Grain growth stagnation and texture development in an irradiated thermally stabilized nanocrystalline alloy

High energy particles such as electrons, neutrons, and ions create point defects in materials and damage their microstructure.¹ Previous studies have shown that the grain boundaries present in polycrystalline metals can act as effective sinks to these defects and help reduce the irradiation-induced damage. The ideal sink strength of grain boundaries $(kgb2)$ in polycrystalline metals is approximately given by

where D is the grain size in centimeters.² Owing to their small grain size, nanocrystalline (nc) metals have better irradiation resistance compared to their coarser grain counterparts.^3,4 This irradiation resistance, however, decreases with the dose because irradiation causes grain growth, which results in lower sink strength. If nc-metals are to be used in a high energy irradiation environment, the grain size stability issue must be addressed.⁵ 

Alexander and Was⁶ proposed that irradiation-induced grain growth (IIGG) is caused by thermal spikes. Their model was modified by Kaoumi et al.⁷ and is widely used to fit the observed data. In this model, an energetic particle passing through a material transfers kinetic energy to target atoms. Each struck atom is known as a primary knock on atom (PKA). If a PKA has sufficient energy, it generates a cascade of vacancies and interstitials in a small volume. Within this cascade, known as a thermal spike, the atoms have high kinetic energy, and the effective temperature is equal to or higher than the melting temperature of the material for a duration on the order of picoseconds. If a thermal spike falls close to a grain boundary, it causes the grain boundary to migrate, resulting in grain growth and consequently lower energy. The equation for IIGG is given as

where $D0$ is the initial grain size, K is a constant that depends on material properties, and $Φ$ is the dose (see  Appendix A). K is directly proportional to the grain boundary energy $γ$⁠, which is the driving force for grain growth. This equation is similar to the annealing equation⁸ where time is used on the right-hand side of the equation instead of dose and the exponent is 2 instead of 3.

As motivated later in this section, we examine nc-NiW, a solid solution, in this work. Fits to data for pure nc-Ni give the exponent n = 2.8⁹ and n = 3.6,¹⁰ in reasonable agreement with the model. However, the implications and assumptions in the IIGG model deserve a closer investigation.

First, Eq. (2) implies that grain growth continues indefinitely. According to Eq. (1), this means that sink strength will continuously decrease. In the model, the origin of the indefinite grain growth is that the grain boundary energy remains constant as irradiation continues. However, as the grain growth progresses, grain boundaries with low stability will be eliminated, and the average grain boundary energy of the system will change. For example, Bufford et al.¹¹ have observed that grain boundaries with low energy survive, while other boundaries disappear as irradiation continues.

Second, the model does not consider the effect of strain energy on grain growth. Grain growth reduces grain boundary energy but increases the tensile stress, and hence the elastic strain energy, of a film deposited on a substrate due to densification and shrinkage. Chaudhari¹² has shown that for thermal growth, if the initial grain size is smaller than a critical grain size, the sum of grain boundary energy and strain energy reaches a minimum resulting in grain growth stagnation. A similar consideration may apply in cases where the nc-material is a coating, as is the case in this study. However, the critical initial grain size required for this mechanism to operate is 4 nm for nc-NiW. The nc-NiW alloy used in this study has an initial grain size of 6 nm. Hence, we shall assume that the mechanism proposed by Chaudhari will not cause stagnation in grain growth during the irradiation process.

With respect to experiments that have been reported, one important consideration is that the films are rather thin compared to the grain size, with a ratio that is usually less than 3. Grain growth in thin films generally stagnates once the grain diameter is similar to film thickness due to grain boundary grooving at triple lines at the surface.¹³ A minor consideration is that the Kaoumi model assumes that the grains are initially spherical in shape. The closest approximation to this in a real material would be equiaxed grains. Although the shape of grains is a minor effect, the model would be better tested if the film thickness were much larger than the grain size and the grains were equiaxed rather than columnar.

A second consideration is that in the Kaoumi model, there is no effect of the grain orientation with respect to oncoming ions on the rate of grain growth. However, it has recently been shown that ion beam bombardment along the channeling direction results in a higher rate of grain growth, with n = 2 and the development of a biaxial texture.¹⁴ The Kaoumi model should not be tested under such irradiation conditions.

A third consideration of current interest is that thermally stabilized nc-metals are now being developed using alloying methods.^15–18 It has been suggested that these will be more resistant to IIGG than pure nc-metals.⁵ However, it is not clear that such metals will be more irradiation resistant because the thermal spike transient temperatures meet or exceed the melting temperature.

In view of these considerations, we choose nc-NiW as a material of interest. Its initial grain size is small, about 6 nm, in comparison with previous studies where the initial grain size was 10 nm or greater.^7,10,19–21 The Kaoumi model can be tested over a wider range with smaller initial grain size. The film thickness of 500 nm is nearly 100 times greater than this initial grain size, and the grains tend to be equiaxed. Finally, it is thermally stable up to 450 °C, in contrast with pure nc-Ni, which is stable only up to 100 °C.²² We irradiate up to a five times greater dose than previous experiments to test whether Eq. (2) continues to hold at high doses. We find that grain growth stagnates at a dose ten times less than the maximum and investigate whether this is due to microstructural evolution or other mechanisms.

To summarize, we address the following questions in this paper:

• What is the IIGG rate in thermally stable nc-NiW and how does it compare to nc-Ni?

• Does the Kaoumi IIGG model apply for nc-NiW up to a high dose?

• How do texture evolution and grain boundary character relate to IIGG in nc-NiW?

The nc-NiW films were grown by reverse pulse electrodeposition,^23,24 which offers a high degree of control over grain size. This method was used to deposit 0.5 μm and 18 μm thick nc-NiW films on copper substrates. Ni⁺ ions with 2 MeV energy were used to irradiate the 0.5 μm film up to a dose of 5 × 10¹⁶ ions/cm². Using high energy self-ion irradiation on a thin film minimizes the changes in chemical composition that occur during the irradiation. Transmission electron microscopy (TEM) along with X-ray diffraction (XRD) was used to characterize the grain size, composition, texture, and crystal orientation of the film before and after irradiation. The experiments and characterization methods are described below; further details can be found in  Appendix B.

The nc-NiW films were electroplated following published recipes.^23,24 The 0.5 μm film was used for irradiation experiments. The 18 μm film was used to analyze the initial texture of the film for reasons explained in the texture analysis Sec. II C 1. The W concentration in both the films was 17%, as determined by energy dispersive spectroscopy (EDS) in scanning electron microscopy (SEM).

The 0.5 μm thick specimen was then irradiated at room temperature. The damage introduced and the ion implantation profile were calculated using the Stopping and Range of Ions in Matter (SRIM) program.²⁵ Our calculations show that 80% of Ni⁺ ions passed through the film and will cause minimal variation in the composition of the film (1.1% change in W concentration at the maximum dose). Doses were from 0.05 × 10¹⁶ to 5 × 10¹⁶ ions/cm², corresponding to 1–100 displacements per atom (dpa). The durations were from 7 to 700 min, whereas the temperature increase during the irradiation was less than 20 °C and reached steady state within 5 min.

Table I summarizes the dose and also includes information on grain size, which was determined as described in Sec. III.

A FEI Tecnai F20 TEM operating at 200 kV was used to characterize the microstructure of the as-deposited and irradiated specimens. A FEI Nova Nanolab 600 Dual beam FIB (focused ion beam) system was used for cross-sectional specimen preparation for TEM. While FIB is an effective method for preparing TEM specimens, it has two limitations that must be addressed before determining the grain size. First, the specimens prepared using FIB give a cross-sectional view that will result in inaccurate grain size determination if the grains are not equiaxed. Second, FIB sample preparation can introduce artifacts into TEM samples.²⁶ To address these issues, we also prepared a TEM plan-view specimen using twin jet electrolytic thinning.

Hollow cone dark field (HCDF) mode²⁷ was used to image the specimens with smaller grain sizes from 6 to 20 nm. This technique illuminates a large number of grains at this scale, as needed for a statistical estimate of grain size.

Both as-deposited and irradiated specimens were investigated to study the texture evolution of nc-NiW due to irradiation.

The as-deposited grain size of 6 nm is beyond the spatial resolution of conventional SEM or TEM-based orientation imaging microscopy (OIM), which was used for the larger grain specimens. Hence, XRD was used to analyze the texture of the as-deposited specimen. However, the film thickness of the thin 0.5 μm nc-NiW specimens is much smaller than a typical X-ray penetration depth (∼25 μm), and the nc-NiW lattice constant is nearly the same as Cu, making it difficult to distinguish between nc-NiW and substrate texture using conventional XRD. Therefore, the 18-μm thick nc-NiW film was used in a Panalytical X'Pert Pro X-ray Diffractometer to gather the texture information. A Cu powder specimen was used to measure the defocusing effect and correct for it.

The grain size of specimens irradiated to ≥10 dpa was 32–35 nm. For these specimens, it is possible to gather the orientation information of each grain using Automated Crystal Orientation Mapping (ACOM) in TEM.²⁸ We used the NanoMEGAS ASTAR™ system installed in a FEI Tecnai F20 TEM to perform ACOM on 10, 30, and 100 dpa specimens.

The upper row in Fig. 1 shows HCDF images of the as-deposited and irradiated specimens. At 0 (as-deposited), 1, and 3 dpa, the grains are small but increasing in size, while the 10, 30 (not shown), and 100 dpa images indicate larger grains of nearly equal size. No voids were observed even at 100 dpa. The 0, 1, and 3 dpa images were filtered using ImageJ²⁹ software to remove the noise and were analyzed to calculate the equivalent diameter, which is reported as grain size D in Table I. The number of grains illuminated in the 10, 30, and 100 dpa images is small, resulting in poor statistics. For these larger grains, we used ASTAR images (Sec. II C 2) to calculate the grain size. Grains below 15 nm were ignored in this calculation to avoid possible biasing of data by poorly indexed grains. Therefore, these values represent upper bound estimates of the grain size.

The lower row in Fig. 1 shows corresponding selected area diffraction patterns (SADPs) with a 10 μm selected area diffraction aperture. It is clear that as dpa increases, the continuous rings become granular, as expected for the increasing grain size. Upon indexing the SADP patterns, only peaks associated with an FCC phase were observed, unlike Ref. 30, where a metastable hcp phase was detected in irradiated nc-Ni.

A plan-view TEM image of the as-deposited specimen prepared by electrolytic thinning is shown in Fig. 2. The D value closely matches (within 5%) that observed by the FIB-prepared cross-sectional samples. As this is the specimen with the smallest D and, therefore, the most sensitive to FIB-induced grain growth, we conclude that no perceptible grain growth has been introduced by the FIB during TEM sample preparation. This result also confirms that grains are equiaxed in shape.

The grain sizes (equivalent circle diameter) and standard deviations are listed against dose in Table I. The grain size as a function of the dose is plotted in Fig. 3 (red circles), where D increases monotonically from 0 to 10 dpa but stagnates at ∼32 nm from 10 to 100 dpa. The standard deviation in grain sizes has not been shown in the plot for clarity and in keeping with the previous literature but is listed in Table I.

The grain size stagnation at a large dose as seen in Fig. 3 is in contrast with the prediction from Kaoumi's model. As discussed in the Introduction, Bufford et al.¹¹ have shown that the grain boundary characteristics play an important role in grain boundary mobility. The nature of grain boundaries and their volume fraction can be characterized by investigating the texture.

Two different techniques were used to evaluate texture in nc-NiW. XRD was used to evaluate the texture of the as-deposited film. This technique can only provide the information on macrotexture, i.e., the distribution of crystallographic poles. There is no information on the local orientation of crystallites or microtexture. Hence, the grain boundary characteristics of the as-deposited film could not be determined. ACOM was used to evaluate local crystal orientations of the 10, 30, and 100 dpa specimens. Both microtexture and macrotexture can be evaluated using this technique. Sections III B 1 and III B 2 discuss the evolution of the macrotexture using pole figures and orientation distribution functions (ODFs) respectively, while Sec. III B 2 also explains the evaluation of grain boundary characteristics.

Figure 4 shows (111) pole figures plotted relative to the normal direction (ND, the direction of film growth) of the as-deposited specimen along with the 10, 30, and 100 dpa specimens. For the as-deposited specimen, the pole figure shows a concentration of (111) poles in the out-of-plane ND direction and a near isotropic distribution for the in-plane directions [conventionally referred to as the rolling direction (RD) and transverse direction (TD)], which is indicative of fiber texture. For the irradiated 10, 30, and 100 dpa pole figures, there is a concentration of (111) planes in the out-of-plane direction as well as some (111) plane concentrations along six in-plane directions, indicative of a biaxial texture.

The pole figures in Fig. 4 qualitatively show the irradiation-induced evolution in nc-NiW from fiber to biaxial texture. However, complete texture information, which involves mapping of intensities (related to volume fraction of grains) in Euler space, is visible only in ODF plots, as discussed below.

Figure 5 shows the orientation distribution function (ODF) plots in Euler space for the as-deposited and irradiated specimens. The three axes in the Euler space are the rotations required for the transformation of specimen coordinate axes to the crystal coordinate axis. Bunge-Euler angles $φ1$⁠, $Φ$⁠, and $φ2$ are defined as passive sequential rotations about the Z-axis, the rotated X-axis, and the rotated Z-axis.³¹ This figure shows variation of intensity as a function of Bunge-Euler angles (⁠$φ1$ and $Φ$⁠) at three sections of $φ2=0°$⁠, 20°, and 45°. (Here, $Φ$ is the second Euler angle and is not to be confused with the same symbol $Φ$ used above for dose.)

Figure 5(a) shows the ODF plots of the as-deposited specimens. There are two distinct regions of high intensity corresponding to two different fiber textures. High intensity centered at $Φ=54.7°$ with $φ2=45°$ corresponds to the (111) fiber texture in the film growth direction (⁠$γ$-fiber texture³¹). Another region of high intensity centered at $Φ=70.5°$ with $φ2=45°$ corresponds to the (221) fiber texture in the film growth direction.

Figures 5(b)–5(d) show the ODF plots for the 10, 30, and 100 dpa specimens. High intensities are observed at $φ1=30°$⁠, 90°, 150°, 210°, 270°, 330°, $Φ=54.7°$⁠, and $φ2=45°$ in all three figures. This corresponds to a $(111)⟨110⟩$ biaxial texture. The volume fraction of this texture was calculated to be 50% for the 10 dpa specimen, 49% for the 30 dpa specimen, and 42% for the 100 dpa specimen, using a 15° acceptance angle. Together, Figs. 4 and 5 indicate that the texture evolves from 0 to 10 dpa, but that it is relatively stable from 10 to 100 dpa.

Figure 6 shows the inverse pole figure (IPF) maps obtained by TEM-ACOM of the 10, 30, and 100 dpa specimens with orientations referenced to ND. The high fraction of blue colored grains further illustrates the prevalence of (111) poles in the normal direction. Grain boundary characteristics determined from these IPF maps are plotted as a function of disorientation angle in Fig. 7. The plots consistently show a high fraction of 60° misorientation angles.

Figure 8 shows grain boundary maps with low angle grain boundaries (LAGBs) (green), high angle grain boundaries (HAGBs) (blue), and coincidence site lattice (CSL) Σ3 boundaries (red). The grain boundaries were classified on the basis of the misorientation angle of adjacent grains. The boundaries with a misorientation angle of 5°–15° are labeled as low angle grain boundaries (LAGBs), and the boundaries with a misorientation angle of 15°–180° are labeled are high angle grain boundaries (HAGBs). CSL Σ3 boundaries are calculated for a misorientation angle of 60° according to Brandon's criterion.³² The grain boundary map shows a uniform distribution of Σ3 boundaries among the HAGBs and a few LAGBs. These Σ3 boundaries may be responsible for the stagnation in grain growth as discussed in Sec. IV B. The overall grain boundary density is higher for 10 and 30 dpa specimens because these specimens had more small grains (<15 nm) with a low confidence index (CI). These grains with a low confidence index were not considered in statistical grain size calculations but are shown here for completeness. This indicates that the true average grain size at 10 and 30 dpa is somewhat smaller than at 100 dpa, but that the maximum grain size does not increase substantially, and clearly remains significantly smaller than the Kaoumi model prediction.

Two major observations can be made from the IIGG results in Fig. 3. For lower doses (Φ ≤ 0.5 × 10⁶ ions/cm² or damage ≤10 dpa), the observed data fit the trend in Kaoumi's model, and nc-NiW IIGG is comparable to nc-Ni IIGG. For higher doses (Φ > 0.5 × 10⁶ ions/cm² or damage >10 dpa), there is a significant deviation between the observed data and Kaoumi's model, and the IIGG stagnates in this regime. These observations are discussed below.

Before we proceed with the discussion on IIGG of nc-NiW, it is important to establish whether grain growth is due to irradiation alone or is thermally assisted. Previous studies have suggested that thermally assisted grain growth in Ni occurs for homologous temperatures (⁠$T/Tm$⁠, where T is the temperature and $Tm$ is the melting temperature) greater than 0.23.³⁰ The solidus temperature of NiW is 1798 K,³³ making the homologous temperature for NiW to be 0.17.

Therefore, the nc-NiW irradiation, performed at 300 K, is in the regime where IIGG will dominate, and it is appropriate to apply the Kaoumi model. To do so, we calculate the value of K in Eq. (2) by evaluating certain material and irradiation parameters.⁷ These parameter values were obtained for Ni and W from SRIM simulation and other sources, and a rule of mixtures was applied ( Appendixes A and C). The value of K = 4.2 × 10⁻³³ cm⁵ is calculated using these values. Figure 3 shows that Kaoumi's model “quantitatively” fits the experimental data well up to a dose of 0.5 × 10¹⁶ ions/cm² using this value of K.

However, the calculation does not explain why the rate of IIGG in nc-NiW is comparable to that of pure nc-Ni. Two factors likely play a role. First, D is only proportional to $γ1/3$⁠, and hence the reduction of $γ$ in nc-NiW (0.4 J/m²)³⁴ relative to nc-Ni (1 J/m²)³⁴ may not be enough to make a large difference. Second, the spike temperature is $≈Tm$⁠, much higher than the temperature of thermal stability of nc-NiW (450 °C).

The IIGG in nc-NiW stagnates at doses higher than 0.5 × 10¹⁶ ions/cm² or damage greater than 10 dpa. Researchers have proposed different mechanisms for grain growth stagnation in thin films. While most of these mechanisms pertain to grain growth in thin films in general, some mechanisms are applicable to IIGG specifically. We discuss these mechanisms and their applicability to our experiment below.

Liu et al.²¹ have reported IIGG stagnation in irradiated nc-Pd films; however, at 50–60 nm, their e-beam evaporated films were much thinner than the present 500 nm NiW film. Their explanation is as follows: when the grains are small, a cascade will damage an entire grain. The damaged region will reorder on adjacent grains acting as seeds and consequently grain growth will take place. As the grain size increases, the damage will tend to be confined to grain interiors, and regrowth will occur from within the grain; therefore, growth will no longer occur. To support this idea, their experiments indicate that the dimension at which the IIGG stagnates depends on the energy and mass of the irradiating species (increases from 100 keV Ne⁺ to 185 keV Ar⁺ to 560 keV Xe⁺). They relate this to the lateral dimension of a collision cascade: once the grain size becomes about twice the cascade size, grain growth stagnates (at 25, 40, and 65 nm for the three energies just mentioned). The model they describe involves cascades in the middle of a grain. When the ion path traversed the grain boundaries, presumably the molten material would grow from each parent grain, which on average would not affect grain size.

While this model of grain growth stagnation can be applied on columnar grains as reported in their paper, it will not be applicable for equiaxed grains. Instead, Kaoumi's model captures the physics of grain growth better than the one suggested by Liu et al., since it allows for the probability of cascades falling close to a grain boundary and causing grain growth. Additionally, as pointed out in the Introduction, previous studies have shown that when the grain size is of the same order as film thickness, grain growth stagnates.¹³ However, the irradiated nc-NiW grain size (32–35) remains much smaller than the film thickness (500 nm). Thus, neither the cascade size effect nor a film thickness effect can explain the observed stagnation in grain growth.

After ruling out cascade size and film thickness as possible causes for grain growth stagnation, we examine texture and grain boundary characteristics. As mentioned in the Introduction, irradiation along easy channeling directions results in a faster grain growth than predicted by Kaoumi's model as well as the development of biaxial texture. Since this study is based on Kaoumi's model, it is important to establish that the irradiation was not performed in an easy channeling direction.

The as-deposited nc-NiW has a FCC crystal structure with a mixture of (111) and (221) fiber textures. In FCC crystals, the easiest channeling direction is [110], which is oriented at 19.5° from the [221] direction and 35.3° from the [111] direction. The ion beam direction in the current experiment was parallel to the surface normal and aligns neither with easy channeling direction of the (221) fiber texture nor with the (111) fiber texture. Even though the beam does not align with an easy channeling direction, we still observe a biaxial texture. Similar texture development in an irradiated Ni film has also been reported by Rajasekhara et al.³⁵ 

Furthermore, Fig. 7 indicates a high fraction of high angle grain boundaries (misorientation angle ∼60°), corresponding to Σ3 CSL boundaries. Based on Brandon's criterion,³² the fraction of Σ3 boundaries is calculated to be 18%, 14%, and 19% for the 10, 30, and 100 dpa specimens, respectively. The grain boundary characteristics of the as-deposited specimen could not be calculated experimentally because of the small grain size (∼6 nm). However, simulations performed by Garbacz and Grabski³⁶ showed that the fraction of Σ3 CSL boundaries in a microstructure with 100% $⟨111⟩$ fiber texture was 5.6%, 2.5% in a microstructure with 50% $⟨100⟩$ and 50% $⟨111⟩$ texture, and a mere 1.5% for a random texture. Hence, there is a potential 3- to 10-fold increase in the fraction of CSL Σ3 boundaries as the texture evolves from a fiber texture to biaxial texture. The CSL Σ3 boundaries have lower grain boundary energy³⁷ and lower mobility³⁸ compared to a random boundary and may be the reason for the stagnation in grain growth. The variation in fraction of CSL Σ3 boundaries for different doses may be attributed to local variations within the specimens. It must be noted that low energy generally means low mobility for thermally driven grain boundary motion, but it is not always the case. Several researchers have shown that some low energy grain boundaries can exhibit high mobility.^39–41 However, as grain growth proceeds, the high mobility grain boundaries will be eliminated, leaving the system with lower mobility grain boundaries.

Solute concentration plays an important role in stabilizing the microstructure of polycrystalline metals. The solute atoms in the grain boundary exert a drag force on the boundary that significantly reduces the grain boundary velocity.⁴² The nc-NiW alloy used for this study has a global W content of 17 at. %. Using atom probe tomography (APT), Detor et al.⁴³ showed that W concentration at grain boundaries of nc-NiW is higher than in the grain interior. We measured the W concentration of this alloy after irradiation using energy dispersion spectroscopy (EDS) in scanning mode TEM. We found no evidence of higher W concentration at grain boundaries. Although STEM-EDS is not as sensitive as APT for determining solute segregation in nanocrystalline alloys, a strong segregation of W at grain boundaries can be ruled out.

While it is difficult to compare quantitatively the effects of low energy Σ3 grain boundaries and solute drag on the grain growth stagnation, it is possible to estimate their relative contribution using the previous literature. Lee et al.⁴⁴ have studied irradiation of nc-NiW (23 at. % W) alloy with a columnar grain structure, which was deposited using sputtering. Unlike the current study, the grains grew from 15 nm to 350 nm when it was irradiated with Kr⁺ ions up to a damage of 83 dpa. Although the texture and grain boundary characteristics were not studied, columnar grain structure may make the formation of low energy CSL boundaries less probable. Hence, a solute drag mechanism cannot be solely responsible for the stagnation in grain growth observed in irradiated nc-NiW.

Therefore, we propose that the formation of low energy Σ3 grain boundaries is the primary mechanism for IIGG stagnation observed in irradiated nc-NiW.

We have analyzed grain growth, texture development, and grain boundary characteristics in a thermally stabilized nc-NiW alloy under high energy irradiation. Although the grains in nc-NiW grow continuously for moderate doses of irradiation (0.5 × 10¹⁶ ions/cm² or damage of 10 dpa), they stop growing at higher doses. This grain growth stagnation at a grain size of ∼32 nm is of practical significance because it will slow down the deterioration of sink strength in nc-NiW. The main conclusions of this study are listed below.

• The irradiation-induced grain growth in nc-NiW is similar to irradiation-induced grain growth in nc-Ni for moderate Ni⁺ doses (0.5 × 10¹⁶ ions/cm² or damage of 10 dpa). Although grain boundary energy of thermally stable nc-NiW is only 40% of nc-Ni, it is not low enough to significantly slow down the grain growth as hypothesized by some researchers.

• Kaoumi's model for irradiation-induced grain growth fits the experimental data well up to a dose of 0.5 × 10¹⁶ ions/cm² (or damage of 10 dpa). For higher doses, Kaoumi's model predicts slower yet perpetual grain growth, but the current study shows that grain growth stagnates. Hence, Kaoumi's model for irradiation-induced grain growth applies to nc-NiW up to a moderate dose but fails at higher doses.

• Irradiation of nc-NiW results in the formation of a strong biaxial texture and a high-volume fraction of low energy Σ3 grain boundaries. These boundaries can exhibit very low mobility and cause stagnation in irradiation-induced grain growth. In future work, it will be of interest to quantify the relative importance of low energy Σ3 boundaries vs fast moving boundaries that are swept out.

This work was supported by the National Science Foundation (NSF) under Grant No. CMMI 1635332, and by the Carnegie Mellon University (CMU) Scott Institute Seed Program. We thank Professor Christopher Schuh (Massachusetts Institute of Technology) for providing the 0.5 um thick NiW specimens and Professor Anthony Rollett (CMU) for help with X-ray pole figures. Lin Shao is partially supported by US National Science Foundation through grant 1708788 (DMR).

Kaoumi et al. derived the following expression for the constant K in Eq. (1) of the main body:

where the definitions and values of these parameters for nc-NiW are shown in Table II.

The 0.5 μm thick specimen was cut into 1 × 0.3 cm² pieces and irradiated with 2 MeV Ni⁺ ions at room temperature. The rate of irradiation was 1.2 × 10¹² ions/cm²/s, and the beam spot size was approximately 7 × 7 mm². Irradiation parameters were calculated using SRIM (Stopping and Range of Ions in Matter) software.²⁵ Doses were from 0.05 × 10¹⁶ to 5 × 10¹⁶ ions/cm², corresponding to 1–100 displacements per atom (dpa) on different samples at a rate of 0.0024 dpa/s.

A platinum layer of 1–2 μm thickness was deposited by electron and subsequently ion beam to form a protective layer against ion beam damage during ion milling. The specimen was ion milled by a 30 kV Ga⁺ ion beam with 7 nA current and welded onto a copper TEM grid. Further cleaning and thinning were done using 30 kV (1 nA) ion beam. An additional final thinning was done by tilting the specimen 3° and milling with a 5 kV (70 pA) ion beam.

For electrojet polishing, a Nital solution (120 ml nitric acid in 400 ml methanol) at −20 °C was used as the electrolyte. The copper substrate was first thinned to approximately 500 μm using mechanical polishing. The nc-NiW side was then covered with scotch tape to protect it from the electrolyte during the electrolytic thinning process.

First, we used a grain dilation filter with a grain tolerance angle of 5° and a minimum grain size of 5 pixels. This process takes care of pixels that are not associated with any grain, yet have neighboring points that do belong to a grain. If the majority of pixel neighbors belong to the same grain, then the orientation of that pixel is changed to match that of majority grains. Second, a confidence index (CI) standardization cleanup method was used again with a grain tolerance angle of 5° and a minimum grain size of 5 pixels. This method changes the CIs of all the points in a grain to the maximum CI found among all the pixels belonging to that grain. Finally, a single average grain orientation per grain with a grain tolerance angle of 5° was used. This method takes care of slight misorientation that arises from minute differences in indexing.

SRIM is a Monte Carlo simulation software that tracks the energy and position of all the recoils as the ion passes through the material. We simulated a bombardment of 10⁴ Ni⁺ 2 MeV ions in 17.5 at. % W in nc-NiW to generate statistically significant data for calculation. A displacement energy of 25 eV was used for both Ni and W. The energy of all the primary knock on atoms (E_PKA) was recorded as the Ni ion passes through this material. All the parameters were calculated using a process similar to Kaoumi as shown below.

For each ion, the energy of PKAs $(EPKA)$ is recorded and compared with thresholds to calculate the number of spikes it generates in the following fashion:

If E_PKA < 2 keV, no spike is generated.

If 2 keV < E_PKA < 200 keV, 1 spike is generated.

If E_PKA> 200 keV, E_PKA/200 is the number of spikes generated.

This process is then repeated for each ion. These numbers were then averaged over the 10⁴ ions and divided by the film thickness to obtain the value of $χ$⁠.

Q is estimated as follows:

where $E¯i$ is the average energy of the spikes created by ion i.

where $a0$ is the lattice parameter of the material in nanometers.