reaction
Ex.
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Eutectoid reaction: α ↔ β + γ
Monotectoid reaction: α1 ↔ β + α2
Peritectoid reaction: α + β ↔ γ
Transformation can only proceed if –ΔGbulk > +ΔGinterface+ΔGstrain
Binary Phase Diagrams: Reactions in the Solid State
Disordered atomic arrangement at grain boundaries will reduce the strain energy factor and the interfacial energy needed to nucleate a new phase.
The finer the grain size, and hence the larger the grain boundary area, the more readily will the transformation proceed.
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Iron-Carbon System
Source: Reed-Hill, Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.
Diagram is not ever plotted past 12 wt%
Cementite
Hägg carbide
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Iron Carbon Phase Diagram
ACM
A3
A1 (Eutectoid Temperature)
Formation of Ledeburite
Formation of Pearlite
Source: Reed-Hill, Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.
Steel Cast Irons
FCC
α ferriteBCC
δ ferrite, BCC
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Cementite – What is it?
• Cementite has an orthorhombic lattice with approximate parameters 0.45165, 0.50837 and 0.67297 nm.
• There are twelve iron atoms and four carbon atoms per
unit cell, corresponding to the formula Fe3C.
Source: http://www.msm.cam.ac.uk/phase-trans/2003/Lattices/cementite.htmlH. K. D. H. Bhadeshia
Purple: Carbon atomsOrange: Iron atoms
Iron Carbide – Ceramic Compound
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Pearlite: What is it?
• The eutectoid transformation:γ (0.77% C) α (0.02%C) + Fe3C (6.67%C)
• Alternate lamellae of ferrite and cementite as the continuous phase
• Diffusional Transformation
• “Pearlite” name is related to the regular array of the lamellae in colonies. Etching attacks the ferrite phase more than the cementite. The raised and regularly spaced cementite lamellae act as diffraction gratings and a pearl-like luster is produced by the diffraction of light of various wavelengths from different colonies
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Pearlite• Two phases appear in definite
ratio by the lever rule:
• Since the densities are same (7.86 and 7.4) lamellae widths are 7:1
• Heterogeneous nucleation and growth of pearlite colonies – but typically grows into only 1 grain
Reed-Hill, Abbaschian, 1994, [5]
%8867.6
77.067.6≈
−=α
%1267.6
077.0≈
−=cementite