C5305 Computational Thermodynamics

Faculty of Science
Spring 2017
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).
doc. Mgr. Jana Pavlů, Ph.D. (lecturer)
prof. RNDr. Jan Vřešťál, DrSc. (lecturer)
doc. Mgr. Jana Pavlů, Ph.D.
Department of Chemistry - Chemistry Section - Faculty of Science
Supplier department: Department of Chemistry - Chemistry Section - Faculty of Science
Basic university level knowledge of physical chemistry (thermodynamics, equilibrium, phase diagrams - contained in courses: C1020, C4660, C4020).
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 the course is directly associated with
Course objectives
Main aims of the course are: - introduction to concepts of thermodynamic and crystallographic background;
- understanding of the base of calculation of phase equilibria and phase diagrams in various systems;
- retrieving of the knowledge of theoretical methods and models for modeling of Gibbs energy of phases;
- retrieving of the knowledge of experimental and theoterical methods providing necessary data for successful calculation of phase diagrams;
- gaining the information how to assess literature data and perform optimization of them together with experimental and theoretical information;
- understanding of principles how to create a consistent database for successful prediction of stable equilibrium state for industrial application;
Learning outcomes
Student will be able to:
- describe and explain the concepts and principles of computational thermodynamics;
- chose the appropriate model for phases contained in given system;
- perform critical assessment of both experimental and theoretical literature data;
- create a consistent database for successful prediction of stable equilibrium state;
- work independently with available software for computational modeling;
- calculate phase diagrams and use them for solution of practical applications;
- present and discuss her / his results in written form and corresponding to standards in the field;
  • 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 algorithm.
  • 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 dependencies, 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 anti corrosion Superalloys,Intermetallic Phases in Lead-Free Soldering, Equilibria with Laves Phases for aircraft engines.
  • 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 and writing a report on the received results; Oral examination
Language of instruction
Follow-Up Courses
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2019.
  • Enrolment Statistics (recent)
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