Lecture

Thermal and Atomic Diffusion

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In course

MSE-101(b): Materials:from chemistry to properties

Ce cours permet l'acquisition des notions essentielles relatives à la structure de la matière, aux équilibres et à la réactivité chimique en liaison avec les propriétés mécaniques, thermiques, électriques, magnétiques et optiques des matériaux. ...

Description

This lecture covers the concepts of thermal and atomic diffusion, including the heat equation, thermal diffusivity, and stationary solutions. It also explores atomic diffusion, activation energy, and the diffusion coefficient. The importance of diffusion in various applications, such as surface treatment, growth of nanowires, and semiconductor doping, is discussed.

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Instructors (4)

Arianna Marchioro

Education PhD Thesis | Interfacial Charge Transfer Dynamics in Solid-State Hybrid Organic-Inorganic Solar Cells 2010 – 2014 EPFL Directed by Prof. J.-E. Moser and Prof. M. Grätzel MSc in Molecular and Biological Chemistry | 2008 – 2010 EPFL and Imperial College London (exchange program) BSc in Chemistry | 2005 – 2008 EPFL Professionals experiences Postdoctoral Research Associate 2014–2016 University of Washington, Seatt

Fabien Sorin

Sep 2002-Oct 2007 Ph.D., Department of Materials Science and Engineering, MIT, USA. Supervisor: Prof. Yoel Fink; Thesis: Multi-material, Multifunctional Fiber Devices. After graduating with an engineering degree and a Master of Science in Physics from the Ecole Polytechnique in Palaiseau, France, Prof. Sorin joined the department of Materials Science and Engineering at the Massachusetts Institute of Technology (MIT) in Cambridge, USA for his graduate studies. He worked as a research assistant in the Photonic Bandgap Fibers and Devices Group of Professor Yoel Fink and graduated with a PhD in 2008. His PhD thesis led to the development of a new class of fiber material and devices and he was a pioneer of the field of multi-material fibers. Mar 2008-Oct 2010 Postdoctoral Associate and Research Scientist, Research Laboratory of Electronics, MIT. He then joined the Research Laboratory of Electronics at MIT as a Postdoctoral Associate, and continued as a Research Scientist associate, where he conducted independent research in the emerging field of multi-material fibers and was involved and led a variety of projects in fundamental research as well as in collaborations with local start-ups. Apr 2011 Feb 2013 Research Engineer, Saint-Gobain Recherche, Aubervilliers, France. Surface du Verre et interface Group In 2011, prof. Sorin returned to Europe and joined the company Saint-Gobain in the Saint-Gobain Recherche center, its biggest research center located near Paris in France. As a research engineer, he developed a new research thrust investigating new photonic materials and nanostructures for the energy and building industries. In particular, he and colleagues developed innovative processing approaches to deploy photonic nanostructures for light management over large area substrates, for applications in energy harvesting and saving, and for building materials and windows. Mar 2013 Present Assistant Professor tenure-track, Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland. Head of the Photonic materials and fibre devices laboratory (FIMAP) Since March 2013, he is in the department of Materials Science (IMX) at the Ecole Polytechnique Fédérale de Lausanne (EPFL) as an assistant professor tenure-track. He is starting a research group on photonic materials and fiber devices (FIMAP), continuing on developing innovative materials processing approaches and photonic device architectures to develop new solutions in energy harvesting, saving and storage, in sensing and monitoring, health care and smart fabrics.

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Related concepts (25)

Diffusion

Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios.

Heat equation

In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. As the prototypical parabolic partial differential equation, the heat equation is among the most widely studied topics in pure mathematics, and its analysis is regarded as fundamental to the broader field of partial differential equations.

Fick's laws of diffusion

Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation. A diffusion process that obeys Fick's laws is called normal or Fickian diffusion; otherwise, it is called anomalous diffusion or non-Fickian diffusion.

Heat kernel

In the mathematical study of heat conduction and diffusion, a heat kernel is the fundamental solution to the heat equation on a specified domain with appropriate boundary conditions. It is also one of the main tools in the study of the spectrum of the Laplace operator, and is thus of some auxiliary importance throughout mathematical physics. The heat kernel represents the evolution of temperature in a region whose boundary is held fixed at a particular temperature (typically zero), such that an initial unit of heat energy is placed at a point at time t = 0.

Secondary treatment

Secondary treatment (mostly biological wastewater treatment) is the removal of biodegradable organic matter (in solution or suspension) from sewage or similar kinds of wastewater. The aim is to achieve a certain degree of effluent quality in a sewage treatment plant suitable for the intended disposal or reuse option. A "primary treatment" step often precedes secondary treatment, whereby physical phase separation is used to remove settleable solids.

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Michel Rappaz

After a PhD in solid state physics (1978) at the Ecole Polytechnique Fédérale de Lausanne (EPFL) and a post-doc at Oak Ridge National Laboratory, Michel Rappaz joined the Institute of Materials of EPFL in 1981. After two years in an engineering company, he came back to EPFL in 1984 where he was nominated Adjunct Professor in 1990 and Full Professor in 2003. He retired from EPFL in 2015 and is now Emeritus Professor and independent consultant for several industries and research centres. His main interests are in phase transformations and solidification, in particular the coupling of macroscopic aspects of heat and mass transfer with microscopic aspects of microstructure and defect formation. Among his diverse achievements, one can mention in particular the development of cellular automata for grain structure predictions and of granular models for hot tearing formation in castings, the coupling of Finite Element method with microscopic models of nucleation and growth, the application of the phase field method to the understanding of various microstructures, the discovery of quasicrystal mediated-nucleation in alloys, and many other studies both fundamental at the microstructure-defect level and more applied at the level of processes. Some of the software developments have been commercialized by a spin-off company founded by his group in 1991 (Calcom SA), now part of the French company ESI. Michel Rappaz initiated in 1992 an annual postgraduate course on solidification which has been attended by more than 900 participants from all over the world. He is presently collaborating closely with another spin-off company started from his group, Novamet SàrL. Michel Rappaz has received several awards, in particular the Mathewson co-author award (1994) and author award (1997) of the American Mineral, Metals and Materials Society (TMS), the Koerber foundation award jointly with Profs Y. Bréchet and M. Asbby (1996), the Sainte-Claire Deville Medal (1996) and the Grand Medal (2011) from the French Materials Society, the Bruce Chalmers Award of TMS (2002), the Mc Donald Memorial Lecture award of Canada (2005), the FEMS European Materials Gold Medal (2013) and the Brimacombe Prize of TMS (2015). He is a highly-cited author of ISI, a fellow of ASM, IOP and TMS, and has co-authored more than 200 publications and two books.

Related concepts (25)

Diffusion

Heat equation

Fick's laws of diffusion

Heat kernel

Secondary treatment