Phase equilibria: solubility limit Introduction – Solutions – solid solutions, single phase – Mixtures – more than one phase Adapted from Fig. 9.1, Callister 7e. Sucrose/Water Phase Diagram • Solubility Limit: Max concentration for 10 0 which only a single phase Solubility L solution occurs. 8 0 Limit (liquid) 6 0 + L S 4 0 (liquid solution i.e., syrup) (solid 20 Temperature (°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 mixture (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) Alloy 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 solid solution) system 1400 • 3 phase fields: L α 1300 liquidus 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 solidus 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 lever rule 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. melting 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 • T : No liquid below T E E 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 crystals. 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): (austenite) 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 steel 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.