SubjectsSubjects(version: 928)
Course, academic year 2019/2020
Equilibria in Heterogeneous Systems - D126002
Title: Chemické a fázové rovnováhy v heterogenních systémech
Guaranteed by: Department of Solid State Engineering (126)
Faculty: Faculty of Chemical Technology
Actual: from 2019
Semester: winter
Points: winter s.:0
E-Credits: winter s.:0
Examination process: winter s.:
Hours per week, examination: winter s.:3/0, other [HT]
Capacity: unlimited / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
For type:  
Note: course is intended for doctoral students only
can be fulfilled in the future
Guarantor: Leitner Jindřich prof. Ing. DrSc.
Sedmidubský David prof. Dr. Ing.
Is interchangeable with: AP126001, P126001
Examination dates   Schedule   
This subject contains the following additional online materials
Annotation -
Last update: TAJ126 (14.05.2014)
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: TAJ126 (14.05.2014)

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. (15.09.2015)

R:Leitner J., Voňka P.: Termodynamika materiálů, skripta VŠCHT, Praha 1992. Skripta jsou dostupná na webu:

A:Gaskell D.R.: Introduction to the Thermodynamics of Materials, 5th Edition (618 pp), Taylor & Francis (2008).

A:DeHoff R.: Thermodynamics in Materials Science, 2nd Edition (624 pp), CRC Press (2006).

Powerpoint presentations are available at

Syllabus -
Last update: TAJ126 (14.05.2014)

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 of N-component solutions, dilute solutions.

3.Sublattice model for solid solutions (ordered alloys, solutions of stoichiometric compounds, interstitial solutions).

4.Associate solution model for liquids, sublattice model for ionic melts.

5.Experimental methods for determination of thermodynamic data for solids.

6.Experimental methods for phase equilibria and construction of phase diagram from experimental data.

7.Methods for estimation of thermodynamic properties of solids.

8.Ab-initio calculations and thermodynamic properties of solids.

9. Thermodynamic description of oxide systems (stoichiometric solid oxides and their solutions, non-stoichiometric solid oxides, oxidic melts).

10. Calculation of phase equilibria and construction of phase diagram from thermodynamic data, thermodynamic description of partially open systems Me-O.

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

12.Thermodynamics of surfaces and interfaces (structure of surfaces, surface energy, surface stress).

13.Influence of surfaces and interfaces on phase and chemical equilibria (vapour pressure, melting, solid-state transformation).

14.FactSage and its application for thermodynamic calculations.

Course completion requirements -
Last update: TAJ126 (14.05.2014)

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

At least 50% successfulness at the exam test.

Coursework assessment
Form Significance
Report from individual projects 40
Examination test 60