Anisotropy of Radiation Damage in Electron-Bombarded Hexagonal Metals. II. A Model for Frenkel-Pair Formation in Single Crystals

Abstract

A "geometrical" model is presented for the hexagonal close-packed lattice proposing several principal mechanisms for the displacement of a knocked-on atom. Using the experimentally determined resistivity-change rates of a previous paper and matching families of cross sections computed with this model, we have calculated sets of thresholds energies for displacement in the directions [0001], [10¯14], [1012], [10¯11], and [11¯20] in cobalt, zinc, and cadmium. The correlation between the resistivity-change rates and the displacement cross sections allowed the determination of the Frenkel-pair resistivity per unit concentration in cobalt and zinc: ${\rho }_F^{\mathrm{Co}}\approx \frac{3{\rho }_{0°\mathrm{C}}^{\mathrm{Co}}}{\mathrm{at}.\%}$, ${\rho }_F^{\mathrm{Zn}}\approx \frac{3.5{\rho }_{0°\mathrm{C}}^{\mathrm{Zn}}}{\mathrm{at}.\%}$; no definite conclusion for ${\rho }_F^{\mathrm{Cd}}$ could be made owing to the proximity of a recovery stage. Expressions for the energies needed to pass across one or several open "windows" in the hcp unit cell were derived, including the possibility of focusing collisions in the [11¯20] direction, and compared with the previously calculated threshold energies for displacement in various directions. This comparison permitted the tentative deduction of interatomic potentials of the Born-Mayer type giving as a possible choice: $U^{\mathrm{Co}}\left(\mathrm{eV}\right)=3300\mathrm{}{e}^{-4.1r\left(\AA \right)}$, $U^{\mathrm{Zn}}\left(\mathrm{eV}\right)=280\mathrm{}{e}^{-2.5r\left(\AA \right)}$, $U^{\mathrm{Cd}}\left(\mathrm{eV}\right)=300\mathrm{}{e}^{-2.0r\left(\AA \right)}$.