Lecture

Diffusion: Fundamental Concepts

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In course

PHYS-307: Physics of materials

This course discusses materials physics associated with the mechanical and structural properties of solids, primarily focusing on the physics of dislocation defect dynamics and linking diffusion kinetics to the fundamental physics of phase transformations. ...

Description

This lecture covers the fundamental concepts of diffusion, including Fick's laws, demonstration of diffusion in one-dimensional systems, solutions of Fick's second law, diffusion coefficient and random walk, temperature dependence, self-diffusion, force applied to diffusing particles, Darken equation, interdiffusion, Boltzmann-Matano method, scaling laws, Heaviside step distribution, and the Kirkendall effect. The instructor explains the concepts with examples and demonstrations.

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Instructor

Thomas La Grange

Expertise Electron Microscopy, Aberration Correct Scanning Transmission Electron Microscopy, Electron Diffraction, Ultrafast Transmission Electron Microscopy, Electron Energy Loss Spectroscopy, Energy Dispersive Spectroscopy, Materials Science, High-speed deformation, Dislocation Dynamics, Skyrmionics, Martensitic Phase Transformation Theory, Solidification Expertise Electron Microscopy, Aberration Correct Scanning Transmission Electron Microscopy, Electron Diffraction, Ultrafast Transmission Electron Micro

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Related concepts (21)

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.

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.

Molecular diffusion

Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of the particles. Diffusion explains the net flux of molecules from a region of higher concentration to one of lower concentration. Once the concentrations are equal the molecules continue to move, but since there is no concentration gradient the process of molecular diffusion has ceased and is instead governed by the process of self-diffusion, originating from the random motion of the molecules.

Heaviside step function

The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or ), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one. The function was originally developed in operational calculus for the solution of differential equations, where it represents a signal that switches on at a specified time and stays switched on indefinitely.

Step function

In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. A function is called a step function if it can be written as for all real numbers where , are real numbers, are intervals, and is the indicator function of : In this definition, the intervals can be assumed to have the following two properties: The intervals are pairwise disjoint: for The union of the intervals is the entire real line: Indeed, if that is not the case to start with, a different set of intervals can be picked for which these assumptions hold.

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