The default theory of radiation damage in graphite invokes Frenkel pair formation as the principal cause of physical property changes. We set out its inadequacies and present two new mechanisms that contribute to a better account for changes in dimension and stored energy. Damage depends on the substrate temperature, undergoing a change at approximately 250°C. Below this temperature particle radiation imparts a permanent, nano-buckling to the layers. Above it, layers fold, forming what we describe as a ruck and tuck defect. We present first principles and molecular mechanics calculations of energies and structures to support these claims. Necessarily we extend the dislocation theory of layered materials. We cite good experimental evidence for these features from the literature on radiation damage in graphite.

Iwata and Watanabe's model for the observed low-temperature specific heat of neutron-irradiated graphite [T. Iwata and M. Watanabe, Phys. Rev. B 81, 014105 (2010)] assumes that self-interstitial atoms exist as clusters of nearly free C-2 molecules. We suggest that their hypothesis is not supported by other experiments and theory, including our own calculations. Not only is it inconsistent with the long-known kinetics of interstitial prismatic dislocation loop formation, density-functional theory shows that the di-interstitial is covalently bonded to the host crystal. In such calculations no prior assumptions are made about the nature of the bonding, covalent or otherwise.

We report calculations in support of the application of LDA within DFT to graphite and go on to report the inner core structure and energetics of prismatic dislocations with Burgers vector c/2: two types of edge and one of screw type. We find the screw dislocations preserve sp(2) hybridisation and graphite bonding, whereas one edge type (zigzag) gives rise to interlayer single bonds and sp(3) hybridisation, while the other type (armchair) does not, preferring instead to rehybridise towards sp and form bonds with itself approaching triple character. For computational and physical reasons these calculations were based on AA graphite, rather than Bernal (AB) graphite.

The story behind radiation damage in graphite is framed in terms of interstitials and vacancies. First principles calculations all show that interstitials are immobile at low (e.g. liquid N2) temperatures. We have performed the first serious and first principles calculations on dislocations in graphite and found some remarkable results, which give clear explanations for the dimensional change and creep in graphite under neutron irradiation. Dimensional change can be substantial (sometimes exceeding 100%) and creep can be a linear (i.e. non-saturating) function of dose. We find that basal dislocations lie at the heart of nearly all these effects, which are not, as was originally thought, exclusively due to the Frenkel pairs formed from irradiation. A more complete explanation lies in prismatic loops and the interactions between basal dislocations, so the structure and energetics of these will be discussed. The physical effects they give are buckling and forming folds, i.e. ‘ruck and tuck’ defects. The findings are expected to be general to layered materials. Dislocations in graphite In every material the shear strength is not limited by the inherent shear strength of the perfect crystal where one plane glides uniformly and simultaneously over another, but rather by progressive movement of slip through the crystal, so that at any one time some of the crystal has slipped and some has not. The boundary between the slipped and unslipped region is a line known as a dislocation. The amount of slippage is the Burgers vector, b, and it is commonly a lattice vector so that both the slipped and unslipped regions are commensurate with the underlying lattice. Dislocations are classified by b and by their line direction (Table 1). Elegant and pioneering work on radiation damage focused on the aggregation of carbon interstitials in interlayer regions into new sections of graphite planes, i.e. interstitial prismatic dislocation loops (Brown et al., 1969, Reynolds and Thrower, 1965). The existence of such loops was proven in transmission electron microscopy. The extra disks of graphene plane are bounded by prismatic dislocations, which have been studied elsewhere (Suarez-Martinez et al., 2007). The loops clearly expand the c direction and can thus cause dimensional change, but the process is irreversible at most temperatures. Annealing would require the emission of interstitials or absorption of vacancies which are both high energy processes. Table 1. Classes of dislocation in graphite after Fujita and Izui (1961) .