C5305 Computational Thermodynamics

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/0. 2 credit(s) (plus 2 credits for an exam). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. Mgr. Jana Pavlů, Ph.D. (lecturer)
prof. RNDr. Jan Vřešťál, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Vřešťál, DrSc.
Department of Chemistry – Chemistry Section – Faculty of Science
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Main aims of the course are: - understanding of the base of calculation of phase equilibria in various systems;
- retrieving of the knowledge of experimental methods necessary for successful calculation of phase diagrams;
- retrieving of the knowledge of theoretical methods for modeling of Gibbs energy of phases;
- gaining the information how to assess literature data and perform optimization of them together with experimental and theoretical information;
- creating consistent database for succesful prediction of stable equilibrium state for industrial application;
At the end of the course, students should be able to calculate phase diagrams and use them for solution of practical applications.
Syllabus
  • 1. Introduction: Computational thermodynamics, past and present of CALPHAD technique.Thermodynamic basis: laws of thermodynamics, functions of state, equilibrium conditions, vibrational heat capacity, statistical thermodynamics.
  • 2. Crystallography: connection of thermodynamics with crystallography, crystal symmetry, crystal structures, sublattice modeling, chemical ordering. Equilibrium calculations: minimizing of Gibbs energy, equilibrium conditions as a set of equations, global minimization of Gibbs energy, driving force for a phase.
  • 3. Phase diagrams: definition and types, mapping a phase diagram, implicitly defined functions and their derivatives. Optimization methods: the principle of the least-squares method, the weighting factor. Marquardt’s algorith.
  • 4. Sources of thermodynamic data: first principles calculations, the density functional theory and its approximations, DFT results at 0 K, going to higher temperatures. Experimental data used for the optimization, calorimetry, galvanic cells, vapor pressure, equilibria with gases of known activity.
  • 5. Sources of phase equilibrium data: thermal analysis, quantitative metallography,microprobe measurements, two-phase tie-lines, X-ray, electron and neutron diffraction.
  • 6. Models for the Gibbs energy: general form of Gibbs-energy model, temperature and pressure dependences, metastable states, variables for composition dependence.
  • 7. Models for the Gibbs energy: modeling particular physical phenomena, models for the Gibbs energy of solutions, compound-energy formalism, the ideal-substitutional-solution model, regular-solution model.
  • 8 .Models for the excess Gibbs energy: Gibbs energy of mixing, the binary excess contribution to multicomponent systems, the Redlich-Kister binary excess model, higher-order excess contributions: Muggianu, Kohler, Colinet and Toop.
  • 9. Models for the excess Gibbs energy: associate-solution model, quasi-chemical model, cluster-variation method, modeling using sublattices: models using two sublattices.
  • 10. Models for the excess Gibbs energy: models with three or more sublattices, models for phases with order-disorder transitions Gibbs energy for phases that never disorder, models for liquids, chemical reactions and models.
  • 11. Assessment methodology: literature searching, modeling of the Gibbs energy for each phase, solubility, thermodynamic data, miscibility gaps, modeling terminal phases.
  • 12. Assessment methodology: modeling intermediate phases, crystal-structure information, compatibility of models, thermodynamic information, determining adjustable parameters, decisions to be made during assessment, checking results of optimization and publishing it.
  • 13. Creating thermodynamic databases: unary data, model compatibility, naming of phases,validation of databases, nano-materials in structure alloys and lead-free solders.Examples using databases: Sigma-Phase Formation in Ni-based anticorrosion Superalloys,Intermetallic Phases in Lead-Free Soldering, Equilibria with Laves Phases for aircraft engines.
Literature
  • Computational Thermodynamics. The Calphad Method. Hans Leo Lucas, Suzana G.Fries, Bo Sundman: Cambridge Univ.Press, 2007, 312 s., ISBN 978-0-521-86811-2.
  • SAUNDERS, Nigel and Peter A. MIODOWNIK. Calphad :calculation of phase diagrams : a comprehensive guide. Oxford: Pergamon, 1998, xvi, 479 s. ISBN 0-08-042129-6. info
Teaching methods
Lectures focused to practical application in calculations of phase diagrams.
Assessment methods
Individual homework: calculation of one phase diagram, Oral exam
Language of instruction
English
The course is also listed under the following terms Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2017, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.