Following the characterization of the initial damage, we have annealed the sample as described in section 9.1.3. We first calculated the displacement of the atoms from their initial position (obtained after a bombardment of twelve atoms at 0 K), as a results of annealing at 3000 K for 20 ps. Averages of the atomic coordinates were computed for every 0.25 ps, for the six samples considered, which differ in their initial conditions (see section 9.1.3). The results of the six calculations were averaged, and are shown in figure (9.12) for both the highly damaged core and the lighter damaged periphery. A clear difference is observed between the atoms of the core which can move the rather long distances of up to several lattice sites, and those in the periphery, whose motion is much more limited. Moreover, the results show that there is very little motion of atoms across the boundary between the core and the periphery.
The number of threefold coordinated atoms in the sample was calculated as a function of annealing time separately for both inside and outside the core. The results, averaged over the six samples studied here (which differed only by their velocity initializations, see section 9.1.3) are shown in figure (9.13). It can be seen from this figure that the number of threefold coordinated atoms increases, predominantly in the periphery of the damage core, whereas the number of threefold coordinated atoms inside the core decreases. The effects of the annealing process are thus rather different for the core in which the defects density is high and in the periphery, which is characterized by the low damage concentration.
The displacement vector of the atoms, defined as the vector pointing from the initial position of the moving atoms to their post-annealing position, when projected on the x,y and z axis, should reveal the direction of motion of the atoms. This projection was calculated for the atoms inside the core (see figure (9.14)). One can see from figure (9.14) that a majority of atoms diffuse, under annealing, in the negative direction of the x-axis. This can be explained by the fact that the damage creating bombardments were carried out so that the largest component of the initial velocity of the 12 atoms displaced was x. Thus, a volume rich in vacancies was created on the left side of the sample while an interstitial rich region is to be expected on the right side. Diffusion can thus occur due to a gradient in the atomic density, and vacancy-interstitial recombinations can take place, leading to the slight decrease in the number of threefold coordinated atoms in the core of the damage. As expected, no assymetry can be observed in the y-z plane.
The radial distribution function g(r) for atoms inside the core after annealing at 3000 K for 20 ps was calculated and compared with that calculated prior to annealing. The results for both cases are shown in figure (9.15). For the six samples created, almost identical radial distribution functions were obtained. One can see that annealing does not affect the shortest and strongest bonds, associated with bonding between threefold coordinated atoms. However, many bonds, mainly between fourfold coordinated atoms, are significantly extended. A most interesting observation is that the very sharp peak centered at 2.1 Å almost disappears upon annealing, suggesting that the quadrilateral structures formed during the bombarding events are very unstable. Moreover, the disorder induced by the bombardment, as reflected in the lack of any structure in the g(r) spectrum for the next nearest neighbor, seems to change over, upon annealing, to a somewhat more ordered phase, as indicated by the appearance of flat ``waves'' following the first peak in g(r).
Figure (9.16(a)) shows the damaged part of the sample to which the above described annealing was applied. Only threefold coordinated atoms and bonds between neighboring threefold coordinated atoms, if they exist, are displayed for clarity. Figures (9.16(b)) and (9.16(c)) show the atomic arrangement of the same sample following heating to 3000K for 16.25 ps and 20 ps respectively. Inside the core of the damage region, the structure seems to maintain its disorder, as will be shown later. However, the formation of several parallel graphitic planes at the periphery of the core region is obvious, and was observed in all the six different samples obtained.
In order to quantify this unexpected graphitization, we have calculated the vectors normal to the planes formed by the three nearest neighbors of each threefold coordinated atom. These vectors were then normalized and projected on the x-y plane. A vector thus defined, when oriented in a <111> direction should have coordinates and . Projections on the x-z or the y-z plane should give similar distribution. Figures (9.17) and (9.18) show, in a polar presentation, the evolution, as a function of annealing time, of the distribution of the vectors defined above, for the threefold coordinated atoms in the core and for those in the periphery, respectively. Indices a and b refer to the configuration of the sample before annealing, and after annealing at 3000 K for 20 ps, respectively. Figures (9.17(a)) and (9.18(a)) show that before annealing, the vectors defined above are distributed rather randomly inside the core. In the periphery, a few vectors are already oriented in the <111> direction prior to annealing. These must be related to isolated threefold coordinated atoms (see 9.2.2). Thus, before annealing, no ordered structure at all is formed by the cluster of threefold coordinated atoms.
Figure (9.18(b)) show that following annealing for 20 ps at 3000K a clear pattern evolves for atoms outside the core of the damage; clusters of oriented sp2 bonded carbon atoms form, with the normal to their planes preferentially pointing in the <111>direction. In contrast, the core of the damage does not evolve to a more structured configuration, as indicated by figure (9.17(b)). The graphitization in the periphery of the damage is obvious (see figure (9.18(b))) and the number of C atoms belonging to the "graphitic" planes increases with annealing time (see also figure (9.13)).
The formation of the graphitic planes at the periphery of the damage region inside the diamond resembles that which occurs at the surface of a diamond crystal, in both the ab initio calculations  and in the present calculations based on the Tersoff potential, described in section 9.1. These calculations show that the graphitization starts from the surface, by outward atomic displacements in the <111> direction, which leads to the breaking of bonds between the first and the second layer. The graphitization then progresses into the diamond sample by correlated breakage of adjacent <111>-oriented bonds. The process of graphitization of damaged regions inside diamond may well proceed in the same manner, namely start from the periphery of the damage region and proceed into the core of the damage until complete graphitization is achieved.