Nanostructuring has been proposed as a method to enhance radiation tolerance, but many metallic systems are rejected due to significant concerns regarding long term grain boundary and interface stability. This work utilized recent advancements in transmission electron microscopy (TEM) to quantitatively characterize the grain size, texture, and individual grain boundary character in a nanocrystalline gold model system before and after in situ TEM ion irradiation with 10 MeV Si. The initial experimental measurements were fed into a mesoscale phase field model, which incorporates the role of irradiation-induced thermal events on boundary properties, to directly compare the observed and simulated grain growth with varied parameters. The observed microstructure evolution deviated subtly from previously reported normal grain growth in which some boundaries remained essentially static. In broader terms, the combined experimental and modeling techniques presented herein provide future avenues to enhance quantification and prediction of the thermal, mechanical, or radiation stability of grain boundaries in nanostructured crystalline systems.

Nanocrystalline metals have received a great deal of research interest due to an assortment of interesting properties that stem from the high grain boundary density.1,2 However, microstructural stability limits this significant potential in many environments. Nanocrystalline metals are known to undergo grain growth not only under anticipated conditions like at elevated temperatures3,4 but also in less intuitive cases like ambient temperature5 and deformation-induced grain growth.6,7 Grain growth mechanisms in nanocrystalline metals are not straightforward to understand, as grain boundary mobility depends sensitively on chemical composition, grain/boundary orientation, grain boundary character, local stress fields, and temperature.8–12 

The high grain boundary density in nanocrystalline metals provides abundant sinks for structural and chemical defects. These aspects have positioned nanocrystalline metals as promising candidates to replace conventional materials in certain radiation environments.13–15 However, radiation has also been found to induce grain boundary motion and grain growth in both pure and alloyed metals.16–18 Some previous work utilizing in situ ion irradiation transmission electron microscopy (TEM) investigated microstructural stability in several nanocrystalline metal systems as a function of temperature, and ion species, energy, and fluence.19 Motivated by the work of Vineyard,20 Kaoumi et al.19 proposed a model for irradiation-induced grain growth based on the direct effects of thermal spikes on grain boundary properties. The authors reported normal grain growth, and attributed it to enhanced grain boundary mobility in the vicinity of cascades. There have also been some experiments combining ex situ irradiation and orientation mapping.21 These sorts of experiments build a statistical understanding of global changes in grain size and texture, but they do not track characteristics of individual grain boundaries, and thus miss the root of the behavior.

In this work, we sought to better understand the finer points governing grain boundary migration and grain coarsening in nanocrystalline metals during ion irradiation. To this end, we used a unique combination of experiments and modeling. Nanocrystalline samples were characterized by advanced TEM techniques before, during, and after in situ ion irradiation. Experimentally obtained initial crystallographic orientation maps were used as initial structures for a mesoscale model. We compare microstructure evolution from the model and the experiment.

Au films approximately 40 nm in thickness were deposited by pulsed laser deposition (PLD) onto single crystal NaCl substrates.3 TEM characterization and in situ ion irradiation at a flux of 6.6 × 1011 ions cm−2 s−1 to a fluence of 2.7 × 1015 ions cm−2 (approximately 0.35 displacements per atom) were performed using the 200 kV JEOL 2100 at the In Situ Ion Irradiation TEM (I3TEM) facility at Sandia National Laboratories.22 The 10 MeV Si beam selected favors electronic over nuclear (collisional) stopping power, and results in mostly linear ion trajectories within the sample. These conditions confine most of the beam interactions to a more spatially localized volume than might be expected with a lower energy and/or heavier ion beam. As will be described in the next paragraph, this sort of localized ion-solid interaction was the most straightforward to implement for an initial version of the model. In addition to standard TEM bright field (BF) imaging and selected area electron diffraction (SAD), orientation maps were collected by a precession-assisted scanning TEM diffraction technique23 that rastered a focused electron probe across the sample. This technique is sensitive to overlapping grains and inclined boundaries within the film, so areas with well-defined grains and boundaries (suggesting through-thickness columnar grains) were selected for in-depth analysis.

The experimentally obtained maps were used as input for a mesoscale simulation of the microstructure evolution based on the phase field method described in Refs. 24 and 25. Given the assumption of through-thickness columnar grains in selected areas of interest, the model was implemented in two dimensions for ease of computation. Model parameters uniquely define grain boundary energy, width, and mobility, enabling studies of grain growth as a function of these parameters. Microstructural change from a single ion is largely confined to the volumes of the collision cascades, which occur mostly along the path of the ion. Hence, we approximate the size of the affected area as having a diameter of a single cascade. The initial kinetic energy transferred to atoms within a collision cascade can be interpreted as a spatially localized thermal event26 with maximum temperature related to the deposited energy density, θD, by 3kBTmax=θD, where kB is the Boltzmann constant.27 Although these events quench in tens of picoseconds, they provide an upper-bound limit for temperature. Subsequent evolution of leftover defects occurs on much longer timescales, but for a single ion much of the evolution is still spatially confined near the initial ion path. The simulations incorporate these drastically different time scales by introducing spatially and temporally localized events as small regions of greatly enhanced mobility, with temperature-dependent grain boundary mobility, Mgb, defined by MgbeΔE/kBT, where ΔE is an activation energy. Thermal events with Gaussian profiles and random spatial distribution are introduced at discrete times, with the number, size, and temperature of the events chosen to match the experimental ion fluence. We note that we have intentionally chosen a system in which the effects can be reasonably simplified to a single spatially and temporally localized event. In principle, this technique could be extended to more complex (e.g., highly branched) cascade geometries. Specifics of the experimental and simulation procedures are described in detail in the supplementary material.28 

The BF micrograph of the as-deposited sample in Fig. 1(a) reveals a broad distribution of grain sizes, from tens of nm to a few hundred nm, a microstructure typical of Au and other metal thin films.29 A video collected during this in situ irradiation is available online (supplementary video SV128). Fig. 1(b) shows the same area after irradiation with 10 MeV Si3+ to a dose of 2.7 × 1015 cm−2. While defect clusters were apparent, we note that this density was quite low in comparison to what would be expected from a beam with higher nuclear stopping power.22,30 Some movement of grain boundaries and grain growth was also immediately apparent, for example, grain 1 (marked in Figs. 1(a) and 1(b)). Also notable were the contrast changes in several grains due to the high sensitivity of diffraction contrast to sample tilt. These changes make the micrographs more difficult to interpret, especially for automated methods. Figs. 1(c) and 1(d) correspond to panels (a) and (b), respectively, and highlight local orientation and grain boundaries by combining orientation and correlation index information.31 The full dataset including separate TEM, correlation index, orientation, and reliability appears in the supplementary Fig. SF1.28 The orientation data were less affected by strain and diffraction contrast, and better highlight the grain boundary areas. Several grains clearly increased in size at the expense of smaller grains, and boundaries migrated. Qualitatively, the finely grained area near the center grew coarser. Overall, (111) oriented grains (blue) mostly grew at the expense of other textures, however, in the upper left, an enlarged area of (100) is apparent. The orientation maps have a powerful benefit of being readily quantified both globally (e.g., average grain size and texture) and locally (e.g., character of individual boundaries).

FIG. 1.

Bright-field TEM images (a) and (b) and associated orientation maps (c) and (d) collected from the same area of the nanocrystalline Au sample before ((a) and (c)) and after ((b) and (d)) in situ TEM ion irradiation with 10 MeV Si3+ to a dose of 2 × 1015 cm−2. Grain 1 is indicated by the number 1. Panels (c) and (d) show combined orientation and index data, with orientation taken normal to the sample surface. (e) and (f) Corresponding grain size histograms from before (e) and after (f) in situ ion irradiation.

FIG. 1.

Bright-field TEM images (a) and (b) and associated orientation maps (c) and (d) collected from the same area of the nanocrystalline Au sample before ((a) and (c)) and after ((b) and (d)) in situ TEM ion irradiation with 10 MeV Si3+ to a dose of 2 × 1015 cm−2. Grain 1 is indicated by the number 1. Panels (c) and (d) show combined orientation and index data, with orientation taken normal to the sample surface. (e) and (f) Corresponding grain size histograms from before (e) and after (f) in situ ion irradiation.

Close modal

Orientation distribution functions in the supplementary Fig. SF228 showed a slight increase in the intensity of the (111) texture. Though the change here was small, such data could feasibly be compared to texture information obtained from larger areas by other techniques like X-ray diffraction, although this was not done in this study. Thus, they provide an important link to other analytical methods. Grain diameter histograms (cf. Figs. 1(e) and 1(f)) indicate a peak in the 20–30 nm bin, and heavy right tails leading to considerably larger average (mean) diameters with large standard deviations. The change in average grain diameter was small, from 43 to 48 nm, and the fraction of grains smaller than 40 nm decreased considerably. Although the number of large grains was small, they covered a significant fraction of the measured area. The five largest grains represented 11% of the total measured area before irradiation, a figure that increased to 16% after irradiation. Finally, the total number of grains counted fell from 485 to 368, a decrease of 25%. These three observations all indicate that larger grains grew at the expense of smaller grains. A closer look at a few grains provides insight into this process.

Images detailing part of the irradiation-induced microstructure change appear in Figs. 2(a) and 2(b), before and after irradiation, respectively. Note that the areas shown are magnified views of Fig. 1. Panels (c) and (d) show the corresponding correlation index maps and computed grain boundaries. Here, orange, yellow, cyan, and blue represent boundaries with misorientation angles, φ, in the respective ranges of φ < 3°, 3° ≤ φ < 15°, 15° ≤ φ < 30°, and 30° ≤ φ. These values correspond to sub-grain (given the ≥3° boundary definition), and low-, medium-, and high-angle grain boundaries. A number and letter, as in grains 7a and 7b, identify sub-grains. For discussion, we will identify boundaries between grains by the grain numbers, e.g., “boundary 1–2” is the boundary between grains 1 and 2. In general, the boundaries were found in the same locations as would be anticipated from the BF micrographs. For example, the boundaries among grains 15 through 19 appear quite clearly in Figs. 2(a)–2(d). There are some areas, particularly those with the smallest grains, in which the boundaries were more difficult to identify in both the BF and index maps. We note that grain boundaries in a TEM foil are not always perpendicular to the foil plane, and the presence of overlapping grains causes uncertainties in the orientation map data. However, Au has a strong tendency for columnar growth, and many grain boundaries appear as sharp orientation changes, suggesting that the sample was composed mostly of columnar grains. To avoid ambiguity issues, most of the following analysis focuses on the areas that were most clearly defined.

FIG. 2.

Closer views of grain 1 from Fig. 1. Bright field micrographs (a) and (b) and index maps (c) and (d) with grain boundaries highlighted before and after irradiation. Orange, yellow, cyan, and blue indicate grain boundaries with misorientation angles in the respective ranges of 0°–3°, 3°–15°, 15°–30°, and ≥30°. Grains are numbered clockwise from the bottom right. Arrows in (d) indicate directions that boundaries moved. (e) Phase field representation of the structure shown in (c). (f) Grain structure after homogenous annealing. (g) Snapshot taken during simulated irradiation. Red spots indicate one set of thermal events. In panels (e)–(g), white (blue) regions represent grain (boundary) regions. (h) Average grain diameter as a function of characteristic time. Red diamonds show the homogenous anneal, while blue circles indicate 5 thermal event runs. The blue line shows the average of these 5 runs.

FIG. 2.

Closer views of grain 1 from Fig. 1. Bright field micrographs (a) and (b) and index maps (c) and (d) with grain boundaries highlighted before and after irradiation. Orange, yellow, cyan, and blue indicate grain boundaries with misorientation angles in the respective ranges of 0°–3°, 3°–15°, 15°–30°, and ≥30°. Grains are numbered clockwise from the bottom right. Arrows in (d) indicate directions that boundaries moved. (e) Phase field representation of the structure shown in (c). (f) Grain structure after homogenous annealing. (g) Snapshot taken during simulated irradiation. Red spots indicate one set of thermal events. In panels (e)–(g), white (blue) regions represent grain (boundary) regions. (h) Average grain diameter as a function of characteristic time. Red diamonds show the homogenous anneal, while blue circles indicate 5 thermal event runs. The blue line shows the average of these 5 runs.

Close modal

Of particular interest are boundaries 1-6b and 1-7b, both approximately 18°. These boundaries are identifiable in the BF micrograph. Though difficult to see in the BF image, a nearby subgrain boundary (<3°) divides the lower grains into 6a,b and 7a,b, as revealed by the orientation maps. After irradiation, however, boundaries 1-6 and 1-7 had advanced approximately 30 nm, stopping near the initial location of the subgrain boundary, and the subgrains disappeared. We note that grain 1 also clearly grew by consuming entire grains as well. Grains 8 and 11 are absent after irradiation (Figs. 2(b) and 2(d)), and grain 1 consumed part of grain 9 as well. Similarly on the other side of grain 1, grains 2-5 were nearly completely consumed, and it appeared that grain 1 was in the process of consuming grain 3. Grain 13 expanded by the movement of low angle boundaries 12-13a and 13a-14. While the general trend suggested by the grain size histograms was mostly consistent, this closer examination revealed a few discrepancies, e.g., the stability among grains 15-17, each of those was initially <50 nm diameter but remained essentially unchanged. These boundaries were likely less mobile, or not exposed to extensive radiation effects, two possibilities that will be discussed further in the following paragraphs.

As mentioned previously, the initial orientation map data (i.e., Fig. 2(c)) was used as an experimentally collected starting structure for the phase field model, as seen in Fig. 2(e), where white and blue areas, respectively, represent grain and grain boundary regions. Fig. 2(f) and the supplementary video SV228 show the microstructure evolution during simulated homogeneous annealing, where grain boundary mobility is uniform everywhere. The rapid loss of smaller grains (e.g., 8, 11, 16, and 17) and evolution towards qualitatively rounder grains and straighter boundaries suggest normal grain growth. A simulation run for the same number of time steps incorporating spatially random thermal events appears in Fig. 2(g) and the supplementary video SV3,28 and again shows the behavior characteristic of normal grain growth. The graph in Fig. 2(h) compares the temporal evolution of the average grain size for each system. To account for the variations stemming from the stochastic nature of the thermal events, five independent runs are included. In comparing these model cases, it is important to note that the evolution is dependent on the far-field temperatures and thermal event parameters (diameter, temperature, and density) chosen. Also, note that the random spatial distribution of thermal events (as was the case experimentally) results in a unique evolution pathway with each run of the simulation, depending on the order in which boundaries are struck (see supplementary Fig. SF328). We note that growth in both simulated cases scaled approximately with T1/n, where n was in the range of 2–3, and nirradiation > nhomogeneous. Similar scaling and flattening of the grain growth curve over time (Fig. 2(h)) has been reported in other studies,17–19,32,33 and is related to the falling probability that a given thermal event will affect a grain boundary. Thermal events occurring far enough from grain boundaries fail to contribute to grain growth, so irradiation-induced growth eventually stagnates. Given the different scaling behaviors, this implies that in the homogenous growth case the grain size should eventually surpass the maximum grain size in the irradiation case.

Experimentally, no obviously “abnormal” grains (i.e., large, rapidly growing grains surrounded by much smaller grains) were noted, which is consistent with results reported in previous investigations.17–19,32,33 However, the observed growth deviated subtly from normal in the sense that some boundaries moved while others remained essentially static. This is most striking in the case of grains 16 and 17 in Fig. (2); both are small, but neither the grains nor the boundary between them changed substantially. In contrast, in both simulations these grains quickly merged and began to shrink away. We first note that grain 1 and most surrounding grains initially had similar {111} orientations (supplementary Fig. SF128), with the exception of grains 8 and 11. Surface energy differences may have played a role in the disappearance of those grains, but are unlikely to have strongly influenced the others. Given the ion fluences, it is unlikely that the area was unaffected by radiation effects. Instead, these observations suggest mobilities that may be non-thermally activated, or anisotropic due to misorientation or inclination.11,34 For example, examination of the orientation data revealed that boundaries 16–17 had a misorientation angle of 60°, and were identified as a Σ3 boundary. These measurements are consistent with a coherent twin, which is anticipated to be rather stable. The implementation of the model used here treated all the grain boundaries similarly; a logical next step would be to include misorientation angle-dependent properties,35–37 or a more refined approach incorporating specific mobilities for individual boundary types computed from molecular dynamics simulations.9 

The combination of orientation mapping with in situ TEM methods has been powerful in resolving microstructure changes at elevated temperatures,4 and those induced by mechanical deformation.38–40 The addition of coordinated modeling further extends this capability. While the ion and target species were selected in this study specifically because they undergo grain growth, this technique can in principle be utilized to probe the fundamental mechanisms of grain boundary migration during irradiation in essentially any crystalline material system. This study may lead to better predictive models of grain boundary migration, and has practical implications in engineering more stable grain boundary structures that resist radiation-induced migration, potentially improving the long term microstructure stability of irradiated nanostructured metals.

A fundamental understanding of grain boundary mobility is crucial for designing nanocrystalline metals that maintain their desirable properties in a variety of environments. TEM orientation mapping provides a practical means of quantitatively characterizing statistically relevant numbers of grains and grain boundaries at the nanoscale, while the combination with in situ ion irradiation yields a way to monitor the radiation stability of individual boundaries. Incorporation of the orientation map data within the phase field model allows for direct comparisons between experiments and modeling. Tunable model parameters for grain boundary energy and mobility allow for exploration of the effects of these parameters. Discrepancies between the experiments and model in this study suggest a degree of anisotropic grain growth in this system, an observation that likely stems from non-thermally activated or anisotropic grain boundary mobility.

We thank A. Darbal (AppFive LLC), D. Kaoumi (University of South Carolina), A. Leff (Drexel University), for valuable discussions, and B. L. Boyce, D. L. Buller, C. Gong, H. Lim, M. T. Marshall, and B. R. Muntifering (Sandia National Laboratories). This work was fully supported by the Division of Materials Science and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

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Supplementary Material