Au Core–Shell Nanowire

Apr 19, 2013 - Jesper Wallentin , Daniel Jacobsson , Markus Osterhoff , Magnus T. Borgström ... Gang Xiong , Oussama Moutanabbir , Manfred Reiche , R...
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Letter pubs.acs.org/NanoLett

Concentration and Strain Fields inside a Ag/Au Core−Shell Nanowire Studied by Coherent X‑ray Diffraction Sabine T. Haag,*,†,‡ Marie-Ingrid Richard,‡,§ Udo Welzel,† Vincent Favre-Nicolin,§,⊥ Olivier Balmes,§ Gunther Richter,† Eric J. Mittemeijer,†,# and Olivier Thomas‡ †

Max Planck Institute for Intelligent Systems (formerly Max Planck Institute for Metals Research), D 70569 Stuttgart, Germany Aix-Marseille Université, CNRS, IM2NP UMR 7334, F 13397 Marseille Cedex 20, France § Aix-Marseille Université, F 13397 Marseille Cedex 20, France § CEA-UJF, INAC, SP2M, F 38054 Grenoble, France ⊥ Université Grenoble-Alpes, F 38041 Grenoble, France # Institute for Materials Science, University of Stuttgart, D 70569 Stuttgart, Germany ‡

ABSTRACT: Three-dimensional coherent diffraction patterns of an isolated, single-crystalline Ag/Au core−shell nanowire were recorded at different X-ray beam energies close to the Au LIII absorption edge. Twodimensional slices of the three-dimensional diffraction pattern, with the diffraction vector oriented perpendicular to the wire axis, were investigated in detail. In reciprocal space, facet streaks with thickness fringes were clearly observed in the two-dimensional diffraction patterns, from which the shape and size of the corresponding cross sections of the nanowire could be revealed. Comparison with simulated diffraction patterns exhibited the coherency strain field in the nanowire. During in situ annealing at temperatures which would lead to significant intermixing by volume diffusion in bulk material, according to literature data, a core−shell morphology was preserved; that is, intermixing in the nanowire was pronouncedly decelerated compared to bulk diffusion. KEYWORDS: Coherent X-ray diffraction, core−shell nanowires, coherency strain, interdiffusion

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retrieved. To this end, phase retrieval algorithms have been developed.3 On this basis, coherent diffraction in Bragg geometry gives access to the local, i.e., three-dimensional (3D) strain distribution.4 If one uses in addition the variation of the atomic scattering factors, of the chemical species (elements) present in the specimen, with energy, “anomalous X-ray diffraction” can provide chemical sensitivity.5,6 The simultaneous assessment of the strain and concentration fields inside nano-objects and their evolution upon annealing is crucial for studying the interaction of stress and interdiffusion at the nanoscale. Steep concentration gradients, specific defect structures, and (exceptionally) large stresses in nanomaterials may either accelerate or decelerate the diffusion kinetics.7,8 Until now, simultaneous mapping of both strain and composition at the nanoscale for a single nanosized particle has not been performed. Presently, a procedure to retrieve the (three-dimensional) strain and composition fields of singlecrystalline nanoparticles using a combination of anomalous and coherent X-ray diffraction was developed.6 In this study, coherent 3D diffraction patterns were recorded from an isolated, single-crystalline Ag−Au core/shell nanowire (NW). Measurements close to the Au LIII absorption edge were employed for obtaining anomalous data in the as-prepared

he unique properties of nanoparticles compared to their bulk counterparts, as e.g. the tunable electrical conductivity, plasmon resonance, or high yield stress, have provoked pronounced scientific and technical interest. To characterize such nanosized systems down to the atomic scale, adaptation of existing and especially development of dedicated new methods have to occur in order to meet the specific requirements of (sub-) nanometer resolution. The large penetration depth and the in principal nondestructive character of X-ray diffraction techniques suggest their application for investigation of a nanosized object as a monolith without destructive sample preparation and, especially, during in situ experiments. Diffraction provides quantitative data on crystallite size and shape, as well as on strain, which can be due to compositional variation or applied internal or external loads.1,2 Conventional (“powder”) diffraction experiments are carried out on a large assembly of particles, thereby yielding averaged structure data. A single nanosized particle could be subjected to “coherent diffraction” analysis: if the whole object under consideration diffracts coherently, by use of a highly coherent, plane wave illumination, the diffracted amplitude is, in the kinematical approximation, proportional to the Fourier transform of the electron density of the object. The phase of the diffracted wave is lost in the recorded intensity. In order to characterize the object in real space, the phase must be © XXXX American Chemical Society

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state, as well as during and after in situ annealing. For the first time, a metallic core−shell NW with such a perfect crystalline quality could be prepared so that a detailed analysis of 2D slices of the 3D diffraction patterns perpendicular to the NW axis was possible. It will be demonstrated that the comparison of measured with simulated diffraction patterns permits drawing conclusions on the shape of the NW and the elemental distribution and the strain state within the NW. Single-crystalline Ag NWs with the crystallographic [110] direction as length axis were grown on a carbon-coated Si(111) substrate by thermal evaporation of Ag in a UHV system (base pressure 10−7 Pa). These Ag NWs (diameters of about 50−500 nm) were subsequently coated with an epitaxial Au shell. A detailed description of the preparation method can be found in refs 9 and 10. Next, single NWs with diameters of about 100− 300 nm and lengths of about 5−20 μm were isolated from the growth substrate, transferred to and glued on Mo grids, for transmission electron microscopy (TEM) analysis, in a dual beam scanning electron microscope/focused ion beam instrument (SEM/FIB). The method is described in detail in ref 11: it is important to note that mechanical loading upon picking the NW from the growth substrate was avoided in this work by gluing the manipulator tip to the bottom of the NW. The original top of the NW was thus finally glued as the base on the TEM grid. The validation of epitaxial growth of the Au shell on the single-crystalline Ag NWs, the determination of the crystallographic orientation of the NW length axis, as well as the verification of the very good crystalline quality was achieved by TEM analysis in a Philips CM200 microscope operating at 200 kV. The X-ray diffraction experiments were conducted at the beamline ID03 of the European Synchrotron Radiation Facility (ESRF). The monochromatic beam (obtained by a channel-cut Si(111) monochromator) was focused with Kirkpatrick-Baez (KB) mirrors to a size (full width at half-maximum) of 15 and 8 μm in the horizontal and vertical directions, respectively. The NW on the TEM grid was clamped vertically on a customdesigned Cu clamping device, mounted on an Anton Paar DHS 900 heating stage equipped with a polyether ether ketone Xray-transparent dome on the horizontal goniometer with vertical z-axis; the diffraction geometry has been depicted in Figure 1. A rough vacuum was reached inside the dome by the use of an oil-free pumping unit consisting of a turbo and a rotary pump. The Au LIII absorption edge was determined by measuring the intensity of the fluorescence signal of a Au standard sample with a multichannel fluorescence detector. This detector was also used to locate, by mapping its Au fluorescence, the NW in the beam. Diffraction patterns around a 111 Bragg reflection, with the diffraction vector oriented perpendicular to the [110] NW axis, were recorded at a detector distance of about 1 m with a MAXIPIX 2D pixel detector with 516 × 516 pixels with a pixel size of 55 μm × 55 μm, with the detector-plane normal pointing to the center of the goniometer (cf. Figure 1). Two energies were chosen for anomalous diffraction: at the Au LIII edge at 11.92 keV and below the edge at 11.80 keV. 3D diffraction patterns were obtained by stacking 2D detector images recorded upon rotating the NW around the z-axis (see Figure 1) incrementally in the range of Δω = ± 0.2°. The intensities recorded by the pixel detector (i) were corrected for intensity fluctuations of the incident X-ray beam (using the counts of the monitor), (ii) were corrected for the

Figure 1. Sketch of the diffraction geometry for measuring a 111 Bragg reflection with the diffraction vector perpendicular to the NW axis of a NW with a [110] crystallographic length axis and a cross-section terminated by four {111} facets and two {100} facets (drawn out of scale for clarity). x⃗, y,⃗ and z⃗ are the specimen-translation axes, q⃗ is the diffraction vector, ω is the rotation angle around the z⃗-axis, δ and γ are the in-plane and out-of-plane angles of the scattered beam (with respect to the diffraction plane normal to the z⃗-axis), ki⃗ and kf⃗ are the wave vectors of the incident and scattered beams, and (i, j) denotes the pixel position on the detector.

nonuniform sensitivity of the detector pixels (by normalization with flood-field intensities), and (iii) the intensities for dead and stuck pixels (identified in the flood-field and dark images, respectively) were masked. In order to record the flood-field, a Au foil was irradiated under 45° with respect to the incident beam at a beam energy of 12 keV and the fluorescence recorded by the 2D pixel detector at δ = 80° (cf. Figure 1; not fully 90° due to geometrical restrictions imposed by the goniometer). An irregular shift in the vertical direction (γ-angle; cf. Figure 1) of the position of the diffraction pattern for each ω angle was observed, which was presumably caused by a small variation of the orientation of the ω axis of the goniometer, causing a varying tilt angle of the NW. The detector images were therefore vertically (i-direction of the detector; cf. Figure 1) shifted with respect to each other such that the centroids of the projections along the j-pixels, obtained by summing all intensities for variable i and the same j, coincided (this shifting occurred with integer numbers of pixels, to avoid interpolation) before stacking them to 3D diffraction patterns. In order to assign reciprocal space coordinates to each pixel, the reciprocal space coordinate system was chosen with qx⃗ parallel to the [1̅10] crystallographic direction, qy⃗ parallel to the [001] crystallographic direction and qz⃗ parallel to the [110] crystallographic direction (= NW axis) with |q⃗| = (2π/d) (d being a spacing in real space). After the examination of the as-prepared NW, diffraction patterns were recorded during annealing at incremental temperature steps up to 400 °C nominal temperature (temperature controller of the heating stage) and after cooling down to 100 °C (see Figure 2). At the beginning of the measurements of the NW in the asprepared state, the diffraction spot of the 1̅11 reflection was split in the direction of the NW axis (see Figure 3a), indicating that different parts of the NW, that are slightly misoriented, diffract separately. Facet streaks emanating from the Bragg maximum position with thickness fringes are clearly visible for both parts (see Figure 3b/c). The angles between the streaks B

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created using the finite element (FEM) software COMSOL Multiphysics.12 The cross-section of the NW with [110] crystallographic length axis is terminated by four {111} facets and two {100} facets. Based on the composition fields and the resulting strain fields from the FEM simulations, diffraction patterns were calculated in the kinematical approximation. For details, see ref 6. The size and morphology of the model NW was refined utilizing the experimentally observed “periodicity” of the oscillations along the intensity streaks emanating from the Bragg maximum position in the experimental diffraction patterns. The experimental pattern is subjected to counting statistics (for reasonable measuring times), and the spatial resolution in reciprocal space is limited by the finite pixel size; increasing the detector to sample distance increases the spatial resolution at the cost of the total range in reciprocal space covered by the detector, i.e., at the cost of the real-space resolution. Additionally, extracting the 2D slices from the 3D patterns causes blurring by integrating and thus averaging over a restricted range in the direction parallel to the NW axis. A (slight) temperature gradient along the NW axis could furthermore contribute to the blurring. The frequencies of the intensity oscillations along the streaks (see Figure 5) are related to the size of the NW in the corresponding direction in real space: the discrete Fourier transforms (dFTs) of the intensities of the 1D profiles exhibit peaks corresponding to a thickness of about 95 nm perpendicular to all three facet pairs. No (additional) “beat frequencies”, from which the shell thickness could be resolved (see below and ref 6), could be observed (see Figure 5). Presumably, the range probed in reciprocal space was not sufficiently large, or the interface between core and shell of the NW was too diffuse to induce distinct beat frequencies. If a sharp interface is assumed, it follows from the range investigated in reciprocal space, Δq, that an upper bound estimate for the shell thickness, Δh, is Δh ≤ (2π)/(Δq/2) ≈ 10 nm (derived from a minimal “beat frequency”). The intensity distribution in-between the streaks in the 2D slice suggests rounded edges of the facets of the NW; the simulation with sharp edges leads to a more “speckled” intensity distribution (cf. Figure 3b and Figure 4e). If the composition field in the NW cross-section is centrosymmetric and no inhomogeneous strain field is present, the diffraction pattern (2D slice) would be centrosymmetric. The observed asymmetry of the experimental diffraction pattern (see Figure 3b) is similar to the one of a simulated pattern for a coherency strain field slightly above room temperature (see Figure 4). This is compatible with an epitaxial Ag/Au core−shell structure and the absence of defects like dislocations or stacking faults. The bottom 2D slice (see Figure 3c) reveals a much more distorted cross-section of the corresponding part of the NW. Additional streaks (as compared to Figure 3b) indicate the presence of several additional minor facets. Beat frequencies are clearly observed along the 1̅11 streak (see Figure 5). On the basis of simulated diffraction patterns, it follows that, for a lighter scattering core (Ag) and a stronger scattering shell (Au), the first peak in the dFT of the 1D intensity profile along the streak represents the thickness of the core plus one time the shell thickness, and the second peak represents the total thickness, i.e. the core plus two times the shell thickness. Thus it follows from the 1̅11 streak in the experimental diffraction pattern, that the cross-section of the part of the NW corresponding to the bottom part of the diffraction pattern

Figure 2. Temperature evolution (see text) during the in situ annealing of the Ag/Au core−shell NW.

Figure 3. 2D slices (logarithmic intensity scale) through the 3D diffraction pattern of the 1̅11 reflection of an as-prepared Ag/Au core− shell NW recorded for an energy of the incident X-ray beam below the Au LIII absorption edge. (a) Detector image (cf. Figure 1), (b−c) 2D slices perpendicular to the NW axis from (b) the top part and (c) the bottom part of the 3D diffraction pattern. The reciprocal-space coordinates qx and qy have been defined parallel to the real-space coordinates x and y, respectively, of the specimen coordinate system shown in Figure 4a. The 1̅11 facet streak is indicated in c. The dark straight lines appearing in the diffraction patterns were caused by dead pixels where the chips of the pixel detector have been joined.

correspond well with the expected four {111} and two {100} facets defining the cross-sectional shape of a NW with a [110] axis (as also revealed by TEM analysis for Cu NWs grown by the same method9). The clearly split nature of the 1̅11 reflection (with very small broadening of each of the parts in the direction parallel to the NW axis) allows the structural analysis of the corresponding cross sections of the separately diffracting parts of the NW by considering the intensity distribution in the corresponding 2D slices of reciprocal space perpendicular to the NW axis (i.e., Figure 3b/c). The top 2D slice (see Figure 3b) resembles the diffraction pattern for a simple model NW well (see Figure 4e). The model of a coherent, strained Ag/Au core−shell NW was C

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Figure 4. Cross-section of the FEM model and corresponding diffraction pattern for an infinitely long Ag−Au core−shell NW with [110] length axis, Ag core, Au shell, and coherency strains at 320 K; (a) the Ag concentration field in at. %, (b−d) the strain components εxx, εyy, and εxy, respectively, in % relative to pure Ag at room temperature, (e) the diffraction pattern (logarithmic intensity scale) of the 1̅11 reflection calculated for an X-ray beam energy of 11 840 eV using the kinematical approximation. The total diameter of the model NW was adjusted according to the experimentally observed “periodicity” of the oscillations along the intensity streaks of the top part (see Figure 3b). The lack of beat frequencies in the experimental diffraction pattern hinders direct adjustment of the Au shell thickness; the upper bound of 10 nm (see text) was used instead.

broadening/elongation in the direction parallel to the NW axis increased with time. These observations signify bending of the NW (cf. simulated 3D diffraction patterns in ref 11) increasing with time. Although anomalous data were obtained in these experiments, the effects of the change in energy of the incident radiation on the diffraction patterns are too small for a qualitative interpretation on the basis of comparison of experimental and simulated patterns. For quantitative evaluation using phase retrieval algorithms,6 the experimental beam conditions (transverse coherence/plane wavefront) were not ideal enough and, moreover, unknown so that phase retrieval was not possible. The actual temperature of the NW could not be measured directly. However, the value of the average lattice-plane spacing, derived from the centroid position of the Bragg peak, can provide an estimate of the actual temperature (i.e., the effect of a strain field on the average lattice parameter then is neglected). In contrast to the determination of an absolute value of the lattice-plane spacing, the measurement of the change in lattice spacing by a change of the temperature is insensitive to inaccurate alignment of the specimen in the center of the goniometer. The thus determined values for the thermal strain, with respect to the strain at room temperature, are shown in Figure 7 as function of the temperature indicated by the thermocouple of the heating stage. As evident from Figure 7, the average thermal strains agree well with the expected values calculated for pure Ag (which is the main material of the NW), adopting literature values for the thermal expansion. The major changes of the diffraction patterns upon annealing (see Figure 8) are attributed to changing curvature of the NW, causing increasing splitting and elongation of the diffraction spots roughly parallel to the NW axis (cf. discussion of Figure 6). These bending-induced elongations (broadening) in the diffraction patterns complicate the creation of meaningful 2D

Figure 5. Intensity profiles (logarithmic scale) along the (1̅11) facet streak of the 1̅11 reflection (cf. Figure 3b/c) of the bottom and top parts of the 3D diffraction pattern of an as-prepared Ag/Au core−shell NW recorded for the energy of the incident X-ray beam at and below the Au LIII absoprtion edge (11.80 and 11.92 keV, respectively).

has a core thickness of about 165 nm and a shell thickness of about 20 nm in the 1̅11 direction (i.e., much larger than the 95 nm total diameter determined from the top 2D slice). The asymmetry as revealed by the 2D slice shown in Figure 3 and by the intensity profile shown in Figure 5 evidence an inhomogeneous strain field and/or a noncentrosymmetric concentration field with respect to the NW axis. A series of consecutive 3D diffraction patterns were measured below and at the Au LIII absorption edge before annealing. The patterns changed (already) pronouncedly only by exposure of the NW to the X-ray beam, i.e., without applying extra heating (see Figure 6). The peak splitting and D

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slices for detailed analysis: when the different (two: top and bottom) parts of the 3D pattern are broadened, there can be no 2D sections identified which are directly correlated to certain cross sections of the NW. The change of bending of the NW was presumably caused by the formation of a C-contamination layer with a final thickness of about 200 nm, as evidenced by transmission electron microscopy (TEM) analysis performed after the synchrotron experiments (see Figure 9). Such C contamination can be caused by photoelectron emission from the NW, leading to cracking of remaining hydrocarbons.14 This effect is enhanced for energies at/above absorption edges (resonant photoelectron emission), as employed for anomalous studies. The C shell could have grown inhomogeneously with internal stress, thereby inducing bending of the NW. An inhomogeneous C-shell thickness furthermore leads to bending upon temperature change as a consequence of the mismatch of thermal expansion of Ag/Au and the C shell. Moreover, possible asymmetry of the cross-section of the Ag/Au NW (e.g., nonconstant Au-shell thickness) causes inhomogeneous thermal expansion, which will induce additional bending of the NW. In the 2D slices in reciprocal space after annealing (see Figure 10), the intensity distribution is still noncentrosymmetric, revealing the presence of an inhomogeneous strain field and/or of a noncentrosymmetric (with respect to the NW axis) elemental distribution. Furthermore, in the bottom part 2D slice of the 3D diffraction pattern, beat frequencies are still present on the intensity streaks. These observations suggest incomplete intermixing of Au shell and Ag core, in contrast to what is expected on the basis of bulk single-crystal diffusion data15 extrapolated to the low temperature of annealing: the mean diffusion lengths thus estimated from d = (2Dt)1/2 for the diffusion coefficient D at T = 400 °C and for the time t = 1 h are 18 and 67 nm for impurity diffusion of Au in Ag and of Ag in Au, respectively. Without sources and sinks for vacancies, the interdiffusion coefficient should approach the smaller value of the two intrinsic diffusion coefficients,16 i.e., still 18 nm here. In the case of a strong diffusion asymmetry, a sharp interface could be preserved upon interdiffusion, but the observed shell thickness should change then, which is not observed here (within the limit of the precision of this analysis). A possible reason for the apparently relatively slow interdiffusion in the NW, compared to that in bulk material, may be a vacancy concentration, which is possibly smaller than the (equilibrium) bulk vacancy concentration, and the absence of dislocations acting as sources and sinks for vacancies (Ag and Au diffuse according to a vacancy diffusion mechanism). The lack of vacancy sources and sinks can lead to the build-up of pronounced stress gradients if the partial molar volumes and/or the fluxes of the diffusing species are different17 (the latter holds particularly for Ag and Au). This may decelerate interdiffusion.7,16 Stress induced by a C shell has been shown to drastically reduce the diffusion of Cu in Si NWs.18 In summary, 3D coherent diffraction patterns of a 111 reflection from an isolated Ag−Au core−shell NW with a ⟨110⟩ wire axis could be recorded for different synchrotron beam energies. Different parts of the NW, slightly inclined relative to each other, diffracted separately. 2D slices through the intensity distribution in reciprocal space perpendicular to the NW axis clearly reveal intensity streaks emanating from the Bragg-peak maximum position in directions perpendicular to the {111} and {100} facets of the NW. The intensity along these streaks is modulated (“periodic” oscillations and beat frequencies) due to

Figure 6. Series of detector images (logarithmic intensity scale) at the maxima of the ω scans of the 11̅ 1 reflection of a Ag/Au core−shell NW with [110] length axis. The evolution with time (total exposure time about 14 h, equal periods between the images) at ambient temperature, recorded alternately at two different energies of the incident X-ray beam, can be followed in the sequence a−h. The dark straight lines appearing in the diffraction patterns were caused by dead pixels where the chips of the pixel detector have been joined.

Figure 7. Average thermal strain deduced from the shift of the centroid of the 11̅ 1 diffraction spots as a function of the display temperature of the controller of the heating chamber during in situ annealing of the Ag/Au core−shell NW, in comparison with literature data.13 Values derived from the bottom part and the top part of the 3D diffraction patterns for different energies and for either heating or cooling have been indicated by different symbols.

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Figure 8. Detector images (logarithmic intensity scale) at the maxima of the ω scans of the 1̅11 reflection of a Ag/Au core−shell NW with [110] length axis recorded for an energy of the incident X-ray beam below the Au LIII absoprtion edge at different temperatures before and during in situ annealing. For the temperature evolution, see Figure 2. Note that, with increasing peak splitting, the bottom and top parts had to be recorded on individual detector images with different γ and δ angles of the detector (cf. Figure 1). The dark straight lines appearing in the diffraction patterns were caused by dead pixels where the chips of the pixel detector have been joined.

Figure 10. 2D slices through the 3D diffraction pattern of the 11̅ 1 reflection of a Ag/Au core−shell NW at 100 °C after annealing, recorded for an energy of the incident X-ray beam below the Au LIII absoprtion edge. 2D slices (logarithmic intensity scale) perpendicular to the NW axis from (a) the top part and (b) the bottom part of the 3D diffraction pattern. The reciprocal-space coordinates qx and qy have been defined parallel to the real-space coordinates x and y, respectively, of the specimen coordinate system shown in Figure 4a. The dark straight lines appearing in the diffraction patterns were caused by dead pixels where the chips of the pixel detector have been joined.

Figure 9. (a) Bright field TEM image and (b) dark field TEM image of the Ag/Au NW with a thick C shell after the ACXD experiment.

the finite total NW thickness and finite shell thickness. Thus, the diameters of two parts of the NW could be determined as about 95 and 165 nm, respectively, and for the thicker part, a value for the shell thickness of 20 nm was obtained. The intensity distribution of the 2D slice corresponding to the thinner part of the NW matches very well with the simulated pattern for a strain field in the NW arising from the epitaxy of the Au shell on the Ag core, thereby confirming the

fully coherent and defect free structure of the corresponding section of the Ag/Au NW. The diffraction patterns changed already upon X-ray measurements performed at room temperature: increasing elongation (broadening) and peak splitting parallel to the NW axis were observed, which could be ascribed to bending, caused F

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by the formation of a thick C contamination layer on the NW surface. Even after annealing for more than one hour at a temperature of 400 °C, beat frequencies for the thicker part of the NW were still detected, and also an inhomogeneous concentration and/or strain field of the thinner part of the NW was still present, indicating preservation of a core−shell structure at this stage: interdiffusion in a perfect, coherent Ag/Au NW may be much slower than expected on the basis of bulk diffusion data because of a possibly smaller vacancy concentration, the lack of dislocations acting as vacancy sources/sinks, and the development of stress gradients upon interdiffusion.

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AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected].

ACKNOWLEDGMENTS We thank Dr. Lars Jeurgens for providing the facility and technical support for NW growth and Ulrike Eigenthaler for SEM/FIB preparation. The ESRF, for providing beamtime, and the ID03 beamline staff, for support during the synchrotron experiment, are gratefully acknowledged.

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ABBREVIATIONS NW, nanowire; dFT, discrete Fourier transform; FEM, finite element method REFERENCES

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