Glassy and ballistic dynamics in collision cascades in amorphous ${\mathrm{TiO}}_2$: Combined molecular dynamics and Monte Carlo based studies across energy scales

Kinetics in amorphous $\mathrm{Ti}{\mathrm{O}}_2$ driven by ion irradiation are discussed in the framework computer simulations. Thermal spike like regions along the path of incident ions are identified and their effects on the glassy system are described. Benefiting from the complementary approaches of purely ballistic TRIM (transport in matter) simulations and molecular dynamics simulations, a distinction between characteristic scales for short-range diffusive relocations ($\lesssim 4.5\text{Å}$) and long-range ballistic relocations is achieved. It is found that diffusion dynamics within thermally activated cascade zones sets in at the critical temperature $T_c$, identified as the critical temperature of the mode coupling theory, while the mean relocation limit for thermal diffusion in the glassy system is attributed to an overlap between the energy regime of purely ballistic and thermally activated relocation processes.

Figure 1

(a) Probability of finding an atom displaced by at least $2.25\text{Å}$ vs the provided kinetic energy. From extrapolating the tangents, the displacement energies, $E_d$ are estimated. The inset shows the radial distribution function of the amorphous simulation cell. (b) Spectrum of the recoil energies, $E_r$, due to ion irradiation. The energy scales for subsequent subcascade simulations employing Ti and O as primary knock-on atoms are highlighted.

Figure 2

(a) Temperature development in visually predetermined thermal spike like regions of highest energy density due to dissipated energy of the collision cascade in the microcanonical ensemble, discriminating the responses to Ti and O primary knock-on atoms. The fit corresponds to the time development of the heat kernel. $T_c\simeq 1492\left(32\right)\mathrm{K}$ denotes the critical temperature of the mode coupling theory. The temperature is represented by the Maxwell-Boltzmann velocity distribution of the thermally activated atoms. (b) Development of the atomic mean squared displacement in the predefined thermal spike volumes due to $10\mathrm{keV}$ Ti and O PKAs. The time-temperature relationship is established by the fit, shown in (a).

Figure 3

(a) Relocation distributions obtained from purely ballistic TRIM trajectories and an exemplary MD distribution for direct comparison. Long-range relocations in MD are only single events, resembling poor statistics. (b) Schematic representation for the decomposition of the entire relocation distribution into several subdistributions for thermally activated random walk propagation and ballistic propagation. (c) Mean relocation distributions after 100 completed O and Ti MD collision cascades induced by primary knock-on atoms at different energies. As the fit, Eq. (11), indicates, the distribution in the range fitted resembles a superposition of ballistic and thermally activated diffusion. The error bars represent the standard deviation of the average.

Figure 4

(a) Time development of the mean relocation parameter $R$ from Eq. (7) at different temperatures. The error bars correspond to the errors according to the least squares fits of the distributions. The dashed line indicates the parameter value thermal relocation limit obtained from the MD simulations. (b) Arrhenius plot of the diffusion coefficients. The critical temperature of the mode-coupling theory, obtained by fitting to Eq. (13), characterizes the transition region of low-temperature and high-temperature diffusive behavior.