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151-0528-00L 4 Credits DR , MSC D-MATL , D-MAVT

Theory of Phase Transitions

Lecturers & Examiners: Prof. Dr. Dennis Kochmann, Dr. Laurent Guin
VVZ CR n/a

Last Updated: 2026-02-05 15:55:05

Abstract

This course addresses two major examples of phase transitions, namely solid-solid phase transformations and solidification. We focus on the modeling of the propagation of phase boundaries (surface of strain discontinuity or solidification front) in continuum media. Both the sharp-interface model and related numerical modeling techniques based on the phase-field method are introduced.

Objective

The students are able to: - Use mechanical and/or thermodynamic balance laws to formulate a continuum model for problems involving phase transformations in 1D, 2D, and 3D. - Distinguish between the different modeling techniques used for the propagation of phase boundaries and discuss their underlying assumptions. - Apply the concepts of thermodynamics to continuous media in order to derive thermodynamically consistent models. - Model the evolution of a solidification front using the phase-field method.

Content

1. Mechanics of bars 2. The Ericksen’s bar problem: solid-solid phase transformation in 1D 3. Review of classical thermodynamics 4. Continuum theory for phase boundaries in 3D 5. Solidification: a free-boundary problem with interfacial structure 6. Phase-field model for solidification 7. Selected topics involving phase transitions

Resources

Lecture Notes

Lecture notes will be provided for reference. Students are strongly encouraged to take their own notes during class.

Literature

No textbook required; relevant reference material will be suggested.

General Information

Language
English
Levels
DR , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 60 minutes
The oral final exam (taking place during the examination session) covers all contents of this course, including lectures, exercises, homework. It counts 50% towards the final grade. It lasts 60 min including 30 min of preparation time and 30 min of examination. All notes are allowed during the final exam.Additionally, there will be a compulsory continuous performance assessment in the form of four projects:- Two assignments involving theoretical/analytical derivations.- One numerical project based on the phase-field method involving programming in matlab.- A review of a research article that involves writing a 1 to 2 page report and giving a 10 min presentation during class.Out of the four projects, at least three must be submitted two weeks after assignment. The best three submitted projects count 50% towards the final grade (16.7% each).Lastly, optional short exercises will be proposed during the semester as learning tasks. Completing and handing in four of them will give a bonus of 0.25 points to the final grade.All notes are allowed during the final exam.

Course Components

Type Title Time & Place Hours
lecture with exercise Theory of Phase Transitions
  • Tue 10:15-12:00 (ML H 34.3)
  • Tue 14:15-15:00 (ML J 37.1)
3 h weekly

Offered In