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Ternary Phase Diagrams
Lesley Cornish
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Know binaries!
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Useful books
Understanding Phase Diagrams – V.B. John Ternary phase diagram books by D.R.F. West – there are several
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Ternary grid
Space diagram C
A B
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Space diagram
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Usually have elements at the corners as the constituents, but can have compounds:
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← For “normal diagrams”, where interested in all components, use the Normal equilateral triangle.
For diagrams where there is a major component, e.g. Fe in Fe-C-Cr, use a right-angled triangle →
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Everything on the outside must be on the inside – at least to some extent.
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Liquidus surface projection: Shows the invariant reactions and the primary surfaces. Should have arrows to Show the direction of Liquid composition With decreasing Temperature,
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Isothermal section – all at same T Useful! Must be at equilibrium.
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Analysing ternary microstructures
• Ensure phases >3µm (interaction volume, which ↓ with ↓ kV
• At least 5 measuremnts on different phases • (but need higher kV to excite necessary
peaks..) • Overall should lie on tie line of 2 phases, else
– Phase missing – At least one inaccurate result – suspect smallest!
• Overall should lie in tie triangle of 3 phases
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Relative proportions ≡ Lever Rule
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Not so useful, although mathematically correct. Not all the compositions Might lie in this section!
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Why vertical sections are limited:
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Binary eutectic in a ternary system: Reaction is on a locus, not invariant
Projected reactions →
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Alkemade’s line: Joins two phases of Constant composition
≡2 phase field “pseudo-binary”
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maximum
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NB Each phase of the “triangle” has Its own isothermal 3-phase tie triangle, Meaning that this is not solidifying as this vertical section suggests – compositions will be different!
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Different eutectic morphologies with different compositions as go along the locus
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Alkemade’s line: Joins two phases of Constant composition
≡2 phase field “pseudo-binary”
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Binary peritectic in a ternary: L + α → β reaction is on a locus, not invariant
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Tie triangles at decreasing temperature
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Isothermal sections ↑ Vertical section →
Rules!
Note: 3 – phase triangle! NB Each phase of the “triangle” has Its own isothermal 3-phase tie triangle, Meaning that this is not solidifying as this vertical section suggests – compositions will be different!
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Rules!
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Transition from a peritectic (higher T) to a eutectic (lower T) (direction is in decreasing T) L + α → β to L → α + β
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Grey plane is the invariant plane, where the invariant reaction occurs
Ternary eutectic reaction
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Space diagram and isothermal sections
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(a)
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Usually do not know exactly where the solidifying phase is (i.e. its composition), except when there is no solubility, then it will always be pure
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Grey plane is the invariant plane, where the invariant reaction occurs
Weak ternary peritectic reaction
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Above reaction T: L → rhombo_A7 + AGS8_ortho L + AGS8_ortho → hcp_A3 Below reaction T: rhombo_A7 + AGS8_ortho + hcp_A3 L → rhombo_A7 + hcp_A3 (now with a 2-phase field between)
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Strong ternary peritectic reaction
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↑tie triangles with decreasing T
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↑isothermal section
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Primary α (dendrites) L → α L → α + β
L + α + β → γ
From the microstructure….
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Ternary eutectic weak ternary peritectic strong ternary peritectic L → α + β + γ L + α→β + γ L + α + β → γ
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For more complex systems, with more than one reaction:
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For more complex systems, with more than one reaction:
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Example of a liquidus Surface. Ternary phases do Not join to the binary.
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A “cascade” of peritectic Reactions in Al-Ni-Re
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Alkemade’s line: Joins two phases of Constant composition
≡2 phase field “pseudo-binary”
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Reaction scheme Shows all the reactions in binaries and ternary
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Quaternary System: Adding V to WC-Co alloys
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Cheating?
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Cheating? Just plot what is relevant:
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