SubjectsSubjects(version: 955)
Course, academic year 2023/2024
Equilibria in Heterogeneous Systems - AP126001
Title: Equilibria in Heterogeneous Systems
Guaranteed by: Department of Solid State Engineering (126)
Faculty: Faculty of Chemical Technology
Actual: from 2019
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0, other [HT]
Capacity: winter:unlimited / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
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 : P126001
Annotation -
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.
Last update: Pátková Vlasta (19.11.2018)
Aim of the course -

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.

Last update: Pátková Vlasta (19.11.2018)
Literature -

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

Last update: Pátková Vlasta (19.11.2018)
Learning resources -

Powerpoint presentations are available at

Last update: Pátková Vlasta (19.11.2018)
Teaching methods -


Last update: Pátková Vlasta (19.11.2018)
Syllabus -

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.

Last update: Pátková Vlasta (19.11.2018)
Course completion requirements -

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

At least 50% successfulness at the exam test.

Last update: Pátková Vlasta (19.11.2018)