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Radiation Effects in Nuclear Ceramics
Due to outstanding physicochemical properties, ceramics are key engineering materials in many industrial domains. The evaluation of the damage created in ceramics employed in radiative media is a challenging problem for electronic, space, and nuclear industries. In this latter field, ceramics can be used as immobilization forms for radioactive wastes, inert fuel matrices for actinide transmutation, cladding materials for gas-cooled fission reactors, and structural components for fusion reactors. Information on the radiation stability of nuclear materials may be obtained by simulating the different types of interactions involved during the slowing down of energetic particles with ion beams delivered by various types of accelerators. This paper presents a review of the radiation effects occurring in nuclear ceramics, with an emphasis on recent results concerning the damage accumulation processes. Energetic ions in the KeV-GeV range are used to explore the nuclear collision (at low energy) and electronic excitation (at high energy) regimes. The recovery by electronic excitation of the damage created by ballistic collisions (SHIBIEC process) is also addressed.
Ceramics are key engineering materials in many domains of human activity due to outstanding physicochemical properties, such as high strength, low-thermal expansion, chemical stability, and good behavior under irradiation. Therefore, these materials are often employed in hostile media where efficient use of energy is a prime need, for example, extreme temperatures, corrosive surroundings, and radiative environment. Industrial applications concern electronic, space, and nuclear fields. For instance, ceramics are nowadays widely used for surface coating and electronic packaging, and they are envisioned in a near future as immobilization forms for radioactive wastes, inert fuel matrices for actinide transmutation, cladding materials for gas-cooled fission reactors, and structural components for fusion reactors. In most of these applications, there is an urgent need of data for a fundamental understanding of the processes of radiation damage.
Information on the radiation stability of nuclear materials may be gained by simulating the different types of interactions (nuclear and electronic) involved during the slowing down of energetic particles with ion beams delivered by various types of low-, medium-, and high-energy accelerators. A rather broad panoply of advanced techniques (e.g., Rutherford backscattering spectrometry in channeling conditions (RBS/C), X-ray diffraction (XRD), transmission electron microscopy (TEM), and Raman spectroscopy), which sense the investigated materials at various spatial scales and with different sensitivities, can be implemented to (i) monitor the damage buildup, (ii) quantify the strain/stress level as a function of ion fluence, (iii) characterize radiation defects, (iv) determine the formation of new phases, (v) specify the parameters which trigger the (micro)structural changes, and (vi) understand the mechanisms involved in the damage formation. Results may then feed databases, be compared to computational works (using for instance molecular dynamics tools), and finally help the development of theoretical models or at least of phenomenological descriptions.
The topic that is concerned here is extremely broad. A huge number of papers were published in the last three decades on the damage production in nuclear materials, and the state of knowledge was regularly upgraded in thorough reviews (see for instance, [1–10]). To deal the subject in a rather short article, we focus our presentation on a few remarkable examples concerning the ion-beam modifications of selected nuclear ceramics, namely, zirconia, urania, spinels, pyrochlores, and silicon carbide, with an emphasis on the damage buildup, the quantification of the strain/stress level, and the determination of the nature of radiation defects. We report results obtained by performing ion irradiation in a broad energy range (from KeV to GeV) in order to explore both nuclear collision (slow ions) and electronic excitation (swift ions) regimes, as well as synergies between the two types of processes.
Section 2 is devoted to the presentation of general considerations about the damage accumulation processes in ion-irradiated materials and to the description of models developed to interpret experimental results. The effects of elastic collisions generated by slow ions and electronic excitations induced by swift ions are addressed in Sections 3 and 4. The last section presents a new phenomenon, due to a synergetic effect between nuclear and electronic interactions, which consists in the recrystallization by electronic excitation of the defective microstructure produced upon ballistic collisions.
2. Models of Damage Accumulation
The topology of the damage resulting from irradiation of a crystal with low- or high-energy ions is schematically represented in Figure 1. For slow ions (i.e., below ~10 KeV/u), the basic process of ion energy loss is the direct transfer of energy to the atoms of the solid by elastic collisions between the projectile and the target nuclei (). Along the ion path, a large fraction of primary knock-on atoms set in motion by incident ions gain a sufficient amount of energy to subsequently displace other target atoms through several secondary and higher-order collisions. These ballistic processes lead to the creation of damage cascades  which are represented by the ovoid objects in Figure 1(a). For swift ions (i.e., above ~1 MeV/u), the electronic energy deposition () induces the formation of electrostatically unstable cylinders of ionized atoms, called latent track , which are represented by the grey objects in Figure 1(b). The resulting atomic rearrangements may be interpreted in the framework of thermal spike [13–16] or Coulomb explosion [17–19] mechanisms.
The first description of the damage buildup in ion-irradiated crystals was provided by Gibbons  which assumed that the radiation-induced damage accumulation (quantified by the parameter ) is due to the overlapping of a number of ion impacts in a given volume of a target, according to the equation: where is the value of at saturation ( in the case where the final state is amorphous) and is the disordering cross-section. More sophisticated models (see ) were then elaborated to account for the experimentally determined damage buildups with more or less complicated shapes. These models are based on a combination of direct-impact and damage-accumulation descriptions with the possibility of considering additional processes such as cascade-overlap, interface-controlled, and defect-stimulated mechanisms.
Another model, referred to as MSDA for multistep damage accumulation , which has been recently improved , was developed to circumvent a number of drawbacks revealed in previous descriptions. This model is based on the hypothesis that the radiation damage results from a series of successive atomic reorganizations (steps) which are triggered by microscopic or macroscopic solicitations, so that the damage accumulation follows the equation: where is the number of steps required for the achievement of the total process, is the level of damage at saturation, is the cross-section for damage formation, and is the threshold irradiation fluence, for the th step. is a function which transforms negative values into 0 and leaves positive values unchanged.
Implementation of this model to the analysis of damage buildups obtained for ion-irradiated test-case ceramics is provided in the following two sections.
3. Effects of Elastic Collisions (Slow Ions)
Defect cascades created by low-energy ion irradiation are responsible for a large variety of (micro)structural modifications (topological or chemical disorder, swelling, phase transformations, polygonization, amorphization, etc.) which obviously depend on the target material but also on several key parameters such as the irradiation temperature, the ion fluence, flux, and energy.
The RBS/C technique is particularly well suited for the determination of damage buildups in ion-irradiated crystalline solids. An example of RBS/C spectra is provided in Figure 2(a) in the case of cubic zirconia crystals irradiated at RT with MeV heavy ions at various fluences. The spectrum registered in a random direction displays a plateau (below 2600 keV) which corresponds to the backscattering of analyzing particles from the Zr atoms of the sample, and a peak (close to 1000 keV) due to the backscattering of analyzing particles from the O atoms. It is worth noting that the O signal is enhanced by the use of the 16O(4He,4He)16O resonance at a 3.04-MeV He energy. The spectrum registered in the -axial direction on a virgin crystal shows the same features with a much lower backscattering yield for both the Zr and O signals due to the channeling effect. Spectra recorded in the -axial direction on irradiated crystals exhibit an increase with increasing ion fluence (at least up to cm−2) of both the Zr and O yields due to the creation of radiation damage. A bump is clearly observed around 2100 keV, indicating that the damage is mostly located at a depth corresponding to this energy. At cm−2, the Zr maximum yield (measured at 2100 keV) surprisingly decreases. RBS/C spectra displayed in Figure 2(a) were fitted (solid lines) by using Monte-Carlo simulations performed with the McChasy computer code [21, 22]. Calculations rely on the basic assumption that Zr and O atoms are randomly displaced from original lattice sites during irradiation. Figure 2(b) shows the variation of the fraction of displaced atoms () as a function of the depth into the sample extracted from McChasy simulations. These data correspond to the Zr sublattice, since the amount of damage created in the O sublattice may only be measured at the depth where the resonance occurs [25, 26]. For the various fluences used exhibits a peak around 500 nm, with an amplitude that increases with increasing ion fluence up to cm−2. Above this fluence (for instance at cm−2), a clear decrease of is observed.
Figure 3(a) displays θ-2θ spectra recorded in the vicinity of the (400) Bragg reflection for cubic zirconia crystals irradiated at RT with MeV heavy ions at various fluences. Note that the (logarithmic) intensity distributions are also plotted as a function of the elastic strain (ε) in the direction normal to the surface of crystals. All spectra exhibit an intense narrow peak on the high-angle side, corresponding to the unirradiated part of samples (since the probed thickness is higher than that of the irradiated layer), which may be taken as an internal gauge to quantify the irradiation-induced normal strain. For irradiated samples, an additional signal appears on the low-angle side (i.e., in the region of higher lattice parameter), which clearly indicates a lattice dilatation along the direction normal to the sample surface. This positive strain is induced by defects with a positive relaxation volume, most likely self-interstitial atoms. The fringe-like patterns depicted on the low-angle side indicate the presence of a nonhomogeneous strain depth distribution that can be retrieved using dedicated computer codes to fit the XRD curves . However, it must be pointed out that the position of the last peak on the low-angle side of the diffraction spectra provides a good approximation of the maximum normal strain magnitude exhibited by the irradiated layer. Figures 3(b) and 3(c) show the distribution in the reciprocal space of the X-ray scattered intensity in the vicinity of the (400) Bragg reflection for samples irradiated at 1015 cm−2 (b) and cm−2 (c). The intensity is in logarithmic scale and the positions are located either by the in-plane () and out-of-plane () components of the scattering vector (2sinθ/λ), or by the corresponding normalized deviations from the reciprocal lattice vector. On these reciprocal space maps (RSMs), a strong signal (square mesh features of the maps) is observed at the bulk theoretical coordinates. It corresponds to the unirradiated part of crystals. From this area of high intensity, the diffracted intensity spreads along the direction normal to the sample surface () in the region of positive strain (Figure 3(b)), or broadens in the direction (Figure 3(c)). The spreading along , which is particularly strong for the crystal irradiated at 1015 cm−2, indicates (as observed for the θ-2θ scans) the presence of a dilatation gradient along this direction. For this crystal, the intensity is confined in a sharp region, which means that the diffuse scattering due to structural defects in the irradiated layer remains very weak. For the crystal irradiated at cm−2, a strong broadening of the intensity is observed in addition to a large strain relief.
Typical damage (determined by RBS/C) and strain (determined by XRD) buildups are represented in Figure 4 in the case of cubic zirconia irradiated at RT with MeV heavy ions . Both sets of data may be accounted for by using the MSDA model (lines in the figure) with a value of for RBS/C and for XRD (where the elastic strain cannot be evaluated in step 3) in (2). TEM micrographs were recorded at typical fluences of the damage buildup (see insets of Figure 4). They indicate that (i) small defect clusters, which lead to a strong increase of the elastic strain and have a weak influence on , are created during the first step (up to ~1015 cm−2); (ii) the second step is due to the formation of perfect dislocation loops and of a network of tangled dislocations, inducing a relaxation of the elastic strain and a sharp increase of (from ~1015 cm−2 up to ~ cm−2); (iii) long dislocations, which induce a reorganization of the crystal, leading to a decrease of , are exhibited in step 3 (above ~ cm−2). A similar behavior (except step 3) was observed in cubic zirconia irradiated with a large variety of slow ions , leading to the conclusion that the number of displacements per atom of the target (dpa) is the key parameter for the evolution of the damage buildup in the nuclear collision regime.
Figure 5 compares the damage buildups (expressed in dpa), as determined by RBS/C, obtained for nonamorphizable (spinel, zirconia, and urania; Figure 5(a)) and amorphizable (titanate pyrochlore and silicon carbide; Figure 5(b)) ceramics irradiated with slow ions [30–35]. It is worth mentioning that the shape of the damage kinetics may slightly differ depending on the irradiation conditions. Nevertheless, the damage accumulation process always occurs in several damage steps, so that RBS/C data may be accounted for by using the MSDA model (lines in the figure) with in (2) for all materials. It must be noted that, except when the implanted impurities play a role in the damage process (e.g., noble gases or Cs ), the existence of a third step was only observed in cubic zirconia (ZrO2) and magnesia (not shown on the figure for the sake of clarity). Nevertheless, some data at very high fluence may be missing for the observation of this third stage (for instance for MgAl2O4 and UO2). The insets show TEM diffraction patterns recorded at the end of irradiation, which indicate that the samples either remain crystalline (Figure 5(a)) or are amorphized (Figure 5(b)) upon slow ion irradiation. It is worthwhile to mention that the value of at the end of the second step of the damage accumulation cannot be taken as a reliable evaluation of the damage level in the crystal in the case of nonamorphizable materials (Figure 5(a)), since this value depends on the geometry of radiation defects via dechanneling effects inherent to the RBS/C technique. Conversely, the dose (Φ2) at which step 2 starts, leading either to the formation of dislocation loops (in zirconia or urania) or to amorphization (in titanate pyrochlore or silicon carbide), is a parameter that can be used as an indicator of the stability of materials upon ion irradiation: the highest Φ2, the greatest resistance to disordering or amorphization. It is worth mentioning that, for the materials selected in this study, the hierarchy is maintained irrespective of the irradiation conditions.
4. Effects of Electronic Excitation (Swift Ions)
The structure of latent tracks created in the wake of swift ions is dependent on both the ion mass (through the energy density deposited in electronic excitations) and the investigated material (insulators are generally more sensitive to than semiconductors or metals).
Example of RBS/C spectra obtained for cubic zirconia crystals irradiated at RT with GeV heavy ions at various fluences is provided in Figure 6(a). Spectra registered in random and -axial directions on a virgin crystal are very similar to those shown in Figure 2(a). However, in contrast to Figure 2(a), no bump is observed around 2100 keV for spectra recorded in the -axial direction on irradiated crystals. Irradiation leads to an increase with increasing ion fluence of the Zr yield in the whole analyzed thickness, with the presence of additional disorder in the near-surface region of crystals, that is, around 2600 keV. RBS/C spectra of Figure 6(a) cannot be fitted with a simple decomposition method since they do not reveal the presence of damage peaks (as in Figure 2(a)), but rather exhibit progressive dechanneling. In such cases, the use of Monte-Carlo simulations (solid lines) performed with the McChasy computer code [21, 22] is mandatory to obtain the damage depth distributions. Here again, calculations rely on the assumption that Zr and O atoms are randomly displaced from original lattice sites during irradiation. Figure 6(b) shows the variation of the fraction of displaced atoms (in the Zr sublattice) as a function of the depth into the sample extracted from Monte-Carlo simulations. It is shown that the amount of radiation damage is almost constant with depth, except for a thin 100 nm layer below the surface where a large increase of is observed. The steady value of increases with increasing ion fluence, but does not exceed 0.4-0.5 at the final fluence of 1013 cm−2.
Typical damage (determined by RBS/C) and strain (determined by XRD) buildups are represented in Figure 7 for cubic zirconia irradiated with GeV heavy ions . Both sets of data may be interpreted in the framework of the MSDA model (lines in the figure) with in (2). TEM micrographs, recorded at typical fluences (see the insets of Figure 7), indicate that (i) tracks are created at low fluences (below ~1012 cm−2); (ii) dislocation loops are formed at higher fluences (around cm−2) due to the overlapping of individual ion tracks; (iii) the final microstructure at very high fluences (1013 cm−2) is the formation of a dense network of dislocations. It is worth noting that a threshold for track formation depending on the material and on the ion velocity (around 20–30 KeV/nm in cubic zirconia) was found in experiments using swift heavy ions of different masses and energies .
Figure 8 indicates that a single-step damage accumulation process ( in (2)) is also observed for other nonamorphizable (spinel and urania; Figure 8(a)) and amorphizable (titanate pyrochlore; Figure 8(b)) ceramics irradiated with swift heavy ions [37–42]. An exception is provided by silicon carbide which shows a very different response to ballistic collisions as compared to electronic excitations, since it is obviously amorphizable by the former process (see Figure 5(b)) and very weakly damaged by the latter one (see Figure 8(b)) . This peculiar behavior is discussed in the next section.
Figure 9 provides the demonstration that amorphization of titanate pyrochlore occurs via the formation of amorphous tracks observed on cross-sectional (Figure 9(a)) or plane-view (Figure 9(b)) TEM micrographs. It is worth mentioning that the mean diameter of the ion tracks exhibited in Figure 9 (d~6-7 nm) is in agreement with the diameter calculated from the damage cross-section derived from the application of the MSDA model to RBS/C data ( nm) . The fact that the thickness of the amorphized layer is well correlated to the profile is evidenced by Raman results shown in Figure 10 . The vibrational mode (at 770 cm−1) related to the amorphous phase is clearly seen from the surface of the sample up to a depth of ~20 μm (Figure 10(a)), in agreement with the depth distribution obtained with the SRIM code (Figure 10(b)). In this compound, irradiations with swift ions of different masses and energies also revealed the existence of a threshold for amorphous track formation of the order of 10 KeV/nm .
5. Combined Effect of Nuclear and Electronic Processes (SHIBIEC)
In previous sections it was shown that nuclear collisions induced by slow heavy ions can lead to the amorphization of irradiated layers in crystals for which electronic excitation is inefficient to produce damage (for instance SiC). In these materials, different approaches can be implemented in order to maintain or restore the crystalline structure. To prevent amorphization, the irradiation temperature can be increased above a given threshold (which is of the order of 250°C in SiC) [46–52]. Annealing of irradiation-induced amorphized samples at elevated temperatures (higher than 1000°C in SiC) [48, 50, 53, 54] induces recrystallization. Another original route lies in the use of ion-beam-induced epitaxial recrystallisation effect [55–57]. This latter methodology, generally referred to as IBIEC, consists in bombarding samples with ion species having an energy such that the slowing down is still dominated by nuclear collisions, but with an ion projected range quite deeper than the thickness of the amorphous layer. An interesting feature of IBIEC in SiC is that it occurs around 300°C [58–60], which is a quite lower temperature than that required for damage recovery by conventional thermal annealing. Recently, more energetic ion beams (GeV range) were used to recrystallize amorphous layers via the so-called swift-heavy-ion-beam-induced expitaxial crystallization (SHIBIEC) process [43, 61]. SHIBIEC does not imply the same mechanisms as those prevailing during IBIEC at low energy, but seems to be more efficient in that sense that the temperature at which recrystallization occurs is lowered as compared to that required for IBIEC.
A SHIBIEC experiment generally involves two sequences: (i) preirradiation with slow ions leading to the progressive formation of a shallow amorphous layer; (ii) postirradiation with swift ions inducing epitaxial recrystallization by electronic energy loss of the layer which was previously amorphized by nuclear collisions. Figure 11 shows an example of SHIBIEC monitored by RBS/C in the case of silicon carbide . Irradiation of SiC crystals with slow Fe ions leads to the formation of an amorphous layer (the aligned signal reaches the random level: Figure 11(a)) in a 20–40 nm depth range (Figure 11(b)). Subsequent irradiation of the same sample with swift Pb ions induces a decrease of the aligned yield with increasing ion fluence (Figure 11(a)), which indicates a partial recrystallization of the amorphized layer (see also the decrease of in Figure 11(b)). Results are summarized in Figure 12 that shows (i) the amorphization buildup due to slow Fe ion irradiation exhibiting a two-step process , and (ii) the SHIBIEC effect at different Fe fluences, which leads to a clear decrease of . It is worth noting that an increase of the temperature at which swift heavy ion post-irradiation is performed leads to an enhancement of the SHIBIEC process.
Energetic ions in the KeV-GeV range can be used to simulate the radiations produced in nuclear reactors or in storage forms. From a fundamental viewpoint, ion irradiations allow exploring separately the nuclear collision (at low energy) and electronic excitation (at high energy) regimes. The damage accumulation processes are generally well interpreted in the framework of the multistep damage accumulation (MSDA) model, with a number of steps strongly depending on whether nuclear collisions or electronic excitations are the dominant processes.
For slow ion irradiation, the damage depth distributions are consistent with the nuclear energy deposition. The defect cascades created by nuclear collisions lead to several steps of disorder accumulation, due to the development and relaxation of radiation-induced (mechanical) stresses. A sharp increase of the damage is most often exhibited in the second step, associated to the creation of either dislocations for nonamorphizable materials, or amorphous layers in the case of amorphizable materials. The dose (in dpa) at which this second step occurs may be used as an indicator of the radiation resistance of materials.
For swift ion irradiation, the damage depth distributions are consistent with the electronic energy loss. Tracks created by electronic excitation cause a direct transformation of the melt volume into a new structure via a single-step process. The overlapping of tracks at high fluences leads to the formation of either dislocations or amorphous layers. Saturation of the damage is observed at fluences at least one order of magnitude lower than those required to obtain the same amount of disorder in the case of slow ion irradiation. Results also show the existence of Se thresholds for track formation, which depend on the materials properties.
Amorphous layers formed by slow ion irradiation can be recrystallized by swift ion irradiation (SHIBIEC). This effect differs from the well-known IBIEC process by the fact that it does not require the assistance of an external heating source. It is related to the energy deposited by the incoming ions into the target electrons and can therefore be interpreted in the framework of thermal spike models. Besides the fact that the SHIBIEC process is important from a fundamental viewpoint, it presents a crucial interest for industrial applications, particularly concerning the operating cycle of nuclear reactors of the next generations. Actually, amorphization due to irradiations with neutrons or heavy ions arising from the alpha-decay of actinides can be detrimental to the physical integrity of a material. However, a balance between amorphization and damage recovery by SHIBIEC may well occur in order to preserve the crystallinity of irradiated nuclear materials, since swift ions (i.e., fission fragments) are also generated in nuclear fuels.
The investigation of the synergy between radiation effects induced simultaneously by slow and swift ions offers interesting prospects in this research field. Such a daunting challenge is reachable by the development of dedicated new facilities able to deliver several ion beams in a unique irradiation chamber, such as the JANNUS platform recently operating in the Orsay-Saclay area.
This work was partially financed by the GNR MATINEX. The experimental program also benefited from grants provided by the French-Polish cooperation Program no. 01–104.
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