Course detail

Theory of Complex Phase Transformations

FSI-WKFAcad. year: 2019/2020

The basic principles of thermodynamics, theory of reaction rates, diffusion, crystallography and theory of phase interface are applied to introduce criteria of phase equilibrium, as well as to explain thermodynamic conditions, kinetics, mechanism and results of various types of phase transformations. Emphasis is placed on the liquid – solid transformation and to solid – solid diffusive and non-diffusive transitions, predominantly in relation to metals and alloys. The course provides only basic information about transitions in ceramics and plastics, because they are dealt with in other specialised courses.

Learning outcomes of the course unit

The acquired knowledge is highly theoretical, still it can be used both in basic and applied fields of research, as well as in practice, e.g. when optimising manufacturing and processing technologies resulting in the development and production of materials proving desired and guaranteed composition, structure and properties, when influencing the stability of the initial structure of materials or controlling the degradation processes in the course of application.


Students are required to have basic knowledge of crystallography, phases and phase diagrams, mechanical and heat treatments of materials, structure and properties of materials. Basic knowledge of phase transformations thermodynamics and kinetics and of diffusion is an advantage.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Cahn, R. W. - Haasen, P. - Krammer, E. J. : Materials Science and Technology. Vol. 5, Vol. Editor Haasen, P.: Phase Transformations in Materials. , , 0
Porter, D. A. - Easterling, K. E. : Phase Transformations in Metals and Alloys. , , 0
Christian, J. W.: The Theory of Transformations in Metals and Alloys, , 0
Ashby, M. F. - Jones, D. R. H.: .: Engineering Materials, an Introduction to their Properties and Applications. Vol. 1,2, , 0
Ohring, M.: Engineering Materials Science. , , 0
Callister, W. D. Jr.: Material Science and Engineering. An Introduction. 3rd Edition, , , 0

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures. Teaching is suplemented by practical laboratory work.

Assesment methods and criteria linked to learning outcomes

Course-unit credit is awarded on conditions: attendance at all seminars and lessons of practical training, knowledge-based and active participation in their programmes, proper fulfilment of all tasks and success in regular tests of knowledge. In justified cases the teacher may set and control an additional homework in order to compensate for failing to meet the above mentioned requirements. Examination: It involves the whole range of knowledge indicated by the teacher and usually has a written and an oral part. In the written exam the student must prove basic knowledge answering the set of key questions. In the oral exam the depth and context of the knowledge, precise interpretation and the ability of independent judgements must be proved. Final classification: The grade is awarded according to the valid grading scheme. It reflects results of the written and oral part of the exam, as well as the overall assessment of the student’s work in seminars and practical training.

Language of instruction


Work placements

Not applicable.


Students are supposed to gain general theoretical knowledge concerning both external and internal conditions influencing the structure stability and the type and course of phase transformations; to make sense of the basis, cause, run-down, results and purpose of individual types of phase transitions. To acquire the know-how and skills enabling controlled applications of the knowledge acquired.

Specification of controlled education, way of implementation and compensation for absences

The attendance at the lectures is optional; with respect to the advanced stage of specialised studies the self-study, professional reports and discussion given by students, project teaching and consultations are preferred. The attendance at the seminars and practical training is compulsory and is always checked by the teacher. Absence may be in justified cases compensated for by the agreement with the teacher

Classification of course in study plans

  • Programme M2A-P Master's

    branch M-MTI , 1. year of study, summer semester, 7 credits, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer


1. Classification of phase transformations.
2. Crystallisation in one component systems.
3. Crystallisation of solid solutions.
4. Crystallisation of solid solutions.
5. Crystallisation of eutectics and peritectics.
6. Allotropic, polymorphic and massive transformations.
7. Allotropic, polymorphic and massive transformations.
8. Eutectoid transformations.
9. Bainitic Transformations.
10. Martensitic transformations.
11. Martensitic transformations.
12. Decomposition of supersaturated solid solutions.
13. Decomposition of supersaturated solid solutions.

Laboratory exercise

14 hours, compulsory

Teacher / Lecturer


1. Assessment of chemical inhomogeneity in cast materials.
2. Assessment of chemical inhomogeneity in cast materials.
3. Evaluation of calorimetric experiments and estimation of the phase transformation energy.
4. Evaluation of calorimetric experiments and estimation of the phase transformation energy.
5. Evaluation of microstructures, solution of the Avrami equation and construction of a part of the transformation diagram.
6. Evaluation of microstructures, solution of the Avrami equation and construction of a part of the transformation diagram.


12 hours, compulsory

Teacher / Lecturer


1. Key words of the first law of thermodynamics, thermochemical principles.
2. Solution of examples.
3. Key words of the second law of thermodynamics, equilibrium and spontaneous processes.
4. Solution of examples.
5. Key words of the phase transformation kinetics.
6. Solution of examples.
7. The laws of diffusion, solution of examples.


eLearning: opened course