The effective diffusion coefficient of a in atomic diffusion of solid

polycrystalline A crystallite is a small or even microscopic crystal which forms, for example, during the cooling of many materials. Crystallites are also referred to as grains. Bacillite is a type of crystallite. It is rodlike with parallel longulites. Stru ...

materials like metal alloys is often represented as a

weighted average The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The ...

of the

grain boundary diffusion coefficient A grain is a small, hard, dry fruit (caryopsis) – with or without an attached hull layer – harvested for human or animal consumption. A grain crop is a grain-producing plant. The two main types of commercial grain crops are cereals and legume ...

and the

lattice diffusion coefficient Lattice diffusion (also called bulk or volume diffusion) refers to atomic diffusion within a crystalline lattice.P. Heitjans, J. Karger, Ed, “Diffusion in condensed matter: Methods, Materials, Models,” 2nd edition, Birkhauser, 2005, pp. 1-9 ...

.P. Heitjans, J. Karger, Ed, “Diffusion in condensed matter: Methods, Materials, Models,” 2nd edition, Birkhauser, 2005, pp. 1-965. Diffusion along both the grain boundary and in the lattice may be modeled with an

Arrhenius equation In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 18 ...

. 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_\text = f D_\text + (1-f) D_\ell

where :

D_\text =

effective diffusion coefficient :

D_\text =

grain boundary diffusion coefficient :

D_\ell =

lattice diffusion coefficient :

f = \frac

q =

value based on grain shape, 1 for parallel grains, 3 for square grains :

d =

average grain size :

\delta =

grain boundary width, often assumed to be 0.5 nm Grain boundary diffusion is significant in

face-centered cubic In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties o ...

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.

Modeling

References

See also