Simulations and discussion

The physical origin for the increase in track radius can be understood within the limits of the inelastic thermal spike model (iTS) [TAD+_{12]. The model explains track formation}

through a melting-process of atoms along the ion trajectory. Hence, the energy required to form a track mainly depends on the difference between melting energyEm and the internal

energy Ei of the atoms. The internal energy changes with irradiation temperature T0,

consequently irradiation at elevated temperatures reduces the amount of energy required for the melting process as shown schematically in Figure 6.3. If the energy difference is reduced, this increases the volume where the deposited ion energy exceeds the melting temperature of the host material. As a consequence, an increase occurs for the radial distance around the ion trajectory where the energy loss is high enough for ion track formation to occur,

92CHAPTER 6. TRACK FORMATION UNDER TEMPERATURE AND PRESSURE

Figure 6.2: SAXS scattering intensities for (a) ion tracks || c (a) and (b) ? c in quartz

for different irradiation temperatures (open circles). A hard cylinder model was used to fit the results (solid lines). SAXS patterns are offset for clarity. Radius obtained from the SAXS patterns for (c) tracks || c and (d)?c for high-T (filled squares). The corresponding

reference samples underwent the same heat cycle (open circles). A linear regression fit was applied between radius and temperature (lines).

6.1. TEMPERATURE-DEPENDENCE OF ION TRACK FORMATION 93

Figure 6.3: Schematic explanation for the larger track radii at ion irradiation high tem- peratures (high-T) in comparison to room-temperature (RT).

yielding larger track radii. For irradiation at sub-zero degree temperatures, the same physical explanation can be applied to the observed reduction in track size. The magnitude of the effect is lower due to the reduced heat capacity of solids at cryogenic temperatures. Calculations using the iTS model by Marcel Toulemonde from the CIMAP Laboratory in Caen, show an increase of 0.07 nm / 100 °C for the radius of tracks in quartz [SLP+_13].

This provides an excellent match to the experimental values of 0.06 ± 0.02 nm / 100 °C

for tracks || c and 0.08±0.02 nm / 100 °C for tracks?c.

Figure 6.4 shows the results of the MD simulations for tracks in quartz, performed by the group of Kai Nordlund at the University of Helsinki in Finland [SLP+_{13]. The values}

display a linear trend of the track radius with a relative increase of 0.10 nm / 100 °C, which is also consistent with the experimental results. Despite the good agreement between MD and SAXS on the relative effects of temperature during irradiation, the absolute track radii differ by 0.7 nm. Such an offset is commonly observed in results from the atomic potential used for SiO2, which may not fully describe this complex phenomenon. It is potentially

affected by the melting point, thermal expansion and elastic properties of the potential, at least. Also the uncertainties in the energy deposition might affect the track size as a function of temperature.

Overall, the MD simulations as well as iTS calculations for ion track formation in quartz confirm the experimental observations by showing a larger track cross-section when they are formed at elevated temperatures. In fact, the calculated increase in radius is of comparable magnitude between the experimental results and those from iTS-calculations and MD simulations.

94CHAPTER 6. TRACK FORMATION UNDER TEMPERATURE AND PRESSURE

Figure 6.4: MD simulations (open diamonds) for ion tracks in quartz at different temper- atures. A linear regression fit was applied between radius and temperature (red line).

In other materials, such as crystals exhibiting a strong ionic binding character like LiF [SBTT01], a linear increase in damage cross-section was also observed (0.04 nm / 100 °C). This is of particular interest, as ion tracks in LiF are not amorphous, but rather consist of discontinuous arrays of point-defect clusters [TTS+_{00]. This shows that the}

increase in damage radius with elevated temperature during formation is not only limited to amorphisable materials such as apatite and quartz, but of a more general character for damage created by swift heavy-ion irradiation. In contrast to the present observation of a constant density change, the density range in LiF decreases with increasing temperature, indicating that while the damage cross-section increases, the damage morphology (possibly point-defect density) decreases. This might be a result of competing processes of dynamic annealing and defect production. For quartz, no measurements of the radius as a function of irradiation temperature are available for comparison [Kla04].

For ion irradiation with low-energy ions in the keV to low MeV range (nuclear range of stopping power), elevated temperatures generally lead to lower defect concentrations, displaying the exact opposite of the findings of this work for high MeV to GeV [DBL99, JZW04]. This is attributed to the thermally induced dynamic defect recovery, so-called dynamic annealing. The present case shows that for the regime of electronic stopping power this negative correlation between temperature and damage sizes is not visible. However, it is possible that if the irradiation was to be conducted at higher temperatures, the effects of dynamic annealing would be visible and the obtained tracks would again be smaller in size than at RT.

In Subsect. 7.2.1 the thermal stability of these tracks upon expose to high temperatures is compared with tracks created under ambient conditions.