Course detail

Modelling of Thermodynamic Stability and Phase Transformations

FSI-9ESMAcad. year: 2020/2021

Understanding of thermodynamic stability of individual phases and processes of their mutual transformation is important condition for design of new complex materials with enhanced properties. Theoretical assumptions can be verified with help of advanced computer modelling before experimental preparation of studied materials. Some of computational methods used experimental data from simple systems like in the case of method for modelling of phase diagrams CALPHAD. Modelling can be based also on fundamentals of quantum mechanics (ab initio methods) and the no experimental data are required. In this course students obtain general knowledge about advanced applications of both method mentioned above and adopt practical experience of of their using, which can utilize within in their thesis.

Learning outcomes of the course unit

The course is focused on advancement and practical applications of early obtained knowledge of material modelling with help of ab initio methods and the CALPHAD method. After finishing the course student will be able to use both method for solving of real problems within their field of study in material engineering.


Basic overview of method for electronic structure calculations and experience with scripting languages (i.e. Python). Advanced knowledge of solid states physic and thermodynamics.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

A.D. Pelton: Phase Diagrams and Thermodynamic Modeling of Solutions. Elsevier, Amsterdam 2019 (EN)
Zi-Kui Liu, Yi Wang: Computational Thermodynamics of Materials. Cambridge 2016. (EN)
Qing Jiang, Zi Wen: Thermodynamics of Materials. Springer 2011 (EN)
M. Hillert: Phase Equilibria, Phase Diagrams and Phase Transformations. Cambridge University Press 2007. (EN)
H.L. Lukas, S.G. Fries, B. Sundman, Computational Thermodynamics: The CALPHAD Method. Cambridge University Press, Cambridge 2007 (EN)
G. Grimvall, Thermophysical Properties of Materials. Elsevier North-Holland, Amsterdam 1999 (EN)

Planned learning activities and teaching methods

The course is provided trough the lectures which will explain theoretical background for solution of selected problems as well as their practical solutions. Particular issues of students with their semester works will be discussed within consultations.

Assesment methods and criteria linked to learning outcomes

Students will work individually on selected topic related to thermodynamic stability and phase transformations of materials. Current state of problematic, solution and results will be reported in written form and introduced at the exam in form of oral defence.

Language of instruction

Czech, English

Work placements

Not applicable.


The Aims of this course is to provided the knowledge about advanced application of material modelling of phase stability and transformation with help of ab initio calculations of electronic structure and the CALPHAD method. The course is focused on practical using of both method.

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

Lectures supplemented with sample solutions of typical problems. Consultation.

Classification of course in study plans

  • Programme D-MAT-P Doctoral, 1. year of study, winter semester, 0 credits, recommended

  • Programme D4F-P Doctoral

    branch D-FMI , 1. year of study, winter semester, 0 credits, recommended

Type of course unit



20 hours, optionally

Teacher / Lecturer


1. Computational thermodynamics, CALPHAD method
2. Phase diagrams, methods for optimalization, Marquard algorithm, estimation of equilibrium
3. Source of thermodynamic data, Models for Gibbs energy
4. Preparation of "assessment", creation of thermodynamic database
5. Ab initio methods for modeling of phase stability
6. Modeling of solid solutions and defects of crystal lattice
7. Calculations of heat of formation, convex hull
8. Calculations of phonon dispersion, harmonic approximation
9. Quasi-harmonic approximation, anharmonic vibrations
10. Calculations of other contributions to free energy
11. Diffusional phase transformation, modeling of diffusion
12. Diffusionless phase transformation, modeling of transformation pahts