Anisotropy of the Threshold Energy for the Production of Frenkel Pairs in Tantalum

Abstract

Thin tantalum single-crystal foils with the $〈110〉$ direction normal to the surface have been irradiated with electrons of energies between 1.0 to 3.2 MeV. By varying the orientation of the foil relative to the direction of the beam over a major part of the fundamental triangle, a strong directional effect in the damage rate was observed for transferred energies of more than 36 eV. In previous measurements especially on the fcc metals copper and gold, much less, if any, anisotropy of the defect production was observed. The data have been corrected for beam spreading due to the finite sample thickness. From the dependence of the defect production on electron energy and foil orientation, the angular dependence of the threshold displacement energy could be fitted. Good over-all fits were only possible when the averaged threshold was about 36 eV in a region of 20\ifmmode^\circ\else\textdegree\fi{} around the $〈111〉$ direction, about 53 eV in a region of 18\ifmmode^\circ\else\textdegree\fi{} around the $〈100〉$ direction, and larger than 130 eV in other directions. The existence of such "windows" along the close-packed directions indicates a sequence of replacement collisions which eventually leads to a stable defect. Computer calculations by the Brookhaven group for bcc iron yielded similar threshold windows around the principal crystallographic directions. However, the ratio of the threshold values for the $〈100〉$ and $〈111〉$ directions obtained by this group does not agree with our result. For the lowest threshold energy in tantalum, we found 32 \ifmmode\pm\else\textpm\fi{} 2 eV, and for the electrical resistivity per unity concentration of Frenkel pairs, we obtained (17 \ifmmode\pm\else\textpm\fi{} 3) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ \ensuremath{\Omega} cm.