Anisotropic Diffusion in Strained Crystals of Cubic Symmetry

The diffusion of the point defects created by the irradiation and their subsequent absorption at
dislocations and interfaces in the material is the most essential process that restores the material to its almost normal state. The adjective of‘almost nor­mal’ is anything but a casual remark here, but it hints at some subtle effects arising in connection with the long-range diffusion that constitute the root cause for the gradual changes that take place in crystalline materials exposed to continuous irradiation at ele­vated temperatures. If these effects were absent, then a steady state would be reached in the material sub­ject to continuous irradiation at a constant rate and temperature in which the rate of defect generation would be balanced by their absorption at sinks, mean­ing the above-mentioned dislocations and interfaces. As vacancies and self-interstitials are created as Frenkel pairs in equal numbers, they would also be absorbed in equal numbers at these sinks. At this point, the microstructure of these sinks would also be in a steady, unchanging state. While this steady state would be different from the initial microstruc­ture or the one reached at the same temperature but in the absence of irradiation, it would correspond to material properties that reached constant values.

The subtle effects alluded to in the above remarks arise from the interactions of the point defects with strain fields created both internally by the sinks and externally by applied loads and pressures on the materials that constitute the reactor compo­nents. The internal strain fields from sinks give rise to long-range forces that render the diffusion migration nonrandom, while the external strains induce aniso­tropic diffusion throughout the entire material. In the

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next section, we derive the diffusion equations for cubic materials to clearly expose these two funda­mental effects.