molecular diffusion in metal alloys aaron morrison me 447
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Molecular Diffusion in Metal Alloys
Aaron MorrisonME 447
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
Background
Diffusing Species Temperature Lattice Structure Presence of Defects Grain size Porosity of the alloy.
Factors that Influence Diffusion
Diffusion occurs faster for Open crystal structures Lower melting temperature materials Smaller diffusing atoms Cations Lower density materials
Factors that Influence Diffusion
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
=exp(-ΔGv/RT) Where, G is the jump frequency of an atom
and XV is the vacancy concentration = Where is the diffusivities of vacancies and
is diffusivity of species A
Self Diffusion
Subsitutional Alloys
Exchange between two atoms similar in size.
Diffusion Follows:
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
Where v is the lattice drift velocity
Where is the net diffusive flux.
Subsitutional Alloys
Carburization Process in which carbon is diffused into low
carbon steel. Increases hardness of steel, fatigue/tensile
strength and wear resistance.
Example Model
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
=[0.07+(0.06*C)]*exp(-32,0o0/RT) /s
In the figure, Carbon concentration vs distance is calculated for treatments at1700°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
Carburization
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
References