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Fully Miscible Solution

Fully Miscible Solution. Simple solution system (e.g., Ni-Cu solution). Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii ( W. Hume – Rothery rules ) suggesting high mutual solubility.

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Fully Miscible Solution

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  1. Fully Miscible Solution Simple solution system (e.g., Ni-Cu solution) • Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility. • Ni and Cu are totally miscible at all mixture compositions – isomorphous

  2. Copper-Nickel Binary Equilibrium Phase Diagram • Solid solutions are typically designated by lower case Greek letters: a, B, g, etc. • Liquidus line separates liquid from two phase field • Solidus line separates two phase field from a solid solution • Pure metals have melting points • Alloys have melting ranges What do we have? What’s the composition?

  3. T(°C) tie line liquidus L (liquid) 1300 a + L B solidus T B a a + L (solid) 1200 S R 20 3 0 4 0 5 0 C C C a L o wt% Ni The Lever Rule • Draw Tie line – connects the phases in equilibrium with each other - essentially an isotherm Derived from Conservation of Mass: (1) Wa + WL = 1 (2) WaCa + WLCL = Co Let W = mass fraction (amount of phase) Adapted from Fig. 9.3(b), Callister 7e.

  4. Example Calculation Cu-Ni system T(°C) C = 35 wt% Ni o liquidus L (liquid) 1300 a + L B T solidus B a a + L (solid) 1200 a At T : Both and L B 32 35 4 3 20 3 0 4 0 5 0 S = WL C C C a L o wt% Ni R + S R = = 27 wt% Wa R + S tie line S R

  5. Equilibrium Cooling in a Cu-Ni Binary • Phase diagram: Cu-Ni system. • System is: --binary i.e., 2 components: Cu and Ni. --isomorphous i.e., complete solubility of one component in another; a phase field extends from 0 to 100 wt% Ni. • Consider Co = 35 wt%Ni.

  6. Cored vs Equilibrium Phases Uniform C : a a First to solidify: 35 wt% Ni 46 wt% Ni a Last to solidify: < 35 wt% Ni • Ca changes as we solidify. • Cu-Ni case: First a to solidify has Ca = 46 wt% Ni. Last a to solidify has Ca = 35 wt% Ni. • Fast rate of cooling: Cored structure • Slow rate of cooling: Equilibrium structure

  7. 60 %EL for pure Cu 400 %EL for 50 pure Ni TS for Elongation (%EL) 40 pure Ni Tensile Strength (MPa) 300 30 TS for pure Cu 200 20 0 20 40 60 80 100 0 20 40 60 80 100 Cu Ni Cu Ni Composition, wt% Ni Composition, wt% Ni Mechanical Properties:Cu-Ni System • Effect of solid solution strengthening on: --Tensile strength (TS) --Ductility (%EL,%AR) --Peak as a function of Co --Min. as a function of Co

  8. Consider Pb-Sn System Simple solution system (e.g., Pb-Sn solution) 13.7% • W. Hume – Rothery Rules: • Atomic size is within 15% • Same electronegativity • Do not have same crystal structure Will have some miscibility, but will not have complete miscibility

  9. Binary-Eutectic System Eutectic Reaction: L(CE) (CE) + (CE) From Greek eut ktos, easily melted Liquidus Solidus Eutectic Point Solvus

  10. Microstructural Evolution in Eutectic T(°C) L: Cowt% Sn 400 L a L 300 L a + a 200 (Pb-Sn a: Cowt% Sn TE System) 100 b + a 0 10 20 30 Co , wt% Sn Co 2 (room T solubility limit) Consider (1): Co < 2 wt% Sn Result: --at extreme ends --polycrystal of a grains i.e., only one solid phase.

  11. Microstructural Evolution in Eutectic L: Co wt% Sn T(°C) 400 L L 300 a L + a a: Cowt% Sn a 200 TE a b 100 b + a Pb-Sn system 0 10 20 30 Co , wt% Sn Co 2 (sol. limit at T ) 18.3 room (sol. limit at TE) • Consider (2): • 2 wt% Sn < Co < 18.3 wt% Sn • Result: • Initially liquid +  • then  alone • finally two phases • a polycrystal • fine -phase inclusions

  12. Microstructural Evolution in Eutectic Micrograph of Pb-Sn T(°C) eutectic L: Co wt% Sn microstructure 300 L Pb-Sn system a L + a b L 200 183°C TE 100 160m a : 97.8 wt% Sn : 18.3 wt%Sn 0 20 40 60 80 100 97.8 18.3 CE C, wt% Sn 61.9 Consider (3): Co = CE • Result: Eutectic microstructure (lamellar structure) --alternating layers (lamellae) of a and b crystals.

  13. Lamellar Eutectic Structure

  14. Microstructural Evolution in Eutectic L a L a R S S R a b + a primary a eutectic b eutectic 18.3 61.9 97.8 Consider (4): 18.3 wt% Sn < Co < 61.9 wt% Sn T(°C) L: Co wt% Sn Result: a crystals and a eutectic microstructure 300 L Pb-Sn system a L + a b b L + 200 TE 100 0 20 40 60 80 100 Co, wt% Sn

  15. Hypoeutectic vs Hypereutectic 300 L T(°C) a L + a b b L + (Pb-Sn 200 TE System) a + b 100 Co, wt% Sn 0 20 40 60 80 100 eutectic hypoeutectic: Co = 50 wt% Sn hypereutectic: (illustration only) 61.9 eutectic: Co=61.9wt% Sn a b a b a a b b a b a b 175 mm 160 mm eutectic micro-constituent

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