Effective diffusion coefficient explained

The effective diffusion coefficient of a in atomic diffusion of solid polycrystalline materials like metal alloys is often represented as a weighted average of the grain boundary diffusion coefficient and the lattice diffusion coefficient.^[1] Diffusion along both the grain boundary and in the lattice may be modeled with an Arrhenius equation. The ratio of the grain boundary diffusion activation energy over the lattice diffusion activation energy is usually 0.4–0.6, so as temperature is lowered, the grain boundary diffusion component increases. Increasing temperature often allows for increased grain size, and the lattice diffusion component increases with increasing temperature, so often at 0.8 T_melt (of an alloy), the grain boundary component can be neglected.

Modeling

The effective diffusion coefficient can be modeled using Hart's equation when lattice diffusion is dominant (type A kinetics):

D _{eff} = f D _{gb} + ( 1- f) D _{\ell}

where

D _{eff} = {} effective diffusion coefficientD _{gb} = {} grain boundary diffusion coefficientD _{\ell} = {} lattice diffusion coefficientf = (q \delta)/(d) q = {} value based on grain shape, 1 for parallel grains, 3 for square grainsd = {} average grain size\delta = {} grain boundary width, often assumed to be 0.5 nm

Grain boundary diffusion is significant in face-centered cubic metals below about 0.8 T_melt (Absolute). Line dislocations and other crystalline defects can become significant below ~0.4 T_melt in FCC metals.

See also

• Kirkendall effect
• Mass diffusivity

Notes and References

1. P. Heitjans, J. Karger, Ed, “Diffusion in condensed matter: Methods, Materials, Models,” 2nd edition, Birkhauser, 2005, pp. 1-965.