Material transport by atomic motion

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• Introduction
• Material transport by atomic motion
• Diffusion couple
• eg., Cu-Ni in close contact hold at elevated
  temperature for extended period and cool to room
  temperature.

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Introduction continue

• Interdiffusion or impurity diffusion
• Self diffusion same type of atoms no
  composition change

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Chapter 5 Diffusion
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Diffusion mechanisms continue
Chapter 5 Diffusion
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Diffusion mechanisms continue
2) Interstitial Diffusion Atoms move from one
interstitial site to another (vacant)
interstitial site.
Chapter 5 Diffusion
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Steady state Diffusion
JM/At If J is constant, steady-state diffusion
exists. Where, J rate of mass transfer with
time, kg/m2-sec or atoms/m2-sec A Area across
which diffusion is occurring t elapsed time, sec
Chapter 5 Diffusion
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Steady state Diffusion continue.
Steady-state diffusion
Concentration profile
Source William Callister 7th edition, chapter 5,
page 113, figure 5.4
Chapter 5 Diffusion
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Steady state Diffusion continue.
Chapter 5 Diffusion
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Steady state Diffusion continue.
Chapter 5 Diffusion
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Steady state Diffusion continue.
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Problem Carbon diffusing through a plate of iron
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Steady state Diffusion continue.


Problem continue
Diffusion coefficient 3 x 10-11 m2/sec
2.4 x 10-9 kg/m2-sec
Chapter 5 Diffusion
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• Non-steady state Diffusion
• Diffusion flux and concentration gradient vary
  with time net accumulation or depletion of
  diffusing species results

Fick second law
Modified Ficks second law
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Semi-Infinite solid Surface concentration at the
other end is constant. eg, Bar of length, l gt
10Dt , i.e., none of the diffusing atoms reach
the bar end during the time-period of diffusion

• Assumptions
• Co Concentration before diffusion
• x Distance at surface it is 0. It increases
  into the solid
• t Time zero(0) at the instant diffusion starts

Chapter 5 Diffusion
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Semi-Infinite solid continue.
We have, for t0, CCo at 0x? For tgt0, CCS
(Constant surface concentration) at x 0
Also, C CO at x?
This equation shows relationship between
concentration, position and time
Error function
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Semi-Infinite solid continue.
erf
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Semi-Infinite solid continue.
If CXC1 at a specific concentration of solute,
constant
Therefore
constant
constant
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Semi-Infinite solid continue.
Chapter 5 Diffusion
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Problem Carburization of steel using methane
(CH4) at 950C (1750F) Steel 0.25 wt Carbon.
Using CH4, carbon at surface is suddenly brought
to and maintained at 1.2 wt carbon. How long
will it take to achieve a carbon content of 0.80
carbon at a position 0.5 mm below the surface?
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Problem continue
D 1.6 x 10-11 m2/sec
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Problem continue
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Problem The diffusion coefficients for copper in
aluminum at 500 and 600 C are 4.8x10-14 and
5.3x10-13 m2/s, respectively. Determine the
approximate time at 500 C that will produce the
same diffusion result (in terms of concentration
of Cu at some specific point in Al) as a 10-h
heat treatment at 600C. To produce the same
effect at 500C, how long will it take?
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Problem continue
Dt constant
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• Factors in diffusion
• Temperature
• Time
• D increases 5 orders of magnitude with
  temperature

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Factors in diffusion continue
Do temperature independent pre-exponential
(m2/sec) Qd the activation energy for
diffusion (J/mol,cal/mol and ev/atom) R gas
constant, 8.31 J/mol-K or 8.62 eV/atom-K T
absolute temperature (K)
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Factors in diffusion continue
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• Summary
• Self Diffusion
• Inter-Diffusion
• Steady state JM/At Ficks First law
• Non-steady state Ficks second law
• Temperature effect
• Activation energy

Chapter 5 Diffusion