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PEM5107 - Phase Diagram

Form professor

Prof. Dr. Carlos Angelo Nunes, Prof. Dr. Gilberto Carvalho Coelho

Workload

Theoretical	Practical	Study	Duration	Total	Credits
4 hours/week	0 hours/week	8 hours/week	15 weeks	180 hours	12

See on Janus (pt-br)

Concentration area

97135 - Conventional and Advanced Materials

Objectives

To enable students to the read and interpret binary and ternary phase diagrams as well as to predict microstructures of alloys in these systems.

Motivation

Because graduate students have in general limited training in reading and interpretation of phase diagram, this course covers the fundamentals of phase diagram that allow the understanding of microstructure formation in metallic and ceramic materials.

Syllabus

1. Introduction; review of solution thermodynamics; basic theory of phase equilibrium; free energy curves versus composition; phase rule.
2. Unary systems, mono-, bi- and and invariant equilibrium.
3. Isomorphous binary systems; the lever rule; equilibrium solidification and non-equilibrium solidification; minimum and maximum in temperature vs composition binary phase diagram.
4. Binary eutectic systems; solidification and microstructures of hypoeutectic, eutectic and hypereutectic alloys; unidirectional solidification of eutectics; eutectic limit cases.
5. Eutectoid binary systems; microstructures of hypoeutectoid, eutectoid and hypereutectoid alloys; Fe-C system.
6. Monotectic systems; monotectoid systems; metatectic systems; congruent transformations.
7. Peritectic binary systems; equilibrium and non-equilibrium cooling of peritectic alloys; peritectoid binary systems; Synthetic binary systems.
8. Isomorphous ternary systems; the Gibbs triangle; isothermal sections; liquidus projections; vertical sections; maximum and minimum; equilibrium cooling.
9. Three phases ternary equilibrium; the lever rule applied to three phase fields; equilibrium cooling.
10. Four phase ternary equilibrium: Class I; Class II and Class III equilibrium.
11. Ternary four phase equilibrium (continued)
12. Complex ternary systems. Thermodynamic modelling of phase diagrams.

Evaluation criteria

References

1. Gordon, P. Principles of Phase Diagrams in Materials Systems, McGraw-Hill, 1968.
2. Rhines, F. N. Phase Diagrams in Metallurgy: Their Development and Applications, McGraw-Hill, 1956.
3. Prince, A. Alloy Phase Equilibria, Elsevier, 1966.
4. Massalski, T. B. Binary Alloys Phase Diagrams, ASM, Metals Park, Ohio, 1986.
5. Alloy Phase Diagrams, ASM Handbook, Volume 3, ASM, Metals Park, Ohio, 1992.
6. Hansen, M. Constitution of Binary Alloys, McGraw-Hill, 1958.
7. Elliot, R. P. Constitution of Binary Alloys: First Supplement, McGraw-Hill, 1965.
8. Shunk, F. A. Constitution of Binary Alloys: Second Supplement, McGraw-Hill, 1969.
9. Levin, E. M. Phase Diagram for Ceramists, The American Ceramic Society, 1964.
10. Rudman, P. S. Phase Stability in Metals and Alloys, McGraw-Hill, 1967.
11. Kaufman, L. Computer Calculation of Phase Diagrams with Special Reference to Refractory Metals, Academic Press.
12. Hack, K. The SGTE Casebook – Thermodynamics at Work. The Institut of Metals, London, 1996.
13. Hillert, M. Phase Equilibria, Phase Diagrams and Phase Transformations. Cambridge University Press, Cambridge, 1998.
14. Thermocalc version M manuals: User Guide and Examples, ThermoCalc AB, Stockholm, 1997.