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. 2020 Aug 10;14(9):11691–11699. doi: 10.1021/acsnano.0c04327

Plastic Forming of Metals at the Nanoscale: Interdiffusion-Induced Bending of Bimetallic Nanowhiskers

Yuanshen Qi †,*, Gunther Richter ‡, Eylül Suadiye ‡, Michael Kalina †, Eugen Rabkin †,*
PMCID: PMC7586402  PMID: 32790344

Abstract

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Controlled plastic forming of nanoscale metallic objects by applying mechanical load is a challenge, since defect-free nanocrystals usually yield at near theoretical shear strength, followed by stochastic dislocation avalanches that lead to catastrophic failure or irregular, uncontrolled shapes. Herein, instead of mechanical load, we utilize chemical stress from imbalanced interdiffusion to manipulate the shape of nanowhiskers. Bimetallic Au–Fe nanowhiskers with an ultrahigh bending strength were synthesized employing the molecular beam epitaxy technique. The one-sided Fe coating on the defect-free, single-crystalline Au nanowhisker exhibited both single- and polycrystalline regions. Annealing the bimetallic nanowhiskers at elevated temperatures led to gradual change of curvature and irreversible bending. At low homological temperatures at which grain boundary diffusion is a dominant mode of mass transport this irreversible bending was attributed to the grain boundary Kirkendall effect during the diffusion of Au along the grain boundaries in the Fe layer. At higher temperatures and longer annealing times, the bending was dominated by intensive bulk diffusion of Fe into the Au nanowhisker, accompanied by a significant migration of the Au–Fe interphase boundary toward the Fe layers. The irreversible bending was caused by the concentration dependence of the lattice parameter of the Au(Fe) alloy and by the volume effect associated with the interphase boundary migration. The results of this study demonstrate a high potential of chemical interdiffusion in the controlled plastic forming of ultrastrong metal nanostructures. By design of the thickness, microstructure, and composition of the coating as well as the parameters of heat treatment, bimetallic nanowhiskers can be bent in a controlled manner.

Keywords: metal nanowhiskers, nanoscale plasticity, interdiffusion, Kirkendall effect, HAADF-STEM

Plastic deformation of polycrystalline bulk metallic materials at ambient temperature is mediated by the glide of pre-existing lattice dislocations and generation of new dislocations by the pre-existing and newly formed dislocation sources,1 formation of stacking faults and deformation twinning,2 grain boundary sliding,3 or phase transformations,4 depending on the grain size, stacking fault energy, strain rate, composition, etc. The typical elastic deformation of bulk metallic materials at the onset of plastic yield is about 0.1–0.2%. In contrast, plastic deformation of single-crystalline nearly defect-free metallic nanocrystals such as nanowhiskers or nanowires (NWs)5 and nanoparticles6 is controlled by the nucleation of new dislocations. In the uniaxial deformation regime, the nanocrystal deforms elastically up to very high strains of several percent and stresses of several gigapascals, followed by a catastrophic plastic collapse.6 This deformation mode is referred to as nucleation-controlled plasticity.7−9

The nucleation-controlled plasticity of nanocrystals, on one hand, leads to high mechanical strength approaching its upper theoretical limit;6−11 on the other hand, it makes the manipulation of the crystal morphologies by the plastic-forming process very difficult12−14 (see Supporting Information Movie 1). Csikor et al. demonstrated that the intermittent dislocation avalanches in microcrystals under loading result in stochastic distribution of plastic strain.12 For this reason, the mechanical loading of defect-free metal nanocrystals cannot be employed for their controlled plastic forming into a desired shape. Such forming may be necessary because the variety of shapes of the as-synthesized defect-free nanocrystals is severely limited by the relative specific surface energies of the crystal facets.15,16

Controlling of the morphology of NWs is critical for their potential applications, such as plasmonic waveguides.17−19 Studies of mechanical behavior of NWs employing three-point bending and cantilever beam bending reveal high elastic strains at the onset of plastic yielding, often followed by a strain burst and abrupt fracture.20−23 Currently, the curvature or morphology of metal NWs cannot be precisely manipulated by plastic deformation via mechanical load.24

Apart from the stress generated by mechanical load, stresses induced by chemical interdiffusion represent an alternative route of plastic deformation.25 For example, the imbalance of atomic diffusion fluxes during the Kirkendall effect results in net vacancy flux and concomitant lattice drift and shape changes due to the climb of edge dislocations.25−28 The scarcity of internal vacancy sinks may result in the generation of high internal elastic stresses and viscous material flow.25,29 In fact, in the past decade, Kirkendall effect has been widely utilized in the synthesis of hollow metallic nanostructures.30−32 It is also worth noting that the chemical diffusion-induced stresses in nanostructured electrodes of rechargeable Li-ion batteries represent a formidable technological problem.33 The insertion and removal of alkali ions such as Li+ and Na+ during charging and discharging operations cause significant shape distortion and fracture of the nanostructured electrodes and decrease the battery cycling capacity.34−36 It was also shown that diffusion- and transformation-induced stresses significantly modify the kinetics of lithiation of the Si NW anodes.37 However, the possibility of using interdiffusion-generated internal stress for controlled plastic forming at the nanoscale has not yet been explored. Herein, we performed annealing of Au/Fe bimetallic NWs to demonstrate the feasibility of controlled plastic forming of NWs by interdiffusion-generated stresses.

Results and Discussion

The bimetallic Au/Fe NWs were fabricated by physical vapor deposition onto W substrates using molecular beam epitaxy (MBE). The as-grown faceted single-crystalline ⟨011⟩-oriented Au NWs (∼360 nm in cross-sectional width and several micrometers in length) were coated on one side with Fe layers ∼200 or ∼50 nm in thickness in the same MBE chamber (see Methods).

One typical as-synthesized bimetallic NW is presented in Figure 1a. The side facets of Au NWs are {111} and {100}, which are closest-packed and second closest-packed planes, respectively, of the face-centered cubic (FCC) lattice. The Fe layers adjacent to the {100} and {111} facets of the Au NW were found to be single-crystalline (SX) and polycrystalline (PX), respectively, and to form coherent SX Fe–Au and incoherent PX Fe–Au interfaces (see Figure S1 in Supporting Information and ref (38)). The coherent interface exhibits the Bain orientation relationship between the SX Fe layer and the Au NW, for example, [01̅1]Au//[001]Fe, (011)Au//(010)Fe, and (100)Au//(100)Fe. It is worth noting the presence of grain boundaries (GBs) and nanocavities in the PX Fe layer and at the interface between PX and SX Fe layers (Figure 1b and Figures S2–S5). We used the easy-lift technique in a focused ion beam–scanning electron microscope (FIB-SEM) dual beam instrument to harvest and transfer individual NWs from the W substrate to Mo foil substrates, see Figure 1c,d.

Figure 1.

Figure 1

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Au/Fe bimetallic NW characterization, harvesting, and mounting. Secondary electron (SE)-SEM micrographs of (a) a NW grown on a W substrate; (b) an enlarged view to distinguish the Fe layer on the Au NW; white arrows mark some of the morphological features on the polycrystalline Fe layer associated with the GBs or nanocavities between the nanocrystalline Fe grains; (c) welding of the probe tip and the NW employing Pt deposition followed by cutting the NW free from the W substrate; (d) mounting of the NW on a Mo foil substrate by Pt deposition and cutting it free from the probe tip; the green dashed line highlights the radius of curvature of the NW. The error in radius of curvature is related to the measurement uncertainties.

The as-synthesized bimetallic NW was slightly bent in the direction toward the Fe coating (Figure 1d), which contrasts with the straight morphology of single-phase Au, as well as Cu and Pd NWs prepared using same MBE procedures.5 This bending can be explained by a combined effect of lattice mismatch strain and island-coalescence stress in the SX and PX Fe layers, respectively (for the estimate of their contributions see Supporting Information and Figure S2). The lattice mismatch strain at the SX Fe–Au interface between (011)Au//(010)Fe can be estimated as εm = (dFe(010) – dAu(011))/dAu(011) = −0.0059, where dFe(010) = 2.867 Å and dAu(011) = 2.884 Å are the interplanar spacings in Fe and Au, respectively.39 The radius of curvature associated with this mismatch strain was estimated to be 40 μm employing the Timoshenko formula.40 Numerous nanocavities at the GBs in the PX Fe layer also cause high tensile stress in the layer, similar to island zipping stress.41 Using the model of Nix and Clemens,41 this stress was estimated to be 19.1 GPa; this tensile stress also contributes to the bending of NWs toward the Fe layer. However, it is worth noting that such high stress is certainly partially relaxed by various plasticity mechanisms,42 such as plastic deformation of the Au NW resulting in the formation of ledges at the PX Fe–Au interface, see Figure S3.

In Situ Heat Treatments of the Nanowhiskers

Three NWs were lifted-out, heat treated, and characterized in this study. NW#1 and NW#2 with ∼200 nm thick Fe layers were employed for in situ annealing experiments, which were conducted in a Zeiss Ultra-Plus SEM. These two NWs were mounted on a Mo foil, which was fitted into the heating stage, and the annealing was performed under vacuum of 5 × 10–5 mbar in the SEM chamber. Before each SEM image acquisition, the temperature was kept constant for 20 min for thermal equilibration and stage stabilization. NW#3 with a ∼50 nm thick Fe layer was annealed ex situ.

During the in situ heating of NW#1, we first observed reversible bending behavior at relatively low temperatures, see Figure 2a–c. The radius of curvature, R, changed from 23 ± 1 μm at room temperature to 18 ± 1 μm at 300 °C, increasing back to 21 ± 1 μm upon cooling to 25 °C after the heating system was switched off. This reversible bending behavior was attributed to elastic deformation due to the mismatch of the thermal expansion coefficients of the Au NW and the Fe coating (14.2 × 10–6 °C–1 and 11.4 × 10–6 °C–1, respectively). Higher thermal expansion of Au compared to that of Fe upon heating from room temperature to 300 °C resulted in the development of compressive stress in the Au NW as the mismatch strain rose from −0.0059 to −0.0067. This increase in the mismatch strain changes the estimated value of R from 40 to 36 μm, in qualitative agreement with the experimental results. It was also noticed in the experiment that the radius of curvature of NW#1 did not fully recover from 18 back to 23 μm upon cooling from 300 to 25 °C, since the measured value of R was 21 μm after the full heating/cooling cycle. This was due to the healing of some nanocavities in the Fe layer at 300 °C, which resulted in volume shrinkage in the Fe coating (see Figures S4–S6 and estimation of nanocavity healing based on Fe GB diffusion in Supporting Information).

Figure 2.

Figure 2

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Reversible and irreversible bending of a Au/Fe bimetallic NW at elevated temperatures. SE-SEM micrographs of (a–c) reversible bending of NW#1 at 300 °C in elastic deformation regime; (d,e) irreversible bending of NW#1 at 400 and 500 °C. (f) Enlarged view of the NW acquired using back-scattered electrons (BSE), visualizing the Au clusters on the Fe layer by their Z-contrast. (g) Schematic illustration of the bending process. The radii of curvature, R, of the NW at each temperature are presented in panels a–e. The error in determining of the radius of curvature was estimated by performing 5–6 independent curvature measurements.

Irreversible bending in the opposite direction occurred when the temperature was increased above 300 °C. NW#1 was nearly straight at 400 °C and kept bending toward the Au NW reaching a curvature of 22 ± 1 μm with an opposite sign at 500 °C, see Figure 2e. At this stage, the Fe coating and Au NW were under compression and tension, respectively. Finally, from the BSE-SEM micrograph shown in Figure 2f, some isolated Au clusters were observed on the outer surface of Fe layer, which indicated significant Au diffusion at elevated temperatures. Indeed, the diffusional penetration of Au along the GBs and nanocavities in the Fe coating can explain the volume expansion and concomitant development of compressive stresses in the latter.

The penetration of Au into the Fe layers via the nanocavities and GBs is demonstrated in Figure 3. This penetration resulted in the formation of Au-rich clusters on the outer surface of the Fe layer shown in Figure 2f and highlighted in both normal (Figure 3a) and longitudinal (Figure 3d) cross-section views of high-angle annular dark-field scanning electron microscopy (HAADF-STEM) images of NW#1. The GB diffusion process led to the formation of characteristic GB grooves at the Au–Fe interface, which are marked in Figure 3d,e. Also, the nanocavities in Fe got partially filled with the Au-rich alloy. The diffusion of Au along and segregation at the GBs in Fe nanostructures attached to the substrate has also been observed earlier by Amram et al.43 These phenomena have been utilized in bulk Fe–Au alloys for filling and healing of creep-induced microcavities at elevated temperatures, thus enhancing the alloy component lifetime.44

Figure 3.

Figure 3

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Plastic bending of the Au/Fe metallic NW induced by interdiffusion. STEM-EDX characterization of bent NW#1 after in situ heating at 500 °C. (a–c) HAADF-STEM images of the normal cross-section of NW#1, imaged along the [01̅1] zone axis (Z.A.) of Au. The diffusion flux of Au atoms into an Fe nanocavity at the intersection of Au (111) and (100) facets is schematically shown by arrows. (b) Nanoroughness developed at the incoherent Au–Fe interface facilitating interface migration and Fe diffusion into Au; inset fast Fourier transform (FFT) image and lattice analysis indicate the incoherency of the interface. (c) Coherent twin boundary (CTB) and incoherent twin boundary (ITB) developed in Au to relax the diffusion-induced stress. (d, e) HAADF-STEM micrograph and corresponding EDX mapping of the longitudinal cross-section of NW#1, imaged along the [2̅11] Z.A. of Au.

As will be detailed below, Au diffusion along and accretion at the GBs in the Fe layer caused its volume expansion and concomitant bending of the NW in the direction of Au. At the same time, Fe also diffused into Au via lattice diffusion. As seen in Figure 3b, the Au-rich phase grew at the expense of Fe, and the Au–Fe interface migrated in the Fe direction. This movement reflects high solubility of Fe in Au and negligible solubility of Au in Fe.45 This volume interdiffusion and interface migration caused volume shrinkage of the Au constituent, since the lattice parameter of the Au–Fe alloys decreases with increasing Fe content. Finally, a twin boundary (TB) consisting of coherent and incoherent sections can be seen in Figure 3c. It nucleated on the free surface of the Au NW, migrated toward the Au–Fe interface, and stopped in the NW interior. This TB can be categorized as a deformation twin nucleated to relieve the diffusion-generated elastic stresses in the Au NW. The twin has nucleated on the free surface of the Au NW rather than at the Au–Fe interface (the source of diffusion-generated stress) because the nucleation of the Shockley partial dislocations (also serving as twinning dislocations) is easier on the free surface than at the interface exhibiting lower diffusion mobility of Au atoms.46 Finally, transmission Kikuchi diffraction (TKD) characterization of a segment (∼4.5 μm) of NW#1 reveals that the bending curvature was induced by a gradual lattice rotation of ∼6° of Au NW about [011] zone axis, which is normal to the Au NW growth direction, [01̅1] (Figure 4). No GBs that could form via the polygonization process at 500 °C were found in the inverse pole figure (IPF, X-axis) image (Figure 4b).

Figure 4.

Figure 4

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Lattice rotation in bent NW#1. (a) Color-coded dark-field (CCDF) image of the longitudinal cross-section of NW#1. (b) Orientation image with an inset illustrating the color codes of normal (Z) grain orientations. (c) Misorientation map of the Au NW where the reference location is marked by the white cross. The legend shows the range of misorientations (1°–6°). (d) Segmented misorientation map, inverse pole figure, and pole figure showing that the Au lattice distortion was caused by the lattice rotation around the [011] zone for 6°. The orientations of two locations at the ends of the segments, d1 and d2, are schematically illustrated; their [011] directions are parallel.

The interdiffusion induced plastic bending was reconfirmed in bent NW#2, which went through the same in situ heating cycle up to 500 °C as NW#1, see Figure 5a,b. Au diffusion via Fe GBs and nanocavities and Fe lattice diffusion into Au and accompanying interface migration are shown in Figure 5c,h,i. These micrographs support the hypothesis that the plastic bending has resulted from the interdiffusion between the Au NW and Fe coating.

Figure 5.

Figure 5

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Plastic bending of the Au/Fe metallic NW mediated by tilt GBs. SEM and STEM-EDX characterization of bent NW#2 after in situ heating at 500 °C. (a, b) SE-SEM images showing the bending of NW#2 at 500 °C. (c–g) HAADF-STEM images of the normal cross-section of NW#2, acquired along the [01̅1] Z.A. of Au. (d, e) A tilt GB formed at the mouth of Au layer penetrating the gap between the PX and SX Fe layers. (f) Deformation twins formed to relax the interdiffusion-induced stresses and to mediate plasticity. (g) Disconnections and a superledge formed at the coherent Au–Fe interface indicating the interface migration toward Fe. (h, i) HAADF-STEM micrograph and corresponding EDX mapping of the longitudinal cross-section of NW#2, imaged along the [2̅11] Z.A. of Au; an Fe grain fully covered with Au GB segregation layer is highlighted.

Furthermore, a ⟨011⟩ asymmetric tilt GB characterized as a special Σ = 43/(455)1/(5̅33)2/99.37° GB was found at the “mouth” of the Au layer protruding into the gap between SX and PX Fe layers, Figure 5c,d. The formation of the GB could be understood in terms of the reduction of the energy of all GBs and interfaces in the system, see Figure S7 and the estimate in Supporting Information. The penetration of Au into the gap between two Fe layers in homoepitaxial orientation relationship with the Au NW would result in the (277) plane of Au abutting the SX Fe layer. Such Au–SX Fe interface exhibits high energy. Instead, Au penetrated the gap between the two Fe layers in a different orientation (rotated about the [01̅1] axis by 99° with respect to the original Au NW), resulting in the low-index (100) plane of Au contacting the SX Fe layer at the interface and reducing the energy of the Au–SX Fe interface.47 The energy “penalty” of this process is the energy of the Σ43 GB formed at the “mouth”, yet because its total length is significantly smaller than the length of the Au–SX Fe interface the process is energetically favorable. Finally, three deformation TBs were observed, extending from the free surface to the Au–Fe interface across the width of the Au NW, see Figure 5c,f and Figure S8. It is worth noting that unlike the TBs formed in Au NWs during tensile testing experiments, which are inclined with respect to the NW growth axis,48 the TBs observed here are parallel to the growth axis and extend over the whole length of the NW. This is due to difference in the stress states and Schmid factors for the {111}⟨011⟩ slip system during uniaxial loading48 and diffusion-induced bending uncovered in the present work.

The irreversible bending of NW#1 and NW#2 caused by in situ heating, together with the STEM-EDX and TKD characterization of the bent NWs, indicates that the diffusion of Au into Fe nanocavities and GBs caused the lateral (i.e., parallel to the NW axis) expansion of the Fe layer. Let us first assume that the partial diffusion coefficients of Au and Fe along the Fe GBs are equal. In this case, all Au atoms penetrating along the Fe GBs will replace the Fe atoms there, and with the average grain size in the PX Fe of 66 nm (see Figure S2), one monolayer of Au at the GB will cause a lateral strain of 6 × 10–4, 1 order of magnitude lower than the initial mismatch strain. However, in the case that Au diffuses along the GBs much faster than Fe (GB Kirkendall effect49), the accretion of excess Au at the GB will not be accompanied by any outdiffusion of Fe. In this case, accretion of one monolayer of Au at the GBs will cause a Kirkendall strain of 0.004, comparable with the lattice mismatch strain (see Figure. 6a, Figure S9, and the estimation in Supporting Information). Formation of the GB diffusion wedge of 2–3 Au monolayers in thickness can fully compensate the initial mismatch strain and cause NW bending of similar magnitude in the opposite direction. Therefore, the main underlying mechanism of the plastic bending at 500 °C is the imbalanced GB interdiffusion in the PX Fe layer and the GB Kirkendall effect.49 A detailed description of the atomic and vacancy fluxes and lattice/grain drifts associated with the Kirkendall effect during Au diffusion along the individual GB in the PX Fe layer is outlined in Supporting Information, Figure S10. Moreover, it should be noted that Fe lattice diffusion into Au contributed to the lateral shrinkage of the Au NW, because the lattice parameter of the Au(Fe) alloys decreases with increasing Fe content,45 and partial lattice diffusivities of Au and Fe in dilute Au(Fe) solid solution are nearly equal.50 This lattice shrinkage in the Au NW also contributes to the NW curvature (Figure 6b).

Figure 6.

Figure 6

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Two mechanisms to modulate the bending curvature of a Au/Fe metallic NW. Schematic illustrations of (a) Au atom accretion at the GBs in PX Fe layer via the GB Kirkendall effect and (b) diffusion of Fe into Au, formation of Au(Fe) interdiffusion zone, and interface migration. Both mechanisms cause lateral expansion of the Fe layer and contraction of the Au NW, which lead to the NW bending toward Au.

Finally, we would like to emphasize that at relatively low temperatures and short annealing times employed in the in situ heating of NW#1 and NW#2, lattice diffusion of Fe into Au is very limited (as evidenced by the limited interface migration distance and formation of disconnections at the interface, see ref (38)), therefore, the GB Kirkendall effect is the dominant factor in the plastic bending of the NWs when annealing was conducted below 500 °C.

Our TKD measurements of the longitudinal cross sections of the Au NWs did not reveal any low-angle GBs (Figure 4b and Figure S8c). Assuming that the bending of Au NWs proceeds by classical dislocation plasticity mechanisms, it was expected that geometrically necessary dislocations (GNDs) would accommodate the plastic bending and self-organize at elevated temperatures in the form of low-angle GBs according to the classical polygonization mechanism.51,52 In contrast, we observed a gradual change of lattice orientation and formation of TBs in the bent Au NWs. This is consistent with the defect-free nature of as-grown Au NWs (no pre-existing dislocations or dislocation sources) and indicates that the energy barrier associated with nucleation of twinning dislocations (Shockley partials) is lower than that of GNDs. It is should be noted that diffusion-controlled irreversible NW bending with little involvement of lattice dislocations uncovered in the present work bears some similarities to the time-dependent plastic deformation by Coble creep53 and Nabarro–Herring creep.54,55 GB Kirkendall effect and Coble creep are active at low homological temperatures at which the GB diffusion is a dominant mode of mass transport and lattice growth and expansion. On the other hand, full diffusion intermixing and Nabarro–Herring creep operate at higher temperatures and longer annealing times at which the plastic bending or deformation are dominated by bulk diffusion.

We also tested the feasibility of using a thin layer of Fe to bend the Au NW and then dissolve the Fe. We employed NW#3 with a ∼50 nm thick Fe layer for this experiment. The NW was annealed in a rapid thermal annealing furnace under forming gas flow (Ar–10% H2, 6N purity) at a temperature of 600 °C for 30 min. As can be seen in Figure 7a–d, the radius of curvature changed from 43 to −56 μm after annealing, with most of the Fe layer being dissolved in the Au NW.

Figure 7.

Figure 7

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Bending by dissolving Fe layer in the Au NW, revealed by the characterization of NW#3 after annealing at 600 °C for 30 min. (a–d) Morphology and cross-section of the as-synthesized and annealed NW#3, (e) dark-field (DF)-STEM image showing the TBs formed in the interdiffusion zone during the bending and interface migration, and (f) HAADF-STEM image characterizing the TB.

We estimated the volume fractions of the Fe layer and the Au NW in the pristine bimetallic NW to be 16.5% and 83.5%, respectively (Figure S11). This is equivalent to the overall composition of Au–13.5 atom % Fe, so that full homogenization of the NW would result in a decrease of lattice parameter from 4.078 Å (in pure Au) to 4.041 Å.45,56 Taking into account that the lattice parameter of body-centered cubic (BCC) Fe is 2.867 Å, full homogenization of the NW would result in a volume swelling of 6.5%. This estimate is very close to the measured increase of the cross-sectional area of 5.5% determined by comparing Figures 7, panels b and d. This indicates that even nearly full dissolution of the Fe layer does not cancel internal stresses in the NW and its plastic bending. This is because the Au NW contracts upon dissolving Fe (due to the decrease of the lattice parameter of the Au(Fe) solid solution), while the former Fe coating expands due to its transformation into the Au(Fe) solid solution (with atomic volumes of 11.78 Å3 and 16.50 Å3 in BCC Fe and in the Au(Fe) solid solution, respectively) (Figure 6b). A closer observation showed a TB formed in the interdiffusion zone and exhibiting both CTB and ITB sections. It formed during the migration of the Au–Fe interface toward the Fe layer and may be responsible for partial relaxation of the bending stresses (Figure S12).

Conclusion

In conclusion, we have successfully demonstrated the feasibility of controlled plastic deformation of the ultrastrong metallic nanostructures through the chemical interdiffusion route, employing either the GB Kirkendall effect or full diffusion intermixing. By performing in situ heating on Au–Fe bimetallic NWs, we systematically studied the evolution of NW curvature associated with lattice mismatch strain, island-coalescence stress, thermal expansion mismatch, imbalanced GB interdiffusion, and full diffusion intermixing. We uncovered that when the GBs represent the main diffusion paths the irreversible plastic bending is dominated by the Au accretion at the GBs in the polycrystalline Fe layer (GB Kirkendall effect). At higher temperatures or longer annealing times, bulk interdiffusion controls the plastic bending through the dependence of the lattice parameter on the composition and the volume effect associated with migrating interphase boundary. Therefore, the design of the thickness and the microstructure of the diffusion layer, as well as the annealing parameters enables the bending curvature of a bimetallic nanowhisker to be fine-tuned. Conversely, the bimetallic nanowhiskers with a known microstructure can be utilized as local temperature nanosensors, converting the temperature and thermal history of the sample into geometrical curvature.

Methods

Fabrication of Au/Fe Bimetallic Nanowhiskers

The preparation of Au/Fe bimetallic nanowhiskers (NWs) is described in detail in ref (38). In short, Au NWs attached to the W substrate were first fabricated employing the molecular beam epitaxy (MBE) method at the temperature of 800 °C and under vacuum of 5 × 10–10 mbar. The as-grown Au NWs were 300–400 nm in diameter and several micrometers in length, and their growth axis was ⟨011⟩. Fe coatings of ∼200 nm and ∼50 nm in thickness were then deposited on the as-grown Au NWs in the same MBE tool. The nominal deposition rates (as measured with the aid of quartz balance) were 0.01 and 0.05 nm/s for Fe and Au, respectively. We found that the inclination angle of the Au NWs has a strong effect on the morphology of the deposited PX Fe layers. Moreover, the shadowing effect resulted in formation of nanocavities in the Fe layers, particularly at the edges between the side {111} and {100} facets of the Au NW.

Preparation of Nanowhiskers for Annealing

Au/Fe bimetallic NWs were harvested using an easy-lift system in a focused ion beam (FIB)–scanning electron microscope (SEM) dual beam instrument (FEI Helios Nanolab Dualbeam G3). For the heat treatments, the NWs were mounted on Mo foil using Pt deposition. The Mo foil substrates were employed because of a favorable combination of their thermal conductivity (ensuring homogeneous distribution of temperature), oxidation resistance, and mechanical strength.57 The NWs have been cut into several segments, thus enabling a comparative analysis of their cross-sectional microstructures before and after heat treatment. Employing very low ion beam currents, small pixel number (738 × 512 or 1536 × 1024), and short dwell time (50–100 ns) for imaging (30 keV, 1.1 pA) and cutting (30 keV, 7 pA) enabled minimizing the damage to the NWs caused by Ga ion beam exposure.

Annealing Treatments of Nanowhiskers

The in situ heating experiments were performed in a high-resolution scanning electron microscope (Zeiss Ultra Plus) equipped with a heating stage (Kammrath Weiss heating module 1050 °C). A heating rate of 5 °C s–1 was used for the annealing. The ex situ heating experiments were performed in a rapid thermal annealing furnace (RTA; ULVAC-RIKO MILA 5000 P–N) under the flow of forming gas (Ar–10 vol % H2, 6N purity). The heating rate was 40 °C s–1, while fast cooling was achieved by switching off the heating.

Characterization of Nanowhiskers

The atomic resolution microstructure features and the composition of the NWs were characterized in a scanning transmission electron microscope (STEM). The cross-sectional TEM lamellae were prepared from the NWs employing standard FIB procedures. STEM was performed with a double Cs-corrected FEI 80-300 Themis G2 operated at 300 kV. A 21 mrad beam convergence semiangle was used, resulting in spatial resolution better than 0.9 Å. With camera length set at 94 mm, inner and outer collection semiangles of 119  and 200 mrad, respectively, were used for the HAADF detector. The low-angle annular dark-field (LAADF) and bright-field (BF) STEM images were also collected in the semiangle ranges of 19–33 and 0–11 mrad, respectively. Energy-dispersive X-ray spectroscopy (EDX) mapping was performed in STEM using a Dual-X detector (Bruker) with an effective solid angle of 1.76 sr. Selected area diffraction patterns (SADPs) were acquired in an FEI Technai T20 TEM operating at 200 keV. Finally, transmission Kikuchi diffraction (TKD) measurements were conducted in the Zeiss SEM equipped with a TKD system (Bruker).

As-Synthesized Au/Fe Bimetallic NWs

The side facets of Au NWs were {111} and {100}, which are the closest-packed and second closest-packed planes, respectively, of the FCC lattice. The Fe layers deposited on the {100} facets were single-crystalline (SX), whereas their counterparts on the {111} facets were polycrystalline (PX).

Typical as-prepared bimetallic NWs exhibiting both SX and PX Fe layers are shown in Figure S1. The SX Fe layer exhibits the Bain orientation relationship with the Au NW, for example, [01̅1]Au//[001]Fe, (011)Au//(010)Fe, and (100)Au//(100)Fe. Most of the nanograins in the PX Fe layers exhibit low misorientation angles, which is confirmed by the diffuse diffraction streaks in the diffraction patterns (Figure S1d). The reason why incoherent PX interface and coherent SX interface were formed on {111} and {100} Au facets, respectively, was probably related to the high difference of the respective values of lattice mismatches between Fe coating and Au substrate. Indeed, it was shown that during initial stages of Fe deposition on Au(111), the first few monolayers of Fe grow pseudomorphically as a FCC phase.58 The corresponding lattice mismatch, however, is very high (about 14%), so that at a thickness of only 2–3 monolayers a set of misfit dislocations is nucleated at the interface. These dislocations serve as heterogeneous nucleation sites of the BCC α-Fe phase, which occurs once the thickness of the Fe layer reaches 5–7 monolayers. The stochastic nature of this nucleation in the strong stress field of misfit dislocations causes a transformation of the single crystalline pseudomorphic γ-Fe layer into the polycrystalline α-Fe. In contrast, very small lattice mismatch between α-Fe and (100) Au of only 0.59% (Bain orientation relationship [01̅1]Au//[001]Fe, (011)Au//(010)Fe, and (100)Au//(100)Fe) probably causes the Frank–van der Merwe growth of α-Fe on {100} facets of Au NW from the onset of Fe deposition.

Acknowledgments

This work was supported by German-Israeli Foundation for Scientific Research and Development, Grant No. I-1360-401.10/2016, and by the Russell Berrie Nanotechnology Institute at the Technion. Helpful discussions with Dr. Leonid Klinger are heartily appreciated. Y.Q. thanks the Technion-Guangdong Postdoctoral Fellowship for support.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.0c04327.

  • Numerical estimates of NW bending due to lattice mismatch strain and island-zipping stress, numerical estimate of NW bending due to the mismatch of thermal expansion coefficients, kinetic model and numerical estimate of nanocavity healing in the PX Fe layer, energy balance of the process of GB formation at the mouth of the Au layer penetrating into the gap between PX and SX Fe layers, estimation of the GB Kirkendall effect induced irreversible bending of the NWs, electron microscopy characterization of interfaces in bimetallic Au/Fe NW, illustration of NW#1 bending and the TKD band contrast image demonstrating its microstructure, electron microscopy micrographs illustrating Fe–Au interface bending at the PX Fe–Au interface and healing of nanocavities in the PX Fe layer, quasi-in situ demonstration of nanocavity healing and Au penetration into Fe after annealing, illustration of the geometric parameters employed in the quantitative model of nanocavity healing, schematic illustration of the energy balance during the GB formation at the “mouth” of Au layer penetrating into the Fe nanocavity, lattice distortion and deformation twinning in bent NW#2 characterized by TKD and LAADF, accretion of Au atoms at the GBs in Fe, schematic illustration of the GB Kirkendall effect, evolution of the cross-sectional dimensions of NW#3, and formation of an incoherent twin boundary induced by interface migration and bulk Fe–Au interdiffusion (PDF)

  • Elastic bending of the bimetallic NW with the aid of nanomanipulator in the focused ion beam (FIB) microscope (MOV)

Author Contributions

G.R. and E.R initiated and directed the study. G.R. and E.S. synthesized the NWs. Y.Q. carried out the experiments and analyzed the data. M.K. took part in the in situ heating experiments. Y.Q. and E.R. wrote the manuscript, with input from all coauthors.

The preprint version of this work was deposited in the arXiv preprint server: Yuanshen Qi, Gunther Richter, Eylül Suadiye, Michael Kalina, Eugen Rabkin, Plastic Forming of Metals at the Nanoscale: Interdiffusion-Induced Bending of Bimetallic Nanowhiskers, 2020, 2005.05241, arXiv [cond-mat.mtrl-sci - Materials Science], arXiv:2005.05241v1.

The authors declare no competing financial interest.

Supplementary Material

nn0c04327_si_001.pdf (1.4MB, pdf)
nn0c04327_si_002.mov (16.6MB, mov)

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Associated Data

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Supplementary Materials

nn0c04327_si_001.pdf (1.4MB, pdf)
nn0c04327_si_002.mov (16.6MB, mov)

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