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Lecture# Diffusion: Fundamental Concepts

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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In course

PHYS-307: Physics of materials

This course illustrates some selected chapters of materials physics needed to understand the mechanical and structural properties of solids. This course deals primarily with the physics of dislocation

Instructor

Related concepts (32)

Related lectures (33)

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.

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.

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.

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.

Darcy's law

Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the hydraulic head difference (which is often just proportional to the pressure difference) via the hydraulic conductivity.

Explores diffusion from a macroscopic perspective, emphasizing the derivation of the diffusion equation through mass conservation and fixed flux law.

Explores diffusion, transport phenomena, Fick's law, thermal and electrical transport, Onsager's relations, and thermoelectric effects.

Explores diffusion coefficients for self-diffusion and suspended particles in fluids.

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Covers mass transport through molecular diffusion, explaining Fick's first law and diffusion coefficient values for various materials.