Point defects

Point defects are defined as crystalline defects associated with one or, at most, several atomic sites [48]. They can be either vacancies, which are normal lat- tice sites with an atom missing or self-interstitials, atoms from the crystal that are crowded into interstitial sites, spaces in the crystal that should not be occu- pied [48]. Usually, vacancies and interstitials are generated simultaneously under radiation, forming Frenkel pairs. Impurities are not of interest here.

Due to their higher formation energy, SIAs are relatively rare in metals com- pared to vacancies under normal equilibrium conditions [57]. However, both are plentiful in irradiated metals. Typically, over a volume of ∼10 nm in diameter hundreds of SIA-vacancy pairs can be formed following the displacement cascade mechanism [42]. It is the intra-cascade fate of these point defects that govern material properties thereafter.

As discussed earlier, the number of point defects remaining in the crystal after the cascade is given either by the NRT formula, or, since NRT gives an overestimate, by equation (2.12) [39]. The probability of point defects clustering with their own kind and the size of the largest clusters increase with increasing PKA energy [39]. In bcc iron, for defect clusters to be observed by TEM, relatively high radiation doses are required; at low radiation doses (∼0.0001 dpa), the very low cascade production efficiency of visible defect clusters can be attributed to the openness of the bcc crystal lattice structure [32].

In the discussion above, clusters are defined suchthat every defect has at least one other in a nearest neighbour position. For vacancies, that would mean vacancy dislocation loops, of which ones with perfect Burgers vector would be glissile and partial ones sessile, sessile stacking fault tetrahedra (in the case of fcc metals) or, of course, voids (or He and H-bubbles) [39]. Loose-vacancy clusters are also possible [27], as both positron annihilation experiments on neutron-irradiated Fe [58] and MD modelling [59, 60, 61] have indicated. SIAs form dislocation loops,

which can be stable or metastable. Vacancy clusters are unstable, due to having lower binding energy per defect, and can dissociate back into single vacancies when temperatures are high enough [28]. This leads to a ‘production bias’ in favour of vacancies compared to SIAs as a result of displacement cascades.

This has also been confirmed experimentally. Reported direct observations of point defects with TEM have shown that SIA clusters exist in Fe (even though they are smaller compared to ones in Cu) [62, 63]. For vacancies, it has been found that they tend not to cluster at all, leaving the whole vacancy population after the cascade intact [64].

For any given temperature, point defects can migrate within the volume of the crystal by random thermally-activated hopping of atoms. There exist several mechanisms under which this can happen, the most important one being vacancy diffusion: an atom changes position from a normal lattice position to an adjacent one; this is equivalent to a vacancy migrating in the opposite direction [48]. For SIAs diffusion of importance is migration through nearest-neighbour translation- rotation jumps of 110 dumbbells (which are the most stable SIA or di-SIA structures [65]) or through the crowdion mechanism: as a crowdion moves from the beginning of its row to the end, each of its atoms is displaced in the row by one interatomic distance in this direction [66].

Point defects interact with dislocations, mainly through the distortion each of them produces in the crystal that surrounds them. This distortion interaction may raise or lower the elastic strain energy of the crystal. It is the sign and the gradient of the interaction energy that determines the direction and the magni- tude of the force exerted on a dislocation by a point defect, respectively. In the simplest model [30], in which a point defect is a misfitting sphere, the interaction energy for a screw dislocation is zero, because a screw dislocation does not create a pressure. For an edge dislocation, however, above the slip plane, where the crystal is compressed, this energy is positive for SIAs and negative for vacancies. Therefore, vacancies are attracted to the line, whereas SIAs are repelled from it. The opposite happens when the point defect is below the slip plane. This is why dislocations act as sinks of point defects.

By emitting or absorbing point defects, often at large numbers, a dislocation undergoes climb. Climb is characterised as positive when a positive edge disloca- tion (i.e. one with an extra half-plane up) moves upwards one atom spacing, or

negative when the line moves down [30]. Absorption of vacancies in the line or the formation of an SIA and its diffusion away can lead to positive climb. Absorption of SIAs in the line or the formation of a vacancy and its diffusion away can lead to negative climb.

Dislocation-point defect interactions have an effect on the mechanical prop- erties of the material: when work is required to seperate the dislocation from the point defect, this leads to an increase in stress required for slip, thus hardening the crystal. Nevertheless, the interactions of dislocations with intrinsic point de- fects are not as important as those with extended defects, which will be the focus of the next sub-sections.