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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
MMK162 - Phase transformations
Syllabus adopted 2019-02-21 by Head of Programme (or corresponding)
Owner: MPAEM
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Chemical Engineering with Engineering Physics, Mechanical Engineering, Industrial Design Engineering, Engineering Physics

Teaching language: English
Application code: 09120
Open for exchange students: Yes
Block schedule: B+

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0111 Examination, part A 6,0c Grading: TH   6,0c   24 Oct 2020 am J   04 Jan 2021 am J,  25 Aug 2021 am J
0211 Project, part B 1,5c Grading: UG   1,5c    

In programs

MPAEM MATERIALS ENGINEERING, MSC PROGR, Year 1 (compulsory elective)


Fang Liu

  Go to Course Homepage


General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

The course is suitable for students admitted to Master's Programmes Advanced Engineering Materials, Applied Physics or any student following the M- or F-programme at Chalmers as well as former IMP Advanced Materials or PhD students in Materials Science and Engineering.


In this course the aim is to develop understanding for and skills to apply basic physical and thermodynamical principles for interpretation of the development of microstructure. These principles serve as tools when you need to understand and solve complex problems which may occur during production or service of materials. Examples are design of heat treatments or alloy composition to minimise growth of precipitates that may impair the creep properties for turbine alloys or formation of brittle intermetallic phases in the heat affected zone formed during welding.

Learning outcomes (after completion of the course the student should be able to)

- calculate expressions or sketch the free energy for ideal, regular and real binary solutions as a function of composition, temperature or pressure taking into account the effect of particle size. From binary free energy diagrams at different temperatures, construct binary phase diagrams.

- apply Ficks first and second law for diffusion in binary system, solve the equation for a few specific applications and for different types of diffusion relate to the expression for the diffusion coefficient D.

- sketch, use and to some extent calculate expressions for the free energy for a surface/interface or grain boundary. From this determine or recognise the equilibrium shape of a precipitate, crystal or grain.

- sketch expressions for free energy of formation of small clusters and discuss the implications for nucleation and nucleation rate.

- describe and discuss driving forces for growth of a pure solid or alloy after nucleation. In particular describe the effects of changing process parameters on the microstructure of ingots and welds.

- describe the mechanisms for diffusionless transformations and discuss which mechanisms that govern nucleation and growth of short-range and long-range diffusional transformations.

- use TTT-diagrams.

- apply a commercial software for phase transformation.


The course is comprised of following:
Thermodynamics and phase diagrams: Free energy, volume and surface energy, equilibrium conditions, modelling of solid and liquid systems, kinetics of phase transformations.
Diffusion: Atomistic and macroscopic modelling, activation, interstitial and substitution diffusion, diffusion in binary and ternary alloys.
Interfaces and microstructures: Free energy of interfaces, coherent and incoherent interfaces, precipitation interface migration, grain growth.
Solidification: Nucleation, growth, single and many component alloys, eutectic and peritectic solidification, ingot structures.
Diffusional transformation: Homogeneous and inhomogeneous nucleation in solids and liquids, grain growth, particle growth, transformation kinetics, different kinds of transformations.
Diffusionless transformation: Nucleation and growth of martensite.
Thermodynamic modelling: Principles and application of commercial software, for instance "Thermocalc".


Lecture series supplemented by exercises and project.


D.A. Porter and K.E. Easterling: Phase Transformation in Metals and Alloys, Chapman & Hall, UK, 2nd edition 1992, (paper back edition).
Thermocalc - Software package. Instruction manuals.

Examination including compulsory elements

Written exam

Page manager Published: Thu 04 Feb 2021.