Voids are a consequence of a supersaturation of vacancies in the lattice and the tendency of excess vacancies to condense into higher-order defect com­plexes (either vacancy loops or voids). However, the root cause ofvoid formation is actually not the vacan­cies, but the interstitials. Each atomic displacement event during irradiation produces a pair of defects known as a Frenkel pair. The constituents of a Frenkel pair are an interstitial (i) and a vacancy (v). Interstitials are more mobile than vacancies at most temperatures (at low-to-moderate temperatures, say less than half the melting point (0.5 T^), vacancies are essentially immobile in most materials), such that i-defects freely migrate around the lattice, while v-defects either remain stationary or move much smaller distances than i-defects. Because i-defects are highly mobile, they are able to diffuse to other lattice imperfections, such as dislocations, grain boundaries, and free surfaces, where they often are readily absorbed. This situation leads to a supersatu­ration of vacancies, that is, a condition in which the bulk vacancy concentration exceeds the complemen­tary bulk interstitial concentration. This is a highly undesirable circumstance for a material exposed to displacive radiation damage conditions, because the v-defect concentration will continue to grow (unchecked) at approximately the Frenkel defect production rate, while the i-defect concentration will reach a steady-state concentration, determined by interstitial mobility and by the concentration of extended defects (extended defects presumably serve as sinks for interstitial absorption). The v-defect concentration will inevitably reach a critical stage at which the lattice can no longer support the exces­sive concentration of vacancies, at which point the v-defects will migrate locally and condense to form voids (or vacancy loops or clusters). This entire pro­cess, initiated by the supersaturation of vacancies, causes the material to undergo macroscopic swelling, and the material becomes susceptible to microcrack­ing or failure by other mechanical mechanisms. This, indeed, is the fate suffered by a-Al2O3 when exposed to a neutron (displacive) radiation environment.

It is interesting that a supersaturation of vacancies can even be established in a material devoid of extended defects, such as a high-quality single crystal or a very large-grained polycrystalline material. Single crystal a-Al2O3 (sapphire) is an example of just such a material.6 When freely migrating i-defects are unable to readily ‘find’ lattice imperfections such as grain boundaries and dislocations, they instead ‘find’ one another. Interstitials can bind to form diin­terstitials or higher-order aggregates. Eventually, a new extended defect, produced by the condensation of i-defects, becomes distinguishable as an interstitial dislocation loop (also known as an interstitial Frank loop). Once formed, such a lattice defect acts as a sink for the absorption of additional freely migrating i-defects. With this, the conditions for a supersatura­tion of vacancies and macroscopic swelling are established.

The defect situation just described can be conve­niently summarized using chemical rate equations as described in detail in Chapter 1.13, Radiation Dam­age Theory. In eqn [1], we employ a simplified pair of rate equations to show the time-dependent fate of interstitials and vacancies produced under irradiation for an imaginary single crystal of A atoms:

^ = Pi (Aa! Ai + Va)

—Ri—v (Ai + VA! AA) Jia]

—N (nucleation rate for interstitial loops)

— G(growth rate for interstitial loops)

= pv (aa! Ai + Va) ribl

—Ri—v (Ai + Va! Aa)

where Ci(t) and Cv(t) are the time-dependent concen­trations of interstitials and vacancies, respectively; Pi and Pv are the production rates of interstitials and vacancies, respectively (equal to the Frenkel pair pro­duction rate); Ri-v is the recombination rate of interstitials and vacancies (i. e., the annihilation rate of i and v point defects when they encounter one another in the matrix); N and G are the nucleation and growth rates, respectively, of interstitial loops; Aa is an A atom on an A lattice site; Ai is an interstitial A atom; and Va is a vacant A lattice site (an A vacancy). (This equation for vacancies assumes low or moderate temperatures, such that vacancies are effectively immobile. Under high-temperature irradiation conditions, we would need to add nucleation and growth terms for voids, vacancy loops, or vacancy clusters. Reactions with preexisting defects are also ignored in eqn [1].) Note in eqn [1] that i—v recombination, Ri-v, is a harmless point defect annihilation mechanism (it restores, locally, the perfect crystal lattice). On the contrary, nucleation and growth (N and G) of interstitial loops are harmful point defect annihilation mechanisms, in the sense that these mechanisms leave behind unpaired vacancies in the lattice, thus establishing a supersaturation of vacancies, which is a necessary con­dition for swelling.

It is interesting to compare and contrast the neu­tron radiation damage behavior shown in Figure 1 of alumina (a-Al2O3) and spinel (MgAl2O4) single crys­tals, in terms of the defect evolution described in eqn [1]. Alumina must be described as a highly radiation-susceptible material, due to its tendency to succumb to radiation-induced swelling. Spinel, on the other hand, is to be considered a radiation — tolerant material, in view of its ability to resist radiation-induced swelling. According to eqn [1], we can speculate that mechanistically, nucleation and growth of interstitial dislocation loops are much more pronounced in alumina than in spinel. Also, eqn [1] suggests that harmless i—v recombination must be the most pronounced point defect annihila­tion mechanism in spinel so that a supersaturation of vacancies and concomitant swelling is avoided. Indeed, it turns out that nucleation and growth of dislocation loops are far more pronounced in alu­mina than in spinel, as discussed in detail next. The dislocation loop story described below is rich with the complexities of dislocation crystallography and dynamics. The unraveling of the mysteries of dislo­cation loop evolution in alumina versus spinel should be considered one of the greatest achievements ever in the field of radiation effects in ceramics, even though this was accomplished some 30 years ago! This story also illustrates the tremendous complexity of radiation damage behavior in ceramic materials, wherein point defects are created on both anion and cation sublattices, and where the defects generated often assume significant Coulombic charge states in highly insulating ceramics (alumina and spinel are large band gap insulators).

The earliest stages of the nucleation and growth of interstitial dislocation loops are currently impossible to interrogate experimentally. TEM has been used as a very effective technique for examining the struc­tural evolution of dislocation in irradiated solids but only after the defect clusters have grown to diameters of about 5 nm. Interestingly, important changes in dislocation character probably occur in the early stages of dislocation loop growth, when loop diameters are only between 5 and 50 nm.10 Therefore, we must speculate about the nature ofnascent dislocation loops produced under irradiation damage conditions.