Thermodynamics and phase equilibria

- Reminder of thermodynamics of single component systems.

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

- Knowledge of thermal analysis techniques that allow the construction of binary/ternary diagrams: TGA, DTA and DSC

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

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

- The supercritical state: definition, thermodynamic properties, most extensive industrial applications.

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

Hourly volumes* :

CM :13

TD :7

- Know how to construct a phase diagram from some thermodynamic data (coordinates of critical points, value of enthalpies of phase change...) and from thermal analysis data.

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

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

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

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

- 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 to anticipate the properties and stability of materials.

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

Bachelor's degree in Chemistry, Physics and Materials Science

Final Examination

- Basic notions of multicomponent thermodynamics. Definition of thermodynamic state functions for a multicomponent system. Definition of the chemical potential. Spontaneous evolution condition and equilibrium condition. Gibbs-Duhem relation. Molar free enthalpy diagrams as a function of composition 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 of a binary liquid mixture. Case of miscible mixture and case of partially miscible mixture. 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 transition in polymers, phase transitions in solid materials (with and without diffusion).

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

- Thermal analysis: Gravimetric thermal analysis, Differential thermal analysis, Differential scanning calorimetric analysis: Definitions, interpretation of curves, usefulness of techniques for the construction of phase diagrams

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

- Ternary temperature-composition diagram: isothermal sections, ternary eutectic,^1st order peritectic,^2nd order peritectic, study of the 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.