The discovery of Fullerenes9 and carbon nanotubes,10 and other nanocarbon structures, has renewed inter­est in high-resolution microstructural studies of car­bon nanostructures and the defects within them.11 This in turn has given new insight to the nature of displacement damage and the deformation mechan­isms in irradiated graphite crystals. The binding energy of a carbon atom in the graphite lattice12 is about 7 eV. Impinging energetic particles such as fast neutrons, electrons, or ions can displace carbon atoms from their equilibrium positions. There have been many studies of the energy required to displace a carbon atom (£d), as reviewed by Kelly,13 Burchell,14 Banhart,11 and Telling and Heggie.15 The value of £d lies between 24 and 60 eV. The latter value has gained wide acceptance and use in displacement damage calculations, but a value of ^30 eV would be more appropriate. Moreover, as discussed by Banhart,1 Hehr et a/.,16 and Telling and Heggie,15 an angular dependence of the threshold energy for displacement would be expected. The value of £d in the crystallo­graphic c-axis is in the range 12-20 eV,11,17 while the in-plane value is much greater.

The primary atomic displacements, primary knock-on carbon atoms (PKAs), produced by ener­getic particle collisions produce further carbon atom displacements in a cascade effect. The cascade carbon atoms are referred to as secondary knock-on atoms (SKAs). The displaced SKAs tend to be clustered in small groups of 5-10 atoms and for most purposes it is satisfactory to treat the displacements as if they occur randomly. The total number of displaced car­bon atoms will depend upon the energy of the PKA, which is itself a function of the neutron energy spec­trum, and the neutron flux. Once displaced, the carbon atoms recoil through the graphite lattice, dis­placing other carbon atoms and leaving vacant lattice sites. However, not all of the carbon atoms remain displaced and the temperature of irradiation has a significant influence on the fate of the displaced atoms and lattice vacancies. The displaced carbon atoms easily diffuse between the graphite layer planes in two dimensions and a high proportion will recom­bine with lattice vacancies. Others will coalesce to form C2, C3, or C4 linear molecules. These in turn may form the nucleus of a dislocation loop — essentially a new graphite plane. Interstitial clusters may, on fur­ther irradiation, be destroyed by a fast neutron or carbon knock-on atom (irradiation annealing). Adja­cent lattice vacancies in the same graphitic layer are believed to collapse parallel to the layers, thereby forming sinks for other vacancies which are increas­ingly mobile above 600 ° C, and hence can no longer recombine and annihilate interstitials. The migration of interstitials along the crystallographic c-axis is discussed later.

Banhart11 observed typical basal plane defects in a graphite nanoparticles using high-resolution trans­mission electron microscopy (HRTEM). These defects can be understood as dislocation loops which form when displaced interstitial atoms cluster and form less mobile agglomerates. Other interstitials condense onto this agglomerate which grows into a disk, pushing the adjacent apart. Further agglomeration leads to the for­mation of a new lattice planes (Figure 4).

Other deformation mechanisms have been pro­posed for irradiated graphite. Wallace18 proposed a mechanism whereby interstitial atoms could facili­tate sp3 bonds between the atomic basal planes, this mechanism allowing the stored energy (discussed in Section 4.10.5.1) to be explained. Jenkins19 argued that the magnitude of the increase in shear

modulus (C44) with low dose irradiation could not be explained by interstitial clusters pinning dislocations, but that a few sp3 type covalent bonds between the planes could easily account for the observed changes. More recently, Telling and Heggie,15 in their ab-initio calculations of the energy of formation of the ‘spiro- interstitial,’ advocate this mechanism to explain the stored energy characteristics of displacement dam­aged graphite, particularly the large energy release peak seen at ~-473 K (discussed in Section 4.10.5.1). The first experimental evidence of the interlayer interstitial-vacancy (IV) pair defect with partial sp3 character in between bilayers of graphite was recently reported by Urita et at20 in their study of double­walled carbon nanotubes (DWNTs).

Jenkins19 invoked the formation of sp3 bonding to explain the c-axis growth observed as a result of displacement damage. If adjacent planes are pinned, one plane must buckle as the adjacent planes shrink due to vacancy shrinkage; buckled planes yield the c-axis expansion that cannot be explained by swelling from interstitial cluster alone. Telling and Heggie15 are very much in support of this position on the basis of their review of the literature and ab-initio simulations of the damage mechanisms in graphite. Their simulations showed how the spiro-interstitial (cross-link) essen­tially locked the planes together. Additionally, diva­cancies could lead to the formation of pentagons and heptagons in the basal planes causing the observed bending of graphene layers and c-axis swelling.11,21,22 The predicted c-axis crystal expansion via this mecha­nism is in closer agreement with the experimentally observed single crystal and highly oriented pyrolytic graphite (HOPG) dimensional change data.

The buckling of basal planes as a consequence of irradiation damage has been observed in HRTEM studies of irradiated HOPG by Tanabe21 and Koike and Pedraza.22 In their study, Koike and Pedraza22 observed 300% expansion of thin HOPG samples subject to electron irradiation in an in-situ transmis­sion electron microscope (TEM) study. Their exper­imental temperatures ranged from 238 to 939 K. They noted that the damaged microstructure showed retention of crystalline order up to 1 dpa (displace­ments per atom). At higher doses, they observed the lattice fringes break up in to segments 0.5-5 nm in length, with up to 15° rotation of the segments with respect to the original {0001} planes.

The evidence in favor of the formation of bonds between basal planes involving interstitials is consid­erable. However, such bonds are not stable at high temperature. As reported by numerous authors and
reviewers11’15’19’20 the sp3 like bond would be ex­pected to break and recombine with lattice vacancies with increasing temperature, such that at T>500K they no longer exist. Indeed’ the irradiated graphite stored energy annealing peak at ~-473 K, and the HRTEM observations of Urita eta/.20 demonstrate this clearly. Figure 5 shows a sequential series of HRTEM images illustrating the formation rates of interlayer defects at different temperatures with the same time scale (0-220 s) in DWNTs. The arrows indicate possi­ble interlayer defects. At T = 93 K (Figure 5(a)) the electron irradiation-induced defects are numer­ous’ and the nanotubes inside are quickly damaged because of complex defects. At 300 K (Figure 5(b)), the nanotubes are more resistive to the damage from electron irradiation, yet defects are still viable. At 573 K (Figure 5(c)), defect formation is rarely observed and the DWNTs are highly resistant to the electron beam irradiation presumably because of the ease of defect self-annihilation (annealing).

In an attempt to estimate the critical temperature for the annihilation of the IV defect pairs, a system­atic HRTEM study was undertaken at elevated temperatures by Urita et a/.20 The formation rate of the IV defects that showed sufficient contrast in the HRTEM is plotted in Figure 6. The reported numbers were considered to be an underestimate as single IV pairs may not have sufficient contrast to be
convincingly isolated from the noise level and thus may have been missed. However, the data was con­sidered satisfactory for indicating the formation rate as a function of temperature. The number of clusters of IV pairs found in a DWNT was averaged for several batches at every 50 K and normalized by the unit area. As observed in Figure 6, the defect for­mation rate displays a constant rate decline, with a threshold appearing at ^450-500 K. This threshold corresponds to the stored energy release peak (dis­cussed in Section 4.10.5.1) as shown by the dotted line in Figure 6. Evidentially, the irradiation dam­age resulting from higher temperature irradiations (above ^473-573 K) is different in nature from that occurring at lower irradiation temperatures.

Koike and Pedraza22 studied the dimensional change in HOPG caused by electron-irradiation-induced dis­placement damage. They observed in situ the growth c-axis of the HOPG crystals as a function of irradiation temperature at damage doses up to ~ 1.3 dpa. Increasing c-axis expansion with increasing dose was seen at all temperatures. The expansion rate was however signifi­cantly greater at temperatures ;S473 K (their data was at 298 and 419 K) compared to that at irradiation tem­peratures ^473 K (their data was at 553, 693, and 948 K). This observation supports the concept that separate irradiation damage mechanisms may exist at low irradiation temperatures (~T<473 K), that is,

buckling due to sp3 bonded cross linking of the basal planes via interstitials, and at more elevated irradiation temperatures (T ^ 473 K), where the buckling of planes is attributed to clustering of interstitials which induce the basal planes to bend, fragment, and then tilt. Koike and Pedraza22 also observed crystallographic a-axis shrinkage upon electron irradiation in-situ at several temperatures (419, 553, and 693 K). The shrinkage increased with dose at all irradiation temperatures, and the shrinkage rate reduced with increasing irradia­tion temperature. This behavior is attributed to buck­ling and breakage of the basal planes, with the amount of tilting and buckling decreasing with increasing tem­perature due to (1) a switch in mechanism as discussed above and (2) increased mobility of lattice vacancies above -~673 K.

Jenkins19,23 also discussed the deformation of graphite crystals in terms of a unit c-axis dislocation (prismatic dislocation), that is, one in which the Bur­gers vector, b, is in the crystallographic c-direction. The c-axis migration of interstitials can take place by unit c-axis dislocations. The formation and growth of these, and other basal plane dislocation loops undoubtedly play a major role in graphite crystal deformation during irradiation.

Ouseph24 observed prismatic dislocation loops (both interstitial and vacancy) in unirradiated HOPG using scanning tunneling microscopy (STM). Their study allowed atomic resolution of the defect structures. Such defects had previously been observed as regions of intensity variations in TEM studies in the 1960s.25

Telling and Heggie’s15 first principle simulations have indicated a reduced energy of migration for a lattice vacancy compared to the previously estab­lished value. Therefore, they argue, the observed lim­ited growth of vacancy clusters at high temperatures (T >900K) indicates the presence of a barrier to further coalescence of vacancy clusters (i. e., vacancy traps). Telling and Heggie implicate a cross-planer metastable vacancy cluster in adjacent planes as the possible trap. The disk like growth ofvacancy clusters within a basal plane ultimately leads to a prismatic dislocation loop. TEM observations show that these loops appear to form at the edges of interstitial loops in neighboring planes in the regions of tensile stress.

The role of vacancies needs to be reexamined on the basis of the foregoing discussion. If the energy of migration is considerably lower than that previously considered, and there is a likelihood of vacancy traps, the vacancy and prismatic dislocation may well play a larger role in displacement damage induced in­crystal deformation. The diffusion of vacancy lines to the crystal edge essentially heals the damage, such that crystals can withstand massive vacancy damage and recover completely.

Regardless of the exact mechanism, the result of carbon atom displacements is crystallite dimensional change. Interstitial defects will cause crystallite growth perpendicular to the layer planes (c-axis direction), and relaxation in the plane due to coalescence of vacancies will cause a shrinkage parallel to the layer plane (a-axis direction). The damage mechanism and associated dimensional changes are illustrated (in sim­plified form) in Figure 7. As discussed above, this conventional view of c-axis expansion as being caused solely by the graphite lattice accommodating small interstitial aggregates is under some doubt, and despite the enormous amount of experimental and theoretical work on irradiation-induced defects in graphite, we are far from a widely accepted understanding. It is to be hoped that the availability of high-resolution microscopes will facilitate new damage and annealing studies of graphite leading to an improved under­standing of the defect structures and of crystal defor­mation under irradiation.

Dimensional changes can be very large, as demon­strated in studies on well-ordered graphite materials, such as HOPG that has frequently been used to study the neutron-irradiation-induced dimensional changes of the graphite crystallite.13,26 Price27 conducted a study of the neutron-irradiation-induced dimensional changes in pyrolytic graphite. Figure 8 shows the crystallite shrinkage in the й-direction for neutron doses up to 12 dpa for samples that were graphitized at a temperature of 2200-3300 °C prior to being irra­diated at 1300-1500 °C. The a-axis shrinkage in­creases linearly with dose for all of the samples, but the magnitude of the shrinkage at any given dose decreases with increasing graphitization temperature. Similar trends were noted for the c-axis expansion. The significant effect of graphitization temperature on irradiation-induced dimensional change accumula­tion can be attributed to thermally induced improve­ments in crystal perfection, thereby reducing the number of defect trapping sites in the lattice.

Nuclear graphites possess a polycrystalline struc­ture, usually with significant texture resulting from the method of forming during manufacture. Con­sequently, structural and dimensional changes in polycrystalline graphites are a function of the crys­tallite dimensional changes and the graphite’s texture. In polycrystalline graphite, thermal shrinkage cracks that occur during manufacture and that are prefer­entially aligned in the crystallographic й-direction will initially accommodate the c-direction expansion, so mainly a-direction contraction will be observed. The graphite thus undergoes net volume shrinkage. With increasing neutron dose (displacements), the incompatibility of crystallite dimensional changes leads to the generation of new porosity, and the volume shrinkage rate falls, eventually reaching zero. The graphite now begins to swell at an

increasing rate with increasing neutron dose. The graphite thus undergoes a volume change ‘turn­around’ into net growth that continues until the gen­eration of cracks and pores in the graphite, due to differential crystal strain, eventually causes total dis­integration of the graphite.

Irradiation-induced volume and dimensional change data for H-451 are shown28 in Figures 9-11. The effect of irradiation temperature on volume change is shown in Figure 9. The ‘turn-around’ from volume shrinkage to growth occurs at a lower fluence and

, there is less accommodating volume