Nanoscale lattice strains in self-ion implanted tungsten
N.W. Phillips, H. Yu, S. Das, D. Yang, K. Mizohata, W. Liu, R. Xu, R.J. Harder, F. Hofmann
NNanoscale lattice strains in self-ion implanted tungsten
N.W. Phillips a* , H. Yu a , S. Das a , D. Yang a , K. Mizohata b , W. Liu c , R. Xu c ,R.J. Harder c , F. Hofmann a+ a Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX13PJ, UK b Accelerator Laboratory, University of Helsinki, P.O. Box 64, 00560 Helsinki, Finland c Advanced Photon Source, Argonne National Lab, 9700 S. Cass Avenue, Lemont, IL,USA * Corresponding author E-mail address: [email protected] (N.W. Phillips) + Corresponding author E-mail address: [email protected] (F. Hofmann)
Abstract
Developing a comprehensive understanding of the modification of materialproperties by neutron irradiation is important for the design of future fis-sion and fusion power reactors. Self-ion implantation is commonly used tomimic neutron irradiation damage, however an interesting question concernsthe effect of ion energy on the resulting damage structures. The reductionin the thickness of the implanted layer as the implantation energy is re-duced results in the significant quandary: Does one attempt to match theprimary knock-on atom energy produced during neutron irradiation or im-plant at a much higher energy, such that a thicker damage layer is produced?Here we address this question by measuring the full strain tensor for twoion implantation energies, 2 MeV and 20 MeV in self-ion implanted tung-sten, a critical material for the first wall and divertor of fusion reactors. Acomparison of 2 MeV and 20 MeV implanted samples is shown to result insimilar lattice swelling. Multi-reflection Bragg coherent diffractive imaging(MBCDI) shows that implantation induced strain is in fact heterogeneousat the nanoscale, suggesting that there is a non-uniform distribution of de-fects, an observation that is not fully captured by micro-beam Laue diffrac-tion. At the surface, MBCDI and high-resolution electron back-scattereddiffraction (HR-EBSD) strain measurements agree quite well in terms of thisclustering/non-uniformity of the strain distribution. However, MBCDI re-veals that the heterogeneity at greater depths in the sample is much largerthan at the surface. This combination of techniques provides a powerful1 a r X i v : . [ c ond - m a t . m t r l - s c i ] J un ethod for detailed investigation of the microstructural damage caused byion bombardment, and more generally of strain related phenomena in micro-volumes that are inaccessible via any other technique. Keywords:
Self-ion implantation, neutron irradiation damage, Bragg CDI,strain tensor, defect microscopy
1. Introduction
Tungsten (W) is an important candidate material for future fusion power,where it is the material of choice for the plasma-facing armour [1, 2]. Thesecomponents will be subjected to extreme environments in-service. Typicaloperating temperatures are expected to be in the region of 570–1270 K [2],with heat loads of 2–20 MW / m and a neutron flux expected to result in theaccumulation of several displacements per atom (dpa)/year [3]. Tungsten’shigh melting point (3422 ◦ C), good thermal conductivity, low sputtering rateand low tritium retention make it a suitable candidate material for the firstwall amour and divertor [2]. However, a significant amount of damage willaccumulate in these environments. Beside neutron-induced cascade damage,transmutation will introduce foreign elements such as rhenium, osmium, tan-talum, hydrogen and helium. Further hydrogen and helium will diffuse fromthe plasma itself [3]. These processes have been shown to alter the materialproperties, resulting in hardening, embrittlement, creep and lattice swelling[1, 2, 4–7]. Resultant residual stresses can act as offsets to other fatigue load-ing, potentially reducing fatigue life, which is likely to be the limiting factorfor plant service life. The combined effects must be better understood in or-der to develop ways to inhibit these changes in the design of power generatingplants and to estimate the lifetime of functional plasma facing components.[1–3, 7].To better understand neutron irradiation damage processes, self-ion im-plantation can be used to mimic fusion neutron-induced irradiation damage.Self-ion analogues are often selected in favour of neutron irradiation as ionfluxes are much higher, enabling the desired dpa level to be obtained inminutes or hours rather than months or years. Furthermore, the neutronspectrum of typical fission sources fails to replicate the high energy neutrons(14 . et al. [9, 10, 13], provide a foundation for such studiesvia molecular dynamics simulations, showing the scale and distribution ofdefect structures within a cascade including the formation of 1 / (cid:104) (cid:105) and (cid:104) (cid:105) interstitial and vacancy type dislocation loops for 100–400 keV self-ionimplanted tungsten at 0–4 K. This provides a fairly complete understandingof individual impacts of energetic particles. By beginning molecular dynam-ics simulations with pre-damaged iron and tungsten systems, Sand et al. have shown that cascade overlap, as well as cascade splitting, are significantfactors resulting in heterogeneity of the damage structure [14]. In situ obser-vation of self-ion implantation in tungsten transmission electron microscopy(TEM) foils by Yi et al. [5], provides further confirmation of the types anddistributions of defects produced as the microstructure evolves [15]. Morerecently, developments in stereo-imaging TEM by Yu et al. [12] have madeit possible to extract the three-dimensional position of irradiation induceddislocation loops in a 40 nm thick foil for low damage levels (0.01 dpa). Inaddition to being restricted to thin foils, three-dimensional imaging becomesproblematic for higher damage levels where defects overlap, and thus far noTEM tomography data for this regime has appeared in the literature.The aforementioned works use a low ion energy (around 150 keV) as it ismost representative of the PKA energy generated by a fusion neutron col-lision [9]. This eases the computational requirement for simulation as therequired volume remains relatively small. However, performing laboratory-based measurements on low energy implanted samples presents a significantchallenge. This is primarily due to two effects. Firstly, the implanted layerfrom 150 keV W + in tungsten is only tens of nanometres thick, making thedetection of signal from such a small volume difficult to separate from thatof the unimplanted bulk. Furthermore, commonly used sample preparationmethods, such as Focused Ion Beam (FIB) liftout procedures for producing For loops visible at a specified diffraction condition. Loop sizes below 1 . et al. [6, 23] have previously used 0.05 to 1.8 MeV He + implanta-tion in tungsten to generate a sufficiently thick (2–3 µ m) implantation layerfor investigation by differential aperture X-ray microscopy (DAXM), whichallows depth-resolved measurements of lattice strain with sub-micron spatialresolution [24, 25]. In the case of heaver ions such as tungsten, the limiteddepth resolution (0 . µ m) of DAXM necessitates the concession of usingimplantation at energies of around 20 MeV to ensure a clearly distinguish-able implantation layer is produced to a depth of 2–3 µ m. In tungsten, aboveion energies of a few hundred keV, it is known that rather than producinga single cascade, splitting into a number of sub-cascades with a PKA en-ergy in the range of 150–300 keV occurs [10, 14]. The potential for cascadeoverlap and higher local energy dissipation may lead to a defect evolutiondistinctly different to that anticipated from 14 . hkl ). The sample is then rotated through the Bragg condition,and an over-sampled diffraction pattern is collected in the far field. Once athree-dimensional reciprocal space map of the intensity surrounding a Braggpeak has been collected, phase retrieval algorithms need to be used to recoverthe complex-valued, real space sample function, where the amplitude is pro-portional to the electron density and the phase is proportional to the latticedisplacement along the direction of the scattering vector [26, 27]. The samplesize is restricted to sub-micron crystals owing to the sub-micron coherencelengths in the hard X-ray regime at current synchrotron sources. Until re-4ently, BCDI has been limited to materials that form isolated, micro-crystals[28–31] and a few samples which can be annealed and retain sub-micron grainsize [32, 33]. By measuring a multi-reflection BCDI (MBCDI) dataset con-sisting of three or more non-parallel reflections, the full lattice strain tensorcan be determined [16, 29]. Applying our recently demonstrated protocolfor top-down fabrication of BCDI strain microscopy samples [34], we demon-strate that using MBCDI, the strain associated with ion implantation can beinvestigated over previously inaccessible length scales in the range of tens ofnanometres up to a micrometre.Here we compare strain in 20 MeV self-ion implanted tungsten, measuredusing DAXM, to the strain distribution in 2 MeV self-ion implanted tungstenmeasured using MBCDI and high-resolution electron back-scatter diffraction(HR-EBSD). This seeks to address the central question: Whether latticestrain is simply a function of dpa, or whether the ion-energy also plays animportant role in defect structure formation and how this structure variesthroughout the implanted layer. BCDI, provides more than an order of mag-nitude improvement in volumetric spatial resolution compared to state-of-the-art DAXM. This enables us to directly probe the full strain field associ-ated with the sub-micron implantation layer and makes it possible to resolvethe spatial heterogeneity of the implantation induced strain and damage mi-crostructure in three-dimensions.
2. Experimental
As rolled tungsten (99.99 % purity) was mechanically ground and thenpolished using a gradient of diamond paste. 0 . µ m colloidal silica was usedto obtain a high quality surface. The material was annealed and fully recrys-tallised in a vacuum furnace at 1500 ◦ C for 20 hours (2 MeV) and 10 hours(20 MeV) using a heating and cooling rate of 4 ◦ C / min. Parallel studiesshowed an annealing time of 10 hours to be sufficient. Grains with the (010)lattice plane aligned parallel to the sample surface, presented a flat surfaceafter annealing (see Figure 1(c)). Some facetting of the surface within differ-ently orientated grains was seen [35]. This did not impact the quality of thepreparation as only the (010) surface normal orientation was investigated.5 .2. Ion implantation Implantation of samples was performed at the University of Helsinki usinga raster scanned beam at room temperature. One sample was implanted with2 MeV W + ions and the second sample with 20 MeV W + ions. The ion fluencewas 1 . × ions / cm for the 2 MeV sample and 2 . × ions / cm forthe 20 MeV sample. Owing to the reduced scattering cross-section at higherenergies, an increased ion fluence is required for the 20 MeV implantation inorder to achieve a comparable dpa. This gave a peak dpa of approximately0 .
07 dpa and 0 . .
07 dpa and 0 . implanted MBCDI sample To produce a sufficiently small strain microscopy sample for BCDI, a sub-micron volume was extracted from the near-surface material of the 2 MeVimplanted sample using FIB milling (Figure 1). This followed our previouslydeveloped protocol [34]: Using EBSD, a (010) orientated grain was selectedand a 300 nm thick protective cap deposited over the implanted surface byelectron beam assisted deposition of platinum. The thickness of the cap wasincreased to 4 µ m using gallium-FIB assisted deposition of platinum (shownin Figure 1(c)). This ensures that the self-ion implanted surface is neverexposed to energetic gallium ions which have been shown to result in strainsextending over hundreds of nanometers into the material [16, 17]. A liftout,similar to that used when preparing a TEM or atom probe tomographysample [40], was prepared on a Zeiss Auriga dual beam FIB/SEM. Thisis used to extract a 25 × × µ m ( L × W × H ) lamella, which is then turnedupside down (Figure 1(d)) and attached to a 2 µ m diameter silicon pillar6sing platinum deposition (Figure 1(e)). This results in the implanted layerbeing at the bottom of the BCDI sample volume. The sample is then milledto a size of approximately 1 µ m in each dimension. Finally, low energy, 2 keV,Ga + polishing was used to clean off the damage from previous FIB milling,removing ∼
100 nm of material from each side of the sample. This eliminatesmost of the damage from previous FIB milling steps [16, 17, 41, 42].7 igure 1: Plot of the expected dpa and injected ion concentration as a function of depthafter 2 MeV (a) and 20 MeV (b) self-ion implantation. (c) SEM micrograph of the sam-ple surface for the (010) orientated grain that was used to fabricate the MBCDI strainmicroscopy sample from the 2 MeV ion-damaged specimen. Here the initial rectangularshaped platinum cap marks the lift-out region and the approximate position of the BCDIsample is shown. (d) Schematic of the MBCDI strain microscopy liftout, highlighting theinitial upwards facing implanted surface layer and its final position at the bottom of thestrain microscopy volume. (e) SEM image of the finished sample with the location of theimplanted layer superimposed in orange. The scale bar for the micrographs (c) and (e) is2 µ m. .4. MBCDI measurement and analysis White-beam micro-Laue diffraction was used to determine the crystal-lographic orientation of the prepared BCDI sample prior to collection ofMBCDI data. This was performed following our previously developed pro-tocol [43], at 34-ID-E of the Advanced Photon Source (APS) using LaueGo[44] for the analysis of the Laue diffraction data. The UB matrix [45] is usedto provide an accurate description of the sample orientation on a kinematicmount, which is in-turn used to mount and pre-align the sample for MBCDImeasurements.MBCDI data were collected at beamline 34-ID-C of the APS using amonochromatic X-ray beam of 10 keV, focused by Kirkpatrick-Baez mirrorsto a FWHM of 1 . µ m × µ m (horizontal × vertical). An MBCDI datasetconsisting of five reflections, (¯101), (011), (110), (1¯10) and (0¯11), was mea-sured as the sample was rocked through the Bragg condition forming a three-dimensional, over-sampled, reciprocal space map for each reflection. An an-gular range of 0 . ◦ using 0 . ◦ increments was used. An ASI Timepixdetector with 256 × µ m square pixels and a GaAs sensor was usedto record the diffraction patterns at a detector distance of 1 m. 30 × .
05 sexposures were taken at each point, with the measurement for each reflectionrepeated 10 times, maximising the intensity between each scan by centringthe sample in the horizontal and vertical directions with respect to the beamand performing the subsequent scan centred about the rocking angle corre-sponding to the peak intensity. This minimises the effect of long timescaledrift on the data quality. For a comprehensive description of the experi-mental geometry see [46]. Diffraction patterns were flat-field and dead-timecorrected, and then aligned to minimise their Pearson correlation coefficientsusing a 3D version of the algorithm described by Guizar-Sicairos et al. [47].Those satisfying the threshold criterion of a correlation coefficient exceeding0.975 were summed for phase retrieval analysis. Ten scans were summed forthe (¯101), (011), (110) and (1¯10) reflections, whilst nine scans were summedfor the (0¯11) reflection.Phasing of BCDI data employed previously established approaches forphase retrieval [48, 49] and was performed over 4 successive cycles, where theprevious result was used to seed the subsequent cycle (with the exception ofthe first cycle, which was initialised using a random phase guess). Details ofthe phasing procedure are given in Supplementary Information Section 1.After applying the appropriate coordinate transform to the retrieveddata [46], the projection of the crystal electron density is given by the ab-9olute value of the recovered data whilst the phase is proportional to thelattice displacement u ( r ), along the direction of the Bragg vector q hkl , i.e. φ ( r ) = q hkl · u ( r ). Employing our recently developed method of accountingfor phase wraps and phase discontinuity due to crystal defects [34], the strainis computed as follows:Firstly, phase offsets of ± π/ π . Then the recoveredphase and the two copies are transformed into an orthogonal sample space[46] common to all reflections in the MBCDI dataset. The spatial derivativesof φ ( r ) are then computed and the pixel-by-pixel gradient with the smallestmagnitude used for computing the lattice strain tensor through the minimi-sation of the squared error of the displacement gradient and the gradient ofthe measured phase for each reflection, E ( r ) i = (cid:88) hkl,j (cid:18) q hkl · ∂ u ( r ) ∂j − ∂φ ( r ) ∂j hkl (cid:19) , (1)where j refers to the spatial x, y or z coordinate.For a complete discussion of this approach the reader should refer to [34].The lattice strain tensor components and lattice rotations are then given by ε ( r ) = 12 (cid:16) grad u ( r ) + [grad u ( r )] T (cid:17) , (2) ω ( r ) = 12 (cid:16) grad u ( r ) − [grad u ( r )] T (cid:17) . (3)For convenience of displaying the results, the ε ( r ) and ω ( r ) tensors cal-culated by Equations 2 and 3 are displayed in a 3 × ε xx = ∂ u x ∂x ε xy = (cid:16) ∂ u x ∂y + ∂ u y ∂x (cid:17) ε xz = (cid:0) ∂ u x ∂z + ∂ u z ∂x (cid:1) ω z = (cid:16) ∂ u y ∂x − ∂ u x ∂y (cid:17) ε yy = ∂ u y ∂y ε yz = (cid:16) ∂ u y ∂z + ∂ u z ∂y (cid:17) ω y = (cid:0) ∂ u x ∂z − ∂ u z ∂x (cid:1) ω x = (cid:16) ∂ u z ∂y − ∂ u y ∂z (cid:17) ε zz = ∂ u z ∂z Table 1: Lattice strain tensor components and lattice rotations. The representation oflattice strain and rotation in Figures 4, 5 and 7 follow this layout. × − [34]. Thisis especially the case for MBCDI, where both the detector and sample aremoved significantly over the course of the measurement and misalignmentbetween rotation centres is often present to some degree. Fortunately, in thepresent sample it is not necessary to have an absolute measurement as theunimplanted region may be used as an in-built reference. X-ray micro-beam Laue diffraction was used to measure the lattice pa-rameter within the implanted layer of the sample exposed to 20 MeV self-ionsand the unimplanted bulk material beneath. This is possible through DAXM[24] and was performed at beamline 34-ID-E of the APS. The differentialaperture, a platinum knife-edge, is scanned across the surface of the samplein sub-micrometre steps, enabling the depth from which the signal originatesto be determined via a ray tracing approach [24, 25]. DAXM was performedfor a range of monochromatic energies, which provides the lattice spacing asa function of depth within the material. An energy-wire scan (EW-DAXM)was performed, collecting the scattered intensity for a single (060) out-of-plane reflection. The spatial resolution of DAXM is closely linked to the sizeof the probe used to illuminate the sample. Here the probe has a full-width-at-half-maximum (FWHM) of 300 nm in both the horizontal and verticaldirections with depth resolution of approximately 500 nm. Strain sensitivityof 1 × − is routinely achieved using this technique. Further details areprovided elsewhere [25, 50]. In total, three sample positions were analysedon the umimplanted reference sample and four positions on the 20 MeV self-ion implanted 0 . .6. HR-EBSD measurements HR-EBSD was used to obtain high resolution maps of the deviatoric straintensor and lattice rotation at the surface of the 2 MeV self-ion implantedtungsten sample. The data were collected on a Zeiss Merlin scanning elec-tron microscope (SEM) equipped with a Bruker eFlash detector, using anaccelerating voltage of 20 keV, a current of 15 nA, with an EBSD patternsize of 800 ×
600 pixels and a step size of 16 . × − [51]. The analysis was performed using the MATLAB-basedHR-EBSD software developed by Britton and Wilkinson [52].In contrast to the aforementioned X-ray diffraction methods, it is worthnoting that HR-EBSD is insensitive to volumetric strains and that the signaloriginates from a sample volume within the first few nanometers of the surface[53].The raw data and analysis code may be made available upon request.MBCDI analysis code is available at [54].
3. Results
Previous studies employing EW-DAXM to investigate He + implantationin tungsten reported that the in-plane strain components are close to zero[6, 23, 55]. Hence, we only measure the depth variation of the out-of-planestrain component. To exclude any systematic dependence on grain orienta-tion, we only consider grains with (010) surface normal. EW-DAXM depth-strain profiles from 20 MeV W + self-ion implantation are displayed in Fig-ure 2. These show a positive strain, i.e. an expansion of the lattice, to adepth of 2 µ m, which is in agreement with the expected thickness for theimplanted layer of approximately 2 µ m, as calculated by SRIM [36], shownin (Figure 1(a-b)). In tungsten the relaxation volume associated with mono-vacancies is small and negative (V = -0.37 Ω, see Hofmann et al. [55] forfurther vacancy configurations), whilst that of a self-interstitial atom (SIA)is larger and positive (SIA = 1.68 Ω) [55]. As vacancies in tungsten are im-mobile at room temperature, whilst SIAs are highly mobile [55], there areat most, similar numbers of vacancies and SIAs within the material. Overallthis results in the observation of lattice swelling as the relaxation volume ofa Frenkel pair, i.e. a vacancy and SIA pair, is positive. Both the nominallyunimplanted bulk and the unimplanted reference sample show little strain,12s is expected for tungsten after annealing at 1500 ◦ C. The small amountof strain observed near the surface of the unimplanted sample is attributedto damage introduced during sample polishing, an observation supported bythe presence of small visible scratches on the sample surface. DAXM mea-surements on purposely introduced scratches in nickel showed that the strainfields associated with scratches can extend to depths tens of times larger thanthe scratch depth [56]. It should be noted that even for specialised micro-beam Laue instruments, these measurements are approaching the limit ofboth depth and strain sensitivity, hence the large standard deviation for thisdata is not unexpected [50, 57]. The increase in standard deviation withinthe implanted layer perhaps hints at spatial heterogeneity caused by the clus-tering of defects within the implanted layer. This demonstrates the need forthe development of methods, such as BCDI, that address these resolutionlimits.
Figure 2: DAXM strain profile for 20 MeV implantation as a function of depth. Shownis the averaged ε yy (out-of-plane) strain component from a series of sample positions,unimplanted (blue) and 0.1 dpa (red). The shaded bounds indicate one standard deviationfor the measured data. The implanted layer extends approximately 2000 nm from thesurface and has an average strain of 3 . × − within the first 1000 nm of the surface. Asexpected, the strain is close to zero for depths below the implantation layer and in theunimplanted reference sample. Amplitude isosurfaces of the object from all five measured reflectionsare shown in Figure 3. Superimposed on this volume are the directions ofBragg vectors q hkl for each of the five reflections. The morphology of the13ample, recovered from different reflections, is consistent. Quantification ofthe spatial resolution was performed by differentiating line profiles in thex, y, z directions of the average electron density. By fitting a Gaussianprofile to the air-crystal interfaces and taking the FWHM, the average spatialresolution was estimated to be 28 nm.Upon recovery of the phase for each of the five reflections, visual in-spection shows little indication of the presence of an implantation layer (seeSupplementary Figure 5). The implantation layer is simply not visible whenonly the phase for each individual data set is considered. The reader shouldnote that, as the sample was turned upside down during the fabricationprocess, the implanted layer will now appear at the bottom of the MBCDIobject. Visibility of the implanted region is only marginally improved whenone considers the strain in the direction of the scattering vector for eachreflection (see Supplementary Figure 5). Upon careful inspection of the re-covered strain, some indication of the implantation layer can be seen, visibleas a layer of strain slightly higher than that of the bulk. The layer is slightlymore visible for the (101) and (0¯11) reflections. Figure 3: Rendering of the sample morphology for each measured reflection labelled withthe scattering vector hkl . The Bragg vector direction for each reflection is indicated by theblack arrows. The averaged strain microscopy sample morphology from all five measuredreflections is shown in the lower right. The 500 nm long arrows, red, green and bluecomprise a right-handed coordinate system designating the x, y and z axis respectively,which later correspond to the strain tensor components. The red y-z (vertical) and greenx-y (horizontal implanted), black x-y (horizontal unimplanted) planes indicate the cut-through sections displayed in subsequent figures. ε yy component, which corresponds to the strain normal to the implanted surface(central component of Figure 4). The layer can be seen within the lower 1 / rd of the sample and extends 200–245 nm into the sample. The in-plane straincomponents are small, as was the case for He implanted W [6, 23, 55]. Themagnitude of the strain for the ε yy component averages 5 × − and reachesa maximum of 2 . × − within the implanted layer. The strain sensitivity ofthe MBCDI measurement is of the order 2 × − [16, 17, 34]. Theoreticallythe strain sensitivity of MBCDI is limited by the numerical aperture to whichdata can be reliably phased. In practice this is affected by the stability ofthe experimental setup, the amount of coherent flux, imperfections such aschip-set boundaries in detectors or beamstops and the precision to whichthe geometry is known [16, 17, 34, 58]. Addressing these factors in orderto improve the strain resolution is an ongoing challenge within the BCDIcommunity. Lattice expansion is again observed within the implanted layer.The measured thickness compares well to the simulated implantation profile,where the depth at which the dpa is half of its maximum was 180 nm. Thestrain tensor and lattice rotation for horizontal slices are shown in Figure 5for the unimplanted (a) and implanted (b) regions of the sample. The readeris encouraged to view Supplementary Movies 5 and 5 that show the straintensor on a slice-by-slice basis through the entire thickness of the sample.Lattice swelling due to self-ion implantation damage is distinguishablefrom gallium (Ga)-FIB damage by the location within the strain microscopysample and the thickness of the damage layer. The protective platinumcap, deposited before manufacture of the MBCDI sample, ensures that thelower surface is free of any Ga-FIB damage, whilst glancing angle Ga + ionincidence and low energy polishing is used to minimise the effects at the FIB-milled surfaces of the sample volume. Even with careful fabrication it is notpossible to completely remove all strain due to FIB damage. In this sample,FIB induced strain can be identified in the corners of the notched regionwhere a combination of geometric shadowing and re-deposition reduces theeffectiveness of low energy polishing. The remaining damage is confined toa thin surface layer, most visible at the top right corner. These features aremarked by arrows in Figure 4. Overall, whilst present, the effects of FIBdamage are small, readily identifiable, and can be excluded during furtheranalysis of the data with respect to the tungsten-ion-damaged implantationlayer. 15 igure 4: Lattice strain tensor and lattice rotations recovered from MBCDI on the verticalsection through the sample (red) shown in Figure 3, the other sections used in subsequentfigures are shown by the dark green and black lines in the ε yy component. Shown arethe six strain tensor components (upper right triangle and diagonal) alongside the threerotation tensor elements (bottom left triangle) as given in Table 1. The lattice swellingresulting from the tungsten self-ion implantation is most evident in the ε yy component.Residual effects from FIB fabrication are observable at the notch at the top left corners andthe top right corner, indicated by the grey arrows. Heterogeneity of the strain within theimplanted layer is indicative of a complex microstructure (particularly visible in the ε xx , ε yy and ε zz components). The green and blue arrows are 500 nm long. Lattice rotationsare given in radians. igure 5: Lattice strain tensor and lattice rotations recovered from MBCDI on (a) thehorizontal unimplanted section (black) and (b) the horizontal implanted (green) sectionmarked by the planes in Figure 3. Shown are the six strain tensor components (upperright triangle and diagonal) alongside the three rotation tensor elements (bottom lefttriangle) as given in Table 1. The lattice swelling resulting from the implantation is mostevident in the ε yy component (the position of the vertical section (red) is also shown forthis component). Heterogeneity of the strain within the implanted layer is indicative ofa complex microstructure (particularly visible in the ε xx , ε yy and ε zz components). Thered and blue arrows are 500 nm long. Lattice rotations are given in radians.
4. Discussion
The in-plane strain components are close to zero throughout the recov-ered volume of MBCDI data, with the exception of some regions where FIBdamage has not been completely removed. This is expected and agrees withreports in the literature for similar systems [6, 23, 55]. Visualisation of theimplanted layer is via an isosurface of the ε yy component, using a threshold of1 × − for positive lattice strain as shown in Figure 6 (a) (see animated ver-sion in Supplementary Movie 5). To make a quantitative comparison betweenMBCDI and micro-beam Laue data, a strain profile as a function of depthwas computed from the averaged strain in the core of the MBCDI sample.The average of the ε yy strain component for a 200 nm diameter region occu-pying the x-z plane is shown in Figure 6 (b). The top 200 nm of the MBCDIsample (regions furthest from the implanted layer) have been excluded asthey are more susceptible to the spurious FIB damage which is not entirely17emoved. Average ε yy strains of 3 . × − and 5 × − are observed withinthe implanted layer for the 20 MeV (within 1 µ m of the surface, measuredby EW-DAXM) and 2 MeV (average of the total implanted layer measuredby MBCDI) implanted samples respectively. This agreement between im-plantation energies differing by an order of magnitude is quite remarkable.Importantly, this lends credibility to the use of higher ion energies for im-plantation when attempting to mimic neutron-based damage cascades. Thisallows for the generation of a sufficiently thick implantation layer for anal-ysis techniques with limited depth resolution, including EW-DAXM, whenthe magnitude of the lattice strain is the primary concern. Figure 6: (a) Rendering of the recovered strain microscopy sample showing a strain iso-surface plotted for the ε yy component using a value of 1 × − . The position of thehorizontal sections in Figure 5 are shown by the black and green indicators. The redand green arrows are 500 nm long. (b) Strain profile as a function of depth for the lower600 nm of the sample. The implanted layer is contained to the lower 200–245 nm, notingthat the implantation was performed into this lower surface and the sample flipped duringfabrication in order to preserve this surface. From the measured lattice strain tensor an estimate of the underlying de-fect population can be made. In tungsten vacancies are essentially immobileat room temperature, whilst SIAs are highly mobile even at cryogenic tem-peratures [59, 60]. The measured lattice swelling suggests that not all SIAsare lost to sample surfaces, but rather that a population of SIAs is retained18ithin the damaged layer. The ratio of retained vacancies to SIAs cannot beunambiguously determined. However, we can make a lower bound estimateof the defect density, assuming retention of a population of Frenkel pairs( i.e. that there are the same number of vacancies and SIAs). Hofmann et al. showed that the out-of-plane lattice strain is related to the defect numberdensity by: ε yy = 13 (1 + ν )(1 − ν ) (cid:88) A n ( A ) Ω ( A ) r , (4)where A is the defect type, and the Poisson ratio, ν = 0 .
28, of tungsten isused [55]. Given the relaxation volumes of vacancies and SIAs from Hofmann et al. [55], the number density of Frenkel pairs in the implanted layer for bothimplantation conditions can be estimated as ∼
400 appm. It is importantto bear in mind that this analysis neglects the effect of SIA clustering onthe relaxation volume, though for interstitial loops containing up to severalhundred SIAs it has been shown that the relaxation volume scales almostlinearly with the number of SIAs in the loop [55]. The number density ofFrenkel pairs estimated from X-ray diffraction data is significantly greaterthan observed by TEM, where the number of defects is typically reported tobe in the range of 10–250 appm [5, 61, 62]. This is because small defects witha size below 1 . ε xx , ε yy and ε zz components of Figure 4 and5(b). The mottled features have a size in the range of 20–70 nm, in somecases forming longer, chain-like features. Independent simulations of irradia-tion damage evolution have concurrently predicted that spatially fluctuatingstress fields within an evolving cascade microstructure will influence the be-haviour of subsequent cascades, resulting in the formation of complex damagemicrostructure with long range order evidenced as strong variations in stressand strain [64]. The measurements of strain heterogeneity presented herecomplement two-dimensional TEM observations of damage microstructureand provide, in three-dimensions, experimental verification of the predicteddefect ordering at length scales considerably larger than those accessible viaatomistic simulation. The observed defect structure is similar to that re-19orted in the TEM study by Ciupinski et al. [20]. Interestingly, both themagnitude of strain and the spatial heterogeneity are reduced near the sur-face of the implanted layer for MBCDI data. This is most clearly capturedin the simulated HR-EBSD map for the BCDI sample, in which only the toptwo voxels (10 nm) adjacent to the sample surface are considered (see Figure7(b)). As the strain is indicative of the defect content, a reduced strain im-plies a reduction of defects near this free surface. This is in line with previousobservations of irradiation damage near free surfaces, where the surface actsas a significant defect sink in the first 10–15 nm [12, 18].The microstructure is qualitatively similar to the non-uniformity observedfor other grains within the same sample measured via HR-EBSD, shown inFigure 7(a). Here the feature size is in the range of 40–120 nm. When com-paring MBCDI measurements with HR-EBSD, we note that the magnitudeand heterogeneity are smaller in the HR-EBSD measurements. This may beattributed to free surface effects that can have a significant influence on HR-EBSD observations, which are sensitive to the deviatoric strain in the first fewnanometers of material [65, 66]. Calculations from 100,000 electron trajec-tories performed by Monte Carlo Simulation of Electron Trajectory in Solids(Casino) [67] show that 50 % of the detected electrons in the HR-EBSD datapresented here originate from the top 9 nm of the material, a distance overwhich some defects may escape to the free surface. The difference in observa-tions for HR-EBSD and TEM, with respect to MBCDI and micro-beam Lauediffraction, highlights that EM methods may only capture the smaller strainsand strain variations at the sample surface. As defects escape to nearby freesurfaces and TEM fails to account for the invisible defect population, thesefactors are thought to contribute to the significantly lower reported defectpopulations from EM methods. MBCDI, on the other hand, shows thatstrains beneath the surface of the sample can be significantly larger. Thisenforces the merit of adopting three-dimensionally resolved techniques whenconsidering strain at the nano-scale. 20 igure 7: Lattice strain tensor and lattice rotations recovered from HR-EBSD (a) of 2 MeVself-ion implanted tungsten captures the fine heterogeneity of strain at the surface of theimplanted layer indicating non-uniformity of the damage. Lattice strain tensor and latticerotations recovered from MBCDI and used to simulate HR-EBSD data (b) by averagingthe first two voxels (10 nm) of the implanted layer. This signal volume mimics the signalexpected from HR-EBSD measurement of the same sample, where the depth-contributionreaches 50 % at 9 nm from the surface when using an accelerating voltage of 20 keV anda sample tilt of 70 ◦ . Note that the pixel size in the transverse direction has been down-sampled to 15 nm to better represent a realistic pixel size for HR-EBSD. Shown are the sixstrain tensor components (upper right triangle and diagonal) alongside the three rotationtensor elements (bottom left triangle) as given in Figure 1. A reduction in the magnitudeof strain is seen when compared to regions deeper within the implanted layer (see Figure5(b)). The red and blue arrows are 500 nm long. Lattice rotations are given in radians. For implantation doses below 0.1 dpa, heterogeneity in strain componentsis no longer visible via HR-EBSD. Here, we attribute this to defects beingrandomly distributed at low doses when there is little cascade overlap. Thisrandom defect population results in similar average strain from the probedvolume across the sample. However, as the dpa increases, so too does theproximity of cascades with respect to one and-other. We hypothesise thatthis results in the new cascades being influenced by the history within thelocal lattice, i.e. the pre-existing defects and associated strain fields. A de-tailed study by Yu et al. [68] using electron channelling contrast imaging(ECCI) and HR-EBSD further supports this. These findings are in line withthe simulation findings of Ma et. al [60], which show that the local lattice21tress has a substantial effect on the evolution of defects. This has also beenobserved by TEM in self-ion implantation of tungsten [5, 62]. Whilst cascadeoverlap is initially a stochastic process, long range order develops as an in-creasing number of cascade events occur and become sufficiently close so as tointeract with the stress field from defects associated with previous cascades.This results in the formation of the heterogeneous microstructure observedin both the MBCDI and HR-EBSD measurements. Damage cascade forma-tion, evolution and eventual spatial heterogeneity may be affected by the ionenergy, especially as the energy approaches the sub-cascade splitting energy.Further, as the implantation thickness decreases, the cascade volume maybecome insufficient to fully accommodate the evolving microstructure whichoccurs at higher implantation energies or when considering neutron irradia-tion. This complicated regime remains largely unexplored. Whether higherimplantation energy increases the heterogeneity of the damage structure dueto increased cascade splitting and overlapping of sub-cascades needs to bestudied in more detail in the future.
5. Conclusions
In this work we have gained insight into damage processes in tungstencaused by self-ion implantation at 20 MeV and 2 MeV. The thirty-fold im-provement in resolution (compared to X-ray micro-beam Laue diffraction)afforded by MBCDI enables non-invasive measurement of the strain tensorassociated with the damaged material in three dimensions. This makes depthresolved strain measurements of samples implanted at significantly lower ionenergies possible. Consequently, this reduces the potential difference in dam-age microstructure due to differences in PKA energy between self-ions andfusion neutrons. We have found that:1. The magnitude of out-of-plane strain is comparable between 20 MeVand 2 MeV implantation energies (3 . × − and 5 × − respectively).This suggests that the average lattice strain is insensitive to the energyof the incident ions.2. Lattice swelling suggests retention of certainly some population of SIAsand a lower bound estimate of this population can be made (400 appm,assuming retention of Frenkel pairs). Interestingly this estimate is sub-stantially larger than previous estimates from TEM observations, sug-gesting that a large number of small point defects remain invisible toTEM. 22. Substantial strain heterogeneity is observed in the ion-implanted layer.This suggests a clustering of defects and the formation of larger struc-tures. At the surface this clustering is also seen by HR-EBSD. It ishoped that these results can be used to inform future models so thatthe effects of spatial heterogeneity in the microstructure of irradiatedsamples might be better accounted for.4. Strains are smaller near the surface than in the bulk, indicating thatthere is a loss of defects to the free surface. Care needs to be taken whenusing surface sensitive techniques to probe strain and microstructuredue to ion-implantation as these may not be wholly representative. Acknowledgements
NWP, DY and FH acknowledge funding from the European ResearchCouncil (ERC) under the European Union’s Horizon 2020 research and inno-vation programme (grant agreement No 714697). HY and SD acknowledgesupport from The Leverhulme Trust under grant RPG-2016-190. The authorsacknowledge use of characterisation facilities within the David Cockayne Cen-tre for Electron Microscopy, Department of Materials, University of Oxford,the use of the University of Oxford Advanced Research Computing (ARC)facility http://dx.doi.org/10.5281/zenodo.22558 and E. Tarlton for the useof computational resources. The Zeiss Crossbeam FIB/FEG SEM used inthis work was supported by EPSRC through the Strategic Equipment Fund,grant