Near-threshold displacements in tantalum single crystals

Abstract

Tantalum single crystals of the four orientations (100), (110), (111), and (112) have been irradiated with electrons in the energy range 1.0-1.7 MeV. A special irradiation procedure has been used which enables us to distinguish between subthreshold and intrinsic defects. The threshold energy for atomic displacement is found to be the lowest in and around the $〈100〉$ direction. Moreover, the defect production in the $〈100〉$ direction is found to be governed by two slightly different threshold energies. An analysis based on a geometrical model for the threshold energy surface leads to the following results: ${T}_{d1}^{〈100〉}=33\ifmmode\pm\else\textpm\fi{}1$ eV, ${T}_{d2}^{〈100〉}=38\ifmmode\pm\else\textpm\fi{}1$ eV, and ${T}_{d}\ensuremath{\ge}55$ eV for all other crystallographic directions. Although several models can account for the observed defect production rates, these two different values for the threshold energy in the $〈100〉$ direction can best be interpreted as corresponding to different separation distances between the interstitial atom and its vacancy; for the closest distance, i.e., the lowest threshold energy, only one of the two possible configurations of the Frenkel pair (depending on the orientation of the split interstitial with respect to the pair axis) is stable at the irradiation temperature. A value of ${\ensuremath{\rho}}_{F}^{\mathrm{Ta}}=16\ifmmode\pm\else\textpm\fi{}3$ \ensuremath{\mu}\ensuremath{\Omega}cm per at.% is deduced for the Frenkel-pair resistivity in tantalum. An empirical interatomic potential of a Born-Mayer form is proposed in the range $1.4lrl2.7$ \AA{}. Finally, a tentative interpretation is given for the tantalum recovery spectrum between 7 and 20 K.