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Volumen II - SAM

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3. RESULTS AND DISCUSSION<br />

Figure 1 gathers the Arrhenius plots for all the considered clusters and the two potentials, namely, ED (a)<br />

and EAM (b). The labels refer to size (number of SIA), and the two numeric columns at bottom right stand<br />

for D0 (left, 10 -5 cm 2 /s) and Q (right, eV). For the curves that are clearly bent, e.g. 3I, 2I EAM, 4I ED, those<br />

values correspond to the few, best aligned, low temperature points.<br />

Figure 1 Diffusion coefficients of small SIA clusters in Mo computed with potentials ED and EAM.<br />

A few general observations are in order. Firstly, the diffusivities of clusters 7I and larger are very similar<br />

among the two models, and there is also an apparent saturation effect of the activation energy to a rather low<br />

value, outcome that has been traced before to the behavior of individual SIA crowdions [12] (7I, 19I, and 39I<br />

are perfect hexagonal in a cross section view). Notably however, the diffusivities of 2I, 3I, and 4I<br />

EAM, are substantially larger than their ED counterparts for T ≤ 900 K. Also worth of noticing are the Q<br />

trends in both models, with a sizable drop for 3I and a marked increase for 4I, the latter most notably in the<br />

ED case.<br />

Partial results for 1I have already been presented in [20]. A striking feature of the Arrhenius plot is the<br />

almost coincidence between the two models, however this is somewhat deceiving because, as already<br />

reported in [20] , most of the underlying atomic mechanisms are different.<br />

Migration of 2I takes place in 3D, with a fairly independent behavior of the two SIA, namely, one advances<br />

then the other eventually follows. The most relevant low T configuration is a nearest neighbors bi-dumbbell<br />

oriented along ; there is also another higher energy relevant configuration whose frequency increases<br />

with T, in the shape of a non-planar three-vertex star. Nevertheless being sessile, it is instrumental, most<br />

notably for ED, in helping 3D motion.<br />

Figure 2(a) shows the minimum energy structure for the case of 3I ED; it is clearly sessile. On the other<br />

hand, the first excited configuration is about 0.2 eV higher in energy. Figure 2(a) is also the fundamental<br />

state for EAM, though at about 0.05 eV above there is a distorted, crowdion-type structure.<br />

Expectedly thus, MD reveals defect migration on segments for both models. The main difference<br />

being that, whereas ED shows fully 3D motion even at the lowest T simulated, EAM's direction changing<br />

rate is very much diminished, registering only a few events at low T. Also in agreement with the<br />

expectations, QEAM < QED .<br />

The two equilibrium structures involved in 4I migration are the rhombus-shaped ones shown in Figure 2(b)<br />

and (c). The former, relevant to ED, can be described as four parallel dumbbells slightly bent from the <br />

direction with the shortest rhombus diagonal contained in a {110} plane; on the other hand the latter,<br />

relevant to EAM, shows the standard four parallel crowdions. Correspondingly, the simulations for<br />

ED, within the times here employed, show a change from 2D migration (where the shortest diagonal lies on a<br />

fixed {110} plane) to 3D one at about 1000 K; differently, EAM simulations only reveal 1D motion. Also,<br />

consistent with the expectations, QEAM < QED holds<br />

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