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Phase equilibria: limit

Introduction – – solutions, single – – more than one phase Adapted from Fig. 9.1, Callister 7e. Sucrose/ Phase Diagram • Solubility Limit: Max for 10 0 which only a single phase Solubility L occurs. 8 0 Limit () 6 0 + L S 4 0 (liquid solution i.e., syrup) (solid 20 (°C) Temperature sugar)

0 20 40 60 80 100

Co =Composition (wt% sugar) Water Pure Pure Sugar Pure Pure 1 Components and phases

• Components: The elements or compounds which are present in the (e.g., Al and Cu) • Phases: The physically and chemically distinct material regions that result (e.g., α and β).

Aluminum- β (lighter Copper phase)

α (darker phase)

Adapted from chapter-opening photograph, Chapter 9, Callister 3e. 2 Phase diagrams

• Indicate phases as function of T, Co, and P. • For this course: -binary systems: just 2 components. -independent variables: T and Co (P = 1 atm is almost always used).

T(°C) 1600 • 2 phases: • Phase L (liquid) Diagram for Cu-Ni 1500 L (liquid) α (FCC ) system 1400 • 3 phase fields: L α 1300 L + α L + α 1200 solidusα Adapted from Fig. 9.3(a), Callister 7e. (FCC solid (Fig. 9.3(a) is adapted from Phase 1100 Diagrams of Binary Nickel Alloys, P. Nash solution) (Ed.), ASM International, Materials Park, OH (1991). 1000 0 20 40 60 80 100 wt% Ni 3 Phase diagrams

• Rule 1: If we know T and Co, then we know: --the # and types of phases present.

T(°C) • Examples: 1600 L (liquid) 1500 Cu-Ni phase 1400 liquidus diagram α 1300 α + L (FCC solid 1200 solution)

Adapted from Fig. 9.3(a), Callister 7e. (Fig. 9.3(a) is adapted from Phase 1100 Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991). 1000 0 20 40 60 80 100 wt% Ni

4 Phase diagrams

• Rule 2: If we know T and Co, then we know: --the composition of each phase. Cu-Ni system T(°C) • Examples:

L (liquid) liquidus 1300 α L +

solidus α α L + 1200 (solid)

20 30 40 50 wt% Ni

Adapted from Fig. 9.3(b), Callister 7e. (Fig. 9.3(b) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991.)

5 Phase diagrams

• Rule 3: If we know T and Co, then we know: --the amount of each phase (given in wt%). Cu-Ni system • Examples: T(°C) C o = 35 wt% Ni T A A tie line At TA : Only Liquid (L) L (liquid) liquidus 1300 α W = 100 wt%, W = 0 + L α B L α T At TD : Only Solid ( ) B R S solidus α W L = 0, Wα = 100 wt% α L + (solid) At T : Both α and L 1200 D B T D

20 3032 35 404 3 50 C LC o C α wt% Ni

Adapted from Fig. 9.3(b), Callister 7e. (Fig. 9.3(b) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991.) 6 The

Tie line – connects the phases in equilibrium with each other - essentially an isotherm

T(°C) How much of each phase? tie line Think of it as a lever (teeter-totter) L (liquid) liquidus 1300 α + M M B L L α T B solidus α α + 1200 L (solid) R S R S

20 30C C 40 C 50 L o α M " !S = M L !R wt% Ni Adapted from Fig. 9.3(b), Callister 7e.

7 Cooling

• Phase diagram: T(°C) L: 35wt%Ni Cu-Ni system. L (liquid) Cu-Ni • System is: 1300 system --binary A α L: 35 wt% Ni + i.e., 2 components: L α: 46 wt% Ni B Cu and Ni. 35 46 32 C --isomorphous 43 i.e., complete D solubility of one 24 36 L: 32 wt% Ni component in α α: 43 wt% Ni 1200 another; α phase L + E field extends from L: 24 wt% Ni 0 to 100 wt% Ni. α α: 36 wt% Ni (solid)

• Consider C = 35 wt%Ni. 1100 o 20 30 35 40 50 Adapted from Fig. 9.4, Co wt% Ni Callister 7e. 8 Binary eutectic systems

has a special composition 2 components with a min. T. Cu-Ag Ex.: Cu-Ag system T(°C) system 1200 • 3 single phase regions L (liquid) (L, α, β ) 1000 • Limited solubility: α L + α 779°C L+β α : mostly Cu 800 β TE 8.0 71.9 91.2 β : mostly Ag 600 • TE : No liquid below TE α + β • CE : Min. melting TE 400

composition 200 0 20 40 60 CE 80 100 • Eutectic transition Co , wt% Ag L(CE) α(CαE) + β(CβE) Adapted from Fig. 9.7, Callister 7e. 9 Binary eutectic systems

• For a 40 wt% Sn-60 wt% Pb alloy at 150°C, find... --the phases present: Pb-Sn T(°C) system

300 L (liquid) α L+α 200 183°C L+β β 18.3 61.9 97.8

100 α + β

0 20 60 80 100 C, wt% Sn Adapted from Fig. 9.8, Callister 7e.

10 Binary eutectic systems

• For a 40 wt% Sn-60 wt% Pb alloy at 200°C, find... --the phases present: Pb-Sn T(°C) system

300 L (liquid) L+ α α 200 L+β β 183°C

100 α + β

0 20 60 80 100 C, wt% Sn Adapted from Fig. 9.8, Callister 7e.

11 Microstructures in eutectic systems

• Co < 2 wt% Sn T(°C) L: Co wt% Sn • Result: 400 --at extreme ends L --polycrystal of α grains α i.e., only one solid phase. 300 L

L+ α α 200 (Pb-Sn T α: Co wt% Sn E System)

100 α+β

0 10 20 30 C Adapted from Fig. 9.11, o Co, wt% Sn Callister 7e. 2 (room T solubility limit) 12 Microstructures in eutectic systems

L: C wt% Sn • 2 wt% Sn < Co < 18.3 wt% Sn T(°C) o • Result: 400 . Initially liquid + α L . then α alone L . finally two phases 300 α  α polycrystal L + α  fine β-phase inclusions α: Co wt% Sn α 200 TE α β 100 α+ β Pb-Sn system

0 10 20 30 C Adapted from Fig. 9.12, 2 o Co , wt% Sn Callister 7e. (sol. limit at Troom) 18.3 (sol. limit at T ) E 13 Microstructures in eutectic systems

• Co = CE • Result: Eutectic microstructure (lamellar structure) --alternating layers (lamellae) of α and β .

T(°C) Micrograph of Pb-Sn eutectic L: Co wt% Sn microstructure 300 L Pb-Sn L+ α system α 200 183°C L + β β TE

100 160 µm α + β Adapted from Fig. 9.14, Callister 7e.

0 20 40 60 80 100 CE Adapted from Fig. 9.13, 61.9 C, wt% Sn 14 Callister 7e. Microstructures in eutectic systems

• 18.3 wt% Sn < Co < 61.9 wt% Sn • Result: α crystals and a eutectic microstructure

T(°C) L: Co wt% Sn α L L 300 L α Pb-Sn L+α system α 200 L+β β TE

100 α+β primary α eutectic α eutectic β 0 20 40 60 80 100

Adapted from Fig. 9.16, 15 Callister 7e. Co, wt% Sn Hypoeutectic & hypereutectic

300 L Adapted from Fig. 9.8, T(°C) Callister 7e. (Fig. 9.8 α L+α 200 L+β β (Pb-Sn adapted from Binary Phase T Diagrams, 2nd ed., Vol. 3, E System) T.B. Massalski (Editor-in- α + β Chief), ASM International, 100 Materials Park, OH, 1990.)

0 20 40 60 80 100 Co, wt% Sn eutectic hypoeutectic: Co = 50 wt% Sn 61.9 hypereutectic: (illustration only) (Figs. 9.14 and 9.17 from Metals Handbook, 9th ed., α eutectic: Co = 61.9 wt% Sn Vol. 9, β Metallography and α β Microstructures, α α β β American Society for α β Metals, Materials Park, OH, 1985.) α β 175 µm 160 µm Adapted from eutectic micro-constituent Adapted from Fig. 9.17, Fig. 9.17, Callister 7e. Adapted from Fig. 9.14, Callister 7e. (Illustration 16 Callister 7e. only) Intermetallic compounds

Adapted from Fig. 9.20, Callister 7e.

Mg2Pb

Note: intermetallic compound forms a line - not an area - because stoichiometry (i.e. composition) is exact. 17 Peritectic & eutectoid

• Cu-Zn Phase diagram

Adapted from Fig. 9.21, Callister 7e.

18 Fe-C phase diagram

• 2 important T(°C) points 1600 δ -Eutectic (A): 1400 L L ⇒ γ + Fe C 3 γ γ +L 1200 A L+Fe C -Eutectoid (B): () 1148°C 3 R S γ ⇒ α + Fe3C 1000 γ γ γ+Fe3C α γ γ + 800α γ B 727°C = Teutectoid C (cementite)

R S 3 600 α+Fe C 3 Fe 400 0 1 2 3 4 5 6 6.7 (Fe) 0.76 4.30 120 µm Co, wt% C Result: Pearlite = Fe3C (cementite-hard) alternating layers of α (ferrite-soft) α and Fe3C phases eutectoid 19

(Adapted from Fig. 9.27, Callister 7e.) C Adapted from Fig. 9.24,Callister 7e. Hypoeutectoid

T(°C) 1600 δ 1400 L (Fe-C γ γ γ γ+L γ γ 1200 1148°C L+Fe C System) (austenite) 3 γ γ 1000 Adapted from Figs. 9.24 γ γ γ + Fe C 3 and 9.29,Callister 7e. (Fig. 9.24 adapted from α 800 αγ γ r s 727°C Binary Alloy Phase α Diagrams, 2nd ed., Vol.

γ γ α R S C (cementite)

3 1, T.B. Massalski (Ed.-in- wα =s/(r+s) 600 α + Fe C Chief), ASM International,

3 Fe wγ =(1- wα) Materials Park, OH, 400 1990.) α 0 1 2 3 4 5 6 6.7 (Fe) C0 Co , wt% C

pearlite 0.76 wpearlite = wγ Hypoeutectoid 100 µm wα =S/(R+S) steel w =(1-w ) Fe3C α pearlite proeutectoid ferrite Adapted from Fig. 9.30,Callister 7e. 20 Hypereutectoid steel

T(°C) 1600 δ 1400 L (Fe-C System) γ γ γ γ+L 1200 1148°C L+Fe C γ γ (austenite) 3 γ γ 1000 γ γ +Fe C Adapted from Figs. 9.24 γ 3 and 9.32,Callister 7e. Fe C 3 r s (Fig. 9.24 adapted from γ γ 800 Binary Alloy Phase Diagrams, 2nd ed., Vol.

γ γ α C (cementite) R S 3 1, T.B. Massalski (Ed.-in- 600 Chief), ASM International, wFe C =r/(r+s) α +Fe C 3 3 Fe Materials Park, OH, wγ =(1-w Fe C) 3 400 1990.) 0 1 Co 2 3 4 5 6 6.7

(Fe) C , wt%C

pearlite 0.76 o wpearlite = wγ wα =S/(R+S) Hypereutectoid w =(1-wα) 60 µm Fe3C steel

pearlite proeutectoid Fe3C 21 Adapted from Fig. 9.33,Callister 7e.