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151-0528-00L 4 Credits DR , MSC D-MATL , D-MAVT
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Theory of Phase Transitions

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

Last Updated: 2026-02-05 15:42:02

Abstract

Phase transitions are responsible for various intriguing phenomena in physics and especially mechanics such as, e.g., superelasticity and the shape memory effect in shape memory alloys, polarization reversal in ferroelectrics, or dendritic solidification in crystal growth. This course surveys different theoretical approaches to phase transistions and introduces related modeling techniques.

Objective

Students learn different approaches to describing phase transitions at the continuum scale (including the sharp-interface approach, regularized and phase-field models) and at the discrete level (e.g., chains of interacting particles). By discussing various physical problems involving phase transitions, while pointing out their common features and specific properties, students acquire a physical understanding of those phenomena. In addition, students learn basic concepts of modeling and numerically simulating problems involving phase transitions.

Content

1. Introduction - review of continuum mechanics and thermodynamics. 2. Stability of equilibria, the Ericksen's bar problem. 3. Equilibrium phase mixtures and quasistatic processes in 1D. 4. Continuum theory of phase boundaries in 3D. 5. Mathematical aspects of phase transitions. 6. A discrete approach with an atomistic basis. 7. Regularized and phase-field models. 8. Polarization switching in ferroelectrics: the Ginzburg-Landau theory. 9. Phase-field modeling of polarization switching. 10. Fourier-based methods for phase-field models. 11. Propagation of solidification fronts: the Stefan problem. 12. Crystal growth on vicinal surfaces. 13. The framework of configurational forces. 14. Phase transitions in metamaterials.

Resources

Lecture Notes

Copies of the lecture notes will be provided for each class, however students are strongly encouraged to take their own notes.

Literature

Evolution of Phase Transitions: A Continuum Theory, R. Abeyaratne & J.K. Knwoles, Cambridge University Press The Classical Stefan Problem, S.C. Gupta, Elsevier (recommended/not required background literature)

General Information

Language
English
Levels
DR , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 60 minutes
- Oral exam (60 min, including 30 min preparation time and 30 min examination)- Lecture notes and personal notes are allowed.

Course Components

Type Title Time & Place Hours
lecture with exercise Theory of Phase Transitions
  • Tue 10:15-13:00 (ML H 34.3)
3 h weekly

Offered In