Molecular Diffusion in Metal
Alloys
Aaron Morrison
ME 447
Background
 Why is this important?
 Case Hardening
 Doping
 Three types of Diffusion within Metals
 Interstitial Diffusion
 Self-Diffusion
 Diffusion in Subsitutional Alloys
Background
 Diffusion occurs because of defects in the solids.
 Diffusion commonly occurs at the grain boundaries,
inner/outer surfaces and dislocations.
 The diffusion along linear, planar and surface defects
is generally faster than diffusion which occurs in the
lattice, they are also termed high diffusivity or easy
diffusion paths
Factors that Influence Diffusion

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Diffusing Species
Temperature
Lattice Structure
Presence of Defects
Grain size
Porosity of the alloy.
Factors that Influence Diffusion
 Diffusion occurs faster for

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Open crystal structures
Lower melting temperature materials
Smaller diffusing atoms
Cations
Lower density materials
Interstitial
Diffusion
 Must assume interstitial
openings for atoms.
 Steady State Diffusion
 D0 is the frequency factor
and QID is equivalent to the
enthalpy of interstitial atom
migration
Self-Diffusion
 Requires adjacent vacancies.
 Diffusion follows:
 QSD is the activation enthalpy
for self-diffusion which includes
both vacancy migration and
formation of enthalpy terms
Self Diffusion
 𝑋𝑣𝑒 =exp(-ΔGv/RT)
 Where, G is the jump frequency of an atom and XV is
the vacancy concentration

𝐷𝐴
𝐷𝑣 =
𝑋𝑣
 Where 𝐷𝑣 is the diffusivities of vacancies and 𝐷𝐴 is
diffusivity of species A
Subsitutional
Alloys
 Exchange between two atoms
similar in size.
 Diffusion Follows:
 𝐷 is the interdiffusion
coefficient. DA and DB are the
diffusion coefficients of A and B
respectively and XA is the molar
fraction of species A
Subsitutional Alloys
 𝑣 = (𝐷𝐴 −𝐷𝐵 )
𝑑𝑋𝐴
𝑑𝑣
 Where v is the lattice drift velocity
 𝐽′𝐴 = −𝐷𝐴
𝑑𝐶𝐴
−𝑣𝐶𝐴
𝑑𝑥
 Where 𝐽′𝐴 is the net diffusive flux.
Example Model
 Carburization
 Process in which carbon is diffused into low carbon
steel.
 Increases hardness of steel, fatigue/tensile strength and
wear resistance.
Carburization
 Assume:
 No volume changes occur in lattice during diffusion.
 Non-steady state (Interstitial concentration varies with
time)
 Diffusivity is independent of composition
 Temperature between 1600°F and 180o°F
 No Reactions
Carburization
 Beginning with Fick’s 2nd Law
 With the assumption DB is not a function of
concentration
Carburization
 Final Solution
Carburization
𝑦
𝐷𝐶 =[0.07+(0.06*C)]*exp(-32,0o0/RT) 𝑐𝑚2 /s
In the figure, Carbon
concentration vs distance is
calculated for treatments at
1700°F with 2 and 16hour
Treatments with
D = f(C) and D ≠ f(c)
Carburization
 Additional types of Carburization:
 Two Step Carburizing
 Variation of Surface Carbon Potential and Temp During
Treatment
 Vacuum Carburization
References
 Porter, D.A., and Easterling, K.E., Phase
Transformations in Metals and Alloys, 2nd ed.,
Chapman & Hall, 1992
 Johnson, D.D. CHAPTER 6: DIFFUSION IN SOLIDS. 1st ed.
Illinois: MSE, 2006. Web. 14 May 2015
 Christian, J.W., The theory of transformations in metals
and alloys, 2nd ed., Pergamon, 1975
 Shewmon, P.G., Diffusion in solids, 2nd ed., TMS, 1989