Figure 1

Variation of $C\left(r\right)r^{\beta }$ as a function of $x=\frac{r}{R_{\text{max}}\left(E_0\right)}$ extracted from our MC simulations performed for various self-ion irradiations of iron at different $E_0$ values (triangles, 5 keV; squares, 10 keV; stars, 50 keV; crosses, 100 keV). All theses points fall on the same universal curve as expected from the fractal feature of a displacement cascade. These curve does not depend on the nature of the material as expected from the fractal geometry framework.Reuse & Permissions

Figure 2

Evolution of $⟨R_{\text{max}}\left(E_0\right)⟩$ versus $L\left(E_0\right)$ extracted from our MC simulations performed at various energies (1, 5, 10, 50, 100, and 500 keV) for different self irradiations (circles, boron; squares, neon; diamond, calcium; up triangles, zinc; left triangles, zirconium; down triangles, indium; right triangles, neodym; plus symbols, lutecium; crosses, gold; stars, uranium). Data can be fitted by the following linear relation $⟨R_{\text{max}}\left(E_0\right)⟩=25L\left(E_0\right)$ (full line) with a good agreement (the linear regression coefficient is equal to 0.999), assessing the proportionality between the characteristic length $L\left(E_0\right)$ and the averaged caliper diameter $⟨R_{\text{max}}\left(E_0\right)⟩$.Reuse & Permissions

Figure 3

(Color online) Evolution of the subcascades threshold energy $E_c$ surface as a function of the atomic number $Z$ and the displacement threshold energy $E_d$. On the slice $E_d=25\text{eV}$, the maximum (open up triangles) and minimum (open squares) values of $E_c$ extracted from experiments [23] are plotted. These experimental points are two orders of magnitude higher than the cascade threshold energy $E_c$ derived from Cheng’s model (full line) but they are in fair agreement with our calculation.Reuse & Permissions

Figure 4

Evolution of the mean number of subcascades, $n^{sc}\left(E_0,E_c\right)$, extracted from our MC simulations as a function of $\frac{E_0}{E_c}$ for three different self-ion irradiations (dots, carbon; triangles, iron; stars, gold). In these calculations, $E_c$ derived from Eq. (4) were equal to 0.8, 8.6, and 51 keV, respectively. Comparison between this mean number of subcascades extracted from MC simulations and calculated from the Lindhard equation (full lines) are in fair agreement.Reuse & Permissions