Nabarro-Herring source

The Nabarro-Herring source is very similar to the Frank-Read source, but the dislocations move by climb instead of glide. 

The creep of materials can also occur solely by diffusion, i.e., without the motion of dislocations. Consider a crystal under the action of a combination of tensile and compressive stresses, as shown in Fig. 7.4. The action of these stresses will be to respectively increase and decrease the equilibrium number of vacancies in the vicinity of the boundaries. (The boundaries are acting as sources or sinks for the vacancies.) Thus, if the temperature is high enough to allow significant vacancy diffusion, vacancies will move from boundaries under tension to those under compression. There will, of course, be a counter flow of atoms. As shown in Fig. 7.4, this mass flow gives rise to a permanent strain in the crystal. For lattice diffusion, this mechanism is known as Nabarro-Herring creep. The analysis showed that the creep rate e is given by... 

In an ultra-high vacuum, no surface hillocks were found to grow on aluminum (Al) surfaces under compression (Ref 24). Hillocks grow on Al surfaces only when the Al surface is oxidized, and Al surface oxide is known to be protective. Without surface oxide, the free surface of Al is a good source and sink of vacancies, so a compressive stress can be relieved uniformly on the entire surface of the Al, based on the Nabarro-Herring model of lattice creep or the Coble... 

Fig. 8 Nabarro-Herring model of stress relaxation it can occur in each of the grains by diffusion to the free surface of each grain, which is a good and effective source and sink of vacancies.

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