mse20_6
Transcript of mse20_6
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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: