Bachelor's Degree in Modeling and Digital Technology in Materials Science Chemistry

Thermodynamics: micro and macroscopic aspects

Thermodynamics is the tool of choice for studying matter on a macroscopic scale. In particular, in the case of chemical reactions, it allows us to predict the direction of their evolution and their state of equilibrium. In the first years of the bachelor's degree, we focus 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 teaching unit will deepen this knowledge in two directions.

First, we will generalize this macroscopic thermodynamic description 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 ruptures and equilibrium displacements.

Next, we will look at the link with 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 state of equilibrium corresponding to the most probable macroscopic state given the constraints applied to the system. This will allow us to deduce the macroscopic thermodynamic properties of a physicochemical system from its microscopic description.

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The first part of the module will consist of presenting metals and alloys through 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 a final part addressing their synthesis through their solid/liquid binary diagram (description and construction) and the various transformations in the solid state.

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This course builds on the mathematics taught in the first year and^first semester of the second year. It will introduce the mathematical tools needed by physicists in integration theory, functional transformations, complex variables, and distributions.

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This module is an introduction to the concepts and methods of statistical physics of systems in equilibrium, using a bottom-up approach: starting with examples and then presenting the general principles. It draws heavily on the course taught by Harvey Gould and Jan Tobochnik. A historical introduction to the development of Brownian motion theory forms the final chapter of the course.

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This course aims to introduce the basics of physical hydrodynamics. Kinematic aspects are covered first: Euler and Lagrange formalism, analysis of the motion of a fluid volume element, introduction of velocity current and potential functions, and applications to different types of flows. In the next part of fluid dynamics, we establish Euler's equation and Bernoulli's relation for the flow of ideal fluids, then Navier-Stokes' equation describing the flow of viscous Newtonian fluids. This section will lead us to define the stress tensor and the Reynolds number, which can be used to determine whether a flow is laminar or turbulent. The course ends with an introduction to the mechanics of deformable solids: displacement field, dilation tensor, and deformation tensor.

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This course will build on the basic concepts previously acquired in Quantum Mechanics in semester 5. The course is structured around the following main topics: extension of wave mechanics formalism, angular momentum theory, hydrogen atom, perturbations, introduction to relativistic quantum mechanics.

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