Radiation damage in nanostructured materials

Abstract

Materials subjected to high dose irradiation by energetic particles often experience severe damage in the form of drastic increase of defect density, and significant degradation of their mechanical and physical properties. Extensive studies on radiation effects in materials in the past few decades show that, although nearly no materials are immune to radiation damage, the approaches of deliberate introduction of certain types of defects in materials before radiation are effective in mitigating radiation damage. Nanostructured materials with abundant internal defects have been extensively investigated for various applications. The field of radiation damage in nanostructured materials is an exciting and rapidly evolving arena, enriched with challenges and opportunities. In this review article, we summarize and analyze the current understandings on the influence of various types of internal defect sinks on reduction of radiation damage in primarily nanostructured metallic materials, and partially on nanoceramic materials. We also point out open questions and future directions that may significantly improve our fundamental understandings on radiation damage in nanomaterials. The integration of extensive research effort, resources and expertise in various fields may eventually lead to the design of advanced nanomaterials with unprecedented radiation tolerance.

Introduction

Nuclear energy accounts for more than 13% of electricity generated worldwide [1]. The design of advanced (next generation) nuclear reactors calls for materials that can survive an exceptionally high radiation dose of 400–600 dpa (displacements-per-atom), equivalent to the service lifetime of more than 80 years in advanced nuclear reactors. However, most materials adopted in the current nuclear reactors have not been tested over a dose of 200 dpa. Fundamental studies show that radiation by high-energy particles, including electrons, protons, neutrons, light and heavy ions, can introduce significant microstructural damage in a variety of metallic materials. Extensive research studies in the past few decades show that although the details of microstructural damage vary drastically for various materials, the nature of the damage in crystalline materials is mostly associated with the formation, distribution and interaction of point defects (vacancies and interstitials), and their clusters, such as Frenkel pairs (vacancy-interstitial pairs), vacancy clusters, interstitial loops, radiation induced dislocation segments and networks, inert gas bubbles and voids [1], [2], [3]. To a large extent, there are nearly no existing materials that are immune to radiation damage. Understanding the mechanisms of radiation damage clearly has a significant impact on the design of radiation tolerant materials for advanced nuclear energy applications.

Radiation involves extensive ion-solid interactions, which may have beneficial or deleterious impacts on the properties of materials [1], [4]. For materials used in nuclear reactors, radiation damage can pose a serious challenge to the structural stability and reliability of these materials over a long period of time, which is relevant to the safe operation of nuclear reactors [5]. In this review article, we summarize recent progress in the investigation of radiation damage in nanostructured materials, focusing on metallic materials and/or metal-ceramic compounds. Radiation damage in nanostructured ferritic alloys and oxide dispersion strengthened (ODS) steels is another important subject that has been intensely studied but will not be covered here as there are several recent reviews and numerous highlights on this subject [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16].

Radiation has also been used to achieve unique properties in various fields. For instance, ion implantation has been routinely adopted by semiconductor industry to tune electrical conductivity or to fabricate semiconductor devices [17], [18], [19], [20], [21], [22]. Ion irradiation has also been applied to introduce various nanofeatures that may drastically change the chemical and physical properties via surface engineering [23], [24]. The subject on nanopatterning using ion irradiation technique is not the focus of the current review and is not included for further discussions.

The architecture of the current review article is organized as follows. Section 1 briefly summarizes some basics on the nature and formation of defects and their interactions. Introducing these concepts is beneficial to understand radiation damage related to microstructure evolution at a fundamental level. The significance of various types of defect sinks is briefly introduced in this chapter. At the end of Section 1, an overview is provided to summarize various types of defect sinks that will be discussed separately in various nanostructured materials in succeeding chapters. Section 2 targets the impact of grain boundaries on the alleviation of radiation damage in fine grained materials. Section 3 focuses on the reduction of radiation damage by using various layer interfaces in metallic and metal/ceramics nanolayer composites. Section 4 eyes on the strategy of using twin boundaries in nano-twinned metals to transport and eliminate radiation induced defects. This chapter also describes the combination of nanotwins and nanovoids to design radiation tolerant materials. In Section 5, we discuss the influence of free surfaces in controlling the radiation tolerance of nanoporous, 0D, and 1D materials.

Most of these sections will begin by discussing the sink strength of each type of defect sinks, present some in situ evidence for the absorption of radiation-induced defects by defect sinks, and discuss the size effect, that is the influence of defect sinks on mitigation of radiation damage. Certain sections will also address the concerns on the limitation of the current models for defect sink strength, and discuss modified sink strength formulas. Each section has its own outlook that is more specific for a particular type of nanomaterials. At the end of the review, a broader view for the future work is presented to engage and stimulate collaborations among nuclear materials, nanomaterials, physics, chemistry, mechanics and modeling community. Intimate collaborations among scientists in these communities may be the key to push the forefront of science forward, and to accelerate the design of radiation tolerant and ultimately “radiation immune” materials for the future generations of nuclear reactors.

Metallic materials with FCC structures are widely used as structural materials in nuclear reactors, including austenitic stainless steels, Ni alloys and certain Cu conducting cables [1], [2], [3], [5], [25]. Very often pure metals are irradiated as model systems, where the influence of chemistry from a second phase does not exist. Yet, the nature of defects induced in these pure metals is often similar to what has been identified in austenitic stainless steels. Also these FCC metals have drastically different stacking fault energy (SFE), which is critical to determine the type and morphology of radiation induced defects [26].

The vacancy migration energy for FCC metals typically varies from 0.7 to 1.7 eV, and it is typically 50–70% less than the vacancy formation energy. Several types of interstitials may exist, including 3 types of dumbbells, 〈1 1 1〉, 〈1 1 0〉, and 〈1 0 0〉 dumbbells, crowdions (shown in Fig. 1.1a), and the classical tetrahedral and octahedral interstitials (not shown here). As the interstitial formation energy is often the lowest for the 〈1 0 0〉 split dumbbells, the corresponding value is widely used to represent the general interstitial formation energy. The interstitial migration energy is typically 0.05–0.1 eV, significantly less than the vacancy migration energy. Hence it is widely accepted that interstitials (and interstitial loops) are highly mobile, even at room temperature, whereas vacancies mostly move at elevated temperatures. Such a drastic difference between vacancies and interstitials has a profound impact on the accumulation of radiation damage and void swelling in FCC metals and alloys. To some extent, the mobile interstitials (which evolve quickly into interstitial loops) leave vacancies behind, and the disparity in mobility of opposite types of point defects often accelerates the accumulation of vacancy and interstitial type clusters respectively.

The volume of a vacancy, $V_V^F$, is known to be less than the volume of one isolated atom, typically 0.75 Ω (Ω is the atomic volume). This is due to the relaxation of surrounding atoms. Such a relaxation volume, $V_V^{\mathit{rel}}$, can be written as:

$$V_V^{\mathit{rel}}=\mathrm{\Omega }-V_V^F\text{,}$$

and is typically ∼0.25 Ω for a suite of FCC metals [28]. The activation volume of self-diffusion ($V_V^{\mathit{SD}}$) in FCC metals is described as

$$V_V^{\mathit{SD}}=V_V^F+V_V^M\text{,}$$

where $V_V^F$,$V_V^M$ are respective activation volume of vacancy formation and migration. Typically, the vacancy migration volume is 0.1Ω and the activation volume for self-diffusion in FCC metals is ∼0.85 Ω. The dilatational volume expansion associated with the insertion of a self interstitial atom (SIA) in an FCC lattice, $V_{\mathit{SIA}}^F$, is ∼1.1 Ω. Considering the volume expansion arising from non-linear elastic strain, δV, the relaxation volume for self-interstitials (${\text{V}}_{\text{SIA}}^{\text{rel}}$), estimated by

$$V_{\mathit{SIA}}^{\mathit{rel}}=V_{\mathit{SIA}}^F+\delta V\text{,}$$

is typically ∼2 Ω. As will be shown later, the $V_{\mathit{SIA}}^{\mathit{rel}}$ for SIA in BCC metals is much smaller. Such a difference has an important implication on different radiation tolerance (such as void swelling resistance) between BCC and FCC metals.

Isolated point defects tend to cluster together. Among the known defect clusters in FCC metals, interstitial loops and vacancy loops are widely observed. Furthermore, vacancy clusters can evolve into stacking fault tetrahedrons (SFTs), which are a type of 3D defect and difficult to be eliminated. In FCC metals with low-to-intermediate SFE, faulted dislocation (both vacancy and interstitial) loops are frequently observed. Many of these faulted loops are immobile. However, abundant Shockley partials (an inherent nature of FCC metals) can glide and interact with these faulted loops and consequently transform the sessile loops into mobile perfect loops, with Burgers vector of ½ 〈1 1 0〉 . The glide plane of these perfect loops is either {1 1 1} or {1 1 0} [2].

Fig. 1.2 collects selected examples of radiation damage in Cu, Ni and Al to a similar dose level by using heavy ions (such as Kr), neutrons and electron beam (e-beam). Under heavy Kr ion irradiation at 273 K to 1–1.5 dpa, a large number of small interstitial dislocation loops are observed in all 3 FCC metals [29], [30]. Defect density appears to be greater in Cu than in Al. Neutron radiation at a higher temperature (455 K) to a similar fluence (1.3 dpa) generates defects with similar morphology (small loops) but with slightly lower defect density [31], [32], [33]. Meanwhile, e-beam (1 MeV) radiations at room temperature introduce rather large isolated interstitial loops in all FCC metals, which are mostly faulted loops on {1 1 1} planes [34]. The different defect morphologies between e-beam and neutron irradiation are mostly due to the fact that e-beam radiation typically gives rise to isolated low energy recoil atoms (0.1–1 kev), whereas neutron irradiations produce much more energetic recoil atoms (>10 kev). Consequently e-beam radiation induces isolated SIAs and vacancies that nucleate and coarsen via diffusion process [2]. In contrast, high-energy neutron radiation generates small defect clusters directly within the cascade. These small defect clusters act as defect sinks and curtail the coarsening of defect clusters [35], [36], [37]. Comparison of weighted average recoil spectra (a measure of fraction of defects with recoil energy) of neutrons, proton and heavy ions shows that Kr provides a much better approximation to neutron irradiation than light ions [38].

SFTs are another intriguing type of defects in irradiated FCC metals, and they often have triangular geometry under TEM. Some examples of SFTs are shown by dark field TEM and HRTEM in Fig. 1.3a and b for Ag [39] and in Fig. 1.3c and d for Au, irradiated by 1 MeV Kr ions to 1 dpa at room temperature [40]. The formation of SFTs has been investigated by MD simulations. In general, SFTs can evolve from vacancy clusters via the classical Silcox and Hirsch [41] mechanism as later visualized by MD simulations [42]. MD simulations of a large number of collision cascades show that a regular SFT or conjoint SFTs can form (Fig. 1.3e) [43]. SFT-like vacancy clusters are also frequently observed in irradiated FCC Cu. SIA loops can be either glissile, in the case of perfect interstitial loops with Burgers vector of ½ 〈1 1 0〉, or sessile, in the case of faulted loops with Burgers vector of 1/3 〈1 1 1〉. Furthermore, the MD simulations also show that SFTs can even stem from a void, instead of Frank loops, as shown in Fig. 1.3f. The transformation is driven by a large increase in entropy, in spite of a high potential energy barrier. Such a mechanism may be applicable to a variety of FCC metals [44].

Large scale MD simulations (Fig. 1.4) also show that at ambient to intermediate (<600 K) temperatures, 40% of the vacancy clusters are composed of more than 3 vacancies; whereas 80% of the interstitial clusters have more than 4 interstitials [43]. The fraction of vacancy clusters decreases with increasing radiation temperature. In contrast, the fraction of interstitial clusters continues to increase at higher irradiation temperatures. The vacancy cluster size in irradiated Cu appears to reach a maximum at 300 K in certain cases, due to a transition from compact cascade below 300 K (yielding large vacancy clusters) to thermal spike promoted destabilization of large vacancy clusters (due to interstitial-vacancy recombination) at elevated temperature. In comparison, the SIA cluster size increases monotonically with increasing temperature due to their higher binding energy [43].

Radiation damage in BCC metals has also been extensively investigated [1], [8], [45], [46]. Similar to FCC metals, a suite of point defects and their clusters are generated in irradiated BCC metals. The vacancy formation energy for BCC metals is typically 1.6–3 eV, and vacancy migration energy is 0.5–2 eV. Various types of interstitial can be generated in BCC metals, including crowdions, 〈1 1 1〉, 〈1 1 0〉 and 〈1 0 0〉 dumbbells (as shown in Fig. 1.1b) and octahedral and tetrahedral SIAs. The activation volume for self-diffusion of interstitials in BCC metals is ∼0.4–0.6 Ω [28], [47], [48], smaller than that in FCC metals, ∼0.85 Ω [28], [47], [48]. In comparison to FCC metal, the volume expansion associated with the insertion of an interstitial atom in BCC metal is much smaller, ∼0.64 Ω (versus 1.1 Ω for FCC) [28], [47], [48], presumably due to the lower packing density of BCC metals. The relaxation volume for self-interstitials in BCC metal is ∼1.0–1.5 Ω [28], [48], also much smaller than that in FCC metals, ∼2 Ω [28], [48]. These differences between FCC and BCC metals may explain the enhanced radiation tolerance of BCC metals vs. FCC metals to some extent.

The generally high SFE of BCC metals prohibits the formation of large faulted dislocation loops [49]. The perfect glissile loops in BCC metals have {1 1 0} habit planes with b = a/2 〈1 1 1〉, whereas the perfect sessile loops are often on {1 0 0} habit planes with b = a 〈1 0 0〉 [34], [50]. Fig. 1.5 shows various types of dislocation loops in BCC Fe, Mo and W irradiated by heavy ions, neutrons or e-beam [25], [34], [51], [52], [53], [54], [55], [56], [57], [58]. In general, the defect clusters induced by heavy ions and neutrons are similar, in form of dislocation loops with dimensions of several to 10 nm, in these irradiated BCC metals. Heavy ion irradiation of Fe induces abundant dislocation loops (string of loops) [51], whereas neutron irradiation induces rafts in Fe [25]. In comparison, e-beam introduces much fewer loops with greater loop diameter. For instance, e-beam irradiation induces perfect {1 0 0} loops in Fe [34]. In comparison to e-beam irradiation of FCC metals, Kiritani reported that no vacancy clusters were observed in e-beam irradiated Fe [34].

Radiation damage in Fe has been extensively investigated by simulations. Recent MD simulation studies (Fig. 1.6a–c) show that the interaction between two ½ 〈1 1 1〉 loops may have 3 scenarios (path A, B and C), one of which leads to the formation of 〈1 0 0〉 loops [45], [59]. The mobility of ½ 〈1 1 1〉 loops is important as such will ensure the probability of interaction among these loops [59]. Furthermore MD simulations have predicted the formation of nanoclusters with C15 structure in Fe (Fig. 1.6d). These C15 nanoclusters are of interstitial types but are immobile and have a low formation energy (Fig. 1.6e) [60].

The investigations on the nature of defects in HCP metals are largely driven by the application of HCP Zr based alloys as fuel cladding tubes in light water reactors. Vacancies and interstitials have much more complicated configurations in HCP metals than in cubic systems. Both monvacancies and divacancies have been investigated in HCP metals. The formation and migration energy for monovacancies are typically 0.6–2 eV and 0.3–1 eV respectively. The formation volume of monovacancies typically varies from 0.78 to 0.97 Ω [27], [61], [62]. Monovacancies can diffuse within or out of the basal planes. Calculations, though somewhat controversial in certain cases, suggest that the activation energy for self-diffusion (summation of vacancy formation and migration energy) is smaller for the non-basal plane for Zr with c/a less than ideal value [27], [61], [62], whereas the vacancy migration is more isotropic for Mg and Co with near ideal c/a ratios.

Two types of divacancies appear stable, including divacancies between the first nearest neighbors and second nearest neighbors. When c/a < 1.633, the first nearest divacancies are out of the basal plane, whereas the second nearest divacancies are within the basal plane [27]. The divacancies have formation energy of 1.1–3.5 eV, and formation volume of 1.5–1.9 Ω [27]. Among numerous migration paths, two paths (within or out-of-basal planes) have the lowest energy of migration, 0.45–0.75 eV [27]. There are 8 different sites for SIAs in HCP metals, as shown in Fig. 1.1c, including octahedron (O), tetrahedron (T), BO and BT in the basal plane underneath the O and T sites. BC and C are crowdions located halfway between the two nearest neighbor atoms along 〈1 1 $\overline{2}$ 0〉 (on the basal plane) and 1/6 〈2 0 $\overline{2}$ 3〉 direction (out of basal plane). BS and S are respective split dumbbells within or orthogonal to the basal plane [27], [61], [62]. In general, the basal split or crowdion is the most stable configuration for HCP metals with a rather large deviation from the ideal c/a value, and the non-basal dumbbell (C or S) is the most stable configuration for metals with near ideal c/a ratios [27]. The interstitial formation energy in HCP metals is also high, typically 2–6 eV, whereas their migration energy is very low, 0.05–1 eV. The formation volume of interstitials is typically 0.6–1.2 Ω [27].

The major types of defect clusters generated by radiation in HCP metals include vacancy clusters and interstitial loops. A perfect vacancy loop resides on {1 0 $\overline{1}$ 0} prismatic plane with Burgers vector of 1/3 〈1 1 $\overline{2}$ 0〉; and a faulted vacancy loop on (0 0 0 1) basal plane has Burgers vector of 1/6 〈2 0 $\overline{2}$ 3〉. A perfect interstitial loop on {1 0 $\overline{1}$ 0} plane also has the Burgers vector of 1/3 〈1 1 $\overline{2}$ 0〉; and faulted interstitial loops are typically observed on (0 0 0 1) plane with Burgers vector of 1/6 〈2 0 $\overline{2}$ 3〉 or 1/2 [0 0 0 1] [50], [61], [63].

Fig. 1.7 shows selected examples of heavy ion, neutron and e-beam irradiation induced damage in Zr and Mg. Heavy ion irradiation induced c-component loops in Zr have been observed (Fig. 1.7a) [64]. The density of c-loops in Zr decreases rapidly when T < 600 K. Neutron (Fig. 1.7b) and e-beam (Fig. 1.7c) irradiations induce both a-loops and c-loops in Zr [65]. In heavy ion (1 MeV Kr²⁺) irradiated Mg [66], nearly all basal loops have Burgers vector of 1/6 〈2 0 $\overline{2}$ 3〉, and are interstitial loops in nature, whereas prism loops (interstitial and vacancy) have Burgers vector of 1/3 〈1 1 $\overline{2}$ 0〉 (Fig. 1.7d). Meanwhile neutron irradiation of Mg induces dislocation networks (Fig. 1.7e) [67]. Griffiths [63] showed that e-beam irradiation of Mg (300 K/5 dpa) led to a-type vacancy (A_v,) and interstitial (A_i) loops with Burgers vectors 1/3 〈1 1 $\overline{2}$ 0〉, and c-component interstitial loop (C_i) with Burgers vector of 1/6 〈2 0 $\overline{2}$ 3〉 (Fig. 1.7f).

The relative stability of the dislocation loops in HCP metals generally depends on the c/a ratio and purity [68]. When c/a < 1.633, {1 0 $\overline{1}$ 0} prismatic plane is the most closely packed plane, and dislocation loops (prism loops) typically have Burgers vector of 1/3 〈1 1 $\overline{2}$ 0〉. When c/a > 1.633, the basal planes are the most closely packed, and dislocation loops (Basal loops) have Burgers vector of 1/6 〈2 0 $\overline{2}$ 3〉 (or ½ [0 0 0 1]). In reality, however, the situation under irradiation is more complex than that dictated by this simple rule. Exceptions have been reported via both experiments and simulations. For instance, basal loops have been observed in Mg [69], Zr [70], Ti [71], in which the c/a ratio is less than the ideal value (1.633). In Zr and Ti, the situation is further complicated by the co-existence of prismatic loops with both vacancy and interstitial character [65]. When c/a < 1.633, the probability of basal loop nucleation increases with increasing impurity concentration. In Mg, for instance, prism loops with Burgers vector of 1/3 〈1 1 $\overline{2}$ 0〉 are dominant; whereas in Mg with low purity, basal loops with Burgers vector of 1/6 〈2 0 $\overline{2}$ 3〉 have been observed.

Void swelling, in the form of a prominent volume increase accompanied with the formation of voids, is a widely observed phenomenon in most neutron and heavy ion irradiated metallic materials [72], [73], [74], [75], [76]. In this review, we will briefly summarize several instances where void swelling can be significantly reduced or suppressed in nanocrystalline materials (Section 2). Furthermore there are numerous cases where voids are shown to shrink, instead of continuous growth, in irradiated nanotwinned (Section 4) or nanoporous (Section 5) materials.

High dose neutron irradiation can introduce volume expansion as large as several tens of percent [74], [77], [78]. Voids in irradiated materials can have various geometries, including faceted, rectangular, or spherical shapes. As voids are typical stress concentrators, and significantly degrade the fracture toughness of irradiated materials, void swelling can be a serious threat to the mechanical and structural integrity of reactor structural materials [72], [74], [79]. The battle against void swelling is manifested by an extensive investigation of void swelling in metals with FCC, BCC and HCP crystal structures and constantly evolving designs of advanced void swelling resistant materials. Fig. 1.8 lists several examples of void swelling in neutron irradiated metals with FCC [3], [80], [81] and BCC [82], [83], [84] crystal structures. It should be noted that heavy ion irradiation typically generates a depth dependent variation of dose, and consequently the size and density of voids also vary as a function of radiation depth [85], [86].

Void swelling is closely correlated to the radiation temperature. As shown in Fig. 1.9a where Cu specimens were irradiated at different temperatures, swelling percentage, represented by density change, can be divided into three temperature dominated phases [3], [87]. Void growth is difficult at temperatures lower than 200 °C (phase 1) because of the poor mobility of point defects. When the temperature is higher than 500 °C (phase 3), defects of opposite types are effectively recombined or trapped by sinks rather than contributing to void growth. Therefore, swelling often occurs at intermediate temperature (phase 2) when the defects are mobile enough to agglomerate into voids, but less likely to be annihilated. Table 1.1, Table 1.2 summarize vacancy migration temperature ($T_V^M$) and peak void swelling temperature ($T_S^P$) for various metallic materials with FCC, BCC and HCP crystal structures. Void swelling is usually observed in metals and alloys at the temperatures of 0.3–0.5 T_m (where T_m is the melting temperature).

Swelling is also dose dependent. As radiation dose increases, swelling curve shows three regimes, which are transient swelling, steady state swelling and saturation swelling respectively. The steady state swelling undergoes the largest swelling rate. It has been reported that the eventual swelling rate of 316SS at all reactor-relevant temperatures is ∼1%/dpa [107]. In comparison, the swelling rate of numerous ferritic/martensitic steels is merely 0.2%/dpa as shown in Fig. 1.9b [1], [78], [88], [89], [90]. A saturation regime may be applicable to only a few materials, and is often not observed in practice because it requires very high dose and most materials usually fail mechanically long before saturation dose.

The void swelling behavior has also been modeled extensively. Phase field modeling has been increasingly used to simulate the formation of voids. Fig. 1.10a1–a4 shows the simultaneous nucleation and growth of voids in irradiated system supersaturated with vacancies [108]. When the temperature gradient is superimposed in the cascade core, the interstitial concentration gradient is established. Consequently voids may grow and migrate towards the interstitial rich region (Fig. 1.10b) [109]. At a much smaller length scale, MD simulations have been applied to show the influence of dislocations on the formation of voids in irradiated Zr. The dislocations were formed as a consequence of tensile strain (applied concurrently with radiation) [110].

Helium (He) also plays an important role in void swelling. In general, He bubbles are preferential nucleation sites for voids. The evolution of void diameter with time, dr/dt, can be expressed by [111]:

$$\frac{\mathit{dr}}{\mathit{dt}}=-\frac{D_V{X}_V^e}{r}\exp \left(\frac{2\gamma \mathrm{\Omega }}{(r-p)\mathit{kT}}\right)\text{,}$$

where D_v is the diffusivity of vacancies, $X_V^e$is the vacancy concentration at equilibrium, γ is the surface energy. p is the He pressure inside cavities, and can be written as [111]:

$$p=\frac{3\kappa \mathit{mkT}}{4\pi r^3}\text{,}$$

where κ is real gas compressibility factor, and m is the He atomic mass. The solution of dr/dt shows that He bubbles will grow (evolve) into voids when they reach a critical radius (typically several nm), or beyond a critical He concentration.

The influence of He on swelling is complicated. In general, there is an optimum He/dpa ratio for maximum void swelling in metallic materials, depending on the nature of nuclear reactors [112]. Meanwhile although He is attributed to the void swelling in many cases, a higher density of small He bubbles appear to suppress the magnitude of swelling [113]. To some extent, pressurized small He bubbles act as defect sinks for vacancies and interstitials and alleviate void swelling [113]. However, the usage of He bubbles to suppress void swelling may not be a straightforward strategy as He bubbles are known to be nucleation sites for voids; and once He bubbles reach critical radius, they may grow continuously, and lead to significant void swelling.

Void formation has been observed in most HCP metals, such as neutron irradiated Mg [114], both neutron and electron irradiated Zr [104], [105], [106], neutron irradiated Ti [114] and Re [115]. Voids in HCP metals are normally faceted along {1 0 $\overline{1}$ 1} and (0 0 0 1) planes and often align in layers parallel to the basal plane, and in many cases, voids are reported to be faceted. For instance, voids formed in Marz-grade Zr during neutron irradiation in DFR at temperatures between 725 and 740 K were faceted along basal, prism, and pyramidal planes [68], and were mostly near grain boundaries.

Radiation damage induced by He ions has been widely investigated in a variety of metallic materials [116]. He is produced in neutron irradiated metallic materials due to the transmutation during neutron radiation. In numerous reactors, the concentration of He in irradiated metallic materials can achieve a few hundred to thousands of PPM level [111]. Fig. 1.11 compares the formation of He bubbles in a variety of irradiated monolithic metals with FCC [117], [118], [119] and BCC [120], [121], [122] crystal structures. He bubbles typically appear spherical in these metallic materials. However faceted (hexagonal) He bubbles emerge near grain boundaries in Al (in Al matrix composites). The faceted He bubbles may form to minimize surface energy of the cavities [118]. Furthermore, He bubbles form superlattices in He ion irradiated Mo [122].

When He/vacancy ratio is high, the pressured He bubbles may lead to lattice expansion as shown in Fig. 1.12a [123]. Interestingly, both lattice expansion (measured from selected area diffraction pattern in cross-sectional TEM studies) and He bubble density reach a peak value at ∼200–300 nm. The equation of state for He has been described by multiple models [54], [124], [125], [126], [127]. Mills et al. provided a reliable empirical relation (MLB model) (based on experimental results) as follows [128]:

$$V=(22.575+0.00646557\text{T}-7.26457{\text{T}}^{-1/2}){\text{P}}^{-1/3}+(-12.483-0.024549\text{T}){\text{P}}^{-2/3}+(1.0596+0.10604\text{T}-19.641{\text{T}}^{-1/2}+189.84{\text{T}}^{-1}){\text{P}}^{-1}\text{,}$$

where the molar volume V has the unit of cm³, the pressure P is in kbar, T is absolute temperature.

The pressurized He bubbles could lead to lattice expansion based on the point source dilatation mechanism [129]. The pressure due to He bubbles is written as:

$$P=\frac{\mu \delta v}{\pi r_0^3}\text{,}$$

where $\mu$ is the shear modulus of the metal matrix, and $\delta v$ is the volume expansion induced by internal pressure, and $r_0$ is the radius of bubbles. Based on the measured peak lattice expansion in Cu/V 50 nm nanolayers, the pressure inside He bubbles is estimated to be ∼3.8 GPa [123]. By using the equation of state of He, the molar volume of He is estimated to be 6.29 cm³/mol, or approximately 1.3 He/vacancy in V, and 1.1 He/vacancy in Cu are obtained, in agreement with literature values (1.4 He/vacancy in He bubbles of 4 GPa pressure in V, and 1.0 He/vacancy in He bubbles of 2.8 GPa pressure in Cu [116]). Wolfer has also described the mechanism of tensile stress induced lattice expansion arising from pressurized He bubbles [130]. He bubble induced lattice expansions have also been observed in numerous other systems, where the magnitude of lattice expansion is proportional to the He concentration [130], [131]. It is well known that the diameter of measured He bubbles varies as a function of under-focus distance in TEM studies. An example of such study is shown in Fig. 1.12b for He bubbles observed in He ion irradiated Cu/V 50 nm multilayers [132].

There are numerous studies that show He can be managed by using a variety of defect sinks, such as phase boundaries (metal/oxide interfaces as shown in ODS alloys) and grain boundaries [6], [9]. The discussion on the influence of defect sinks on He management is distributed in several succeeding sections in this review. Furthermore He tends to combine with vacancy and vacancy clusters to form pressurized He bubbles. Additionally He may segregate to the grain boundaries and lead to grain boundary embrittlement, often referred to as He embrittlement [133], [134], [135].

Forgoing sections describe the nature and types of defects that are generated by irradiations. Extensive studies have been carried out in the past few decades to improve the radiation tolerance of materials. An effective approach to mitigate radiation damage is to introduce various types of defect sinks, such as grain boundaries, phase boundaries and dislocations. These defect sinks interact with and eliminate, to a greater extent, the irradiation induced point defects and defect clusters.

The interaction of various types of defects with defect sinks has been described by using kinetic rate theory. In general the defect-sink reaction rate is estimated, followed by derivation of a sink strength formula.

For vacancy and interstitials, the following equations sustain [136], [137]:

$$\frac{\partial C_V}{\partial t}=K_0-K_{\mathit{iV}}{C}_i{C}_V-K_{\mathit{VS}}{C}_V{C}_S+\nabla •D_V\nabla C_V$$

$$\frac{\partial C_i}{\partial t}=K_0-K_{\mathit{iV}}{C}_i{C}_V-K_{\mathit{iS}}{C}_i{C}_S+\nabla •D_i\nabla C_i$$

where C_v, C_i are vacancy and interstitial concentration; K₀ is defect production rate; K_iV is the vacancy-interstitial recombination rate coefficient; K_VS and K_iS are the vacancy-sink and interstitial-sink reaction rate coefficient. The reaction rate constants are estimated as follows:

$$K_{\mathit{iV}}=4\pi r_{\mathit{iv}}(D_i+D_V)\approx 4\pi r_{\mathit{iv}}{D}_i$$

$$K_{\mathit{iS}}=4\pi r_{\mathit{iS}}{D}_i$$

$$K_{\mathit{VS}}=4\pi r_{\mathit{VS}}{D}_V$$

Note that the defect absorption rate can be rewritten with the concept of defect sink strength, k²:

$$K_{\mathit{jx}}{C}_j{C}_X=k^2{C}_j{D}_j\text{,}$$

where K_jx the reaction rate between defect sink (X) and a mobile point defect (j). The sink strength k² has a unit of cm⁻². The inverse of k represents the average distance (or mean free path, λ) a mobile point defect can travel before being captured by a defect sink. It follows that in nanostructured materials, λ is limited by the density of defect sinks, and its value would be similar to the value of grain size (d), twin spacing (t) or individual layer thickness (h) as illustrated in the following formula:

$$k^{-1}=\lambda =d\text{or}t\text{or}h(\text{distance between defect sinks})$$

Hence to enhance the defect sink strength, it is critical to scale down the dimension of nanofeatures or increase the density of defect sinks. When considering the defect-GB reaction rate, the steady-state atomic concentration of point defects is given by:

$$D\left[\frac{d^{2}c}{{\mathit{dr}}^2}+\frac{2}{r}\frac{\mathit{dc}}{\mathit{dr}}\right]+K-{\mathit{Dk}}_{\mathit{sc}}^{2}c=0\text{,}$$

and the solution to the formula (assuming that GB is an ideal sink) is written as:

$$k_{\mathit{gb}}^2=\frac{k_{\mathit{sc}}^2[k_{\mathit{sc}}R\coth k_{\mathit{sc}}R-1]}{\left[1+\frac{k_{\mathit{sc}}^2{R}^2}{3}-k_{\mathit{sc}}R\coth k_{\mathit{sc}}R\right]}\text{,}$$

where R is the radius of grains (half of grain size d). When the point defects are lost mostly to GB sinks, then it can be shown that [136], [137]:

$$k_{\mathit{gb}}^2=15/R^2$$

Note the derivation is based on the cellular model using the average point defect concentration within a grain. When an embedding model is used, the GB sink strength becomes 14.4/R², very close to the value derived from the cellular model. Clearly the smaller the grain size, the greater the sink strength.

Similarly using the cellular model, the sink strength for a void, $k_V^2$, is described by:

$$k_V^2=4\pi {\mathit{aC}}_V^0{f}_c\text{,}$$

$$C_V^0=\frac{3}{4\pi R_0^3}\text{,}$$

$$f_c=\frac{5{(R_c^3-a^3)}^2}{[5R_c^6-9{\mathit{aR}}_c^5+5a^3{R}_c^3-a^6]}\text{.}$$

where a is void radius, R_c is the radius at zero flow condition, that is dc/dr = 0, when r = R_c. To a first approximation, R_c may be estimated as the void-to-void separation distance. $R_0^3=R_c^3-a^3$; and $C_V^0$ is the initial volume distribution of voids. Note the sink strength formulas for twin boundaries or layer interfaces have not been derived to date.

To date, there is literally no material known to be immune to radiation damage, especially beyond a dose level of several hundred dpa. As stated in the previous sections, all crystalline materials, regardless of their crystal structures (FCC, BCC or HCP), are vulnerable to radiation damage. Although a large number of point defects may recombine immediately after damage cascade, the residual defects can lead to the accumulation of radiation damage in terms of microstructural evolution. It remains a major challenge to design materials that have significantly enhanced radiation tolerance at extreme conditions.

Zinkle and Snead [138] reviewed several strategies to alleviate radiation damage in irradiated materials. First, metallic materials with BCC structures appear to be more resistant to radiation damage compared with those with FCC structures, presumably due to the higher number density, smaller defect clusters generated during cascade in irradiated BCC metals than in FCC metals [50], [138], [139], [140], [141]. Second, when either vacancies or interstitials are immobile at the operation temperature, the immobile point defects may facilitate recombination of opposite type of point defects [138]. Third, high sink strength or high sink density reduces radiation damage.

The adoption of predesigned defects (sinks) to eliminate radiation induced defects, though appears counterintuitive at the beginning, is in fact a very effective approach. Defects in crystalline materials can be characterized by their dimensions, including 0D – point defects, 1D – dislocations, 2D – grain boundaries, phase boundaries and surfaces, and 3D – voids, pores, precipitates and 2nd phase, etc. The applications of point defects to alleviate radiation have been mostly implemented through the design of solid solutions or alloys, where solid solution can assist the recombination of defects and reduce radiation damage [6], [142], [143], [144], [145]. Dislocation networks have also been used to reduce radiation damage, although dislocations are often considered as biased defect sinks, which may accelerate the formation of voids in certain cases [110]. There are numerous examples that show dislocations, including mobile dislocations, can interact with SFTs and sweep them away [146], [147], [148], [149]. Other widely used defect sinks include grain boundaries, phase boundaries, voids and He bubbles. Literature data show that a sink strength of 10¹⁶/m² may be necessary to curtail void swelling in steels to less than 5% [138]. Such a high sink strength is difficult to achieve in conventional materials. We will show in the succeeding chapters that various types of nanomaterials may reach such a high sink strength depending on the characteristic defect spacing.

The influence of point defects and dislocations on radiation induced damage will not be covered in this review. Instead we will focus on the following nanostructured materials: nanocrystalline materials with fine grains, nanotwinned metals with a high density of twin boundaries, nanolayer composites with layer interfaces, and nanoporous materials, nanoparticles and nanowires with abundant free surfaces. Fig. 1.13 illustrates the application of these defect sinks in various nanostructured materials to alleviate radiation damage.

The review article covers the emerging field (nanomaterials under extreme radiation environments) and emergent needs for the design of superior radiation tolerant nanomaterials. This article highlights what the community has learned to date on the radiation response of various nanomaterials, and points out future directions to move forward. We hope the article can stimulate broad interest in the field of “nano under radiation” with the ultimate goal to discover new strategies (including nanoengineering) and design novel materials with unprecedented radiation tolerance.