Range Measurements in Oriented Tungsten Single Crystals (0.1-1.0 MeV). I. Electronic and Nuclear Stopping Powers

Range distributions of ${\mathrm{Na}}^{24}$, ${\mathrm{P}}^{32}$, ${\mathrm{K}}^{42}$, ${\mathrm{Cr}}^{51}$, ${\mathrm{Cu}}^{64}$, ${\mathrm{Br}}^{82}$, ${\mathrm{Kr}}^{85}$, ${\mathrm{Rb}}^{86}$, ${\mathrm{Sb}}^{122}$, ${\mathrm{Xe}}^{125}$, ${\mathrm{Xe}}^{133}$, ${\mathrm{W}}^{187}$, and ${\mathrm{Rn}}^{222}$ ions in the energy region 0.1-1.0 MeV have been measured in oriented tungsten single crystals by means of the electrochemical peeling technique. Wide-angle scattering of protons has, in some cases, been used to align the crystals to within ±0.1°. The range distributions consist of two peaks—a broad one at approximately the depth predicted for an amorphous target, and a sharp one at a much larger depth. The latter, caused by channeling, falls off very sharply on the more penetrating side. This well-defined paximum range has approximately an $E^{\frac{1}{2}}$ dependence, characteristic of electronic stopping. From range-energy relations, electronic-stopping cross sections are derived at a constant velocity of 1.5×${10}^8$ cm/sec. The electronic stopping is roughly $\frac{1}{3}$ of that predicted for amorphous tungsten, but exhibits a strongly oscillating dependence on $Z_1$. These $Z_1$ oscillations are much larger than those reported previously in amorphous foils. Alto, the range dispersion between the $〈100〉$ and $〈110〉$ directions exhibits an oscillating $Z_1$ dependence. For perfectly channeled Xe ions along the $〈100〉$ directions, electronic stopping is shown to dominate down to a few keV. The contributions from nuclear and electronic stopping become equal at about 4 keV, whereas the corresponding transition energy in amorphous tungsten would be ∼2.5 MeV. The nuclear stopping contribution can be fitted theoretically by means of the momentum approximation down to ∼0.5 keV. It is shown that, under certain conditions, range measurements in monocrystals provide information about amorphous ranges that is otherwise difficult to obtain. Good agreement between experiments and theoretical predictions is obtained. The present experiments also provide some information on the highly penetrating tail (supertail), earlier reported in tungsten. For comparison, a few range distributions have been measured in aluminum single crystals. The observed behavior is similar to that in tungsten, but the channeling is much less pronounced.