L9 Diffusion3 Mechanisms

# L9 Diffusion3 Mechanisms - Lecture 9 Diffusion III Atomic...

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Lecture 9 Diffusion III Atomic Mechanisms of Diffusion And The “Random Walk”

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Previously on Diffusion. .. Macroscopic picture of diffusion Knowing c(x), we can predict J x and dc/dt using Fick’s 1 st and 2 nd laws. Solutions to these differential equations exist for many boundary conditions and initial conditions. BUT, they provide no information on HOW the atoms are moving.
Today’s Learning Objectives Explain why there is an activation energy for diffusion Explain why defects are important for diffusion Be able to describe the Random Walk nature of diffusion Recognize and describe vacancy diffusion and interstitial diffusion Predict which mechanism is most likely List ways to increase or decrease the Diffusion rate in a material

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Microscopic Æ Macroscopic Using a microscopic (atom-level) picture of what happens during diffusion, we should be able to explain the macroscopic behavior observed.
A physical description of Diffusion Diffusion can be modeled as the jumping of atoms from one plane to another Calculate the net number of A atoms moving from plane 1 to plane 2 per unit area and unit time This is called the Diffusion Flux [atoms/(cm 2 -s)] Concentration of A atoms on plane 1 and 2 Are denoted by c 1 and c 2 atoms/cm 3 Spacing between adjacent planes Δ x

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How are atoms able to move in a solid? Recall the E(r) Bond-Energy curves we have seen for 2 atoms or ions. In a crystal, there is a perfect 3D array of atoms. This creates a periodic array of potential wells.
Egg Carton Demo The egg carton is a small 2D array of potential wells. Each atom has some kinetic energy that depends upon the temperature. It is jiggling around in its potential well. The higher the temperature, the more energy it has. If a particular atom gets enough energy… it can jump out of its well. But: where will it go? Stop and think about this for a moment. What are the possibilities? Can atoms double up on one location? Can atoms leave the solid?

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Activation Energy for Diffusion There is an activation energy barrier between the lower-energy atom sites in the crystal If an atom has enough thermal energy, it can overcome this barrier and move to a neighboring site, IF IT IS VACANT. The higher the temperature, the more probable an atom can move.
Arrhenius Relationships This type of equation describes the number of particles that can overcome and energy barrier with their thermal energy. To linearize the equation, take the natural log of both sides: = T k E N N B a highE exp 0 T k E N N B a highE = 0 ln ln

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Atomic Movement in Diffusion is Random Motion can be modeled as a Random Walk In a 1-dimensional case, each atom can move to the left or to the right. Atoms don’t know or care which way they are going.
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## This note was uploaded on 11/28/2010 for the course MTE 209 taught by Professor Tanyafalten during the Fall '09 term at Cal Poly Pomona.

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L9 Diffusion3 Mechanisms - Lecture 9 Diffusion III Atomic...

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