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;
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
Lectures focused to practical application in calculations of phase diagrams.
Individual homework: calculation of one phase diagram and writing a report on the received results;