L9 Diffusion3 Mechanisms

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

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 9 Diffusion III Atomic Mechanisms of Diffusion And The “Random Walk”
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Microscopic Æ Macroscopic Using a microscopic (atom-level) picture of what happens during diffusion, we should be able to explain the macroscopic behavior observed.
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 6
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?
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 8
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
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 47

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

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online