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# Lecture 9

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## Lecture 9

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1. Lecture 9 Phase Diagrams 8-1

2. Introduction • Phase: A region in a material that differs in structure and function from other regions. • Phase diagrams: • Represents phases present in metal at different conditions (Temperature, pressure and composition). • Indicates equilibrium solid solubility of one element in another. • Indicates temperature range under which solidification occurs. • Indicates temperature at which different phases start to melt. 8-2

3. Phase Diagram of Pure Substances • Pure substance exist as solid, liquid and vapor. • Phases are separated by phase boundaries. • Example : Water, Pure Iron. • Different phases coexist at triple point. Figure 8.2 Figure 8.1 8-3 After W. G. Moffatt, et al., “The Structure and Properties of Materials,” vol I: “Structure,” Wiley, 1965, p.151

4. Gibbs Phase Rule P = number of phases that coexist in a system C = Number of components F = Degrees of freedom • P+F = C+2 • For pure water, at triple point, 3 phases coexist. • There is one component (water) in the system. • Therefore 3 + F = 1 + 2 F = 0. • Degrees of freedom indicate number of variables that can be changed without changing number of phases. 8-4

5. Cooling Curves • Used to determine phase transition temperature. • Temperature and time data of cooling molten metal is recorded and plotted. • Thermal arrest : heat lost = heat supplied by solidifying metal • Alloys solidify over a range of temperature (no thermal arrest) Pure Metal Iron

6. Binary Isomorphous Alloy Systems Mixture of two systems Two component system • Binary alloy • Isomorphous system: Two elements completely soluble in each other in liquid and solid state. • Example: Cu-Ni solution. Composition at liquid and solid phases at any temperature can be determined by drawing a tie line. Figure 8.3 8-5 Adapted from “Metals Handbook,” vol. 8, 8th ed., American society of Metals, 1973, p. 294.

7. Phase Diagram from Cooling Curves • Series of cooling curves at different metal composition are first constructed. • Points of change of slope of cooling curves (thermal arrests) are noted and phase diagram is constructed. • The greater the number of cooling curves the more accurate the phase diagram. Figure 8.4 8-6

8. The Lever Rule • The Lever rule gives the weight % of phases in any two phase regions. Wt fraction of solid phase = Xs = w0 – w1 ws – w1 Wt fraction of liquid phase = Xl = ws – w0 ws – w1 W0 is the weight percentage of the alloy. Ws is the weight percentage within the solid phase Wl is the weight percentage in the liquid phase Figure 8.5 8-7

9. Non Equilibrium Solidification of Alloys • Very slow cooling (equilibrium) gives rise to cored structure as composition of melt continuously changes. • Rapid cooling delays solidification but also leads to cored structure . • Homogenization: Cast ingots heated • to elevated temperature to eliminate • cored structure. • Temperature of homogenization • must be lower than lowest melting • point of any of the alloy components. W0=30% Cu Figure 8.7 Figure 8.8 8-8

10. Binary Eutectic Alloy System • In some binary alloy systems, components have limited solid solubility. Example : Pb-Sn alloy. • Eutectic composition freezes • at lower temperature than all • other compositions. • This lowest temperature is • called eutectic temperature. Figure 8.11 Eutectic temperature α solid solution + β solid solution Liquid Cooling 8-9

11. Liquid at 3000C. At about 2450C first solid forms – proeutectic solid. Slightly above 1830C composition of alpha follows solidus and composition of sn varies from 40% to 61.9%. At eutectic temperature, all the remaining liquid solidifies. Slow Cooling of 60% Pb – 40% Sn alloy Figure 8.12 Figure 8.13 • Further cooling lowers alpha Sn content and beta Pb. • (They try to move to equilibrium) 8-10 From J. Nutting and R. G. Baker, “Microstructure of Metals,” Institute of Metals, London, 1965,p.19.

12. Various Eutectic Structures • Structure depends on factors like minimization of free energy at α / β interface. • Manner in which two phases nucleate and grow also affects structures. Figure 8.14 8-11 After W. C. Winegard, “An Introduction to the Solidification of Metals,” Institute of Metals, London, 1964.

13. Binary Peritectic Alloy System • Peritectic reaction: Liquid phase reacts with a solid phase to form a new and different solid phase. Liquid + α β cooling • Peritectic reaction occurs • when a slowly cooled alloy • of Fe-4.3 wt% Ni passes • through Peritectic • temperature of 1517C. • Peritectic point is invariant. Figure 8.16 cooling Liquid(5.4 wt% Ni) + δ (4.0 wt% Ni) γ 4.3 wt % Ni 8-12

14. At 42.4 % Ag & 14000C Phases present LiquidAlpha Composition 55% Ag 7%Ag Amount of Phases 42.4 –7 55-42.4 55 – 7 55 - 7 = 74% = 26% At 42.4% Ag and 11860C – ΔT Phase Present Beta only Composition 42.4% Ag Amount of Phase 100% At 42.4% Ag and 11860C + ΔT Phases present LiquidAlpha Composition 66.3% Ag 10.5%Ag Amount of Phases 42.4 –10.5 66.3-42.4 66.3 – 10.5 66.3–10.5 = 57% =43% Peritectic Alloy System Figure 8.17 Figure 8.18 8-13

15. Rapid Solidification in Peritectic System • Surrounding or Encasement: During peritectic reaction, L+ α β , the beta phase created surrounds primary alpha. • Beta creates diffusion barrier resulting in coring. Figure 8.19 Figure 8.20 8-14 After F Rhines, “ Phase Diagrams in Metallurgy,”McGraw- Hill, 1956, p. 86.

16. Binary Monotectic Systems • Monotectic Reaction: Liquid phase transforms into solid phase and another liquid. L1α + L2 Cooling • Two liquids are immiscible. • Example:- Copper – Lead • system at 9550C and 36% Pb. Table 8.1 Eutectic Eutectoid Peritectic Peritectoid Monotectic Figure 8.23 8-15 Metals Handbook,” vol. 8: “Metallography Structures and Phase Diagrams,” 8th ed., American Society of Metals, 1973, p. 296.

17. Terminal phases: Phases occur at the end of phase diagrams. Intermediate phases: Phases occurin acomposition range inside phase diagram. Examples: Cu-Zn diagram has both terminal and intermediate phases. Five invariant peritectic points and one eutectic point. Intermediate Phases and Compounds Figure 8.25 “Metals Handbook,” vol. 8: “Metallography Structures and Phase Diagrams,” 8th ed., American Society of Metals, 1973, p. 301 8-16

18. Intermediate Phases in Ceramics • In Al2O2 – SiO2 system, an intermediate phase called Mullite is formed, which includes the compound 3Al2O3.2SiO2. Figure 8.26 8-17 After A. G. Guy, “Essentials of Materials Science, “McGraw-Hill, 1976

19. Intermediate Compounds • In some phase diagrams, intermediate compound are formed – Stoichiometric • Percent Ionic/Covalent bond depends on electronegativeness • Example:- Mg-Ni phase diagram contains • Mg2Ni : Congruently melting compound • MgNi2 : Incongruently melting compound. Figure 8.27 8-18 Metals Handbook,” vol. 8: American Society of Metals, 1973, p. 314.

20. Ternary Phase Diagrams • Three components • Constructed by using a equilateral triangle as base. • Pure components at each • end of triangle. • Binary alloy composition • represented on edges. Figure 8.28 Temperature can be represented as uniform throughout the Whole Diagram Isothermal section. 8-19

21. Ternary Phase Diagram (Cont..) • Example:- Iron-Chromium-Nickel phase diagrams. • Isothermal reaction at 6500C • for this system • Composition of any metal • at any point on the phase • diagram can be found by • drawing perpendicular • from pure metal corner to • apposite side and calculating • the % length of line at that • point Figure 8.30 8-20 After “Metals Handbook,” vol. 8: American Society of Metals, 1973, p. 425.