1. Diffusion Thermally activated process
CC512
Chapter 5
Diffusion
Thermally activated process
Thermal production of point defects
Point defects and solid-state diffusion
Steady state diffusion
Alternate diffusion paths
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2. Thermally activated processes
For a large number of processes in MS&E,
Rate rises exponentially with temperature
Examples: diffusivity, creep rate, electrical conductivity of semiconductors
Mechanical analog:
the box must overcome an increase in potential energy, ΔE,
in order to move from one stable position to another
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3. Activation energy _ Indication of the mechanism of the process
Example:
Calculate the activation energy
of the oxidation process of a Mg alloy
Data:
the oxidation rate (r1) at 300º C = 1.05 x 10-8 kg/(m4.s);
The rate r2 at 400º C = 2.95 x 10-4 kg/(m4.s)
Q = [8.314(J/mol)x ln[(2.95x10-4)/(1.05x10-8)]
/ [(673 – 573)/(673x573)]
= kJ/mol
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4. Thermal production of point defects
At a given temperature,
-the thermal energy of given material is constant
-the thermal energy of individual atom varies over
a wide range of energy_ Maxwell-Boltzmann dist.
-A certain fraction of atoms have sufficient thermal
energy to produce the point defects
-This fraction increases exponentially with
temperature
Thermal production of vacancies in Al
-the overall thermal expansion (ΔL/L)
greater than the lattice parameter expansion (Δa/a)
-the difference is due to the production of vacancies
Example_
Vacancy fraction at 400C = 2.29 x (EV = 0.76 eV)
Calculate the fraction at 600C:
C = (nV/nsites)exp(EV/kT) = 11.2 (k = 8.62x10-5 eV/K)
nV/nsites = 8.82 x 10-4
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5. Point Defects and Solid State Diffusion
-Migration of molecules (or atoms) from high to low concentration region
at sufficiently high temperatures
-Example_ a drop of ink in water at RT; ink molecules move from high to low conc. region
until reaching a uniform concentration
-Easy to observe in gaseous (i.e., perfume) or liquid states due to high molecular mobility
-Difficult to observe in solid state because high energy is required for an atom to move
in a tightly squeezed state.
-Atomic migration can only occur through vacancy mechanism at sufficiently high temperatures
-Net migration of atoms (from high conc. to low conc. region) results from a series of
random walk motions (jumps) of atoms.
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6. Interdiffusion_ A - B atoms system
Random walk motion of atoms (at sufficiently high temperature)
-Probability of randomly “walking” (atomic jumps) in any direction is equal
-High conc. of A- atoms on the left-side of couple (i.e., concentration gradient of A-atoms)
cause such random motion (jumps) to produce a net flow of A- atoms into solid B.
-Likewise, B- atoms move into solid A, i.e., an interdiffusion occurs.
Temperature, say, 800 ºC
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7. Fick’s Laws
_ formal mathematical treatment of diffusion
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8. Fick’s 2nd Law Application_ Carburization
Gradient of flux in a unit volume = concentration variation with time
Application_ Carburization
: Diffusion of carbon atom in steel
from carbon rich environment
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9. Diffusion coefficient_ Diffusivity
Diffusivity obeys an Arrhenius equation
Note that carbon atoms diffuse in steel by
Interstitialcy mechanism.
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10. Diffusivity_ non-metallic systems
-Smaller ionic species (e.g., Al+3) diffuse much more readily
through the material
-The Arrhenius behavior of ionic diffusion is similar to that of conductivity
of certain ceramic semiconductor (e.g., ZnO)
-This ionic (not electron) transport mechanism is responsible for semiconducting behavior of
such ceramics.
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11. Example
Example 5.4
The carbon environment (a hydro-carbon gas) is used to set the surface carbon content (cs) at cs = 1.0 wt.%. The initial carbon content of steel (c0) is c0 = 0.2 wt.%.
Using the error function table, calculate how long it would take at 1000C to reach a carbon content of 0.6 wt.% at a distance of 1mm from the surface.
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12. Steady-State Diffusion
-Diffusion through thin membrane;
-Surface concentration are fixed at both surfaces
: Ch = const.; Cl = const.
-For long times,
A linear concentration profile is established
Concentration remains constant regardless of diffusion time
, Steady state diffusion,
i.e., mass-transport unchanging with time
Example 5.7
A 5mm thick sheet of Pd membrane with cross-section area A = 0.2m2
is used as a steady state diffusion membrane for purifying hydrogen.
If the hydrogen conc. on the high pressure side (impure gas) is 0.3 kg/m3
And the diffusion coefficient for hydrogen in Pd is 1.0x10-8m2/s,
Calculate the mass of hydrogen being purified per hour.
Solution:
J = -D[-(ch – cl)/x0] kg/m2.s
Total mass m = J x A x 3600s = x 10-3 kg/h
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13. Alternate Diffusion Paths
Possible diffusion paths:
-Volume diffusion
-Surface diffusion
-Grain boundary diffusion
-Qv> Qgb > Qs
Self-diffusion coefficient for Ag
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