1. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 1 Growth of Solid Equilibrium ( = very slow cooling)  In solid + liquid phase region: Solid forms gradually upon cooling from liquidus line  Composition of solid and liquid changes gradually (determine by tie-line method)  At the solidus line: solid nuclei grow to consume all the liquid

2. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 2 Microstructure in isomorphous alloys Non-equilibrium cooling Compositional change requires diffusion Liquid: diffusion if fast (tie-line OK) Solid state: diffusion is SLOW (no tie line)  New layers solidifying on grains have the equilibrium composition at that T  Formation of layered (cored) grains On heating: grain boundaries melt first. Can lead to premature mechanical failure.

3. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 3 Non-equilibrium Cooling  Develop microstructure

4. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 4 Average Ni content of grains is higher? Application of the lever rule  Greater proportion of liquid phase as compared to equilibrium at the same T  Solidus line is shifted to the right  higher Ni content Solidification complete at lower T  Outer part of grains are richer in the low-melting component (Cu).

5. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 5 Mechanical properties of isomorphous alloys Solid solution strengthening

6. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 6 Binary Eutectic Systems Alloys with limited solubility silver (Ag) copper (Cu) alloy/ system: radii differ The melting point of eutectic alloy is lower than that of the components (eutectic = easy to melt in Greek)

7. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 7 Three single phase regions  - solid solution Ag in Cu matrix,  = solid solution of Cu in Ag matrix, L - liquid Three two-phase regions (  + L,  +L,  +  ) Solvus separates one solid solution from a mixture of solid solutions. Solvus  limit of solubility Copper – Silver phase diagram Binary Eutectic System

8. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 8 Binary Eutectic System Eutectic (invariant) point Liquid + two solid phases co-exist Eutectic composition C E Eutectic temperature T E. Eutectic Isotherm- horizontal solidus line at T E Lead – Tin phase diagram Invariant or eutectic point Eutectic isotherm

9. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 9 Binary Eutectic System Eutectic Reaction – transition from liquid to mixture of two solid phases,  +  at eutectic concentration C E. At most two phases can be in equilibrium Three phases (L, ,  ) may be in equilibrium only only at a few points along the eutectic isotherm. Single-phase regions are separated by 2-phase regions.

10. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 10 Binary Eutectic System Compositions + relative amounts of phases  Tie line and lever rule  C  B  A

11. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 11 Microstructure in eutectic alloys Cooling of liquid lead/tin system at different compositions Lead-rich alloy (0-2 wt% tin) Solidification proceeds as for isomorphous alloys L   +L  

12. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 12 Higher tin concentration:  phase nucleates as  solid solubility is exceeded at solvus line L  +L   + 

13. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 13 No changes above eutectic temperature, T E At T E liquid transforms to  and  phases (eutectic reaction) L   +  Solidification at Eutectic composition

14. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 14 Solidification at Eutectic composition  and  compositions are very different  Eutectic reaction  redistribution of Pb and Sn atoms by diffusion Simultaneous formation of  and  phases  layered (lamellar) microstructure: eutectic structure Formation of eutectic structure in lead-tin system. Dark layers are lead-rich  phase. Light layers are the tin-rich  phase.

15. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 15 Compositions other than eutectic but near the eutectic isotherm Primary  phase is formed in the  + L region Eutectic structure (layers of  and  called eutectic  and eutectic  phases) is formed upon crossing Eutectic isotherm. L   + L   + 

16. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 16 Microstructure in eutectic alloys Microconstituent – element of microstructure having a distinctive structure. For previous page: microstructure  two microconstituents: primary  and eutectic structure. Although the eutectic structure consists of two phases, it is a microconstituent with distinct lamellar structure and fixed ratio of the two phases.

17. Introduction to Materials Science, Chapter 9, Phase Diagrams University of Virginia, Dept. of Materials Science and Engineering 17 Relative amounts of microconstituents Treat eutectic as separate phase + apply lever rule Fractions: primary  phase (18.3 wt% Sn) and eutectic structure (61.9 wt% Sn): W e = P / (P+Q) ; W  ’ = Q / (P+Q)