Factors affecting diffusion

5.4.3 Factors affecting diffusion

The two most important factors affecting the diffusion coefficient D are temperature and composition. Because of the activation energy term the rate of diffusion increases with temperature according to

equation (5.12), while each of the quantities D, D 0 and Q varies with concentration; for a metal at

= 10 2 −12 m s −1 . Because of this variation of diffusion coefficient with concentration, the most reliable investigations into the effect

high temperatures Q ≈ 20RT m ,D 0 is 10 −5 to 10 −3 m 2 s −1 , and D ∼

of other variables necessarily concern self-diffusion in pure metals. Diffusion is a structure-sensitive property and therefore D is expected to increase with increasing lattice irregularity. In general, this is found experimentally. In metals quenched from a high tem- perature the excess vacancy concentration

≈10 9 leads to enhanced diffusion at low temperatures, since D =D 0 c v exp( −E m /kT ) where c v is the vacancy concentration. Grain boundaries and dislo-

cations are particularly important in this respect and produce enhanced diffusion. Diffusion is faster in the cold-worked state than in the annealed state, although recrystallization may take place and

Physical properties 251 tend to mask the effect. The enhanced transport of material along dislocation channels has been

demonstrated in aluminum, where voids connected to a free surface by dislocations anneal out at appreciably higher rates than isolated voids. Measurements show that surface and grain boundary forms of diffusion also obey Arrhenius equations, with lower activation energies than for volume

diffusion, i.e. Q vol ≥ 2Q g ·b ≥ 2Q surface . This behavior is understandable in view of the progressively more open atomic structure found at grain boundaries and external surfaces. It will be remembered, however, that the relative importance of the various forms of diffusion does not entirely depend on the relative activation energy or diffusion coefficient values. The amount of material transported by any diffusion process is given by Fick’s law and for a given composition gradient also depends on the effective area through which the atoms diffuse. Consequently, since the surface area (or grain boundary area) to volume ratio of any polycrystalline solid is usually very small, it is only in particular phenomena (e.g. sintering, oxidation, etc.) that grain boundaries and surfaces become important. It is also apparent that grain boundary diffusion becomes more competitive the finer the grain and the lower the temperature. The lattice feature follows from the lower activation energy, which makes it less sensitive to temperature change. As the temperature is lowered, the diffusion rate along grain boundaries (and also surfaces) decreases less rapidly than the diffusion rate through the lattice. The importance of grain boundary diffusion and dislocation pipe diffusion is discussed again in Chapter

6 in relation to deformation at elevated temperatures, and is demonstrated convincingly in the defor- mation maps (see Figure 6.67), where the creep field is extended to lower temperatures when grain boundary (Coble creep) rather than lattice diffusion (Herring–Nabarro creep) operates.

Because of the strong binding between atoms, pressure has little or no effect, but it is observed that with extremely high pressure on soft metals (e.g. sodium) an increase in Q may result. The rate of diffusion also increases with decreasing density of atomic packing. For example, self-diffusion is slower in fcc iron or thallium than in bcc iron or thallium when the results are compared by extrapolation to the transformation temperature. This is further emphasized by the anisotropic nature of D in metals of open structure. Bismuth (rhombohedral) is an example of a metal in which D varies

by 10 6 for different directions in the lattice; in cubic crystals D is isotropic.