Modeling Irradiation Damage Accumulation in Crystals

Bombardment of crystalline solids by energetic particles produces lattice defects, the accumulation of which is the origin of the macroscopic effects of irradiation damage. In an all-inclusive theory, the defects produced fall into two categories: (1) atomic displacements creating freely migrating vacancies and interstitials and their clusters, both mobile and immobile; and (2) transmutations creating impurity elements, such as helium. The first type of damage is called displacement damage, and is recoverable via the recombination of the vacancies and the interstitials before they disappear into grain boundaries, voids and dislocations, but the second type is not. In the present article, our attention is on the former. Depending on the energy transfer between the projectile particle and the atom of first encounter in the irradiated material, i.e., the primary knock-on atom or PKA, the initial displacement damage may take the form of (i) vacancy–interstitial (Frenkel) pairs, when the energy transferred is just sufficient to overcome the displacement threshold, e.g., irradiation by MeV electrons; or (ii) cascades and sub-cascades, when the energy transferred is substantially higher, e.g., irradiation by fast neutrons and heavy ions. The lattice defects generated directly from the displacement damage in case (i) are isolated vacancies and interstitials, and their generation rates can be approximated by the displacement rate [1], after discounting the recombination of correlated pairs [2]. In case (ii), due to the high concentration of displacement damage produced in the small cascade volume, and the high mobility of atoms resulting from the energy deposited by the PKA, substantial recombination of the lattice defects takes place already during the coolingdown phase. The final numbers of interstitials and vacancies produced from the cascade are only small fractions of those estimated from the available energy due to the PKA. While the recombination is taking place, a significant fraction of interstitials and vacancies cluster at the same time. The fraction