Bachelor's Degree (3rd Year) in CPES: Modeling and Numerical Methods in Materials Science—Chemistry

Thermodynamics: Microscopic and Macroscopic Aspects

Thermodynamics is the tool of choice for studying matter on a macroscopic scale. In particular, when it comes to chemical reactions, it allows us to predict the direction in which they proceed and their equilibrium state. In the early years of the bachelor’s program, the focus is on describing the principles of thermodynamics and their direct application to chemistry in the case of simple, single-phase equilibrium reactions or reactions between homogeneous phases. This course will expand on this knowledge in two directions.

First, we will generalize this macroscopic thermodynamic descriptive framework to more complex systems, such as interfacial systems where surface tension plays a role, or non-uniform phases where the composition is not the same everywhere due to an external field. We will also study phase transitions and equilibrium displacements.

Next, we will examine the connection to the microscopic world, where matter is described at the atomic scale. We will show that the evolution predicted by thermodynamics is statistical in nature, with the equilibrium state corresponding to the most probable macroscopic state given the constraints imposed on the system. This will allow us to deduce the macroscopic thermodynamic properties of a physicochemical system from its microscopic description.

View the full page

The first part of the module will introduce metals and alloys through the lens of crystallography (from the “ideal” crystalline solid to defects and solid solutions), followed by a second part devoted to their characterization by X-ray diffraction, and the final part will address their synthesis using their solid-liquid binary phase diagram (description and construction) and the various solid-state transformations.

View the full page

View the full page

View the full page

View the full page

This course builds on the mathematics covered in the first year (L1) and the^first semester of the second year (L2). It will introduce the mathematical tools that physicists need in the areas of integration theory, functional transformations, complex variables, and distributions.

View the full page

View the full page

View the full page

View the full page

This module provides an introduction to the concepts and methods of statistical physics for systems at equilibrium, using a bottom-up approach: starting with examples and then deriving the general principles. It draws heavily on the course by Harvey Gould and Jan Tobochnik. The final chapter of the course offers a historical introduction to the development of the theory of Brownian motion.

View the full page

View the full page

This course aims to introduce the fundamentals of physical hydrodynamics. The kinematic aspects are covered first: Eulerian and Lagrangian formalisms, analysis of the motion of a fluid volume element, introduction to the stream and potential velocity functions, and applications to various types of flows. In the next section on fluid dynamics, we derive Euler’s equation and Bernoulli’s equation for the flow of ideal fluids, followed by the Navier-Stokes equation describing the flow of Newtonian viscous fluids. This section will lead us to define the stress tensor as well as the Reynolds number, which allows us to determine whether a flow is laminar or turbulent. The course concludes with an introduction to the mechanics of deformable solids: displacement field, strain tensor, and deformation tensor.

View the full page

View the full page

View the full page

In this course, we will build upon the basic concepts previously covered in Quantum Mechanics in Semester 5. The course is organized around the following main topics: extension of the wave mechanics formalism, angular momentum theory, the hydrogen atom, perturbations, and an introduction to relativistic quantum mechanics.

View the full page

View the full page