Deformation of as-fabricated and helium implanted 100 nm-diameteriron nano-pillars

Peri Landau a,n,1, Qiang Guo a,b,1, Peter Hosemann c, Yongqiang Wang d, Julia R. Greer a,e

a Department of Materials Science and Applied Physics, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USAb State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, PR Chinac Department of Nuclear Engineering, University of California at Berkeley, Berkeley, CA 94720, USAd Ion Beam Materials Laboratory, Los Alamos National Laboratories, Los Alamos, NM 87545, USAe The Kavli Nanoscience Institute, California Institute of Technology, USA

a r t i c l e i n f o

Article history:Received 24 March 2014Received in revised form12 June 2014Accepted 14 June 2014Available online 20 June 2014

Keywords:Nanoscale plasticityTension testCompression testIronHelium implantation

a b s t r a c t

⟨101⟩-oriented cylindrical single crystalline Fe samples with diameters of 100 nm and heights of 1 μmwere implanted with 0.3670.06 at% helium throughout their gauge sections. Uniaxial deformationexperiments revealed a 40% higher yield and ultimate strengths in tension and a 25% higher yieldstrength and flow stress at 10% plastic strain in compression for implanted samples compared with as-fabricated ones. Observed tension–compression asymmetry in implanted pillars was attributed to thenon-planarity of screw dislocation cores and to twinning-antitwinning deformation typical of bcc metalsand the interaction between dislocations and He bubbles. Compressive stress–strain data in both sets ofsamples had three distinct regimes: (1) elastic loading followed by (2) discrete strain bursts duringplastic flow with significant hardening up to strains of 5%, and (3) “steady state” discrete plasticitycharacterized by nearly-constant average flow stress. Each regime is discussed and explained in terms ofcompetition in the rates of dislocation multiplication and dislocation annihilation.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Numerous experimental and theoretical studies on small-scaleplasticity in metals unraveled the origins and physical mechan-isms of size effects. For example, micron- and sub-micron sizedmetallic single crystals with non-zero dislocation densities havebeen ubiquitously reported to exhibit the “smaller is stronger”phenomenon, whereby the strength is inversely related to thesample size through a power law [1–13]. Most of the attention insmall-scale plasticity has been devoted to studying face-centeredcubic (fcc) metals (see, for example: [1,2,5,12–14]), where theproposed mechanisms responsible for the increased strength weresingle-arm dislocation source exhaustion [15–17], weakest linktheory [18,19], and dislocation starvation [1,2,5,6]. The mechanicalbehavior of small-scale body-centered cubic (bcc) materials, whichare characterized by more complex dislocation behavior, has notbeen explored as extensively. The mechanical deformation of bccmetals is strongly influenced by temperature, strain rate andorientation [1,4,6,8–11,20–26]. Bcc metals also exhibit tension–

compression asymmetry, which has been explained by the break-down of Schmid's law in these metals, whereby slip may occur oncrystallographic planes, which do not necessarily have the max-imum resolved shear stress (MRSS) [22,23,27,28]. These phenom-ena were attributed to the presence of twinning-antitwinning slipasymmetry caused by the non-planar screw dislocation cores, aswell as to the propensity of screw dislocation to cross-slip[24,27,29]. Another factor that affects the mechanical response ofmetals, particularly at the nano-scale, is the initial dislocationdensity. For example, uniaxial compressive stress–strain data ofpristine Mo alloy columns contained elastic loading virtually up totheir theoretical strengths, which was followed by abrupt soft-ening, a hallmark of dislocation-free metals [30,31]. This is incontrast to the same samples that were pre-strained to increasethe dislocation density before testing, whose deformation wascharacterized by work hardening and bulk-like behavior, attainingthe strengths of �2.5 GPa (9–15% pre-strain) [8,11,32–36].Chisholm et al. [32] observed higher strengths and the operationof spiral, single-arm dislocation sources during tension of155 nm�8 μm single crystalline Mo-alloy samples with pre-existing uniformly distributed tangled dislocations. In contrast tothese reports, Schneider et al. [11] reported that pre-straining to10–40% had a negligible effect on the stress–strain behavior of Mopillars with diameters of several microns down to �300 nm [11].

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Materials Science & Engineering A

http://dx.doi.org/10.1016/j.msea.2014.06.0520921-5093/& 2014 Elsevier B.V. All rights reserved.

n Corresponding author. Tel.: 972 54 8181159.E-mail address: landperi@gmail.com (P. Landau).1 These authors equally contributed to this work.

Materials Science & Engineering A 612 (2014) 316–325

Kim et al. [10] has reported a strong size dependence of the yieldstrength of tensile-tested ⟨011⟩-oriented single crystalline W, Mo,Ta and Nb with diameters ranging between 243 and 973 nm. Thedegree of strain-hardening in these samples did not exhibit a trendas a function of size, which implied that hardening was a strongerfunction of initial microstructure. The formation of complex forest-like dislocation networks in deformed Mo [10] and Nb nano-pillars[21] was attributed to mutual interactions and entanglement ofmobile dislocations in the course of deformation.

Iron is a bcc metal widely used in structural applications, forexample as the main component in ferritic and ferritic–martensiticstainless steels, which renders it a particularly important materialfor deformation studies. Xie et al. [37] performed in-situ transmis-sion electron microscopy (TEM) compression experiments on400 nm wide, 100 nm thick bcc-Fe blades. These authors observedthat the deformation was inhomogeneous, characterized by aseries of short strain bursts, which were attributed to the collec-tive release of dislocations from their pinned positions, as well asby the more extensive intermittent displacement bursts caused bythe formation and propagation of slip bands, which nucleated atthe surface. Griveson et al. [38] showed that compressive stress–strain data of Fe micro-pillars with diameters of �1 μm wascharacterized by strain bursts that correspond to the plastic flowalong a visible slip line. The authors attributed these character-istics to the critical temperature (Tc¼350 K) at which it is equallyeasy to propagate screw or edge dislocations, similar to thatobserved in Mo [8,10] and the deformation mechanism in Fecontrolled by the activation of dislocation sources [38].

Ferritic and ferritic–martensitic steels are being considered forcladding in the next generation nuclear reactors [39,40] as well asfusion applications and spallation source materials. For theseapplications, radiation damage and for fusion and spallationsource particular relevant helium (He) accumulation due to thehigh appmHe/dpa ratio, represent a matter of concern rooted inthe detrimental effects of irradiation on the mechanical perfor-mance [39,41–44]. Bombardment with energetic ions duringirradiation leads to the generation of collision cascades withinthe atomic make-up of the structural components, which formirradiation-induced defects like vacancies, interstitials, dislocationloops, and stacking fault tetrahedra (SFT) [45,46]. The productionof helium is an intrinsic response of the alloy during high-energyneutron irradiation due to nuclear cross sections for (n,α) reactionsof specific elements [44,47]. He atoms are insoluble in metals andcommonly combine with vacancies to form bubbles [45,46] at theright conditions, for example temperature. These effects contri-bute to the deterioration in the mechanical properties of structuralmaterials, which lead to high temperature embrittlement [46]. Toextend the lifetime and efficiency of nuclear reactors andto develop new materials immune to radiation damage, it is vitalto understand the physical mechanisms associated withirradiation-induced disorder in structural materials and theirimpact on mechanical properties. The investigations of the effectsof ion beam irradiation on mechanical properties of iron representa useful way to simplify the complexity of irradiation process. In areactor, structural materials are subjected to different conditionssimultaneously that cause the formation of defects – for exampledose, He content, activation, etc; irradiation with specific ions atknown energies allows separating these factors and studying theeffects of individual defect types on deformation. This study isfocused on the effects of mostly He bubbles on tensile strengthand embrittlement, with only a minor contribution from atomicdisplacements.

Controlled ion implantation into small samples has been usedto imitate the generation and agglomeration of radiation-induceddefects in nuclear reactor-relevant materials. A typical penetrationdepth of ions in such experiments is �10 μm, which has led to

nanoindentation being the prevalent methodology for studyingmechanical behavior of implanted metal systems [38,48–51].Recent developments in miniaturized uniaxial mechanical experi-ments with a defined gauge section offer the advantage ofattaining a simple stress state within the deforming volume[1,2,7,12,52,53]. Further, reducing the volume of the radioactivematerial when examining radiation-induced effects in nuclearreactions, improves safety and costs of handling and transporting[40,43]. Griveson et al. [38] reported similar compressive strengthsexhibited by Fe micro-pillars with diameters of �1 μm in their as-fabricated vs. implanted with Feþ ions at 2 MeV and 0.5 MeV at275 1C. These implantation energies were chosen to produce thedamage of �6 dpa in a �1 μm-thick sample. In their work, thestress–strain data of implanted pillars showed more frequent andshorter strain bursts in implanted pillars. The authors attributedthese differences to the emergence of a unique deformation modein the implanted samples, which was characterized by a single,thick set of parallel glide planes. The increased frequency and areduced extent of strain bursts in the implanted samples wasattributed to the presence of dislocation sources within the glideband, which reduced the mean free path of mobile dislocations[38]. One possibility is that the interstitial loops formed as a resultof irradiation were acting as dislocation sources in the indentationplastic zone. This was deemed to be unlikely because of therelatively low yield stresses measured in micro-compressionexperiments (�0.25 GPa) compared to discrete dislocation models(2–10 GPa) for interstitial dislocation loops in iron [38]. Kieneret al. [7] reported the mechanical response of uniaxially com-pressed single crystalline Cu cylinders with diameters between 80and 1500 nm, which were irradiated with 1.1 MeV protons into thebulk sample, i.e. before the small-scale samples were carved outusing FIB [7]. The authors reported a transition diameter of400 nm, below which the pillar strengths followed a power lawas a function of sample diameter, identical to that for the as-fabricated single-crystalline Cu, and plasticity was carried out bythe operation of single arm dislocation sources. Compressivestrengths of larger samples were independent of size, which wasexplained by their bulk-like plasticity mechanism via interactionsbetween mobile dislocations and irradiation induced defects(SFTs) [7]. Li et al. [53,54] reported that the compressive flowstresses of 500 nm-diameter Cu pillars, fabricated by a similarmethodology to Kiener, et al.'s and implanted with an averageconcentration of 7 at% He, more than doubled compared with theas-fabricated samples. This was attributed to the He bubbles actingas obstacles to gliding dislocations and thereby hardening thecrystals [54]. Guo et al. [52] showed that the compressive stressesof the electroplated 120 nm-diameter Cu cylinders, which wereimplanted with He ions with multiple energies ranging between50–400 keV directly into the small-scale samples (to produce auniform distribution of He, average concentration of 0.35 at%)increased by 30% compared to the as-fabricated pillars. Beyondsingle crystals, uniaxial compression of 500 nm-diameter multi-layered Cu/Nb samples, implanted with an average concentrationof 7 at% of He and compressed orthogonally to the interfaces,revealed the strengthening effect was less pronounced in sampleswith thinner layers: the strengths of implanted 70 nm-spacedsamples were 30% higher than as-fabricated samples while thestrengths of implanted 2.5 nm-spaced samples were only 10%higher compared to the as-fabricated ones [53,55]. In-situ uniaxialtension of l00 nm-diameter Cu/Fe bi-crystals, which were irra-diated with 200 keV He directly into the centrally located inter-face, showed 60% higher yield and ultimate tensile strengthscompared with the as-fabricated bi-crystals [55]. These samplesalso failed gradually rather than brittle, which was attributed to theinability of 1–2 nm He bubbles to serve as sufficient stress concen-trators for cracking. While the brief overview of micromechanical

P. Landau et al. / Materials Science & Engineering A 612 (2014) 316–325 317

tests performed on ion beam irradiated materials are radicallydifferent from one another and study different phenomena it doeshighlight the importance of (1) the irradiation species, (2) thespecific details of the radiation-induced defects, and (3) the materialmicrostructure and composition as contributing factors to themeasured mechanical properties [52]. Additional fundamental workto help understand effects of different types of irradiation onmechanical properties of metallic systems is clearly needed.

In this work, in order to further elucidate the mechanicalbehavior and irradiation effects on Fe nano-pillars, we report theresults of uniaxial tension and compression experiments on100 nm-diameter, 1 μm-tall ⟨110⟩ single crystalline Fe samples,both as-fabricated and implanted with He with energies rangingbetween 50 and 400 keV to produce a uniform distribution of Hethroughout the pillar height. Samples were fabricated by tem-plated electroplating [56], followed by implantation directly intothe pillars with no subsequent patterning. We observed similarstrengths in tension and compression of the as-fabricated sam-ples; compression–tension asymmetry was observed in implantedpillars. We discuss the mechanical behavior and deformationmechanisms operating in these materials and examine the effectof He implantation on the mechanical behavior of nano-sized bccmetals.

2. Experimental

2.1. Sample fabrication

Leica Electron-Beam-Pattern-Generator (EBPG) 5000þ wasused to pattern 100 nm-diameter cylindrical pores into the spin-coated PMMA (polymethyl methacrylate), as described in detail inRef. [56]. Fe was electroplated into the patterned pores from aferrous ammonium sulfate electrolyte [57] to produce pillars withthe intentionally over-plated heads [56] for tensile testing (Fig. 1a).The PMMA layer was subsequently dissolved in the acetone bath[56]. Specimens for uniaxial compression tests were prepared by“chopping off” the over-plated heads using FIB (FEI Nova 200Nanolab™) at 30 kV voltage and 10 pA current to produce a flatpillar top, as shown in Fig. 1c. The heights of the chopped pillarswere 300–600 nm, corresponding to an aspect ratio (pillar height/pillar diameter) of 3–6 [56].

2.2. Helium implantation

He was implanted directly into the free-standing Fe nano-pillars after removing the PMMA matrix using a Danfysik™ ionimplanter at Los Alamos National Laboratory, with varying

energies and doses chosen based on SRIM (The Stopping andRange of Ions in Matter) [58] calculations (Fig. 1b), with an ionbeam that was parallel to the pillar axis. The individual Gaussianprofiles for He distribution at each energy were combined toproduce a calculated overall uniform He concentration of0.3670.06 at% over a 1 μm penetration depth. The correspondingaverage displacement per atom (dpa) was calculated to be0.770.2 by utilizing the Damage Event output files from the SRIMcalculation [58] by assuming threshold displacement energy of25 eV for Fe. The implantation did not appear to change themorphology of the pillar surface. The heads of the implantedpillars for nano-compression experiments were “chopped off”after implantation to ensure a uniform distribution of He and asimilar microstructure of the pillar.

2.3. Nano-compression experiments

Uniaxial compression tests were performed in the HysitronTriboscope nanoindenter equipped with an 8 μm-diameter dia-mond flat punch tip, operated under load controlled conditions ata nominally constant prescribed loading rate of 0.5 mN/s, to amaximum load of 25 mN for as-fabricated pillars and 29 mN forimplanted pillars. The nominal constant loading rate of 0.5 μN/s inthe nano-compression tests corresponds to a strain rate of about3�10�4/s, estimated using the pillar diameter of �100 nm andthe Young's modulus of Fe (�200 GPa). This is about 1/3 of thenominal strain rate of 10–3/s in the nano-tension test. It has beenreported that the strain rate sensitivity of the flow stress (σflow) ofbcc-typed micro-/nano-pillars (such as Mo), reflected by the slopeof the log σflow vs. log _ε plot, is in the range of 0.07–0.1 [59]. Usingthe upper limit of 0.1, a difference in strain rate of a factor of3 would lead to about 10% difference in the flow stress, which iswithin the errors associated with both nano-tension and nano-compression tests.

A NanoDMA controller module was used to monitor the contactstiffness of the pillars during each test at a frequency of 200 Hz.Only the data where the calculated stiffness overlaid the measuredvalue were analyzed [3].

2.4. In-situ nano-tension experiments

In-situ uniaxial nano-tension experiments on the implanted andas-fabricated Fe nano-pillars were performed in InSEM (SEMentor), acustom-built nano-mechanical instrument, comprised of a scanningelectron microscope (FEI Quanta200™ FEG) and a nanomechanicalmodule similar to the nanoindenter (Nanomechanics, Inc.) asdescribed in detail in Refs. [5,9,55]. The adhesion between the Fenano-pillars and the Au film initially evaporated on the Si substrate is

Fig. 1. (a) A scanning electron microscopy (SEM) image of a 100 nm-diameter Fe pillar with over-plated head for uniaxial tensile test. (b) The He concentration profile in theFe pillars over 1 mm penetration depth according to SRIM [58] calculations at multiple energies (all numbers in the figure have units of keV). (c) An SEM image of a 100 nm-diameter Fe pillar used for uniaxial compression test, produced by chopping the head of an over-plated pillar using focus ion beam (FIB) at 30 kV and 10 pA.

P. Landau et al. / Materials Science & Engineering A 612 (2014) 316–325318

not well and does not enable the performance of a tensile test sincethe pillars are detached from the substrate at minute load. Therefore,the pillars were effectively glued to the substrate using electron-beam deposition of W to produce an organometallic layer at thesubstrate-pillar interface. The detailed procedure is described byJennings et al. [5].

All experiments were performed at a constant nominal strain rateof �1�10–3 s�1 through a custom-written feedback loop. Theexperiments were conducted in the continuous stiffness mode(CSM) with the harmonic displacement amplitude of 1 nm at 75 Hzoscillation frequency, collecting instantaneous contact stiffness datathroughout the experiment, which allowed the detection of fullcontact between the tensile grips and the pillar top, as well as offailure. The uniaxial strain was determined by correlating andadjusting the raw length change data collected by the nanoindenterby the displacement visually obtained from the recorded videoframes. A total of 4 experiments on each sample type, as-fabricatedand implanted, were performed. Only data from those experimentsthat did not suffer from sample bending or misalignment wereanalyzed. The bottoms of samples for tensile experiments were gluedto the substrate by localized tungsten electron-beam deposition inFEI's Nova 200™ FIB, as described in detail in Ref. [5]. Stresses andstrains were calculated according to the assumption of volumeconservation during plastic deformation in a manner described indetail in Ref. [9] and somewhat resemble true stresses and strainswhen no localization occurs. True stress was evaluated as σ¼PL/A0L0where P is the measured force, L is the instantaneous gauge length,A0 is the initial cross sectional area and L0 is the initial lengthassuming there is no volume change of the material. True strain ε

was calculated as ε¼ ln(L/L0). The gauge length was evaluatedinstantaneously by the “length change” data collection channeltogether with the measured length from SEM images collectedduring the test [9].

2.5. Microstructural characterization

Selected implanted nano-pillars were lifted away from the sub-strate using SEMentor grips and glued onto the TEM grids by Wdeposition for microstructural analysis. This sample preparationtechnique did not require any additional thinning because the100 nm-diameter samples were transparent to the electron beam.Hence, no additional microstructural damage was accumulated – aswould be the case with FIB-based preparation techniques. Site-specific microstructural characterization was performed in a FEITecnai™ TF20 transmission electron microscope (TEM) on the indi-vidual pillars. He bubble size and distribution was examined bythrough-focus imaging in the TEM [60].

3. Results

3.1. Microstructural characterization

The morphology and microstructure of the implanted Fe nano-pillars are shown in Fig. 2. Fig. 2a shows SEM image of a typical100 nm-diameter Fe nano-tensile sample whose overplated top isshaped like a triangular prism. TEM analysis revealed single crystallinemicrostructure, with the typical growth orientation (pillar axis) close

Fig. 2. (a) A SEM image of a typical over-plated 100 nm-diameter Fe nano-pillar at an orientation that shows the shape and contour of the pillar's triangular-prismatic top.The facets in the top prism are inclined at �451 to the pillar axis. (b) Bright field TEM image of a Fe nano-pillar with the corresponding diffraction pattern. The pillar axis isclose to the [101] direction. (c) Under-focus image of He bubbles that appear as bright dots with a dark fringe. (d) Over-focus image of He bubbles that appear as dark dotswith a bright fringe. The He bubbles form a herring-bone-like arrangement parallel to {110} planes throughout the pillar height that is marked with dashed lines on theimage. (e) Over-focus image of He bubbles at an orientation �901 away from the orientation in (d) where the rectangular facet of the prism-shaped head is perpendicular tothe electron beam, showing a uniform distribution of bubbles throughout the pillar height. A few bubbles are pointed to by the arrows in the image.

P. Landau et al. / Materials Science & Engineering A 612 (2014) 316–325 319

to ⟨101⟩, as shown in the diffraction pattern in Fig. 2b. The size of Hebubbles was estimated to be �1–2 nm based on the through-focusimaging (Fig. 2c,d), with bubbles distributed uniformly throughout thepillar height, consistent with the predictions by SRIM [58]. SRIMcalculations likely overestimate the He concentration within the Fenano-samples and represent its upper bound because this modelaccurately describes ion implantations into continuous bulk materialbut does not account for the possibility of He escaping from thesample at the free surfaces. Systematic under- and over-focus images(Fig. 2c,d) revealed that He bubbles were arranged in a herring-bone-like pattern, which was likely caused by the trajectories of implantedspecies following the triangular-prismatic shape of the pillar top(Fig. 2a). The {110} inclined surfaces of the prism led to differentpenetration distances of He into the pillar, which resulted in theimplanted ions tracing the shape of the contact surface and resulted inHe bubble formation on {110} planes while the centerline along thepillar shows a uniform distribution of He bubbles along it. The herring-bone-like arrangement of bubbles was also observed in the samplesthat were lifted out via Omniprobe™ using the FIB, which suggeststhat most likely the methodology of TEM sample preparation did notsignificantly alter the microstructure and bubble distribution. Whenthe pillar was tilted away from this orientation by 901 away to anorientation that showed only the rectangular shape of the prismfacets, the bubbles appeared to be distributed uniformly, and theaverage bubble size was estimated based on these types of images(Fig. 2e). It was difficult to estimate the average bubble spacing in thesample since bubbles could be located on different planes in thesample (2D image of a 3D sample) resulting in a view of a smallerbubble spacing.

3.2. Nano-compression experiments

SEM image of a compressed He-implanted pillar shown in Fig. 3ademonstrates that the pillar likely deformed via crystallographic slipon {110} planes, as evidenced by the shear offsets oriented at �571from the ⟨101⟩-oriented loading axis. Fig. 3d shows that the compres-sive true stress vs. true strain for the implanted nano-pillars containedstrain bursts characteristics of small-scale plasticity and was similar tothat of the as-fabricated samples. The stress–strain data for both setsof microstructures displays 3 distinct regions: (1) elastic loading up to�2% strain, (2) substantial strain hardening, where flow stressincreases from 1.2370.24 GPa at 2% strain up to 1.6270.16 GPa at

�5% strain for as-fabricated samples and from 1.7370.16 GPa at 2%strain up to 2.0670.10 GPa at �5% strain for implanted samples, and(3) a “steady state” region where the average flow stress remainsvirtually unchanged for the duration of the remaining deformation.The approximate transitions between these regions in Fig. 3b aredenoted by the dashed lines parallel to the elastic unloading slope andare provided as a guide.

The compressive yield strengths of the deformed pillars weredefined as the stress at 2% plastic strain, following the methodology ofJennings et al. [61] and Schneider et al. [11]. This methodology waschosen to avoid the ambiguity in determining yield stress in nano-compression experiments caused by the geometric imperfections inthe pillar tops [56,61], as well as the possible uncertainty andmisalignment at the initial loading between the pillars and theindenter grips [3,11]. Detailed analysis of the contact stiffness datasuggests that a full contact between the pillar top and the grips wastypically established at or after 1–2% strain. The average compressiveyield strengths of the He-implanted Fe nano-samples, measured over15 tests, were estimated to be 1.6270.16 GPa, a value 40% higher than1.2370.24 GPa for the as-fabricated samples. The flow stresses of theimplanted and the as-fabricated samples at 10% strain were2.0670.10 GPa and 1.7370.15 GPa, corresponding to �40%(0.5 GPa) and �20% (0.4 GPa) increases over their respective 2% yieldstrengths, with the relative difference in strength between the twosets of samples remaining at �0.4 GPa.

3.3. In-situ nano-tension experiments

Time-lapsed images from a representative in-situ tension experi-ment are presented in Fig. 4a(i–iii) with the self-consistent markers inthe load vs. length change data (Fig. 4b) and the contact stiffness data(Fig. 4c). True stresses and strains were calculated from the load-length change data by using the initial cross sectional area and gaugelength of the cylinders, which excluded the bottom �200 nm of thepillar coated withW. The boundary of this adhesion layer is marked bya dashed line in Fig. 2a. It is unlikely that the presence of the W layerat the bottom of the pillar contributed significantly to the measuredtensile strength, as reported by Jennings et al. [5]. The sample shownin Fig. 4 reached the yield stress of 1.46 GPa at the axial strain of�2.5% upon yield (Fig. 4c). Full failure occurred after a rapid vanishingof the applied force from 0.016 mN between the displacements of 20and 70 nm. Between UTS and fracture, a length change of

Fig. 3. (a) A SEM image of a post-compression Fe pillar. The measured angle between the slip planes and the � ⟨110⟩ loading axis is �571, so the slip planes are likely to be{110} planes. (b) Compressive true stress vs. true strain curves for a typical as-fabricated and He-implanted single crystalline 100 nm-diameter Fe pillars, which display3 distinct regions: (I) elastic loading up to �2% strain (II) steep strain hardening between �2 and 5% strains, and (III) “steady state” flow at a virtually constant flow stressbeyond 5% strain. Dashed lines represent approximate boundaries between these regions as guides.

P. Landau et al. / Materials Science & Engineering A 612 (2014) 316–325320

approximately 50 nm occurred over the time period of �0.15 sresulting in a strain rate of �1 s�1, three orders of magnitude higherthan the prescribed strain rate of 10�3 s�1. This may be attributed tothe fracture of the pillar, which greatly exceed the response limit of thefeedback loop of the nanoindenter. Careful examination of the in-situSEM images during this process was not conclusive to determinewhen the samples became fully severed.

Fig. 5a and b displays the plots of true stress vs. strain data for 4 as-fabricated and 4 He-implanted samples. The scatter in the initialloading slope is likely a result of some misalignment between thetensile grips and the sample head, as well as the surface roughness ofthe sample's head. The yield stress was measured at the point ofdeparture from linearity, with dashed lines in the figures marking theloading slopes for each set of curves to guide the eye. Once full contactwas established, typically at �0.5% strain, the deformation was self-consistent, and the sample-to-sample variation in the data wasmarginal. Fig. 5c presents representative curves for as-fabricated andimplanted nano-pillars for comparison. The stress–strain signature inboth types of samples is characterized by elastic loading up to thestrain of �2%, yielding at approximately 2%, and attaining themaximum tensile strength at the strains close to 3–5% after a relatively

limited post-yield plastic flow. The yield stresses were estimated to be1.4570.30 GPa for the as-fabricated pillars and nearly 40% higher,2.0170.18 GPa, for the implanted samples. This relative differencewasalso manifested in the ultimate tensile strengths (UTS): 2.3570.13GPa for the implanted samples vs. 1.7070.33 GPa for the as-fabricatedones. The plastic flow region in both the implanted and as-fabricatessamples was less than 3%.

Post-fracture snapshots (Fig. 4a(iii)) of the pillars showed nolocalized reduction of cross-sectional area suggesting that neckingdid not occur. Fracture surface was serrated and did not appear tooccur via shearing-off.

4. Discussion

4.1. As-fabricated samples

The 3-region characteristic of compressive stress vs. strain dataof as-fabricated single crystalline Fe pillars has important implica-tions for developing an understanding of deformation mechanismsin bcc single crystals at the nano-scale. The significant strain

Fig. 4. (a) Snapshots from an in-situ tension experiment of an as-fabricated single crystalline Fe nano-pillar correlated with the marked points in the (b) load–displacementcurve. (c) Contact stiffness as a function of length change, with the point of full contact between the tensile grips and the pillar denoted as (i), ultimate tensile strengthdenoted as (ii) and fracture denoted as (iii).

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hardening between the strains of 2% and 5%, labeled as Region II,suggests that extensive dislocation interactions and multiplicationoccurred, which led to their accumulation and storage. Thismechanism might be equivalent to forest hardening, where eachgliding dislocation has to overcome a denser forest of sessiledislocations and other obstacles, which requires the application ofhigher forces. Dislocation dynamics and molecular dynamics simu-lations [4,62] have suggested that the residence time of dislocationloops in bcc pillars is longer than that in fcc nano crystals becausethe screw components of dislocation loops in bcc metals are notrestricted to any particular set of glide planes and can have a factorof �50 lower mobility than that of the edge components [50,63,64].This leads to additional mutual interactions, which results indislocation storage and junction formation and leads to strainhardening [4,62]. This argument was corroborated by TEM analysison post-compression Mo [10] and Nb [21] single crystalline nano-pillars, where intricate, forest-like dislocation networks containingloops, junctions and entanglements [10,21] were observed. Thesefindings suggest that some bcc pillars were unlikely to attain adislocation-starved state upon deformation.

Schneider et al. [11] studied the compressive properties of as-fabricated and pre-strained single crystalline Mo micro-/nano-pillars,as well, and found that the pre-straining did not affect the yieldstrengths and strain hardening. The authors attributed these obser-vations to the shutdown of dislocation sources during deformationand argued that dislocation storage did not occur in small-scale bcc

specimens [11]. In-situ tensile experiments performed inside TEM byChisholm et al. [32] revealed progressive dislocation source exhaus-tion in single crystalline Mo alloy (Mo–10Al–4Ni at%) nano-fibers,which contained intermediate dislocation densities on the order of1012/m2 [33]. It was also reported that plastic deformation in theheavily pre-strained Mo-alloy fibers was accompanied by hardeningand slip events leading to load drops [32].

We attribute the hardening observed in compression and tensilestress–strain curves to an increase in dislocation density due todislocation multiplication and dislocation pinning. We can estimatethe increase in dislocation density necessary to cause the observedincrease in strength between yield and flow stress or UTS incompression and tension, respectively. We use the modified expres-sion from the originally used single arm source (SAS) model[17,61,65]:

σ ¼ 1M

τ0þ0:5μbffiffiffiffiffiffiffiffiρtot

p þ μb4πλi

lnλib

� �� �ð1Þ

where σ is the axial stress measured in the test, M is the Schmidtfactor, τ0 is the friction stress for α-iron [66,67], ρtot is the totaldislocation density, μ is the shear modulus, and λi is the length of theith single arm dislocation source and represents the shortest distancebetween the source pinning point and the free surface within thesame elliptical plane. We estimate the dislocation density increasefrom the measured stress using Eq. (1) by assuming forest hardeningi.e., neglecting the friction stress at room temperature [66,67] and the

Fig. 5. True stress–strain curves of (a) as-fabricated 100 nm-diameter Fe pillars. (b) Helium implanted 100 nm-diameter Fe pillars. (c) Representative curves for as-fabricatedand implanted pillars. For all the plots, the elastic loading slope is marked by a dashed line.

P. Landau et al. / Materials Science & Engineering A 612 (2014) 316–325322

expression related to the operation of single-arm sources (last termin Eq. (1)). Using the same approach to calculate dislocation densityduring flow stress and prior to failure, it was found that thedislocation density increases by Δρ¼4�1015 m�2. In a constantflow stress regime/UTS the model predicts a dislocation density of�8�1015 m�2, a value that is �2 times higher than the dislocationdensity at the yield point, �4�1015 m�2. The dislocation density atthe yield point is in agreement with initial dislocation densitiesmeasured for as-fabricated electroplated pillars [68]. An increase indislocation density by a factor of 2 appears to be reasonable.

For bcc nano-crystals, such as the Fe nano-pillars studied in thiswork, the possible occurrence of dislocation starvation is stillbeing debated. The hardening region is followed by a steadyplastic flow at a virtually constant overall stress of �1.7 GPabeyond �5% strain, labeled as Region III. This suggests that atthese strains the rates of dislocation generation and annihilationmay become comparable with one another, with the overalldislocation density remaining virtually unchanged. In thismechanism, new dislocations may be produced via multiplicationprocesses and possibly from nucleation events; the annihilation ofgliding dislocations may be accommodated by their escape at thefree surfaces and through cross-slip [1,3,17].

The transition from a pronounced strain hardening regime(Region II) to a regime of steady flow at a nearly constant stress(Region III) may indicate that both dislocation multiplication anddislocation starvation were operating during the deformation ofbcc single crystalline Fe nano-pillars. Their overall deformationbehavior was governed by the competition of the two processes(1) dominated by dislocation multiplication, which led to strainhardening and (2) a steady flow which is a result of comparablerates of dislocation generation and annihilation via escape at freesurface and cross-slip. Recently, Cai et al. [69] reported thatplasticity of bcc micro-pillars is controlled by the competitionbetween dislocation multiplication and dislocation depletion bydislocation dynamics (DD). These authors consider a surface-controlled cross-slip process, involving image forces and non-planar core structures of screw dislocations, following themolecular dynamics (MD) simulations of Weinberger et al. [62].The DD simulations show dislocation density fluctuations and thatdislocation multiplication occurs intermittently, supporting ourassumption of competing mechanisms. Further in-situ TEM stu-dies are needed to monitor the dislocation density evolutionduring deformation.

4.2. Effects of He implantation on the mechanical properties

We observed strengthening as a result of He-implantation, asdemonstrated in Figs. 3b and 5c, which has been previouslyreported for various bulk material systems [42,50,53,54,70,71].This strengthening has been usually attributed to He bubblesacting as obstacles for gliding dislocations [46,54,72,73], whichare forced to bow around the bubbles and require the applicationof higher applied shear stresses to break through and carry theplastic strain [50,54,72,73]. This results in an average �0.4 GPaincrease in yield strength and flow stress/UTS for both compressedand tensile-tested samples. The strengthening effect of He bubblesis often described by the Friedel–Kroupa–Hirsch (FHK) hardeningmodel [45,70]:

Δσ ¼ 18Mμb dN2=3

Bubble ð2Þ

where Δσ is the increase in yield strength, M is the Taylor factor,m is the shear modulus, b is the Burgers vector, d is the bubblediameter, and NHe is the bubble density.

We calculate the bubble density according to the pressure-based method adopted by Knapp et al. [74]:

p¼ 2γ þ μbr

ð3Þ

where p is the bubble pressure, γ¼2.5 J/m2 is the surface energyfor Fe [75], μ is the shear Modulus, b is the Burgersvector and r is the bubble radius. We then calculate the molarvolume using the Equation-of-State of He [54] at 300 K andp¼32.5 GPa: V¼3.18 cm3/mole. The bubble radius 0.65 nm ismeasured from the TEM images so that the volume of one bubbleis 1.15 nm3. We assume that all He resides within the bubblesso that the number of He atoms in a single bubble NHe ¼Vbubble=Vmole, is 217. The bubble density was estimated to beNbubble ¼ RHe � NFe=NHe ¼ 0:0014 bubbles=nm3, where RHe¼0.36at% is the atomic concentration of He in the pillar and NFe¼84.8/nm3 is the atomic density of Fe. This value is in good correlationwith the bubble density in the TEM images. Taking M¼3.06 for fccand bcc metals [70], m¼64.8 GPa for single crystalline Fe [76],b¼0.249 nm for the {110}⟨111⟩ slip system in Fe, d¼1.3 nm asobtained from the TEM analysis, and NBubble¼0.0014 nm�3 theincrease in the yield strength due to He bubbles was 0.1 GPa.Assuming radiation hardening is primarily from He bubbles andradiation-induced defects, the difference between the measuredincrease in yield strength and the strengthening due to bubbles is0.3 GPa and is due to radiation-induced defects such as interstitialloops [70,77]. The density of these defects can be estimated byusing the dispersed barrier hardening model [77]:

Δσ ¼Mαμb=l¼MαμbffiffiffiffiffiffiffiffiffiffiffiffiffiNloopd

qð4Þ

where α is the barrier strength and l is the average spacing

between obstacles that can be estimated as 1=ffiffiffiffiffiffiffiffiffiffiffiffiffiNloopd

q, where

Nloop and d are the average loop density and loop diameter,respectively [70,77]. Considering the typical barrier strength ofdislocation loops, α is taken as 0.45. Such an analysis yields a loopdensity of 3.65�1022 loops/m3 assuming the loop diameter is5 nm. This value is in good agreement with the calculated value ofinterstitial loops in irradiated bulk Fe [78], Al/Nb [70] and Fe/W[77] layers and corresponds to an average loop spacing of �75 nm.

Extensive work has been done on bulk polycrystalline Fe andvarious bulk bcc stainless steels to study radiation-induced hard-ening. For example, Tanigawa et al. [44] reported that theindentation hardness of pure polycrystalline Fe increased by�0.5 GPa when subjected to He implantation to a peak dose of0.2 dpa and a He concentration of 0.2 at%. This increase in hard-ness corresponds to �0.2 GPa increase in yield strength, assuminga Tabor's factor of 3 [79]; 0.3–0.4 GPa increase in yield strengthwas observed in Henry et al. [80] for a 9Cr martensitic steel wherethe uniform He implantation dose was 0.4 dpa and the corre-sponding concentration was 0.25 at%. The �0.4 GPa increase inyield strength and in UTS at 0.7 dpa and 0.36 at% of He observed inthis work are comparable with the degree of strengthening atsimilar implantation doses and He concentrations reported in theliterature for bulk bcc iron and bcc stainless steel. This implies thatthe results obtained from these nano-scaled testing specimensmay be used to extract bulk properties of irradiated materials.Contrary to bulk specimens, He implantation does not appear tocause embrittlement of the nano-samples.

He implantation did not affect the presence of the threedescribed regimes in the compressive stress–strain signature,including inter-regime transition strains of 2% and 5%. To quanti-tatively evaluate the extent of overall strain hardening in Region II,the nominal strain hardening exponent n was estimated betweenthe 2% yield point and the 5% flow stress point from the slope inthe log–log plot of the true stress and strain. The nwas found to be

P. Landau et al. / Materials Science & Engineering A 612 (2014) 316–325 323

0.4870.08 for the as-fabricated Fe pillars and 0.4170.08 for theimplanted ones, both of which are in the same data range reportedfor the strain hardening exponents of single crystalline bcc Monano-pillars (0.2–0.6) [8]. The difference in n caused by implanta-tion being within the experimental errors may suggest that the Hebubbles had little effect on the strain hardening behavior anddislocation multiplication process. The uniaxial pillar strengths isincreased by an offset of 0.4–0.5 GPa due to He bubbles andradiation induced defects acting as obstacles for dislocation glide[45]. In Region III, the strain bursts become shorted and morefrequent after implantation in both compression and tensionexperiments (see Figs. 3b and 5c) similar to previous observationsin He implanted monolithic Cu nano-pillars [52]. This suggeststhat the He bubbles and radiation-induced defects trap disloca-tions and hinder their escape from the surfaces. The radiation-induced defects, both bubbles and dislocation loops, appear to playa role in the competition between deformation mechanisms –

dislocation escape and dislocation multiplication. However, theyare not strong enough to prevent dislocations' escape from thepillar.

Table 1 summarizes the yield and ultimate tensile strengths, aswell as compressive flow stresses of all deformed 100 nm-diameter single crystalline electroplated Fe nano structures. WhileUTS and compressive flow stresses of as-fabricated samples weresimilar, tensile yield strengths were higher than compressive ones,and for He implanted pillars tensile yield strength and UTS werehigher than the corresponding compression values. The averagetensile yield stresses of the as-fabricated samples, 1.4570.30 GPa,were �18% higher than the compressive ones, 1.2370.24 GPawhile the UTS and flow stress values were similar. This discre-pancy might emanate from the different methods of measuringthe yield strengths in compression and tension. The compressiveyield stress was measured at 2% plastic strain while the tensileyield stress was taken as the stress at the initial deviation fromlinearity. This discrepancy might also be caused by the differencesin the initial dislocation density among the samples, as reportedfor deformation of Mo nano-fibers of that contained dislocationdensities between �1�1013 m�2 (4% pre-strained) and �4.4�1013 m�2 (16% pre-strained) and had shown a decrease in yieldstress by �0.5 GPa in the 16% pre-strained samples [11,32,34].

The difference in yield strengths in tensile vs. compressiveresponse of Fe nano structures studied in this work is notsurprising because tension–compression asymmetry is typical forbcc metals [24,27,81,82]. The different response of screw disloca-tions to the direction of applied stress was originally reported byVitek et al. [22,23], where twinning vs. anti-twinning sense ofatomic re-arrangements caused non-Schmid behavior during slip.Also reported for pure bulk Fe that when the maximum resolvedshear stress plane (MRSSP) was not {110} or {112}, the slipdeviated towards {110} planes [81]. Kim et al. [10] studied tensileand compressive deformation of nano-sized single crystalline bccmetals with dimensions similar to the ones in this work, andfound that these metals exhibit a strong size dependence. Kim

et al. [20] showed that [011] oriented Mo nano-pillars exhibit atension–compression asymmetry for samples with diameters ran-ging from 1200 nm to 200 nm. In that work, the tensile stresseswere higher than compressive flow stresses, with the differencebetween them reduced to nearly zero at smaller dimensions of�200 nm. The vanishing of tension–compression asymmetry wasexplained by the lesser role of screw dislocation motion indetermining overall plastic flow because of their annihilation atthe free surfaces [20]. The similar values of yield strengths and UTSand flow stress in tension and compression can indicate thediminishing in the compression–tension asymmetry phenomenain 100 nm-diameter Fe nano-pillars, in a similar manner to the onedescribed in detail in [20].

Nevertheless, He implanted pillars exhibit yield tensile stressesand UTSs that are higher than corresponding compressive stresses.This implies that for He implanted ⟨101⟩-oriented single crystallineFe nano-pillars there exists a compression–tension asymmetry,similar to observations reported for similarly oriented singlecrystalline Mo nano-pillars [20]. We suggest that this asymmetryis more pronounced than that observed for the as-fabricatedpillars probably due to the interactions between dislocations andHe bubbles. The bubbles are arranged in a herring-bone-likepatters, parallel to the {110} planes and parallel to the pillar topfacets, as can be seen in Fig. 2(a), (c) and (d). Since slip in bcc Feoccurs on {110} planes [81], the bubbles enhance the effect of theasymmetry. Contrary to as-fabricated Fe pillars that show adiminished compression–tension asymmetry due to the smalldiameter preventing the formation of intricate dislocation struc-tures, the He bubbles serve as obstacles to dislocations and hindertheir escape of through the free surfaces, making the tension–compression asymmetry more pronounced in the implantedpillars.

5. Summary

We report the fabrication and mechanical properties of elec-troplated ⟨101⟩-oriented single crystalline Fe nano structures with100 nm-diameters. Some of these nano-cylinders were implantedwith He to produce a calculated overall uniform He concentrationof 0.3670.06 at% over a 1 μm penetration depth by varying theenergy between 50 and 400 keV. Uniaxial deformation experi-ments reveal a 40% higher yield and ultimate strength in tensionand a 25% higher yield strength and flow stress at 10% plasticstrain in compression for implanted pillars compared to as-fabricated ones.

Uniaxial compressive stress–strain data for as-fabricated andirradiated samples revealed the presence of three distinct regimes:(1) elastic loading up to �2% strain, (2) strain hardening of�0.5 GPa between 2% and 5% strains, and (3) a steady state flowwith intermittent strain bursts at an unchanging global stress forstrains over 5%. These findings were rationalized in terms of thedislocation driven plasticity mechanisms and the rates of disloca-tion annihilation and accumulation.

TEM analysis of implanted samples revealed a herring-bone-likedistribution of 1–2 nm-diameter He bubbles on {110} planes.Irradiation hardening due to He bubbles and dislocation loops werelikely the reason for the observed �0.4 GPa increase inthe yield strengths and flow stresses/UTSs of implanted vs. as-fabricated pillars. These findings are consistent with observations ofbulk Fe and bcc stainless steels under similar He implantationdoses, which suggests that the results obtained from nano-scaledtest specimens may be used to extract bulk properties of irradiatedmaterials. Implanted Fe nano-pillars show compression–tensionasymmetry, with the tensile stresses on the order of 15–20% higherthan the compressive ones. This is attributed to dislocation–bubble

Table 1Yield stress and UTS/flow stress values for as fabricated and He implanted 100 nm-diameter Fe nano-pillars.

Tension Compression

Asfabricated

Heimplanted

Asfabricated

Heimplanted

Yield strength [GPa] 1.4570.30 2.0170.18 1.2370.24 1.6270.16UTS/flow stress[GPa]

1.7070.33 2.3570.13 1.7370.16 2.0670.10

P. Landau et al. / Materials Science & Engineering A 612 (2014) 316–325324

interactions on {110} planes that encourage the formation ofintricate dislocation structures.

These findings shed light on deformation mechanisms of bccnano structures and the effect of He implantation on the mechan-ical behavior of nano structures, and may help in the developmentand design of new materials for structural applications in nextgeneration nuclear reactors.

Acknowledgments

The authors gratefully acknowledge the financial support of theU.S. Department of Energy, Office of Basic Energy Sciences throughJRG's Early Career grant DE-FOA-00003951. The authors alsoacknowledge support and infrastructure provided by the KavliNanoscience Institute (KNI). Helium implantation was supportedby Center for Integrated Nanotechnologies (CINT), a DOEnanoscience center jointly operated by Los Alamos and SandiaNational Laboratories.

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