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Fundamentals of Materials Science and Engineering

MSE 20 (B2 and B3)

Vera Marie M. Sastine

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Phenomenon of material transport by atomic motion

The net flux of any species, such as ions, atoms, electrons, holes

In materials processing technologies, control over the diffusion of atoms, ions

molecules, or other species iskey

Application Examples:

Carburization for

Surface Hardening of

Steels

Sintering ofbarium

magnesium

tantalate (BMT)

ceramic

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Diffusion Couple

- Formed by joining bars of two different

metals together so that there is intimate

contact between the two facesBefore heat

treatment

After heat

treatment

Interdiffusion / Impurity

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Vacancydiffusion

Intediffu

The diffusion of atoms in one direction corresponds

to the motion of vacancies (or impurity/substitute

atoms) in the opposite directionThe diffusion of interstitials ismore ra

they are smaller and thus more mobile

also more empty interstitial sites than

The probability of interstitial atomic movement is greater than for vacancy di

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Diffusion flux,J

- the rate of mass transfer; a function of time

- Mass (of the atoms) Mdiffusing through and

perpendicular to a unit cross-sectional areaA

of solid per unit of time t

Differentially,

If the diffusion flux does not change with time

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Concentration profile:

Concentration C plotted versus position (or distance) within the solidx

Concentration gradient:

the slope at a particular point on this curve

diffusion flux for

diffusion (in one

Driving force* of F

Concentration gra

*what compels a

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The diffusion flux and the concentration gradient at some particula

a solid vary with time, with a net accumulation or depletion of the

species resulting.

diffusion equatio

state diffusion (in

Ficks 2nd Law

Solutions to this are possible when physica

boundary conditions are specified

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1. For at

For example, consider a semi-infinite solid** with a constant surface concentration

diffusing material is in gas phase whose partial pressure is maintained at a certain c

Assumptions on the system are:

**A solid is semi-infinite if none of th

atoms reaches the end during the tim

diffusion takes place.

A bar of length l is considered to be s

when Dtl 10

1. Before diffusion, any of the diffusing solute

atoms in the solid are uniformly distributed

with concentration of C0.

2. The value of x at the surface is zero and

increases with distance into the solid.

3. The time is taken to be zero the instant

before the diffusion process begins.

These boundary conditions are sim

0;0 CCt x0

2. For (constant sur

at . Ats

CCt ;00x

0

CC x

Solution toFicks 2ndlaw for the condition

of constant surface concentration

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CS - constant

surface concn.CX -concn. below surface

(varies wrt x& time)

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Diffusing species:

The magnitude of the diffusion coefficientD is

indicative of the rate at which atoms diffuse. Thediffusing species as well as the host material

influence the diffusion coefficient.

Temperature:

Temperature dependence of the diffusion

coefficient, D, is

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Sample Problem 1:

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Sample Problem 3:

The purification of hydrogen gas by diffusion through a palladium sheet was discusse

5.3. Compute the number of kilograms of hydrogen that pass per hour through a 5-m

of palladium having an area of 0.20 m2 at 500C. Assume a diffusion coefficient of 1.0

that the concentrations at the high- and low-pressure sides of the plate are 2.4 and 0.6

hydrogen per cubic meter of palladium, and that steady-state conditions have been a

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Sample Problem 4: