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The '''effective diffusion coefficient''' (also referred to as the apparent diffusion coefficient) of a diffusant in [[atomic diffusion]] of solid [[polycrystalline]] materials like [[metal alloy]]s is often represented as a [[weighted average]] of the [[grain boundary diffusion coefficient]] and the [[lattice diffusion coefficient]].<ref name=Heitjans>P. Heitjans, J. Karger, Ed, “Diffusion in condensed matter: Methods, Materials, Models,” 2nd edition, Birkhauser, 2005, pp. 1-965.</ref> 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.<ref name=Heitjans />  Increasing temperature often allows for increased grain size, and the lattice diffusion component increases with increasing temperature, so often at 0.8T<sub>melt</sub> (of an alloy), the grain boundary component can be neglected.
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==Modeling==
The effective diffusion coefficient can be modeled using Hart's equation when only grain boundary and lattice diffusion are dominant:
 
:<math> {D^{\mathrm{eff}}} = f</math> D<sub>gb</sub> <math> + (1-f) </math>D<sub>l</sub>.
 
where
:<math> {D^{\mathrm{eff}}} = </math> effective diffusion coefficient.
:D<sub>gb</sub> = grain boundary diffusion coefficient.
:D<sub>l</sub> = lattice diffusion coefficient.
:<math> f = \tfrac{q}{d} </math>.δ
:<math> q = </math> value based on grain shape, 1 for parallel grains, 3 for square grains.
:<math> d = </math> average grain size.
:δ <math> = </math> 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<sub>melt</sub> (Absolute). Line dislocations and other [[Crystallographic defect|crystalline defects]] can become significant below ~0.4 T<sub>melt</sub> in FCC metals.
 
== References ==
{{reflist}}
{{refbegin}}
{{refend}}
 
== See also ==
* [[Kirkendall effect]]
* [[Phase transformations in solids]]
* [[Mass diffusivity]]
 
[[Category:Diffusion]]

Latest revision as of 17:27, 24 September 2014

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