Post-Irradiation Annealing of Bi Ion Tracks in Si₃N₄: In-Situ and Ex-Situ Transmission Electron Microscopy Study

Abstract

High-energy (710 MeV) Bi ion track morphology in polycrystalline silicon nitride was investigated during post-irradiation annealing. Using both in-situ and ex-situ transmission electron microscopy, we monitored the recovery of crystallinity within initially amorphous ion track regions. In-situ annealing involved heating samples from room temperature to 1000 °C in 50 °C increments, each held for 10 s. We observed a steady decrease in both the size and number of tracks, with only a small number of residual crystalline defects remaining at 1000 °C. Ex-situ annealing experiments were conducted at 400 °C, 700 °C, and 1000 °C for durations of 10, 20, and 30 min. Complete restoration of the crystalline lattice occurred after 30 min at 700 °C and 20 min at 1000 °C. Due to inherent differences in geometry, heat flow, and stress conditions between thin lamella and bulk specimens, in-situ and ex-situ results cannot be compared. Molecular dynamics simulations further revealed that track shrinkage begins in cells within picoseconds, supporting the notion that recrystallization can start on very short timescales. Overall, these findings demonstrate that thermal recrystallization of damage induced by swift heavy ion irradiation in polycrystalline Si₃N₄ is possible. This study provides a foundation for future research aimed at better understanding radiation damage recovery in this material.

1. Introduction

Silicon nitride (Si₃N₄) is an important material widely used in nuclear and radiation environments due to its excellent mechanical strength, thermal stability, and radiation resistance [1,2,3]. Understanding how Si₃N₄ recovers from SHI-induced damage is essential for predicting its long-term reliability and performance under harsh radiation conditions. The knowledge about the recrystallization pathways at elevated temperatures is very important for nuclear applications when materials operate under high temperature [4,5]. Insights into this recovery process reveal the mechanisms of recrystallization and defect migration at the nanoscale, advancing fundamental materials science and radiation physics, and support the development of more durable materials for nuclear reactors and other radiation-exposed applications [6,7,8].

Recent studies have revealed some specific features of SHI induced tracks in polycrystalline silicon nitride. In addition to electronic stopping power, their morphology is also dependent on Al impurity concentration used as sintering aid during synthesis [9,10]. Track region overlapping led to amorphization of the irradiated material [11,12,13,14] and tracks were detected in completely radiation amorphized targets [15]. During long term examination of Si₃N₄ it was found that ion tracks induced by 220 MeV Xe ions tend to recrystallize, leading to structural recovery (see Figure 1). These findings motivated a detailed study of the recrystallization behavior of corresponding radiation damages. Furthermore, molecular dynamic (MD) simulations predicted amorphous tracks in pure silicon nitride for several different interatomic potentials. It was found that SHIs induce a molten volume but no recrystallization occurs during cooling, unlike in non-amorphizable solids, e.g., Al₂O₃ and CeO₂ [16,17]. This implies that recovery of SHI tracks in Si₃N₄ occurs over longer timescales than those considered during MD simulation (~200 ps).

Most studies related to annealing induced structural transformations of ion track associated defects have focused on oxide materials (e.g., ref. [18,19,20,21,22]). To the best of our knowledge, no data have been published on thermal annealing-induced recovery of ion tracks in nitride ceramics. Recently, we published the first results on the annealing behavior of xenon-irradiated silicon nitride [23]. The present study is a continuation of that work, offering a more detailed analysis and an expanded experimental dataset. In this study, we focus on the annealing-induced recovery of amorphous, continuous tracks formed by Bi ion irradiation, in contrast to our earlier work [23], where the tracks were predominantly crystalline and discontinuous. Transmission electron microscopy (TEM) in both in-situ and ex-situ modes, as well as molecular dynamics simulations, were used to study annealing-induced structural evolution.

2. Materials and Methods

Polycrystalline β-Si₃N₄ ceramics (density: 3.21 g/cm³) doped with 3 at.% aluminum and with a thickness of 1 mm were purchased from MTI Corporation, Richmond, CA, USA (http://www.mtixtl.com). The samples were irradiated with 710 MeV bismuth ions at the U-400 cyclotron (Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Reactions, Dubna, Russia) to a fluence of 6 × 10¹¹ cm⁻², with an average ion flux of 3 × 10⁸ cm⁻²·s⁻¹. Beam scanning in both horizontal and vertical directions ensured uniform irradiation, with homogeneity better than 10% across the sample surface.

TEM lamellae were prepared parallel to the irradiated surface using FIB lift-out technique on an FEI Helios Nanolab 650 (Thermo Fisher Scientific, Hillsboro, OR, USA). To minimize FIB-induced damage, the final polishing step was performed using Ga ions at 500 eV.

Structural changes were examined using a ARM 200F transmission electron microscope (JEOL, Tokyo, Japan) operated at 200 kV at the Centre for High Resolution Transmission Electron Microscopy, Nelson Mandela University (Gqebertha, South Africa). Annealing was performed both in-situ and ex-situ. In-situ heating was carried out inside the TEM using a Wildfire In-situ Heating Holder (Dens Solutions, Delft, The Netherlands), while ex-situ annealing was done in a tube furnace under argon atmosphere. For the ex-situ annealing experiments, the plates were divided into smaller specimens of approximately 5 × 5 mm².

The in-situ annealing covered a temperature range from room temperature to 1000 °C, with 50 °C steps, for 10 s. Ex-situ annealing was conducted at three temperatures: 400 °C, 700 °C, and 1000 °C for 10, 20, and 30 min.

3. Results

3.1. TEM Examination

The lamellae were cut by FIB in a planar-view geometry from the near-surface region. The value of the electronic energy loss during irradiation with 710 MeV Bi ions at that depth was found to be approximately 36 keV/nm. It was calculated using the SRIM-2008 code in the Ion Distribution and Quick Calculation of damage mode [24]. This value is sufficient to induce local amorphization along the ion trajectory, resulting in the formation of cylindrical defects—ion tracks. The average radius of tracks was found to be 1.6 ± 0.2 nm. Details of measurements are given in in our previous work [25]. Bright-field (BF) and high-angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) images demonstrating these features are shown in Figure 2.

Annealing was carried out in situ in 50 °C increments, starting from room temperature. Each temperature step was reached within 10 s. At every stage, a bright-field TEM image was taken. As shown in Figure 3, the number of visible defects clearly decreases as the temperature increases. By the time the sample reaches 1000 °C, many of the ion tracks are barely visible. At this point, most tracks no longer appear as continuous amorphous regions but rather as discontinuous crystalline ones. However, they still produce contrast, indicating the presence of residual defects even at 1000 °C. This contrast likely arises from internal lattice strain or other crystallographic imperfections that remain after recrystallization—features that, while crystalline, still affect the electron scattering and appear in TEM images. This interpretation is further supported by Figure 4, which presents high-resolution (HR) TEM images. Before annealing, the tracks appear fully amorphous, as clearly demonstrated in Figure 4a. In Figure 4b, although the image quality is reduced due to in-situ imaging at elevated temperature, some contrast indicating lattice distortion is still visible, while no amorphous regions are detected. The reduced image quality can be attributed to the challenges of high-temperature in-situ TEM, such as thermal drift and instability, which limit the achievable resolution.

Based on these observations, the temperatures selected for ex situ annealing were 400 °C, 700 °C, and 1000 °C. At each temperature, annealing was performed for 10, 20, and 30 min to study the effect of duration. Figure 5 shows representative BF STEM images obtained after ex situ annealing. The crystallization process is observed at all annealing temperatures and durations; however, complete lattice recovery—with no visible crystalline defects—is achieved after 30 min at 700 °C and 20 min at 1000 °C. The uniform contrast in TEM images indicates that stress relaxation has occurred.

Ion tracks in dielectrics are known to be formed when electron energy losses exceed a certain threshold, causing a transient thermal spike that induces nanoscale melting [26,27,28]. The subsequent rapid cooling prevents recrystallization, resulting in the formation of amorphous tracks. Thermally activated recrystallization proceeds via atomic diffusion and is influenced both by temperature and the duration of annealing. It requires overcoming the activation energy barrier for atomic diffusion [29]. At temperatures above the material’s crystallization threshold, atoms gain sufficient mobility to transition from a metastable amorphous state back to a stable crystalline lattice [30]. The total extent of this transformation also depends on how long the material remains above the threshold temperature, as insufficient annealing time may result in only partial recrystallization.

In our experiments all ex-situ annealing modes led to recrystallization of the tracks, which is clearly seen in Figure 5: the previously amorphous regions now exhibit a crystalline lattice structure. We see a clear reduction in both the number and visibility of crystalline defects as the annealing time increases, indicating steady structural recovery. Complete recrystallization—where no defects are visible—was achieved after 20 min at 1000 °C and 30 min at 700 °C (see Figure 5).

All ex-situ annealing treatments led to recrystallization of the tracks, as evidenced by the appearance of a crystalline lattice in previously amorphous regions (Figure 5). The reduction in both the number and visibility of defects correlates with longer annealing times, with complete recrystallization observed after 20 min at 1000 °C and 30 min at 700 °C.

In-situ annealing at 1000 °C was conducted mainly to estimate recrystallization temperatures and observe initial defect evolution under controlled conditions (Figure 4b). Due to inherent differences such as sample thickness and preparation-induced stresses, we do not compare in-situ results directly with ex-situ bulk annealing. Instead, these methods complement each other in providing insights into the recrystallization process.

While this mechanism is well established in many dielectric materials [19,31,32], only limited data on defect recovery behavior in polycrystalline Si₃N₄ is available [23]. Our study provides preliminary insight into the material’s recrystallization process following ion irradiation, which is critical for evaluating its stability under radiation and heat exposure.

3.2. Molecular Dynamics

To model SHI effects in silicon nitride, we have applied a multiscale model combining the Monte-Carlo TREKIS code [33,34] and classical molecular dynamics. The approach implies scattering cross-sections of charged particles calculated using the dynamic structure factor—complex dielectric function formalism [35,36], accounting for a collective response of a target to excitation induced by SHI. The TREKIS describes: (a) SHI passage and ionization of medium; (b) subsequent movement of electrons, their elastic and inelastic interaction; (c) relaxation of holes in deep atomic shells; (d) spatial redistribution of valence holes and their interaction with a target. A detailed description of the model can be found in Ref. [33]. The reconstructed energy loss function of crystalline silicon nitride in the form of a sum of oscillator functions as well as calculated ion energy losses and the parameters of excited electrons/lattice were published in [25]. The radial distributions of the excess lattice energy around the SHI trajectory calculated with TREKIS were converted into the atomic velocities in cylindrical layers surrounding the ion path. The relaxation of the excited lattice was traced using molecular dynamics code LAMMPS [5].

The interatomic forces of silicon nitride were described by the three-body Vashishta potential with the parametrization from [37]. A supercell of β-Si₃N₄ having the size of 35 × 35 × 15 nm³ and the periodic boundary conditions in all directions was used in the MD simulations. To imitate the heat removal by the surrounding unperturbed material, the supercell boundaries (0.5 nm in thickness) in the X and Y directions were cooled by the Berendsen thermostat [38] to 300 K with the characteristic time of 2 ps. Track evolution was traced until 200–300 ps before the temperature dropped below 400 K. The results of simulations were visualized with OVITO 2.9.0 software [39].

Figure 6 shows the results of the simulation of 700 MeV Bi ion impact in silicon nitride within the used approach. The SHI trajectory in this case was parallel to the c-axis of the hexagonal unit cell. The SHI track in this case is the continuous amorphous cylinder of ~2.5 nm in diameter, similarly to the previous work [25]. The calculation of atomic displacements shown by color in Figure 6b reveals that all displaced atoms are observed only in the amorphous track region, which means no recrystallization occurs during the first 200 ps of SHI track kinetics. However, the recovery process in such complicated crystal structure material may happen at much longer times, probably even at microscopic scales.

To simulate the processes of annealing of the SHI track in silicon nitride, the simulation cell was kept at an elevated temperature for a prolonged time. The recovery of ion-induced damage during experimental investigation at temperatures < 1000 °C takes macroscopic times—tens of minutes. It is not possible to trace the atomic processes for such a long period using atomistic simulations. To stimulate the recrystallization, in the modeling the temperature was set to be 2000–2100 K (1727–1728 °C). In order to speed up the simulation, the MD cell was reduced from the original size of 35 × 35 × 15 nm³ to 13.5 × 13 × 15 nm³ preserving periodic boundary conditions. The dynamics of atoms was modelled using the NPT ensemble with an MD timestep of 2 fs.

Figure 7 demonstrates that the initially cylindrical amorphous ion track reduces its size with time at the elevated temperature. After 70–90 ns of annealing, the recovery process occurs not radially, forming an irregular shape of the damaged region. In the transversal direction, the ion track is not continuous at these times, in contrast to the initial state illustrated in Figure 5. The recovery of the crystalline state takes about 90 ns. By this time, we still observe some damage and point defects, but no amorphous phase was detected. The simulation results demonstrate the principal feasibility of the recovery of the SHI damage in silicon nitride and possible microscopic kinetics of the annealing, even though it was done under conditions different from the experimental investigation.

4. Conclusions

The manuscript presents a study on the thermally-induced recovery of amorphous, continuous ion tracks in silicon nitride, which, to our knowledge, has not been studied before. Given the importance of Si₃N₄ in nuclear applications, understanding its recovery behavior is essential for evaluating its long-term performance in radiation environments. Our results highlight the potential of thermal annealing as a way to reverse such damage and offer both experimental and modeling insights that can serve as a foundation for future research.

The in-situ annealing experiments covered a temperature range from room temperature up to 1000 °C, with 50 °C increments, each step lasting 10 s. Throughout this range, we observed a continuous reduction in both the size of the ion tracks and the number of defects. At the final step of 1000 °C, only a significantly reduced number of residual crystalline defects remained, as indicated by the weak contrast in the TEM images. These results confirm that recrystallization occurs under these conditions.

To further explore these effects, ex-situ annealing was performed at three selected temperatures—400 °C, 700 °C, and 1000 °C—with annealing durations of 10, 20, and 30 min. These specific conditions were chosen based on the in-situ observations, not for direct comparison, but rather to provide reference points, because of the limited literature available on the thermal recovery of SHI-induced damage in silicon nitride. Complete recovery of the crystalline lattice was achieved after 30 min at 700 °C and 20 min at 1000 °C.

Molecular dynamics simulations show that, within the MD cell, ion tracks begin to shrink on picosecond timescales, indicating the onset of recrystallization. While no quantitative comparison with experimental timescales was possible to make, the simulations qualitatively confirm that recrystallization is thermodynamically feasible under appropriate conditions and may initiate at relatively short annealing durations, potentially leading to complete structural recovery over time.

At this stage, the findings represent a set of modeling observations rather than a complete mechanistic model. More studies are required to identify the specific conditions and mechanisms of defect recovery in this system.