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Next: Annealing of the damaged Up: Properties of the damaged Previous: The thermal spike

   
The structure of the damage region

The radius of gyration Rn, calculated as a function of the number N of atoms knocked out (with initial kinetic energy of 416 eV) of their lattice site into the same volume, as described above, is shown in figure (9.7). It can be seen that with increasing number of bombarding atoms the affected volume increases, however Rnapproaches a saturation at about Rmax =6.85 Å for twelve bombarding atoms. This saturation was expected since the bombarding atoms are directed toward a similar region in space. This prevent the extension of the damage area by successive bombardments.

We are interested in analyzing separately the core of the damage, defined to be the volume inside a sphere of radius Rmaxcentered on $\vec{r}_{cm}$, and its periphery, defined as the volume outside this sphere, up to a radius of about 2Rmax, since these may contain different amounts and kinds of defects, and may thus respond differently to annealing (as will be discussed in the next section).


  
Figure 9.7: Radius of gyration (defined in the text) as a function of the number of bombarding atoms.
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The percentage of atoms inside the core that are threefold and fourfold coordinated has been calculated as a function of N, and the results are shown in figure (9.8). The diamond lattice is, as expected, destroyed by the bombarding atoms and as the number of bombarding atoms increases the number of threefold coordinated atoms increases at the expense of fourfold coordinated atoms. The structural change to the diamond lattice can be further analyzed by studying of the bond length distribution.


  
Figure 9.8: Percentage of threefold and fourfold coordinated atoms inside the core as a function of the number of bombarding atoms.
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The radial distribution function g(r) is calculated as a function of N for the atoms within the core and is shown in figure (9.9) for selected values of N. It can be seen that the long range order of the diamond lattice completely disappears for N=12, and only short range order remains. The coordination number obtained by calculating the area inside the first peak of g(r), (figure (9.10)) decreases as N increases, consistently with the amorphization observed. The first peak, that was centered at 1.545 Å (which corresponds to the bond length in diamond) decreases and broadens with increasing number of bombarding atoms, and its center shifts toward the graphite bondlength (1.46 Å as calculated with the Tersoff potential). In other words some bonds are shortened and others are extended (see the insert in figure (9.9), that shows the first peak of the radial distributions), spanning all lengths from below the bond length in graphite, to above that of diamond. It should also be noted that the unimodal distribution of the first peak of g(r) for N=12 indicates that no distinct configuration (graphite-like or diamond-like) dominates in the heavily damaged region.


  
Figure 9.9: The radial distribution function g(r) as a function of the number of bombarding atoms, for three, five and twelve atoms. The first peaks of the distributions are shown in the insert.
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Figure 9.10: Coordination number as a function of the number of bombarding atoms.
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For N=12, the partial radial distribution function between threefold coordinated atoms in the core, g33, between threefold and fourfold coordinated atoms, g34, and for fourfold coordinated atoms only, g44, are calculated and are shown in figure (9.11). One can see from the insert in figure (9.11), in which the first peak of the partial distributions is enlarged, that the bond length increases with the coordination number. That is, the shortest bond lengths are those between threefold coordinated atoms, and the longest bond lengths can be attributed to bonds between fourfold coordinated atoms.

An important feature of our damage sample is the presence of a second very sharp peak observed at about 2.1 Å in g33. Since this appears exclusively in g33, one must attribute this peak to the second nearest neighbors of threefold coordinated atoms. Such a short second neighbor distance can exist only as the diagonal distance in quadrilaterals. It will be shown that these quadrilateral structures are highly unstable and almost entirely disappear upon annealing. It has to be mentioned that this relatively short distance second peak has been experimentally found in tetrahedral amorphous carbon by Gilkes [116], using high-resolution neutron scattering. It has also been obtained by Marks et. al. [44] by ab initio MD calculations.

In summary, the structure obtained after repeated bombardments of the same region in the diamond lattice is heavily damaged, containing more than 60 % of threefold coordinated atoms, yet with no distinct diamond or graphite like character. Since the simulation is performed at 0K, interstitial-vacancy recombinations due to some diffusional process are inhibited after the cooling down of the thermal spike. The rapid increase in Rn and the decrease in fourfold coordinated atoms found here, as a function of the number of bombarding atoms, is thus due to bond breakage induced by both the initial energetically displaced atoms and by the recoiling "higher generation" atoms involved in the damage cascade. As expected, the number of fourfold coordinated atoms decreases by the bombardment process, while the number of threefold coordinated atoms increases. The bombardment does not only induce transformation of fourfold to threefold coordinated atoms by bond breakage, but it also gives rise to the formation of clusters of threefold coordinated atoms, as reflected by the increase in g33(r) as N increases. Indeed, in the core, each threefold coordinated atom is found to be connected on the average to 1.74 other threefold coordinated atoms, for N=12, while in the periphery, this average is only 0.7. That is, the core of the damage contains a cluster of connected threefold coordinated atoms, while in the periphery the threefold coordinated atoms are isolated point defects.


  
Figure 9.11: Partial radial distribution functions g33, g34 and g44 for N=12 ( g33+g34+g44=g(r)). The first peaks of the distributions are shown in the insert.
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next up previous contents
Next: Annealing of the damaged Up: Properties of the damaged Previous: The thermal spike
David Saada
2000-06-22