On the Nature of Grain Boundaries in Nanocrystalline Diamond
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of three-coordinated Si atoms each having one unsaturated, bound electron in an otherwise more or less tetrahedrally coordinated environment.7 In contrast to silicon, carbon can form both sp3- and sp2-hybridized electronic states as evidenced by the existence of two energetically similar bulk phases— diamond and graphite. Also the typically three-to-five-times-higher elastic moduli of diamond in comparison to those of Si indicate much stiffer nearestneighbor bonds with respect to both bond bending and stretching. One might ask what role these differences play in the atomic structures of diamond GBs in comparison to those of silicon. Intuitively one would expect that, because of the greater bond stiffness of diamond, even relatively small bond distortions are energetically very costly, thus favoring a change to s/?2-type local bonding. Amorphous carbon, in which up to 80% of the atoms are threefoldcoordinated,8 provides evidence for this behavior. This should translate into considerably more ordered GB structures in diamond than in Si, however at the price of many C atoms being only threefoldcoordinated. We therefore anticipate that the high degree of structural disorder in the mostly fourfold-coordinated Si GBs will be replaced by bond-coordination disorder in the mostly threefold coordinated diamond GBs. Like the dangling bonds in the silicon GBs, threefold-coordinated C atoms in diamond GBs can be expected to be electrically and optically active. Moreover, in contrast to silicon, the n electrons in sp2-bonded, graphitelike local environments can at least in prin-
ciple be expected to be rather mobile— provided the threefold-coordinated C sites are spatially connected among themselves. The graphitelike electrical conductivity of amorphous carbon provides evidence for such behavior.9 It > therefore appears that, in contrast to Si, j diamond GBs have potential for becoming electrically conductive. The main goal of the study reported > here is to elucidate the effects of sp3 versus sp2 bonding, with particular emphasis on the role of nearest-neighbor coordination in the atomic structures and properties of those types of GBs predominantly present in nanocrystalline diamond films. A comparison between silicon and diamond is helpful because Si provides a basis for understanding GB structural disorder in a purely sp3-bonded material, against which the greater bond stiffness in diamond combined with its ability to ' change hybridization in a defected environment can be elucidated. Molecular-Dynamics Synthesis of Nanocrystalline Microstructures In our simulations of nanocrystalline microstructures, we use Tersoff's semiempirical C and Si potentials1"11 instead of a more sophisticated, electronic-structurebased approach (such as the tight-binding or Car-Parrinello methods) because our simulations can involve up to 10s atoms in the simulation cell and very long simulation times. These simulations allow us to identify the types of bicrystalline GBs representative of the highly constrained interfaces present in the nanocrys
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