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Stability of amorphous carbon and of point defects in the diamond lattice

The P,T phase diagram of carbon proposed by F. B. Bundy [3] (figure 2.1) suggests that graphite is the stable phase at low temperature and pressure. Thus, if high pressure, at which the diamond phase is stable, is released, diamond undergoes a very slow transformation to graphite. Therefore, the sp2 bonding configuration is expected to be the stable structure for a crystal of carbon. Indeed, P. C. Kelires showed [48] that the diamond-like lattice he generated was not stable under further annealing at higher temperature. Many of the sp3 bonds disappeared (the weaker ones, with large angle distortion), the sample created remaining quite dense (2.8 gr/cm3) but with a majority of threefold sp2 bonds and a mean bond length of 1.48 Å. G. Comelli et alreport [38] that the sp2 fraction can range from 60% at 30oCto 90% at 1050oC. In the same way, increasing temperature promotes the creation of graphite-like bonds in the sample created by G. Galli et al [50]. Therefore, the amorphous state is metastable and thermal annealing promotes a sp3 to sp2 bonds transition, when the sp3 bonds are sufficiently distorted and unstable.

In the same manner, the stability of point defects in irradiated diamond is expected to be related to the thermodynamic stability of the sp2 bonds. Many investigations were carry out to calculate the formation energy of defects in diamond and their relative stability. ab initio calculations of J. Bernholc, A. Antonelli and T. M. Del Sol [55] concluded that the bond-centered interstitial has the lowest formation energy of 15.8 eV, even lower than that of the <100> split interstitial (16.7 eV). In contrast with them, S. J. Breuer and P. R. Bridden [56] found by means of similar calculations that the <100> split-interstitial is the only truly stable structure for an interstitial. They proposed that one possible reason for the stability of the <100> split interstitial defect is the preference in diamond for sp2 bonding, since the configuration of the <100> split interstitial very much resembles that of sp2 bonds in graphite, with the major difference that the latter is a planar structure. Finally, by means of molecular dynamics and Monte Carlo techniques, D. Saada et. al. [20,57] found that the <100> split interstitial is the most stable defect, with a formation energy of 16.5 eV, in agreement with S. J. Breuer et al [56].


next up previous contents
Next: Impurities and defects in Up: Structural modifications induced by Previous: Structure of amorphous carbon
David Saada
2000-06-22