Thermodynamics and phase equilibria

- Thermodynamics of single-component systems.

- Basic thermodynamics of multicomponent systems. Chemical potential, Gibbs-Duhem relationship, variance.

- Thermal analysis techniques used to construct binary/ternary diagrams: ATG, ATD and DSC

- Construction and interpretation of binary phase diagrams based on thermodynamic quantities. Diagrams of Gibbs free enthalpy, pressure and temperature as a function of binary mixture composition. Liquid-liquid, liquid-vapor, solid-liquid mixtures.

- Phase transformation: first- and second-order transitions, critical points. Examples.

- The supercritical state: definition, thermodynamic properties, wide-ranging industrial applications.

- Construction and interpretation of ternary phase diagrams: variance, definitions of ternary eutectic, first- and second-order peritectic, isothermal section, study of alloy cooling.

Hourly volumes* :

CM :13

TD:7

- Construct a phase diagram using thermodynamic data (coordinates of critical points, enthalpy of phase change values, etc.) and thermal analysis data.

- Understand the concepts of first- and second-order phase transitions.

- Identify regions associated with phase equilibrium in diagrams. Give the evolution of appropriate thermodynamic functions from the interpretation of a binary diagram (phase-change enthalpy estimation, Clapeyron formula).

- Identify critical points in a binary diagram. Differentiate the supercritical state from liquid and gas states in terms of its thermodynamic properties. Understand the main industrial applications of supercritical fluids.

- Identify characteristic reactions in a ternary diagram: ternary eutectic, 1st-order peritectic and 2nd-order peritectic.

- Know how to interpret a binary or ternary diagram to know the conditions for obtaining the desired phases or, conversely, to avoid the formation of undesirable phases and anticipate the properties and stability of materials.

General chemistry, Principles of thermodynamics. Phase transition thermodynamics of a single-component system. Phase diagrams of a single-component system. Spontaneous evolution and equilibrium conditions of a single-component system.

Bachelor's degree in chemistry, physics and materials science

Final Examination

- Basic concepts of multicomponent thermodynamics. Definition of thermodynamic state functions for a multicomponent system. Definition of chemical potential. Spontaneous evolution and equilibrium conditions. Gibbs-Duhem relationship. Molar free enthalpy versus composition diagrams for a mixture. Variance of a system.

- Vapor pressure diagram - composition of a binary liquid mixture. Construction and interpretation. Ideal solution, Raoult's law, Henry's law. Colligative properties.

- Temperature-composition diagram for a binary liquid mixture. Miscible and partially miscible mixtures. Azeotropic mixtures. Construction and interpretation.

- Temperature-composition diagram of a binary solid mixture. Eutectic. Construction and interpretation.

- Phase transitions. Order parameters, first- and second-order transitions. Critical points. Examples: changes of state, phase transitions in polymers, phase transitions in solid materials (with and without diffusion).

- The supercritical state. Definition, thermodynamic properties, wide-ranging industrial applications (e.g. caffeine extraction with supercritical_CO2 ).

- Thermal analysis: Gravimetric thermal analysis, Differential thermal analysis, Differential scanning calorimetry: Definitions, interpretation of curves, usefulness of techniques for constructing phase diagrams.

- Ternary diagrams: Definitions, variance, inverse segment rules, liquidus surface, solidus surface

- Ternary temperature-composition diagram: isothermal sections, ternary eutectic,^1st-order peritectic,^2nd-order peritectic, study of slow cooling of a molten composition

• "Physical Chemistry: Thermodynamics, Statistical Thermodynamics and Kinetics", Thomas Engel & Philip Reid, Pearson, 2018.
• "Atkins' Physical Chemistry", Peter Atkins, Julio de Paula & James Keeler,^11th edition, OUP Oxford, 2017.
• "Phase Equilibria, Phase Diagrams and Phase Transformations: Their Thermodynamic Basis", Mats Hillert, Cambridge University Press,^2nd edition, 2007.
• "Ternary Phase Diagrams in Materials Science", D. R. F. West, CRC Press, 2017.
• "The Liquid and Supercritical States of Matter", John E. Proctor, CRC Press, 2020.
• "Computational Thermodynamics of Materials", Zi-Kui Liu &Yi Wang, Cambridge University Press, 2016.