Volumen II - SAM

Table 1 reports the first few processes involving the 2I cluster. (D/C)n stands for a pair of
dumbbells/crowdions located at n th nearest neighbors, whereas the star indicates variant forms. In bold is the
proposed activation energy, that for both models entails a jump at 1nn with rotation of the common
dumbbells' axis ( e.g. (000) → 1/2(111) ). However, the (optimum) two-steps mechanism that
accomplishes the jump is model dependent. For EAM, one of the dumbbells moves first to a 3nn position,
then the other follows, whereas for ED the first step involves the 2nn; this is shown in figure 3, where one
should interpret, e.g., the 2I EAM sequence as ( ab → ab1 → a2b1 ).
Due to the number of possible structures, the precise description of the 3I case becomes more intricate,
though qualitative arguments can still be given. For EAM the relevant structure consists of three
(distorted) crowdions; the one located at the cluster tail is the least extended and rests misaligned with the
other two. The latter feature entails that the jump is (slightly) sense dependent, being 0.22 eV the activation
energy for motion along the row. On the other hand, the defect may exchange directions
through an immobile configuration, involving a barrier of 0.23 eV.
The situation regarding 3I ED is better described in terms of dumbbells, though motion still happens along
the rows and involves a sequence of individual jumps. The behavior resembles somewhat the EAM
case in that the dumbbell more advanced' may eventually lock motion. The sequence comprises 4 steps, the
2 nd (and 3 rd ) being the critical one, with a barrier of 0.31 eV.
Regarding the 4I cluster, as stated for the MD simulations, migration is tied to the row. Being the
Burgers vector of the ED rhombus -type in nature, a sizable amount of activation is needed; it was
found that the activated form is reached in about half a dozen steps with 0.82 eV as overall barrier.
Other processes, not leading to migration, also compete, e.g. a non-dissociative jump of the dumbbells
located across the longest rhombus diagonal. Applied to the EAM case, the method turns out to be very
inefficient; in particular no barrier for rotation could be determined. On the other hand, the overall barrier for
motion was computed to be 0.33 eV.
4. CONCLUSIONS
Though the main characteristics of migration of SIA clusters beyond some 7 units, are most likely dominated
by lattice structure, we have shown that the behavior of clusters of up to 4 SIA may be influenced by the
kind of interaction model chosen. This is true at the level of the size of the quantities involved, such as
activation energy, but also when considering the relevant micromechanisms, e.g., for the central force EAM,
extended structures are clearly preferred..
We have also shown the usefulness of a (static) transition state finding technique, the Monomer, at filling in
details where MD can hardly do, and also at providing comparable activation energies at a fraction of the
computational cost. Besides some points discussed below, a drawback of the static technique (at least in the
current naive implementation) is the increased inefficiency with cluster size. Perhaps a combined strategy,
with MD providing initial configurations and search directions, may alleviate this pitfall.
Overall, the agreement between Monomer and MD is reasonable. However, even though inherent statistical
errors might be invoked where disagreement is more apparent, one may wonder, for instance, why for the
simplest case of the 1I cluster the static technique obtains values systematically larger. Part of the answer
may lie in entropic contributions present in MD, that relatively stabilize easier migrating structures beyond
their naive Boltzmann weights [19]. Entropy effects were also reported in [21] to stabilize immobile cluster
configurations in Fe; however, noting the rather high temperatures involved in this effect, one may question
their importance to cascade damage conditions. In any case, the link between the static results and the
dynamic ones is not straightforward. The former can be refined by computing vibrational spectra and attack
frequencies in the spirit of transition state theory, though at the expense of new questions on their reliability
with current potentials. The central difficulty however is that these clusters, complex objects after all, may
not suit the picture of random walkers. In fact, under certain conditions not even the single SIA does, as
found in recent models for V and W [22,23]. Nevertheless, considerations such as these are too fine details to
be accounted for within the higher hierarchy theories of radiation damage evolution, which simulations like
the present ones try to inform.
ACKNOWLEGMENTS
Partial support from CONICET-PICT 5062 is gratefully acknowledged. Thanks also to Dr. G. Simonelli for
sharing her results during the initial stages of the current research.
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