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