Thermodynamics and Phase Equilibria

- Review of the thermodynamics of single-component systems.

- Fundamentals of thermodynamics for multicomponent systems. Chemical potential, the Gibbs-Duhem relation, variance.

- Overview of thermal analysis techniques used to construct binary and ternary phase diagrams: ATG, ATD, and DSC

- Construction and interpretation of binary phase diagrams based on thermodynamic variables. Gibbs free energy, pressure, and temperature diagrams as functions of the composition of the binary mixture. Liquid-liquid, liquid-vapor, and solid-liquid mixtures.

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

- The supercritical state: definition, thermodynamic properties, and the most widespread industrial applications.

- Construction and interpretation of ternary phase diagrams: variance, definitions of ternary eutectics, first- and second-order peritectics, isothermal sections, and study of alloy cooling.

Hourly volumes*:

CM: 13

TD: 7

- Know how to construct a phase diagram based on thermodynamic data (coordinates of critical points, enthalpy values for phase changes, etc.) and data from thermal analyses.

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

- Identify the regions associated with phase equilibrium in the diagrams. Determine the changes in the appropriate thermodynamic functions based on the interpretation of a binary diagram (estimation of the enthalpy of phase change, Clapeyron’s equation).

- Identify critical points in a binary phase diagram. Be able to distinguish the supercritical state from the liquid and gaseous states in terms of their thermodynamic properties. Understand the main industrial applications of supercritical fluids.

- Identify characteristic reactions in a ternary phase diagram: ternary eutectic, first-order peritectic, and second-order peritectic.

- Be able to interpret a binary or ternary phase diagram to determine the conditions for obtaining the desired phases or, conversely, to prevent the formation of undesirable phases and to predict the properties and stability of materials.

General Chemistry, Principles of Thermodynamics. Thermodynamics of Phase Transitions in a Single-Component System. Phase Diagrams of a Single-Component System. Conditions for Spontaneous Change and Equilibrium in a Single-Component System.

Bachelor's Degree in Chemistry, Physics, and Materials Science

Final Exam

- Fundamentals of multicomponent thermodynamics. Definition of thermodynamic state functions for a multicomponent system. Definition of chemical potential. Condition for spontaneous change and condition for equilibrium. The Gibbs-Duhem relation. Diagrams of molar free enthalpy 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 for a binary liquid mixture. Miscible and partially miscible mixtures. Azeotropic mixtures. Construction and interpretation.

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

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

- The supercritical state. Definition, thermodynamic properties, and the most widespread industrial applications (e.g., caffeine extraction using supercritical_CO2 ).

- Thermal analyses: Gravimetric thermal analysis, Differential thermal analysis, Scanning differential calorimetry: Definitions, interpretation of curves, and applications of these techniques in the construction of phase diagrams

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

- Ternary temperature-composition diagram: isothermal sections, ternary eutectic,^first-order peritectic,^second-order peritectic, study of the slow cooling of a molten composition

• “Physical Chemistry: Thermodynamics, Statistical Thermodynamics, and Kinetics,” by Thomas Engel and Philip Reid, Pearson, 2018.
• “Atkins’ Physical Chemistry,” by Peter Atkins, Julio de Paula, and 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,” by D. R. F. West, CRC Press, 2017.
• “The Liquid and Supercritical States of Matter,” by John E. Proctor, CRC Press, 2020.
• “Computational Thermodynamics of Materials,” by Zi-Kui Liu and Yi Wang, Cambridge University Press, 2016.