TMT4260 - Modelling of Phase Transformations


Examination arrangement

Examination arrangement: Work
Grade: Letters

Evaluation form Weighting Duration Examination aids Grade deviation
work 100/100

Course content

The course includes the theoretical basis for understanding phase transformations in metals as well as models and methods for a mathematical and numerical description of some technological important phase transformations in metals (with emphasis on aluminium) that are determining for the evolution of microstructure and properties during casting/solidification and thermal processing (heat treatments/welding). The course starts with a short description of the thermodynamical basis for phase transformations, based on the consideration of simple binary phase diagrams. It is followed by an atomistic and mathematical description of diffusion together with structural aspects of phase boundaries. After that a more detailed presentation of phase transformations by nucleation and growth is given, including homogeneous and heterogeneous solidification, precipitation, growth and dissolution of second phase particles, recrystallization and grain growth, including the concepts of Johnson-Mehl-Avrami-Kolmogorov (JMAK) kinetics, additivity and iso-kinetic reactions. The topics will be presented and analysed by means of relevant mathematical/numerical models which the students themselves should implement and use/explore through 3-4 relevant mini projects.

Learning outcome

After the course is finished the students should be able to:
- Be able to describe and make use of binary phase diagrams to perform relevant thermodynamical calculations.
- Be able to use simple thermodynamical data models based to calculate and analyse simple binary phasediagram, incl. stable and metastable solvus lines.
- Account for the atomistic description of diffusion, and moreover be able to use this in analytical and numerical calculations of a selection of relevant diffusion problems.
- Describe geometrical and structural aspects of phase boundaries and explain how these aspects relate to interfacial energies and mobilities.
- Describe the theoretical basis for, be able to formulate mathematically and apply classical models for phase transformations by nucleation and growth, including homogeneous/heterogeneous solidification, precipitation, growth and dissolution of second phase paticles, recrystallisation and grain growth, and be able to make use of this knowledge to carry out relevant quantitative calculations (analytical and/or numerical) of kinetics and microstructure evolution during iso-thermal as well as non-isothermal thermal processing.
- Analyse and describe how alloy composition and heat-treatment procedures influence growth and dissolution of second-phase particles in binary/quasibinary alloys during isothermal as well as non-isothermal heat treatments, including the theoretical basis for and use of iso-kinetic solutions.
- Analyse and discuss limitations and validity of relevant theoretical models in relation to real life problems and industrial process conditions.
- Evaluate and suggest suitable heat-treatment procedures in order to obtain desired microstructural conditions and properties by thermo-mechanical processing and welding of a selection of metals and alloys for structural purposes.

Learning methods and activities

Lectures and computational mini-problems. Moreover 3-4 modelling projects, involving small written reports, plenary presentations and individual questioning. The computational problems and the modelling projects are mandatory activities which will serve as basis for the marking.
Total work load is estimated to be about 200 hrs (incl. independent home work).

Further on evaluation

If a student has to take the course over again, all evaluations in the course has to be repeated.

Course materials

Extracts from D.A. Porter and K.E. Easterling, Phase Transformations in Metals and Alloys and seleceted relevant journal papers. In addition lecture notes will be made available via internett.

More on the course



Version: 1
Credits:  7.5 SP
Study level: Second degree level


Term no.: 1
Teaching semester:  AUTUMN 2020

No.of lecture hours: 4
Lab hours: 2
No.of specialization hours: 6

Language of instruction: English, Norwegian

Location: Trondheim

Subject area(s)
  • Materials Science and Engineering
  • Physical Metallurgy
  • Technological subjects
Contact information
Course coordinator: Lecturer(s):

Department with academic responsibility
Department of Materials Science and Engineering



Examination arrangement: Work

Term Status code Evaluation form Weighting Examination aids Date Time Digital exam Room *
Autumn ORD work 100/100
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

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