Diffusion And Its Role In Material Property Control

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Diffusion And Its Role In Material Property
Control

• R. Lindeke, Ph. D.
• Engr 2110

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DIFFUSION
IN LIQUIDS
IN GASES
Carburization
Surface coating
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Diffusion
Interdiffusion In an alloy, atoms tend to
migrate from regions of high conc. to
regions of low conc.
Initially
After some time
Adapted from Figs. 5.1 and 5.2, Callister 7e.
This is called a DIFFUSION COUPLE a sketch of Cu
Ni here
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Diffusion Mechanisms
Vacancy Diffusion
atoms exchange with vacancies applies to
the atoms of substitutional impurities rate
depends on -- number of vacancies --
activation energy to exchange a function of
temp. and size effects.
increasing elapsed time
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Diffusion Mechanisms

• Interstitial diffusion smaller atoms can
  diffuse between atoms.

More rapid than vacancy diffusion
Adapted from Fig. 5.3 (b), Callister 7e.
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Processing Using Diffusion

• Case Hardening
• Diffuse carbon atoms
• into the host iron atoms
• at the surface.
• Example of interstitial
• diffusion to produce a surface (case) hardened
  gear.

Adapted from chapter-opening photograph, Chapter
5, Callister 7e. (Courtesy of Surface Division,
Midland-Ross.)
The carbon atoms (interstitially) diffuse from a
carbon rich atmosphere into the steel thru the
surface. Result The presence of C atoms makes
the iron (steel) surface harder.
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Diffusion

• How do we quantify the amount or rate of
  diffusion? we define a mass flux value
• Flux is Commonly Measured empirically
• Make thin film (membrane) of known surface area
• Impose concentration gradient (high conc. On 1
  side low on the other)
• Measure how fast atoms or molecules diffuse
  through the membrane

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Simplest Case Steady-State Diffusion
The Rate of diffusion is independent of time
? Flux is proportional to concentration gradient
This model is captured as Ficks first law of
diffusion
D ? diffusion coefficient which is a function of
diffusing species and temperature
For steady state diffusion? concentration
gradient dC/dx is linear
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F.F.L. Example Chemical Protective Clothing (CPC)

• Methylene chloride is a common ingredient in
  paint removers. Besides being an irritant, it
  also may be absorbed through skin. When using
  this paint remover, protective gloves should be
  worn.
• If butyl rubber gloves (0.04 cm thick) are used,
  what is the diffusive flux of methylene chloride
  through the glove?
• Data
• diffusion coefficient in butyl rubber D
  110 x10-8 cm2/s
• surface concentrations

C1 0.44 g/cm3
C2 0.02 g/cm3
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Example (cont).

• Solution assuming linear conc. gradient

glove
C1
paint remover
skin
C2
x1
x2
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What happens to a Worker?

• If a person is in contact with the irritant and
  more than about 0.5 gm of the irritant is
  deposited on their skin they need to take a wash
  break
• If 25 cm2 of glove is in the paint thinner can,
  How Long will it take before they must take a
  wash break?

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Another Example Chemical Protective Clothing
(CPC)

• If butyl rubber gloves (0.04 cm thick) are used,
  what is the breakthrough time (tb), i.e., how
  long could the gloves be used before methylene
  chloride reaches the hand?
• Data (from Table 22.5)
• diffusion coefficient in butyl rubber
• D 110 x10-8 cm2/s

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Example (cont).

• Solution assuming linear conc. gradient

Equation 22.24
Time required for breakthrough ca. 4 min
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Diffusion and Temperature
Diffusion coefficient increases with
increasing T
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Diffusion and Temperature
D has exponential dependence on T
So Note
Adapted from Fig. 5.7, Callister 7e. (Date for
Fig. 5.7 taken from E.A. Brandes and G.B. Brook
(Ed.) Smithells Metals Reference Book, 7th ed.,
Butterworth-Heinemann, Oxford, 1992.)
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Example At 300ºC the diffusion coefficient and
activation energy for Cu in Si are D(300ºC)
7.8 x 10-11 m2/s Qd 41.5 kJ/mol What is the
diffusion coefficient at 350ºC?
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Example (cont.)
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Non-steady State Diffusion

• If the concentration of diffusing species is a
  function of both time and position that is C
  C(x,t)
• In this case Ficks Second Law is used

Ficks Second Law
Concentration (C) in terms of time and position
can be obtained by solving above equation with
knowledge of boundary conditions ? The solution
depends on the specific case we are treating
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One practically important solution is for a
semi-infinite solid in which the surface
concentration is held constant. Frequently
source of the diffusing species is a gas phase,
which is maintained at a constant pressure value.

A bar of length l is considered to be
semi-infinite when

• The following assumptions are implied for a good
  solution
• Before diffusion, any of the diffusing solute
  atoms in the solid are uniformly distributed with
  concentration of C0.
• The value of x (position in the solid) at the
  surface is zero and increases with distance into
  the solid.
• The time is taken to be zero the instant before
  the diffusion process begins.

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Non-steady State Diffusion
Adapted from Fig. 5.5, Callister 7e.
Notice the concentration decreases at increasing
x (from surface) while it increases at a given x
as time increases!
Boundary Conditions
at t 0, C Co for 0 ? x ? ? at t gt 0, C
CS for x 0 (const. surf. conc.) C Co
for x ?
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Solution

• C(x,t) Conc. at point x at time t
• erf (z) error function
• erf(z) values are given in Table 5.1

CS
C(x,t)
Co
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Non-steady State Diffusion

• Sample Problem An FCC iron-carbon alloy
  initially containing 0.20 wt C is carburized at
  an elevated temperature and in an atmosphere that
  gives a surface carbon concentration (C0 )
  constant at 1.0 wt. If after 49.5 h the
  concentration of carbon is 0.35 wt at a position
  4.0 mm below the surface, determine the
  temperature at which the treatment was carried
  out.
• Solution use Eqn. 5.5

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Notice that the solution requires the use of the
erf function which was developed to model
conduction along a semi-infinite rod as we saw
earlier
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Solution (cont.)

• t 49.5 h x 4 x 10-3 m
• Cx 0.35 wt Cs 1.0 wt
• Co 0.20 wt

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Solution (cont.)
We must now determine from Table 5.1 the value of
z for which the error function is 0.8125. An
interpolation is necessary as follows
Now By LINEAR Interpolation
z 0.93
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Solution (cont.)

• To solve for the temperature at which D has above
  value, we use a rearranged form of Equation
  (5.9a)

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Following Up

• In industry one may wish to speed up this process
• This can be accomplished by increasing
• Temperature of the process
• Surface concentration of the diffusing species
• If we choose to increase the temperature,
  determine how long it will take to reach the same
  concentration at the same depth as in the
  previous study?

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Diffusion time calculation

• X and concentration are equal therefore
• Dt constant for non-steady state diffusion!
• D1300 2.6x10-11m2/s (1027?C)

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Summary
Diffusion FASTER for... open crystal
structures materials w/secondary
bonding smaller diffusing atoms lower
density materials
Diffusion SLOWER for... close-packed
structures materials w/covalent bonding
larger diffusing atoms higher density materials