SubjectsSubjects(version: 879)
Course, academic year 2020/2021
Equilibria in Heterogeneous Systems - P126001
Title: Chemické a fázové rovnováhy v heterogenních systémech
Guaranteed by: Department of Solid State Engineering (126)
Actual: from 2019
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0 other [hours/week]
Capacity: winter:unlimited / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type: doctoral
Note: course is intended for doctoral students only
can be fulfilled in the future
you can enroll for the course in winter and in summer semester
Guarantor: Leitner Jindřich prof. Ing. DrSc.
Sedmidubský David prof. Dr. Ing.
Interchangeability : D126002
Z//Is interchangeable with: AP126001
Annotation -
Last update: Pátková Vlasta (19.04.2018)
Thermodynamic calculations are common part of theoretical modeling of various processes of preparation, treating and utilization of materials. The course Equilibria in Heterogeneous Systems is focused on this field and, in advanced form, goes over pVT relations and thermodynamic properties of solids, experimental as well as theoretical (computational) methods for their determination and methodology of phase and chemical equilibrium calculations in complex heterogeneous systems (including systems with significant influence of surfaces and interfaces). Practical demonstrations of the FacfSage system and model thermodynamic calculations are also included.
Aim of the course -
Last update: Pátková Vlasta (19.04.2018)

Students will be able to:

Apply proper thermodynamic models for various types of melts and solid solutions.

Assess reliability of experimentally determined, empirically estimated and theoretical calculated thermodynamic data.

Calculate of equilibrium composition of complex heterogeneous systems including those with significant influence of surfaces and interfaces.

Literature -
Last update: Leitner Jindřich prof. Ing. DrSc. (14.09.2018)

A: Gaskell D.R., Laughlin D.E.: Introduction to Thermodynamics of Materials, 6th edition (694 pp). CRC Press (2017), ISBN-13: 978-1498757003

A: DeHoff R.: Thermodynamics in Materials Science, 2nd edition (624 pp). CRC Press (2016), ISBN-13: 978-0849340659

Learning resources -
Last update: Leitner Jindřich prof. Ing. DrSc. (16.06.2018)

Powerpoint presentations are available at

Teaching methods -
Last update: Leitner Jindřich prof. Ing. DrSc. (12.09.2018)


Syllabus -
Last update: Leitner Jindřich prof. Ing. DrSc. (16.06.2018)

1. PVT equations of state and thermodynamic properties of solids under high pressures, magnetic contribution to thermodynamic functions, extrapolation of heat capacity of solids and liquids out of range of their stability.

2. Substitutional solutions, mixing and excess properties, model of associate solution. Sublattice model for solid solutions (solutions of stoichiometric compounds, interstitial solutions, ionic melts).

3. Experimental methods for determination of thermodynamic data for solids. Experimental methods for phase equilibria and construction of phase diagram.

4. Methods for estimation of thermodynamic properties of solids. Ab-initio calculations and thermodynamic properties of solids.

5. Thermodynamic description of partially open systems (non-stoichiometrc phases, fixed chemical potential). Calculation of phase equilibria and construction of phase diagram from thermodynamic data in partially open systems Me-O.

6. Calculation of complex equilibria in multicomponent heterogeneous systems by Gibbs energy minimization method, equilibria in ionic systems (aqueous solution of electrolytes, ionic melts).

7. Thermodynamics of surfaces and interfaces (structure of surfaces, surface energy, surface stress). Influence of surfaces and interfaces on phase and chemical equilibria (vapour pressure, melting, solid-state transformation).

8. FactSage software and its application for thermodynamic calculations.

Course completion requirements -
Last update: Pátková Vlasta (19.04.2018)

Right solution at least of two from three exercises assigned as individual homework.

At least 50% successfulness at the exam test.