CHAPTER 9 Phase Diagrams— Equilibrium Microstructural Development The microstructure of a slowly cooled “eutectic” soft solder ( ≈ 38 wt % Pb − wt % Sn) consists of a lamellar structure of tin-rich solid solution (white) and lead-rich solid solution (dark), 375X. (From ASM Handbook, Vol. 3: Alloy Phase Diagrams, ASM International, Materials Park, Ohio, 1992.) Figure 9-1 Single-phase microstructure of commercially pure molybdenum, 200 × . Although there are many grains in this microstructure, each grain has the same, uniform composition. (From Metals Handbook, 8th ed., Vol. 7: Atlas of Microstructures, American Society for Metals, Metals Park, Ohio, 1972.) Figure 9-2 Two-phase microstructure of pearlite found in a steel with 0.8 wt % C, 500× . This carbon content is an average of the carbon content in each of the alternating layers of ferrite (with < 0.02 wt % C) and cementite (a compound, Fe 3 C, which contains 6.7 wt % C). The narrower layers are the cementite phase. (From Metals Handbook, 9th ed., Vol. 9: Metallography and Microstructures, American Society for Metals, Metals Park, Ohio, 1985.) Temperature T(°C) Gas Steam 100 Water Liquid 0 Solid 1 atm (a) Ice Pressure (log scale) (b) Figure 9-3 (a) Schematic representation of the one-component phase diagram for H 2 O. (b) A projection of the phase diagram information at 1 atm generates a temperature scale labeled with the familiar transformation temperatures for H 2 O (melting at 0 ◦ C and boiling at 100 ◦ C). T(˚C) Temperature Gas Liquid Liquid 1538 1394 910 1 atm Pressure (log scale) (a) (b) Figure 9-4 (a) Schematic representation of the one-component phase diagram for pure iron. (b) A projection of the phase diagram information at 1 atm generates a temperature scale labeled with important transformation temperatures for iron. This projection will become one end of important binary diagrams such as Figure 9–19. Liquidus Melting point of B Temperature L L + SS Melting point of A Solidus SS A 0 100 20 80 40 60 60 40 80 20 B 100 ← wt % B 0 ←wt % A Composition (wt %) Figure 9-5 Binary phase diagram showing complete solid solution. The liquidphase field is labeled L and the solid solution is designated SS. Note the two-phase region labeled L + SS. Composition of L at T1 State point L System temperature T1 L + SS Composition of SS at T1 SS A X1 B System composition Figure 9-6 The compositions of the phases in a two-phase region of the phase diagram are determined by a tie line (the horizontal line connecting the phase compositions at the system temperature). Temperature F=C–P+1 F =2–1+1=2 F =1–2+1=0 F =2–2+1 =1 F =2–1+1=2 A B Composition Figure 9-7 Application of Gibbs phase rule (Equation 9.2) to various points in the phase diagram of Figure 9–5. Lsystem Temperature T1 All liquid (Lsystem) Crystallites of SS1 in matrix of L1 L1 SS1 Polycrystalline solid (SSsystem) SSsystem A B System composition Composition Figure 9-8 Various microstructures characteristic of different regions in the complete solid-solution phase diagram. Atomic percentage nickel ˚C 1500 10 20 30 40 50 60 70 80 90 1455˚ L 1400 1300 1200 1100 1084.87˚ 1000 900 800 700 600 500 Cu 10 20 40 30 50 60 70 Weight percentage nickel 80 90 Ni Figure 9-9 Cu–Ni phase diagram. (After Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, Ohio, 1973, and Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, ed., American Society for Metals, Metals Park, Ohio, 1986.) ˚C 2800 L 2600 L + SS 2400 SS 2200 2000 NiO 20 40 60 80 MgO Mole % MgO Figure 9-10 NiO–MgO phase diagram. (After Phase Diagrams for Ceramists, Vol. 1, American Ceramic Society, Columbus, Ohio, 1964.) Temperature L Liquidus A+L Eutectic temperature L+B Solidus A+B A B Eutectic Composition Composition Figure 9-11 Binary eutectic phase diagram showing no solid solution. This general appearance can be contrasted to the opposite case of complete solid solution illustrated in Figure 9–5. Temperature All liquid (Leutectic) Crystallites of A in matrix of L1 Crystallites of B in matrix of L2 L1 L2 Eutectic microstructure— fine, alternating layers of A and B Leutectic A B Composition Figure 9-12 Various microstructures characteristic of different regions in a binary eutectic phase diagram with no solid solution. Atomic percentage, silicon ˚C 1500 10 20 30 40 50 60 70 80 90 1414˚ 1400 1300 L 1200 1100 1000 900 800 700 660.452˚ 600 1.6 577˚ 12.6 500 400 300 A1 10 20 30 40 50 60 70 80 90 Si Weight percentage, silicon Figure 9-13 Al–Si phase diagram. (After Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, ed., American Society for Metals, Metals Park, Ohio, 1986.) Temperature L A B Composition Figure 9-14 Binary eutectic phase diagram with limited solid solution. The only difference from Figure 9–11 is the presence of solid-solution regions α and β . Temperature All liquid (Leutectic) Leutectic L1 L2 A B Composition Figure 9-15 Various microstructures characteristic of different regions in the binary eutectic phase diagram with limited solid solution. This illustration is essentially equivalent to Figure 9–12 except that the solid phases are now solid solutions ( α and β ) rather than pure components (A and B). Atomic percentage tin ˚C 400 10 20 30 40 50 60 327.502˚ 70 80 90 L 300 231.9681˚ 200 19 183˚ 61.9 97.5 100 0 Pb 13˚ 10 20 30 40 50 60 Weight percentage tin 70 80 90 Sn Figure 9-16 Pb–Sn phase diagram. (After Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, Ohio, 1973, and Binary Alloy Phase Diagrams, Vol. 2, T. B. Massalski, ed., American Society for Metals, Metals Park, Ohio, 1986.) Temperature L Eutectic temperature Eutectoid temperature A B Eutectoid composition Eutectic composition Composition Figure 9-17 This eutectoid phase diagram contains both a eutectic reaction (Equation 9.3) and its solid-state analog, a eutectoid reaction (Equation 9.4). Temperature A B Composition Figure 9-18 Representative microstructures for the eutectoid diagram of Figure 9–17. ˚C 1700 2 1600 1538˚ 1500 1400 Atomic percentage carbon 10 15 20 5 1495˚ 25 L 1394˚ 1300 1227˚C 1200 L + Fe3C 1148˚ 1100 4.30 2.11 6.69 1000 900 912˚ 800 700 727˚ 0.02 0.77 600 Fe3C (cementite) 500 400 300 200 100 0 Fe 1 2 3 4 5 6 7 Weight percentage carbon Figure 9-19 Fe–Fe 3 C phase diagram. Note that the composition axis is given in weight percent carbon even though Fe 3 C, and not carbon, is a component. (After Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, Ohio, 1973, and Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, ed., American Society for Metals, Metals Park, Ohio, 1986.) ˚C 2200 2 Atomic percentage carbon 10 15 20 5 25 2100 2000 1900 1800 1700 1600 1538˚ 1500 1400 1300 L+C 1495˚ 1394˚ 1200 1154˚ 1100 1000 900 912˚ 800 700 600 4.26 2.08 738˚ 0.02 0.68 C (graphite) 500 400 300 200 100 0 Fe 1 2 3 4 5 6 Weight percentage carbon 99 100 Figure 9-20 Fe–C phase diagram. The left side of this diagram is nearly identical to that for the Fe–Fe 3 C diagram (Figure 9–19). In this case, however, the intermediate compound Fe 3 C does not exist. (After Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, Ohio, 1973, and Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, ed., American Society for Metals, Metals Park, Ohio, 1986.) Temperature Composition of liquid formed upon melting of AB L+B L A + L L + AB AB + B A + AB A AB B Composition Figure 9-21 Peritectic phase diagram showing a peritectic reaction (Equation 9.5). For simplicity, no solid solution is shown. Temperature Crystallites of B in matrix of L1 L Polycrystalline solid (compound AB) A AB B Composition Figure 9-22 Representative microstructures for the peritectic diagram of Figure 9–21. ˚C 2200 2100 2054˚ L 2000 L + Al2O3 1900 1890˚ SiO2 (cristobalite) + L 1800 1700 1726˚ L + mullite(SS) Al2O3 + mullite(SS) 1600 1500 1400 SiO2 mullite(SS) 1587 SiO2 (cristobalite) + mullite(SS) 10 20 30 40 50 60 70 80 90 Al2O3 Mole % Al2O3 Figure 9-23 Al 2 O 3 –SiO 2 phase diagram. Mullite is an intermediate compound with ideal stoichiometry 3Al 2 O 3 · 2SiO 2 . (After F. J. Klug, S. Prochazka, and R. H. Doremus, J. Am. Ceram. Soc. 70, 750 (1987).) Temperature L A+L AB + L L + AB A B+L AB + B A + AB AB B Composition (a) L Temperature Figure 9-24 (a) Binary phase diagram with a congruently melting intermediate compound, AB. This diagram is equivalent to two simple binary eutectic diagrams (the A–AB and AB–B systems). (b) For analysis of microstructure for an overall composition in the AB– B system, only that binary eutectic diagram need be considered. A+L AB + L L + AB AB + B A + AB A B+L AB Composition (b) B Temperature L A A 2B AB AB2 AB4 B AB4 B Composition (a) Temperature L A A 2B AB Composition AB2 ˚C 3000 L 2500 L + spinel (SS) 2000 Periclase (SS) +L L + Al2O3 Periclase (SS) 1500 1000 MgO Spinel (SS) Periclase (SS) + spinel (SS) 10 20 30 40 Spinal (SS) + Al2O3 50 60 70 80 90 Al2O3 Mole % Al2O3 Figure 9-26 MgO–Al 2 O 3 phase diagram. Spinel is an intermediate compound with ideal stoichiometry MgO · Al 2 O 3 . (After Phase Diagrams for Ceramists, Vol. 1, American Ceramic Society, Columbus, Ohio, 1964.) Atomic percentage, copper ˚C 0 1100 10 20 30 40 50 60 70 80 90 100 1084.87˚ 1000 L 900 800 700 660.452˚ 53.5 600 η1 548.2˚ 500 5.65 32.7 567˚ 52.5 400 300 Al 10 20 30 40 50 60 Weight percentage, copper 70 80 90 Cu Figure 9-27 Al–Cu phase diagram. (After Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, ed., American Society for Metals, Metals Park, Ohio, 1986.) ˚C 700 Atomic percentage, magnesium 10 20 30 40 50 60 70 80 90 660.452˚ 100 650˚ 600 L 35.6 500 450˚ 17.1 400 36.1 455˚ 59.8 66.7 437˚ 87.4 δ 300 200 100 Al 10 20 30 40 50 60 70 Weight percentage, magnesium 80 90 Mg Figure 9-28 Al–Mg phase diagram. (After Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, ed., American Society for Metals, Metals Park, Ohio, 1986.) Atomic percentage, zinc ºC 1300 10 20 30 40 50 60 70 90 Atomic percentage Cu 1 2 3 450 L 1.7 424 1250 1200 400 1150 1100 80 1084.87º 2.7 350 L 300 1050 250 1000 200 950 903º 900 32.5 37.5 150 36.8 850 56.5 800 100 1 Zn 2 3 Weight percentage Cu 59.8 835º 750 700 73.0 700º 69.8 80.5 650 78.6 598º 600 558º 550 74.1 500 39.0 450 456º 48.9 98.3 468º 45.5 87.5 400 424º 97.3 419.58º 350 300 250 200 99.7% at 100º 150 100 50 0 Cu 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 Zn Weight percentage, zinc Figure 9-29 Cu–Zn phase diagram. (After Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, Ohio, 1973, and Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, ed., American Society for Metals, Metals Park, Ohio, 1986.) 4 ˚C 8 CaO (wt %) 12 16 20 24 28 500 0 ZrO2 Cubic ZrO2SS + ZrCaO3 Monoclinic ZrO2SS + Cubic ZrO2SS 1000 Cubic ZrO2SS 1500 Tetragonal ZrO2SS 2000 Tetragonal ZrO2SS + Cubic ZrO2SS 2500 10 20 30 CaO (mol %) 40 Figure 9-30 CaO–ZrO 2 phase diagram. The dashed lines represent tentative results. (After Phase Diagrams for Ceramists, Vol. 1, American Ceramic Society, Columbus, Ohio, 1964.) 50 Temperature L A A2B AB Composition AB2 AB4 B Temperature L L + SS T1 SS 0 A 30 50 80 100 Composition (wt % B) B mL + mSS = mtotal 0.30mL + 0.80mSS = 0.50mtotal →mL = 0.60mtotal mSS = 0.40mtotal Figure 9-31 A more quantitative treatment of the tie line introduced in Figure 9–6 allows the amount of each phase (L and SS) to be calculated by means of a mass balance (Equations 9.6 and 9.7). (a) Fulcrum (b) Figure 9-32 The lever rule is a mechanical analogy to the mass balance calculation. The (a) tie line in the two-phase region is analogous to (b) a lever balanced on a fulcrum. Temperature Lsystem 100% liquid (Lsystem) L1 T1 SS1 L2 T2 10% SS1 in matrix of L1 SS2 L3 T3 SS3 40% SS2 in matrix of L2 90% SS3 in matrix of L3 SSsystem A Composition B 100% Solid (SSsystem) Figure 9-33 Microstructural development during the slow cooling of a 50% A–50% B composition in a phase diagram with complete solid solution. At each temperature, the amounts of the phases in the microstructure correspond to a lever rule calculation. The microstructure at T2 corresponds to the calculation in Figure 9–31. Temperature Leutectic 100% liquid (Leutectic) T1 T2 A Composition B *The only differences from the T1 microstructure are the phase compositions and the relative amounts of each phase. For example, the amount of b will be proportional to Figure 9-34 Microstructural development during the slow cooling of a eutectic composition. Temperature 100% liquid (Lsystem = 80% B) Lsystem L2 L1 T2 (= Teutectic + 1 ) T3 (= Teutectic – 1 ) 0 A 30 60 80 Composition (wt % B) 90 100 B Figure 9-35 Microstructural development during the slow cooling of a hypereutectic composition. Temperature Lsystem 100% liquid (Lsystem = 40% B) L1 T2 (= Teutectic + 1 ) T3 (= Teutectic – 1 ) 0 A 30 40 60 Composition (wt % B) 90 100 B Figure 9-36 Microstructural development during the slow cooling of a hypoeutectic composition. Temperature Lsystem 100% liquid (Lsystem = 10% B) L1 0 A 10 Composition (wt % B) (a) Temperature Lsystem 100% liquid (Lsystem = 20% B)uid (Lsystem = 20% 100 B L1 0 A 10 20 Composition (wt % B) (b) 100 B Temperature 100% liquid (3% C) L1 0 3.0 6.7 Weight percentage carbon Figure 9-38 Microstructural development for white cast iron (of composition 3.0 wt % C) shown with the aid of the Fe–Fe 3 C phase diagram. The resulting (low-temperature) sketch can be compared with a micrograph in Figure 11–1a. Temperature 0 0.77 6.7 Weight percentage carbon Figure 9-39 Microstructural development for eutectoid steel (of composition 0.77 wt % C). The resulting (low-temperature) sketch can be compared with the micrograph in Figure 9–2. Temperature Proeutectoid cementite + pearlite 0 1.13 6.7 Weight percentage carbon Figure 9-40 Microstructural development for a slowly cooled hypereutectoid steel (of composition 1.13 wt % C). Temperature Proeutectoid ferrite + pearlite 0 0.50 6.7 Weight percentage carbon Figure 9-41 Microstructural development for a slowly cooled hypoeutectoid steel (of composition 0.50 wt % C). Temperature 100% liquid (3% C) L1 C flakes (from eutectic and eutectoid reactions) in matrix of ferrite 0 3 100 Weight percentage carbon Figure 9-42 Microstructural development for gray cast iron (of composition 3.0 wt % C) shown on the Fe–C phase diagram. The resulting low-temperature sketch can be compared with the micrograph in Figure 11–1b. A dramatic difference is that, in the actual microstructure, a substantial amount of metastable pearlite was formed at the eutectoid temperature. It is also interesting to compare this sketch with that for white cast iron in Figure 9–38. The small amount of silicon added to promote graphite precipitation is not shown in this two-component diagram. The phase diagram for this alloy system is T A B