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C: Physical Processes in Nanomaterials and Nanostructures

3D Maps of Helium Nanobubbles to Probe the Mechanisms of Bubble Nucleation and Growth Noelle R. Catarineu, Norman C. Bartelt, Joshua D. Sugar, Suzanne Vitale, Kirk L. Shanahan, and David B. Robinson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00709 • Publication Date (Web): 10 Jul 2019 Downloaded from pubs.acs.org on July 17, 2019

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The Journal of Physical Chemistry

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3D Maps of Helium Nanobubbles to Probe the Mechanisms of Bubble Nucleation and Growth Noelle R. Catarineu,†,a Norman C. Bartelt,† Joshua D. Sugar,† Suzanne Vitale,†,b Kirk L. Shanahan,‡ David B. Robinson†,* †Sandia National Laboratories, Livermore, California 94551, United States ‡Savannah River National Laboratory, Aiken, South Carolina 29808, United States aCurrent

address: Lawrence Livermore National Laboratory, Livermore, California 94551, United States

bCurrent

address: Carnegie Institution for Science, Washington, DC 20015, United States

*[email protected], +1 925-294-6613

ACS Paragon Plus Environment

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2 Abstract

We present and analyze a 3D volume of nanoscale helium bubbles in a tritium-exposed palladium alloy that we have reconstructed by transmission electron tomography. Helium nanobubbles commonly form within metals during exposure to radiation and radioactive substances. The radioactive decay of tritium stored in metal tritides often results in a high density of these nanoscale helium bubbles. A persistent question about the mechanisms of bubble nucleation and growth has been the role of lattice defects and impurities. To address this matter, we have determined the 3D positions of helium nanobubbles in a palladium-nickel alloy exposed to tritium for 3.8 years. We introduce methods to determine the 3D shapes, volumes, and spatial positions of helium bubbles as small as 1 nm within solids. We find that the size and spacing of observed nanobubbles are not correlated. Our results suggest that previous models, which hypothesize initial, rapid homogeneous nucleation of nanobubbles followed by diffusion-limited growth as helium atoms join the nearest bubble, are inadequate. We propose that the lack of size and spacing correlation is due to traps of atomic helium in the metal lattice that allow bubbles to nucleate even at low average helium concentration. This work will facilitate development of high-fidelity models of helium nanobubble formation in radiation-exposed metals.


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3 Introduction

Helium atoms are introduced into metals in a variety of radiation environments, including implantation from ion beams or plasmas,1  self-irradiation by actinides,2  decay of tritium to helium-3 in metal tritides,3 and reaction of metals with energetic neutrons.4,5 In these situations, nanometer-scale bubbles often form. These bubbles can degrade the mechanical properties of the metal, 6,7,8 motivating the long-standing effort to understand the factors that control their size, spatial arrangement, and density.

Current understanding holds that bubble nucleation can in principle occur homogeneously. It has been long known that the clustering of helium interstitial atoms within a metal lattice is energetically favored.9 Since these helium clusters are sinks for additional helium, they grow and eventually displace metal atoms to form bubbles. The bubbles are then believed to act as sinks for helium atoms as well.10 Accordingly, after sufficiently many bubbles have nucleated, any lattice helium quickly diffuses to existing bubbles. In that case, the helium concentration in the metal lattice becomes so low that nucleation of new bubbles becomes unlikely, and bubble density approaches a constant value.

Helium atoms and clusters, however, are also likely to be trapped by defects such as vacancies and atomic impurities.11 In fact, without defects, helium atoms and clusters may be mobile enough to diffuse out of a sample before they can nucleate new bubbles or enter existing bubbles.12 We seek to elucidate the role of defects in the evolution of helium bubbles generated by the decay of tritium within metal tritides. Our analysis focuses on determining the correlation between a bubble’s size and its distance to neighboring bubbles. In the case of homogeneous bubble



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4 nucleation, after nucleation stops, each bubble will grow at a rate proportional to the volume and helium concentration of the metal lattice closest to this bubble. Therefore, after nucleation ceases, bubble size correlates with distances to neighboring bubbles. However, trapping mechanisms may exist that break this correlation. First, the presence of traps that bind helium but do not nucleate a bubble would prevent helium from joining the nearest bubble. Second, if defects are continuously generated by growing bubbles, 13 they could act as traps that induce nucleation of new bubbles after previously nucleated bubbles have grown significantly. Third, trapping sites could allow bubbles to nucleate at very low average helium concentrations in the metal lattice, again allowing bubbles to nucleate after other bubbles have grown significantly.

Little reliable information about the relationship between bubble size and spacing is available because bubbles have only been studied by 2D imaging. We applied electron tomography to this outstanding question to generate a 3D reconstruction of bubble sizes and locations that is mathematically derived from a series of 2D images obtained through a series of tilt angles.14,15 This technique has proven valuable in prior studies of noble metal nanostructures. We have previously applied this method to palladium samples with surfactant-templated nanopores.16,17 Recent reports also include tomography of nanoporous platinum,18,19 metal and alloy nanoparticles near atomic resolution,20,21,22 and defects in gold nanoparticles.23 In the work presented here, we performed electron tomography on a palladium-5 atom% nickel solid-solution sample24,25 (Pd95Ni5) stored in the β-phase as a concentrated tritide for 3.8 years. We observe bubbles with diameters typically of 1 – 3 nm with an average density of about 1 x 1025 m-3.


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5 An advantage of palladium alloys for study of helium bubbles is their reversible tritide formation near room temperature and pressure. Desorption of tritium causes a simple lattice contraction of palladium and likely preserves the configuration of the helium bubbles. Further, palladium and its dilute alloys are resistant to oxidation, which allows handling in air. Despite these advantages, the number of prior studies of tritium-induced helium bubbles in palladium and its alloys by electron microscopy remains small. Thomas and Mintz reported 1.5 – 2.0 nm diameter bubbles with densities of 5 – 10 x 1023 m-3 in a palladium foil aged for 66 days. 26 Thomas reported another sample aged to produce 0.01 helium atoms per metal atom, which would be expected after about 3 months of aging. Bubble density in this sample was lower within 5 nm of the surface than the bulk metal, presumably because helium near the surface escaped.27 More recently, bubble concentrations of 0.3 – 2 x 1025 m-3 were measured in palladium and palladium alloys aged for 1 – 8 months.28,29,30,31 A similarly aged Pd-Y-Rh alloy, subject to thermal desorption of tritium at 200 °C after aging, contained bubbles with diameters of about 1 nm.32

Uncovering the relationship between lattice defects and bubble growth requires experimental methods that minimize the production of additional defects in the metal. Introduction of helium into a metal by processes that displace host metal atoms, such as ion implantation or  decay, generates lattice vacancies that trap helium and presumably serve as bubble nucleation sites. This type of damage is not expected for helium generated by  decay of tritium as studied here. However, the lattice expansion of palladium and its alloys upon exposure to tritium may create defects capable of trapping helium.27,33 The palladium alloy sample studied here was subjected to hydrogen isotope absorption and desorption cycles at several stages of its life to study its bulk tritium absorption properties and to remove tritium for safe handling. An alternative method of



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6 studying helium trapped within metals without displacement damage involves implanting with helium ions at energies below the metal displacement threshold of a few hundred eV.34 However, this technique exposes only a nanometer-scale surface layer of the metal to helium.

In our sample, we find no clear correlation between bubble size and spacing. This result is inconsistent with the assumption that bubbles nucleate in a narrow time window and subsequently grow by simple diffusion of helium atoms to the nearest bubble. The lack of such a correlation suggests the presence of trapping sites for helium that are not resolved by the microscope, such as very small bubbles that nucleated but did not grow, or atomic-scale traps such as impurities or vacancies that have not nucleated bubbles.

Experimental Methods Sample preparation and tritium exposure The palladium-nickel sample described in this report has been the subject of prior publications that further detail the sample history.24,25 The sample was prepared as cold-rolled foil pieces with dimensions of about 0.1, 3, and 6 mm. It was subject initially, after 1 year, and after 2.5 years to cycles lasting a few days between the concentrated β-phase tritide and the dilute α-phase tritide by controlling the tritium overpressure at temperatures between room temperature and 338 K. After these experiments, the sample was stored in the concentrated β-phase. The sample was returned to the dilute α-phase after 3.8 years of storage as a β-phase tritide. It was stored in this form for about 3 months and then treated to four cycles between the concentrated β-phase deuteride and the dilute α-phase deuteride by controlling the deuterium overpressure to exchange trace tritium. The sample was stored as an α-phase deuteride for 15 years and then subject to two more deuterium cycles.


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7 The sample container was opened to reveal that the sample had decrepitated into particles with dimensions not significantly greater than the foil thickness. To determine residual radioactivity, a small quantity was dissolved in a 1:3 mixture of concentrated hydrochloric and nitric acids by shaking in a closed container. The sample was sealed for 24 hours and then diluted with an equal volume of water. A volume of 0.1 mL of this solution was withdrawn, and the container was closed. The withdrawn amount was diluted by a factor of 260, and 0.1 mL of this solution was added to 20 mL of Ultima Gold AB liquid scintillation cocktail. However, this solution was too dilute for detection of tritium. Seven days later, 5 mL was withdrawn from the dissolution container and diluted by a factor of 2. This solution was steam distilled to collect 1 mL of distillate, which was added to 19 mL of Ultima Gold AB and analyzed for tritium. The residual radioactivity of the sample was found to be 38 µCi/g. Particles were then affixed to a scanning electron microscope stub by double-sided conducting carbon tape. A sample of this age is expected to contain a helium-to-metal ratio of about 0.12, assuming no escape of helium from the sample.

TEM sample preparation Some samples for 2D imaging described here were prepared by encapsulation of particles in Cotronics Durapot 861 low-viscosity epoxy, curing at room temperature, and microtomy in a Leica EM UC7 ultramicrotome using a diamond knife following initial trimming with glass and diamond knives. The sample was captured on a water drop and transferred to a 200 mesh copper TEM grid. Other samples for 2D imaging were prepared by conventional lift-out techniques with a Thermo Fisher Scientific Helios NanoLab 660 Dualbeam Focused Ion Beam-Scanning Electron Microscope system (FIB-SEM).



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8 TEM tomography samples were prepared on a Fischione Instruments atom probe tomography sample post using the FIB-SEM. First, the sample post was mounted in a Ted Pella tube/needle clamp. The diameter of the end of the post was reduced from about 200 µm to about 2 – 3 µm using high ion current (65 nA) annular milling patterns. Ion beams were gallium except as specified. Next, a specific area of interest was identified from the sample particles. The surface of this area was protected by a thin layer of electron beam carbon deposition (about 50 nm) and a thicker layer of ion beam carbon deposition (1 µm). Using an ion beam current of 9.3 nA, a rectangle pattern was milled at an angle of 22° incident to the bulk surface above the carbon deposition layer. The stage was then rotated 180°, and the same rectangle pattern was milled above the carbon deposition layer. The triangular sample was lifted out of the bulk using the Thermo Fisher Scientific EasyLift in situ micromanipulator and was welded to the top of the sample post using platinum ion deposition. Starting at a beam current of 9.3 nA, annular milling patterns in decreasing diameters and currents were used to reduce the sample to a sharp tip. The final 30 kV ion beam current used was 24 pA. Low energy (5 kV) clean up milling (0.12 nA) removed any amorphous surface damage. The final sample tip diameter was about 12 nm.

TEM imaging 2D imaging of microtomed samples was performed on a JEOL 2010F field-emission electron microscope operating at 200 kV. Other 2D imaging was performed with a 300 kV Thermo Fisher Scientific Titan Themis Z electron microscope. 3D representations of the bubble structure were generated by 3D electron tomography. The needle shaped specimen was loaded into a Fischione Model 2050 on-axis tomography TEM holder that is specifically designed for needle geometries. A series of 141 high-angle annular dark field scanning transmission electron microscopy (HAADF


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9 STEM) images were collected at 1° increments from -70 to 70° of α tilt such that the needle was rotated about its symmetric axis. The 2048 x 2048 16-bit grayscale HAADF images were collected on a Thermo Fisher Scientific Titan 80 – 200 probe-corrected instrument with a Fischione HAADF detector and a pixel dwell time of 6 µs at a magnification of 450 kX corresponding to a pixel size of 89.3 pm. The STEM convergence angle was 20 milliradians and HAADF detection range was 50 – 200 milliradians. The 0° image was collected both at the start and halfway through the dataset. Alignment and overlay or mutual subtraction of the two images showed no perceptible evidence of beam damage.

Reconstruction of 3D bubble map Images were preprocessed with GNU Octave scripts.35 SER files generated by the instrument were converted to TIFF images using a script by Peter Ercius of Lawrence Berkeley National Laboratory.36 Some images included in the analysis display distortions due to environmental perturbations near the microscope. Images were initially scaled so that their minimum and maximum intensities were 0 and 65,535. To roughly align the images along the rotational axis, each image row was summed. A row in each image was identified that had a sum closest to a chosen threshold value representative of the tip. These rows were aligned, while cropping data that shifted beyond the top row. Each column was then summed and aligned versus the zero-angle image using a cross-correlation script available on the website of the John Miao group at the University of California, Los Angeles,37,38 with the maximum of the zero-angle image aligned with the center line. The images were then rescaled to make the sums of their intensities equal. A mask for each image was created by assigning a threshold that eliminated most of the carbon on the edges of the sample. To reduce edge roughness and stray pixels in the masks, dilation and erosion



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10 operations were performed. A 60 x 60 pixel Blackman-Nuttall low-pass filter was applied to each image. Each unfiltered image was then subtracted from its correspoding low-pass filtered image, retaining data as signed 16-bit integers with -32,768 representing black and 32,767 representing white. This operation causes voids in the sample to appear in the filtered projections as highintensity features. Masks were then applied to the filtered images, and the resulting set of images converted to the mrc file format. The 3D volume was then further translationally aligned by iterations of 2D cross-correlation of images at adjacent angles, and rotationally aligned by identifying the tilt axis in the Fourier domain, using Thermo Fisher Scientific’s Inspect3DTM software. Reconstruction was performed by the weighted back projection algorithm in Inspect3DTM with filter settings of 0.1 max and sigma.39 This filter ramps linearly from zero to 1 over frequencies of zero to 0.1 times the maximum spatial frequency and then decays from 1 at that frequency back to zero at the maximum spatial frequency according to a Gaussian curve with sigma (width) equal to 0.1 times the maximum spatial frequency. Visualization and analysis of the 3D data was performed with Thermo Fisher Scientific’s Avizo Fire using an intensity threshold of 4,000 to define bubble volumes. This intensity was chosen by inspection of 2D grayscale slices and 1D intensity line scans of the reconstruction to distinguish apparent bubbles from noise and reconstruction artifacts. Erosion and dilation steps with a mask size of 3 pixels were applied to merge small, closely spaced bubbles, based on the assumption that the separation of these bubbles was an artifact of noisy signals crossing a fixed threshold. Voronoi tessellations for the bubble distributions were computed with the open-source software Voro++.40,41


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11 Results and discussion 2D electron microscopy of the Pd95Ni5 sample shows an array of circular features of about 2 nm diameter spaced 5 – 10 nm apart (Figure 1). Imaging at overfocus and underfocus conditions with the objective lens induces Fresnel contrast reversal with bright circular features at underfocus and dark circular features at overfocus.42 As expected in the case of bubbles or voids, this contrast inversion indicates lower electron density in the circular features than the surrounding metal. Bubbles were not observed in a control sample of the same alloy that was not exposed to tritium; no contrast reversal between underfocus and overfocus conditions was observed when imaging this non-tritiated control sample. No significant differences in bubble size or spacing were observed between samples sectioned by focused ion beam (FIB) or microtome, or from cycles of hydrogen exposures of a FIB-prepared sample under conditions expected to cause phase transitions between the dilute  phase and concentrated  phase. (Figure 2). These data confirm that the observed features are bubbles caused by exposure to tritium and are not sample preparation artifacts or pre-existing defects in the palladium alloy. Our comparison of bubbles before and after hydrogen exposure suggests that decontamination of a tritium-exposed sample by hydrogen cycling does not disrupt existing bubbles. However, it does not rule out the possibility of hydrogen cycling impacting the bubble evolution of a subsequent tritium exposure.



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Figure 1. TEM images of (left) Pd95Ni5 sample exposed to tritium for 3.8 years; (right) Pd95Ni5 sample never exposed to tritium. Top: in focus; middle: underfocused by 417 nm (left) and 2,152


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13 nm (right); bottom: overfocused by 762 nm (left) and 1,586 nm (right). Sample thicknesses are estimated at 50 – 100 nm based on electron energy loss spectra.

Figure 2. Scanning transmission electron microscopy high-angle annular dark field images of tritium-exposed Pd95Ni5 sample. Top: prepared by microtomy. Middle: prepared by FIB. Bottom:



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14 prepared by FIB and then exposed to 5 cycles of hydrogen at room temperature between 345 kPa and vacuum, spending 5 minutes at each pressure.

To produce a 3D map of bubbles in the material, a sample was prepared with a tip geometry, as typically employed in atom-probe tomography. The advantage of this geometry is the ability to mount on a stage and rotate about its central axis without occlusion from other parts of the sample or holder, facilitating high-quality reconstructions.43 The tip geometry also provides a well-defined sample boundary that aids the accurate image alignment necessary for tomographic reconstructions. In the HAADF STEM imaging mode, the signal intensity scales approximately with the quantity of metal intersecting the electron beam, and diffraction effects are less significant. The metal appears bright and bubbles are dark in the series of collected images (Figure 3). During animation of the entire set of aligned images, the bubbles appear as dark spots that shift in position as the sample is rotated on its long axis (Supporting Movie 1). Some carbon contamination is present on the surface of the tip. We applied a high-pass filter to obtain a flat baseline intensity and invert the image contrast as described in the methods section. The set of filtered images is included at the end of Supporting Movie 1.


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15

Figure 3. Scanning transmission electron microscopy high-angle annular dark field images of tomography sample tilted about the central axis by 45° increments. Supporting Movie 1 contains an animation of the complete tilt series.

Because quantitative accuracy in bubble positions and sizes is crucial to our analysis, we now describe in detail the techniques we employed to locate the nanoscale bubbles of helium. We performed a 3D reconstruction using the weighted back projection method of the Inspect3DTM software. To gain confidence that our results are insensitive to the chosen reconstruction method, we generated reconstructions with both the Inspect3DTM weighted back projection and SIRT (Simultaneous Iterative Reconstruction Technique) methods while employing several filter settings. We reconstructed our data set with the GENFIRE (GENeralized Fourier Iterative REconstruction) software as well.44 We then compared lines and planes through the 3D images and found that the various algorithms yielded similar results. Animations of the set of slices through the reconstructed 3D image are provided as Supporting Movies 2 and 3. Bubbles can be easily identified by inspection of slices parallel to the tip/tilt axis, whereas slices perpendicular to the axis show streaks and ripples that make interpretation more difficult (Figure 4). These artifacts result from the finite number of tilt angles measured, filtering applied to the images, imperfect



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16 spatial alignment, and the interaction of these effects with noise in the projections. We presume the resolution limits of the imaging may cause sub-nm bubbles to be undetected and/or noise and artifacts to occasionally be interpreted as small bubbles. However, the agreement between the 3D reconstruction and 2D images in terms of bubble diameters and densities is satisfactory.


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Figure 4. Slices through the 3D reconstruction of the sample (A) parallel and (B) – (D) perpendicular to the tip/tilt axis. Supporting Movies 2 and 3 are animations of larger sets of these parallel and perpendicular slices, respectively.



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18 Regions in the 3D dataset were categorized as bubbles through several segmentation steps. First, we applied an intensity threshold below which we judged a voxel not part of a bubble. A histogram of image intensities for the entire dataset did not yield a bimodal distribution in which the threshold could be set at the minimum between peaks, in part because the intensities within bubbles were broadly distributed. Similarly, we also did not observe bimodal intensity distributions in 2D HAADF images of the sample. However, inspection of smaller regions of the data provided a systematic method to distinguish signal from noise. Figure 5 shows plots of line scans through apparent bubbles and through regions near the edge of the sample that contained no features resembling bubbles. We chose an intensity threshold of 4,000 that included nearly all lines through apparent bubbles and excluded nearly all lines without apparent bubbles. It is apparent from Figure 5 that if the threshold is too high, the number and size of bubbles will be underestimated, whereas if it is too low, many false bubbles could be included. To further distinguish bubbles from noise, and to take advantage of the 3D nature of the dataset toward this goal, we applied an erode and dilate function with a cubic mask size of 3 voxels. The erosion eliminated small bubbles that are indistinguishable from noise as well as thin streaks of reconstruction artifacts. The dilate step approximately restored the original size of bubbles prior to erosion.


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19

Figure 5. Vertical line scans through a slice of the 3D reconstruction perpendicular to the tilt axis. Red traces are line scans that intersect features suspected to be bubbles. Black traces are line scans near the edge of the sample and do not intersect features suspected to be bubbles. Dashed line represents the chosen intensity threshold.

By this segmentation process, we extracted from the 3D reconstruction the set of nanoscale helium bubbles within the metal, including the 3D size, shape and position of each individual bubble. Figure 6 depicts 2D projections of the reconstructed 3D bubble map with bubbles colorcoded by size. An animation of a finer range of viewing angles is available as Supporting Movie 4. There is some distortion of bubble shape due to the incomplete range of tilt angles measured.



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20 The bubbles have a characteristic size and spacing with some random variation and no apparent spatial ordering. Bubbles appear to increase somewhat in size closer to the sample tip. We believe this effect is due to the higher resolution expected in thinner sample regions45 but may also involve more focused ion beam damage in thinner regions.


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Figure 6. Projections of the 3D bubble map tilted about the central axis in 90° increments. Bubbles are color-coded by size, with larger bubbles red and smaller bubbles blue. Supporting Movie 4 is an animation of these projections.



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22 As discussed in the Introduction, if bubbles are the only sinks of helium generated by tritium decay, then after nucleation has stopped, the amount of helium diffusing to a given bubble will be proportional to the volume of the region nearer to this bubble than to any others. We performed a 3D Voronoi tessellation of the sample to determine the volume nearest each bubble (Figure 7 and Supporting Movies 5 and 6). From the tessellation, we also obtained the distributions of numbers of neighboring bubbles and of distances to each neighboring bubble. In short, this 3D Voronoi tessellation allowed us to quantify the spacing and density of the bubbles. Due to difficulties in the definition of an outer boundary of the solid that is recognized by the tessellation software, we discarded volumes that intersected the boundary of the reconstruction volume from our analysis. We also sought to reduce the number of volumes that protrude out of the sample volume, which are not representative of the interior of a bulk sample, while ensuring that a negligible number of volumes within the sample were discarded. To accomplish this, we discarded volumes with face areas exceeding 7,000 pixels (55.9 nm2). The area threshold was chosen by identifying a region on a histogram of face areas above which the number of faces per bin was less than 0.67% of the peak. We observed that the bubble density is approximately constant when the tip diameter is less than about 50 nm but decreases where the tip is wider. This difference in bubble density is consistent with the greater difficulty of resolving small bubbles in the thicker region of the sample given the fixed number of projections.45 The limited depth of field afforded by the STEM probe in each projection could also contribute to the decrease in observed bubble density in the thicker sample region.46 We omitted this thicker region of the sample from further analysis, leaving a population of 395 bubbles.


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23

Figure 7. Left: Outer surface defined by Voronoi tessellation. Right: View of Voronoi polyhedra obtained by scaling their coordinates by one-third. Top and bottom images are offset by 90°. Supplementary Movies 5 and 6 are animated versions of these representations of the polyhedra.



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24 A central question of our investigation is whether the bubbles we have detected in the above analysis are the only traps of helium. To answer this question, it was necessary to approximate the total amount of helium stored in the bubbles. We first estimated an upper bound on the concentration of helium in the bubbles based on our 3D representation. We found an average Voronoi volume of 90 nm3, corresponding to an average bubble density of 1.1 x 1025 m-3. The average bubble volume is 3.5 nm3. Bubbles thus occupy 3.9% of the sample volume. The expected ratio of helium to metal based on the sample age is about 0.12, including helium in bubbles, trapped within the lattice, or that escaped from the sample. Based on prior studies,47,48 we expect that less than 10 percent of the helium has escaped. We assume that bubbles are all pressurized to values near the requisite value to displace metal atoms such that their helium content is proportional to their volume. If all helium within the sample resides in bubbles, the helium concentration would be about 220 atoms/nm3, which by most estimates of the helium equation of state would correspond to implausibly high pressures in the tens of GPa or more.49 This result is strong evidence that some helium in the sample does not reside in the nanoscale bubbles we have identified. We hypothesize that additional helium remains in the metal lattice as helium atoms or clusters at atomic-scale traps or in sub-nm helium bubbles that were not detectable.


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25 Further evidence for these additional sinks for helium atoms comes from our examination of bubble size and separation. Our analysis of bubble volumes and nearest neighbor distances produced broad and asymmetric distributions (Figure 8B and C) and reveals the extent to which average bubble density is an incomplete characterization. If bubbles nucleate randomly in 3D space, their Voronoi volume distribution should be approximately log-normal.50,51 We indeed observe a log-normal distribution of 3D Voronoi volumes in this sample (Figure 8A), a result expected by current theories of helium bubble nucleation.52 The black curve in Figure 8A is an example of a log-normal distribution that closely resembles the histogram. Voronoi volumes are most commonly between about 50 and 100 nm3. In contrast, the bubble size distribution is not lognormal, a result that is independent of the chosen segmentation threshold. Even if some small bubbles were missed or noise was occasionally mistaken as small bubbles, it would be difficult to describe the observed distribution as log-normal. As an additional check, we have analyzed a 2D HAADF image of a thin lamellar sample at about twice the magnification of the tomography sample with the "Analyze Particles" function in ImageJ,53 which involves similar thresholding procedures. After converting the bubble areas to volumes by assuming spherical bubbles, we obtained a similarly shaped distribution to that shown in Figure 8B. This comparison indicates that the distribution graphed in Figure 8B is not specific to our chosen 3D analysis methods. To investigate the number of neighbors for each bubble, we determined the number of faces of a bubble’s Voronoi polyhedron and obtained a typical result of approximately 15, close to the value expected for randomly chosen points (Figure 8D).50 The distribution of nearest neighbor distances of bubbles is depicted in Figure 8C with an average of 3 nm. A sphere of this radius corresponds to a volume of about 100 nm3 which is similar to the average Voronoi volume. This result suggests that the Voronoi volumes are not far from spherical.



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Figure 8. Histograms of bubble statistics. (A) Voronoi volumes, (B) bubble volumes, (C) nearest-neighbor distances, and (D) number of Voronoi polyhedron faces for 395 bubbles near the thin end of the sample tip. Voronoi volumes that intersect the sample boundary or have faces larger than 55.9 nm3 were omitted. The black curve depicts a log-normal distribution.


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27 If we assume that: a) helium bubbles nucleate within a narrow, early time window, b) subsequent helium diffuses within the lattice to the closest bubble, and c) a bubble’s volume is proportional to its helium content, then a bubble’s size should strongly correlate with its Voronoi tessellation volume. However, if any of these assumptions regarding bubble formation are invalid, we no longer expect a correlation of bubble size and position. Regarding the conjecture of early stage nucleation of bubbles, similar bubble densities to our 3.8 year aged sample were found in a 1month-old sample,28 providing some justification that a large fraction of bubbles nucleated at early times in our sample. However, we did not observe a correlation between the volume of a bubble and its Voronoi volume (Figure 10A) nor between the radius of a bubble and its nearest-neighbor distance (Figure 10B). These interesting results indicate that at least one of the assumptions regarding bubble nucleation and growth is incorrect.

Figure 9. Scatter plots of (A) the Voronoi tessellation volume of a bubble versus the bubble volume and (B) nearest-neighbor distance of a bubble versus its radius for the bubble population described in Figure 8.



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28 To further investigate this intriguing lack of correlation between bubble size and spacing, we determined the effect that a missing set of undetectable, sub-nm bubbles would have on our data analysis. We first generated a set of test data consisting of theoretical bubbles nucleated randomly in space that we presumed had bubble volumes proportional to their Voronoi volumes. We then discarded bubbles with volumes less than the peak volume of their log-normal distribution. We recomputed the Voronoi volumes after deletion of the small bubbles and found no correlation between the originally determined Voronoi volume for each remaining bubble and its Voronoi volume obtained after deletion of small bubbles. This analysis suggests that if the resolution of an electron tomography data set precludes the detection of a significant number of small bubbles, a clear correlation of bubble size and Voronoi volume may not be obtained. This exercise demonstrates the possibility of sub-nm helium bubbles that grew slowly or that nucleated relatively late in the life of the sample. Equivalent results could be expected from trapped helium clusters that have not displaced metal atoms. If enough of these clusters or small bubbles are present, they could account for a significant fraction of the helium in the sample.

Insights into the bubble nucleation process were made by computation of the radial distribution function of the bubbles. For each bubble, the distance to all other bubbles was computed, and a histogram of these distances was made. These histograms were averaged, and each bin was normalized by the volume of the spherical shell of radius equal to the given distance. If helium bubble nucleation is entirely random over all space in the metal, the radial distribution function is unity everywhere. For bubbles in a sample of finite size, the function decays to zero at large radius, though a more sophisticated approach than described here can minimize this.54 Completely random nucleation would only be expected if bubble nucleation is independent of helium concentration,


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29 such as if nucleation is determined by randomly distributed defects in the metal lattice. In contrast, if bubble nucleation is indeed dependent on helium concentration, bubbles will tend to nucleate away from existing bubbles in regions of the metal lattice where helium concentrations are highest. The radial distribution function for the bubble population considered here is less than unity below 3 nm (Figure 10A), consistent with the nearest-neighbor distribution shown in Figure 8. This investigation suggests that bubble nucleation is not entirely random, and there is a length scale at which a bubble suppresses nearby nucleation of other bubbles.

Figure 10. (A) Radial distribution function averaged over the bubble population described in Figure 8. (B) Histogram of estimated thinnest ligament width assuming spherical bubbles.

To clarify the effect of suppression of nucleation near existing bubbles, we calculated the thinnest ligament widths of all bubbles by subtracting the radius of each bubble in a nearestneighbor pair from the nearest-neighbor distance, assuming that bubbles are spherical (Figure 10B). Ligaments are typically 1 – 2 nm wide. In addition to the explanation that existing bubbles suppress nearby nucleation of new bubbles, another reason for these observations is that bubbles



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30 nucleate randomly but coalesce in cases when two bubbles nucleate in close proximity. The minimum ligament width may result from both mechanisms.

Conclusions The results presented here expose the inadequacy of the simple model of helium bubble evolution that stipulates that nucleation occurs exclusively at early times following tritium exposure and that growth occurs by all helium atoms entering the nearest bubble. Our 3D electron tomography experiments and subsequent analysis present a more detailed description of the behavior of helium in metals. Transport of helium as atoms or clusters through interstitial sites in a perfect crystal is believed to be quite rapid.12,55,56,57 However, the helium can be trapped at interstitial or substitutional impurities,26 self-interstitial atoms,11 vacancies58 that may be abundant due to stabilization by hydrogen,27,33 and dislocations that may include those produced by growing bubbles.59,60 Dilute substitutional copper in palladium has been predicted to trap helium atoms with a heat of formation of –0.2 eV; similar results could be expected for the substitutional nickel in the palladium sample presented here.61 This trapped helium may still be mobile at room temperature, but much less so, especially if several helium atoms are trapped at a defect.62,63,64 Bubbles that are smaller than those that are resolvable could serve a similar function as traps in the lattice. If the concentration of traps is comparable to the number of observed bubbles, they could effectively reduce the Voronoi volumes of the observable bubbles. It then follows that if samples with different concentrations of hypothetical traps result in different bubble sizes and spacing, our electron tomography and analysis methods will be valuable techniques to more precisely identify the nucleation mechanism in the presence of different microsctructural features.


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31 Our tomography results, combined with these considerations, stimulate new hypotheses regarding the mechanism of bubble formation. Trapping of helium within the lattice appears to be an essential first step because it explains the low percentage of helium that escapes the metal. Traps could provide sites that seed bubble nucleation by allowing atomic helium to accumulate locally prior to formation of a bubble through metal atom displacement or vacancy accumulation. A trap that has not nucleated a bubble could slowly release helium to a nearby bubble or cause nucleation late in the metal tritide’s lifetime. These traps may facilitate nucleation of bubbles over a broader range of times rather than exclusively within a narrow, early time window following tritium exposure. Bubble nucleation is believed to result from ejection of metal atoms from sufficiently large clusters of trapped helium9 or by coprecipitation of helium with vacancies.57 These mechanisms are consistent with our observations of a lack of correlation between a bubble’s volume and its Voronoi volume and an average thinnest ligament width of a few nm. In our sample, hydriding and dehydriding cycles may have also provided opportunities for late nucleation by creating a fresh set of dislocations and/or hydrogen-stabilized vacancies.65 Bubbles may achieve finite mobility by ejecting dislocation loops preferentially away from other bubbles13 and by thermal coarsening or ripening mechanisms.66 Changes in bubble positions after their initial nucleation or the destruction of bubbles by a coarsening mechanism could disrupt a correlation between bubble volume and Voronoi volume. Applying our electron tomography and analytical techniques to samples of varying age will further clarify the time dependence of nucleation.

Summary We have leveraged electron tomography to determine properties of helium nanobubbles generated in a metal tritide that were not previously discernible from 2D images, including the



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32 nanobubbles’ 3D spatial positions, volumes, morphologies, and Voronoi polyhedra. We find that the distribution of Voronoi volumes is log-normal, but the distribution of bubble volumes is not. Additionally, the bubble volumes and Voronoi volumes are not correlated. These results suggest that a simple model of bubble growth, based on all bubbles forming during an early nucleation stage followed by helium migration to the closest bubble, is inadequate. In this scenario, Voronoi and bubble volume distributions would be log-normal, and a correlation between the two would be anticipated. A model that accounts for further details of helium trapping and transport may be more accurate. We have demonstrated that electron tomography proves to be a powerful technique for characterization of nanoscale helium bubbles trapped in metals. Recent demonstrations of atomic-resolution tomography have involved sample volumes of only about 10 of our measured Voronoi volumes. It might then be feasible to achieve this resolution for one set of nearest neighbors around a central bubble.20,21 More generally, the methodology developed for atomicresolution tomography could allow for improved identification of sub-nm bubbles in future work. Electron tomography could also be applied to samples prepared under a range of tritium exposure times, with varying quantities of microstructural trap sites, or subjected to a series of annealing steps.22 Information from such experiments may help validate the new insights gained by our work toward improving models of helium bubble nucleation and growth.

Supporting Information Animations of the aligned tilt series, reconstruction slices, segmented bubbles, and Voronoi tessellations have been provided as supporting information.


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Acknowledgment Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. Work at Savannah River National Laboratory (SRNL) was performed under contract number DE-AC09-08SR22470 with the U.S. Department of Energy (DOE) Office of Environmental Management (EM). This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. At SRNL, E. Lynn Bouknight performed the decontamination of the sample, and David DiPrete measured its residual tritium. At Sandia, Warren L. York prepared conventional FIB liftouts.

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