Equilibrium Diagrams

Code:

EMM0015

Acronym:

DEQUI

Keywords
Classification	Keyword
OFICIAL	Engineering Sciences

Instance: 2014/2015 - 1S

Active?	Yes
Responsible unit:	Department of Metallurgical and Materials Engineering
Course/CS Responsible:	Master in Metallurgical and Materials Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEMM	39	Syllabus since 2006/2007	2	-	6	56	162

Teaching language

Portuguese

Objectives

Knowledge and understanding of Phase Equilibrium Diagrams is important to materials engineering since properties of materials are controlled by the thermal history of the alloys. Phase Equilibrium Diagrams are the foundation in performing basic materials research in such fields as solidification, crystal growth, joining, solid-state reaction, phase transformation, oxidation, etc. On the other hand, a phase diagram also serves as a road map for materials design and process optimization since it is the starting point in the manipulation of processing variables to achieve the desired microstructures.

The purpose of this curricular unit is to use Phase Equilibrium Diagrams to develop an understanding of the phase transformations and the interpretation of the microstructural evolution of the alloys. Even if most phase equilibrium diagrams relate to equilibrium state and microstructure, they are also useful to understand nonequilibrium structures, that are often more desirable than those of equilibrium states due to the properties values attained. Materials of interest range from single to multi-component systems. While many industrial important systems can be adequately represented by binary equilibrium diagrams, ternary or higher order diagrams are often necessary to the understanding of more complex systems, like certain industrial alloys, slags or ceramic materials.

Learning outcomes and competences

This curricular unit will prepare students to: 1) understand of scientific bases of Phase Equilibrium Diagrams; 2) know the relations between the composition, temperature and phases volume, being able to apply it to Phase Equilibrium Diagrams of different systems; 3) possess the understanding of how the microstructure is formed, and how this structure influences materials properties; 4) use Phase Equilibrium Diagrams as a point of departure to establish the microstructural evolution of materials with temperature.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Recommended prerequisites: concepts learnt on the course units of Chemistry I and II, and Introduction to Materials Engineering I and II.

Program

Introduction. Gibbs’ phase rule. Unary phase diagrams. - Allotropy. Binary phase diagrams. - Isomorphic binary systems. - The lever rule. - Binary reactions: eutectic, eutectoide, monotectic, peritectic, metatectic, peritectoide and sintetic. - Congruent transformations. - Complex binary equilibrium diagrams. Ternary phase diagrams. - The ternary space model. - Tie lines and tie triangles. - Isomorphic systems. - Three-phase equilibrium. - Four-phase equilibrium. - Intermediate phases (congruent and non-congruent fusion). - Immiscibility in liquid state. - Complex ternary equilibrium diagrams

Mandatory literature

Rhines, Frederick N.; Phase Diagrams in Mettalurgy
D. R. F. West; Ternary equilibrium diagrams. ISBN: 0412493101

Complementary Bibliography

Saunders, N.; Calphad. ISBN: 0-08-0421296
João Lopes Baptista, Rui Ferreira e Silva; Diagramas de fases. ISBN: 972-8021-72-0

Teaching methods and learning activities

Short tutorials followed by the presentation and discussion of several cases, mainly phase diagrams of industrial importance in order to improve the understanding of scientific concepts. Problems of phase diagram interpretation, structure development and solidification paths are solved by students in small groups. Case studies are accompanied by the teacher in order to develop student skills in the analysis and resolution of engineering problems.

keywords

Technological sciences > Engineering > Materials engineering

Evaluation Type

Evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Not applicable

Calculation formula of final grade

Final grade = 100% of the exam grade

Examinations or Special Assignments

Not applicable

Internship work/project

Not applicable

Special assessment (TE, DA, ...)

Special cases will be assessed based on a closed book written exam which is 2 h 30 min long.

Classification improvement

Students have to enrol after getting the passing grade.

Observations

Classes will be taught in English if students do not master the Portuguese language.