Fully Miscible Solution Simple solution system (e.g., Ni-Cu solution) Crystal Structure electroneg r (nm) Ni FCC 1.9 0.1246 Cu 1.8 0.1278 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

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?

The Lever Rule Draw Tie line – connects the phases in equilibrium with each other - essentially an isotherm wt% Ni 20 1200 1300 T(°C) L (liquid) a (solid) L + liquidus solidus 3 4 5 B T tie line C o S R 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.

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

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.

Cored vs Equilibrium Phases • 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 First a to solidify: 46 wt% Ni Uniform C : 35 wt% Ni Last < 35 wt% Ni

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

Consider Pb-Sn System Simple solution system (e.g., Pb-Sn solution) Crystal Structure electroneg r (nm) Pb FCC 1.8 0.175 Sn Tetragonal 0.151 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

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

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

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

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

Lamellar Eutectic Structure

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

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