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**MSE 559 Phase Equilibria in Multicomponent Systems**

Sem. 1. Class 3, cr. 3. (offered in alternate years). Prerequisite: senior or graduate standing in engineering or science.

MSE 559 is an elective course.

Weekly Schedule: Three 50-minute lectures.

A detailed examination of the thermodynamics of phase equilibria in multicomponent systems, experimental methods of determining these equilibria by measurements of thermodynamic activity and graphical method of representing the equilibria. This is followed by an examination of theoretical models of the behavior of solutions and an examination of the extent to which observed phenomena can be understood and predicted in terms of the models. Offered in alternate years.

**Relation of Course to Program Outcomes**

1. an ability to apply knowledge of mathematics, science, and engineering to problems in materials engineering.

5. an ability to identify, formulate, and solve engineering problems, particularly in the context of materials selection and design.

**Goals**

- To understand the criteron for equilibrium in a materials system under conditions of constant temperature and constant pressure.

- To understand graphical representation of phase equilibria in materials systems containing one, two and three components.

- To understand the atomic-scale interactions which determine the thermodynamic stabilities of phases.

- To understand the difference among stable, metastable and unstable states of existence of phases in materials systems.

**Course Objectives**

- calculate a unary phase diagram from fundamental thermodynamic properties; changes in enthalpy and volume accompanying phase transitions,

- be capable of drawing isobaric and isothermal sections of the 3-dimensional phase diagrams for binary systems drawn in pressure-temperature-composition space,

- be capable of recognizing the nine 3-phase equilibria that can occur in binary systems; eutectic, eutectoid, peritectic, peritectoid, monotectic, monotectoid, metatectic, metatectoid, syntectic),

- be familiar with these 3-phase equilibria as they occur in the real binary systems Fe-Mn, K-Zn, Pb-Sn, Al-Zn, Fe-Cu, Cu-Pb, K-Mg, Li-Na and Mg-Ca,

- be familiar with the thermodynamic requirements of 3-phase equilibria in binary systems,

- be capable of calculating phase diagrams for binary system assuming combinations of ideal, regular and sub-regular solution behavior,

- be familiar with the origins of the Gibbs Phase Rule,

- understand the difference between species and components and be capable of calculating the number of independent reaction equilibria which can occur in multicomponent systems,

- calculate phase stability diagrams for metal-oxygen-carbon, metal-oxygen-sulfur and metal-oxygen-nitrogen systems as isobaric diagrams and diagrams with temperature and a partial pressure of a gaseous species or the activity of a component as independent variable,

- be familiar with phase equilibria in ternary systems containing eutectics, peritectics, liquid immiscibility, compound formation and combinations thereof,

- be familiar with the influence of partial pressure of oxygen on phase equilibria in oxide systems containing cations of variable valence,

- be capable of drawing isothermal and vertical sections of real ternary systems such as Na2O-CaO-SiO2 (sheet and container glass), CaO-Al2O3-SiO2 (iron blast furnace slag), MgO-Al2O3-SiO2 (ceramic ware) and FeO-Fe2O3-SiO2 (steelmaking slags),

- be capable of explaining phase equilibria in the real systems Fe-Si-O, Fe-Mn-O, Fe-Ni-O, Fe-Cr-O, Fe-Cr-C; understand oxidation behavior in those systems containing oxygen and phase equilibria in ferritic stainless steels in the system Fe-Cr-C,

- Be capable of calculating phase stability diagrams in ternary system containing two metals and oxygen from known Gibbs free energies of formation of the oxides and assumptions as to the thermodynamic solutions that can occur.

**Instructor(s)**

**Contribution of course to meeting the professional component: **MSE 559 is a materials-specific technical elective course.

**Prepared by:** Elliott Slamovich **Date:** April 25th, 2007