Article pubs.acs.org/crystal
Crystallization Pathway for Metastable Hexagonal Close-Packed Gold in Germanium Nanowire Catalysts Ann F. Marshall,* Shruti V. Thombare, and Paul C. McIntyre Department of Materials Science and Engineering and Stanford Nano Shared Facilities, Stanford University, Stanford, California 94305, United States ABSTRACT: The recent discovery of hexagonal-close-packed (hcp) Au nanoparticles, crystallized at the tips of Ge nanowires following vapor−liquid−solid (VLS) growth, prompts interest in the mechanism of metastable phase formation in the Au catalyst. The equilibrium structure of Au is face-centered cubic, and observation of hexagonal close-packing in Au is very rare. Here we report on eutectic melting of Au nanocatalysts in the transmission electron microscope (TEM), followed by rapid quenching, and subsequent in situ annealing at intermediate temperatures. A metastable hexagonal Au−Ge alloy phase solidifies during quenching of the Au−Ge liquid in the TEM, and it is a likely precursor to formation of metastable hcp Au during nanowire post-VLS cooling. A novel aspect of the hcp Au phase formation is the rejection of quenched-in Ge from the alloy during low-temperature in situ TEM annealing, while maintaining the metastable hcp crystal structure, indicating that this is the likely pathway for hcp formation following nanowire growth. The kinetics of metastable phase formation are discussed in relation to the unique characteristics of VLS nanowire growth: Ge supersaturation during growth and undercooling of the nanoscale liquid catalyst prior to crystallization at the end of growth.
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INTRODUCTION Synthesis of nanoscale materials such as nanowires offers novel kinetic pathways for metastable phase formation that are not available in bulk materials, or in other, more traditional, morphologies such as thin films. For example, metastable phases have been reported in nanowires of silver, tin, vanadium oxide, cadmium telluride, iron silicide, and boron carbide, and attributed to specific aspects of the growth conditions and size of the nanowires.1−8 Metastable phase formation in such structures is nontrivial, as size effects in nanomaterials can provide additional barriers to equilibrium phase formation compared to the situation for bulk samples. The use of catalysts in vapor−liquid−solid (VLS) or vapor− solid−solid (VSS) growth of nanowires broadens the range of materials in which metastable phases may form in nanowire systems. Metastable phase formation in the nanocatalysts can occur during nanowire synthesis,9,10 and can also be investigated by postgrowth in situ transmission electron microscopy (TEM) heating and cooling experiments.11,12 The morphology of a nanowire provides an ideal structure for such studies: it is a nanoscale pedestal that has a small, defined volume of catalyst at the top, with an isolated interface for characterization of melting, crystallization, and phase formation, and that is readily observed in TEM with minimal sample preparation. Gold is the most widely used catalyst for semiconductor nanowire growth, and the phase diagrams of the Au−Si and Au−Ge systems in particular, including metastability, have long © XXXX American Chemical Society
been of interest for both fundamental reasons and practical applications. These include the use of gold alloys as solders in the semiconductor industry;13,14 studies of the metal−semiconductor liquid structure15,16 and of metastable structures achieved by rapid quenching of the liquid,15,17,18 and the growth of semiconductor nanowires.19 We have previously reported the discovery of metastable hexagonal close-packed (hcp) Au nanoparticles that form following Ge nanowire growth when the Au−Ge liquid catalyst droplet crystallizes.9 The crystallization process leaves a volume of Au from the initial catalyst particle remaining at the tip of the nanowire; we found that this Au nanoparticle may have either the fcc or hcp crystal structure.9 Observation of an hcp structure in Au is very rare, and had previously been reported only under conditions of ultra high pressure,20 or in the vicinity of special grain boundaries,21,22 i.e., under conditions of mechanical pressure or strain. More recently, Huang et al. demonstrated the formation of ultrathin (2.4 nm) square sheets of hcp Au on graphene oxide substrates, which were stable under ambient conditions.23 These ultrathin structures developed fcc segments as they grew beyond 6 nm thickness. The Au hcp nanoparticles that we observed at the tips of Ge nanowires are three-dimensional, typically on the order of 40 nm in size, and also remain stable indefinitely under ambient conditions.9 The mechanism of formation of this unique Received: March 12, 2015
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DOI: 10.1021/acs.cgd.5b00803 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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structure. As these furnace holder cooling rates are of the same order of magnitude as the rate of cooling in the nanowire reactor following VLS growth, this observation suggested that hcp formation was dependent on factors specific to the nanowire growth chamber environment. However, when we rapidly quenched the liquid droplets in the Aduro holder, we were able to form the hcp metastable Au−Ge alloy structure, the β phase, that has previously been reported in conventional splat-cooling experiments performed on bulk-like Au−Ge liquid droplets.15,17,18 The metastable β phase is reported to have a composition range of 17−25 atom % Ge, and to have lattice parameters similar to those expected for hcp Au (within 1%).25 Figure 1 shows a nanoparticle quenched from the melted state
metastable form of Au is therefore of considerable interest. We note that the nanowires are grown with the catalyst still liquid at temperatures well below the eutectic melting temperature, so that the crystallization of the catalysts takes place under already metastable conditions of undercooling.24 We suggested that the formation of hcp Au can be attributed to three intersecting characteristics of Ge nanowire VLS growth: the occurrence of the hcp metastable alloy phase (beta phase) in the Au−Ge binary system,25 the large liquid undercooling prior to solid nucleation at the nanoscale,24 and barriers to fcc Au nucleation that occur as a result of Ge supersaturation of the liquid catalyst droplet during nanowire growth.26 In this paper we present in situ melting, quenching, and heating TEM studies of the Au nanocatalysts at the tips of VLSgrown Ge nanowires, along with X-ray diffraction (XRD) analysis, to determine the mechanism of formation of the metastable hcp Au phase that occurs following nanowire growth. In particular, we test the hypothesis that the hexagonal β AuGe metastable phase is a precursor to formation of nearly pure hcp Au at the tips of Ge nanowires. Instead of a conventional TEM furnace heater, we utilize a microfabricated heater that allows us to access rapid quenching rates comparable to standard splat cooling studies,27 as well as to carry out in situ compositional analysis. Such novel TEM heating stages enable direct in situ studies of rapidly quenched structures at very small length scales. We find that solidification of the metastable alloy beta (β) phase is the precursor to formation of hcp Au at the tips of VLS-grown Ge nanowires. Reproducible data on hcp Au formation following post-VLS growth cooling and TEM quenching studies were obtained from numerous Ge nanowire samples deposited over a period of several months. It should be noted that observation of hcp Au phase is not reported in the prior rapid solidification literature. The results give insight into the role of undercooling, dynamics, Ge supersaturation, and crystallographic orientation in enabling formation of this rare Au crystal structure at the cessation of VLS nanowire growth.
Figure 1. (a) A TEM in situ rapidly quenched nanocatalyst exhibits the hcp structure. The angle between the (0001) hcp planes and the (111) nanowire growth planes is 42°. (b) The enlarged image shows the signature 4.7 Å hcp (0001) spacing visible in the image and diffraction pattern (inset, arrows). A few stacking faults are visible to the righthand side of the image, and the 4.7 Å fringes, although present, become less regular in contrast, which is to be expected in areas where the thickness or strain (due to the stacking faults) changes. This change in contrast is also visible around the thinner top edges of the particle.
to room temperature in the Aduro holder by setting the heating bias to zero from a starting state of 370 °C. The quench rate is estimated to be 106 °C/s.27 Lattice fringes of 4.7 Å are observed, consistent with the {0001} interplanar spacing expected for the hcp phase, and a clear signature of its presence.9 We note that these fringes are oriented at a 42° angle to the Ge {111} planes at the catalyst/nanowire interface and that stacking faults are present in the right-hand side of the image intersecting the interface. EDS analysis indicates a Ge content of about 8% in the quenched structure solidified in the TEM. This is much less than the 17−25 atom % reported for the alloy phase, but more than the ≤3% that we measured and previously reported for as-grown nanowire samples.9 This result, along with the results on the as-grown nanowires, suggests that the range of Ge content in the metastable β phase is much broader than the 17−25 atom % reported in the early rapid quenching literature.25 It suggests that the range may vary continuously from about 25 atom % to a minimum Ge content of 3 atom % Ge or lower, which is comparable to the solubility of Ge at equilibrium at the eutectic temperature in fcc Au. If Ge has the same equilibrium solubility in hcp Au as in fcc Au, then we will expect to always find a few atom % Ge in the hcp gold nanoparticles, regardless of heat treatment or cooling history. A mechanism to achieve this minimal Ge content in the hcp phase becomes apparent when the quenched β nanocatalyst is heated in the TEM at temperatures below the eutectic melting temperature: Ge from the nanowire appears to diffuse easily into and out of the hcp crystal structure at temperatures above
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RESULTS AND DISCUSSION VLS-grown Ge nanowires with solid Au nanocatalyst tips were heated above the eutectic melting point, using a MEMS-based resistive heating holder (Protochips Aduro), in order to melt the nanocatalyst, form the eutectic liquid, and apply rapid quenching to the melt. The nanowire growth parameters are described in the Methods section. The initial crystal structure of the Au tips has been analyzed in previous publications: using diffraction and energy dispersive spectrometry (EDS) analysis, we found that the Au nanoparticles remaining at the tips of the nanowires after VLS growth have either the fcc or hcp structure and contain little to no Ge.9 The hcp nanoparticles frequently contain stacking faults. Regardless of the initial crystal structure of the catalyst before heating, we expect that melting a given volume of Au catalyst to the same melting temperature achieves the same initial liquid state for quenching experiments. The Aduro holder has three advantages, relative to a standard furnace holder, that enable the studies reported here: (1) much higher heating and quench rates, on the order of 106 °C/s;27 (2) much lower specimen drift rates allowing the area of interest to stay in view and in relatively good focus while heating; (3) a direct line of sight to the X-ray detector allowing for the collection of EDS compositional data. Previously, when melting the catalyst and then cooling at the relatively slow rates allowed by a furnace holder, we had not found the hcp Au B
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∼175 °C. An example is shown in Figure 2 for a nanocatalyst that was melted and quenched from 400 °C to RT. During
nanoparticle in Figure 1 indicating that the amount of Ge retained during quenching can vary. However, a noticeable amount, e.g., the 8−16 atom % reported here, was always retained during in situ TEM quenching, relative to the very low amounts, ≤ 3 atom %, found in the as grown nanowires. The EDS results are shown in Figure 3. The heating data show that Ge diffuses out of the quenched nanoparticle when it is heated, reaching a minimum composition of 3−7 atom % Ge in the range of 250−270 °C. We have not measured the composition between room temperature and 175 °C, because we typically do not observe the samples during the initial stages of heating. This minimizes carbon contamination layers that form on the nanocatalyst in the electron beam at the lower temperatures. However, interface motion suggests that out-diffusion of Ge begins at ∼175 °C. Because the sample was quenched from the melt to room temperature, and EDS analysis during the quench is not possible, details regarding compositional changes during the quench (the blue line) are not accessible, so it is simply shown as a straight line from melt to room temperature in Figure 3. The data of the melted eutectic liquid were used to calibrate the k-factors in this analysis (see Methods). Along with the measured data points, the red trend line is consistent with the observed movements of the interface during heating. We note that, as the Ge concentration decreases to very low values, the scatter in the data tends to increase, both because of the statistical nature of the analysis and the limitations in the software modeling of such small peaks. As shown in Figure 3, the Au catalysts of the as-grown nanowires have, on average, a residual Ge content that is slightly less (1−4 atom %) than the minimum value observed during heating of in situ TEM quenched nanowires (4−7 atom %). These values approach the limit of Ge solubility in fcc Au; therefore, the kinetics of removal of the last few atomic percent of Ge from the hcp Au particles may be very slow. We note that, during heating in the TEM, the sample was held at each temperature for a period of about 15 min during data acquisition. In addition, we held the sample at 260 °C for 10 additional minutes. We observed no systematic decrease in composition during these periods of constant temperature that would indicate further out-diffusion of Ge with time. The changes that we did observe during heating occurred immediately upon increasing the temperature, and further annealing thereafter at the same temperature appeared to have no effect. We have reported previously that an approximate orientation relationship between a nanowire and its as-grown hcp nanocatalyst was frequently observed and proved to be useful in finding the hcp structure in the TEM: When the nanowire was oriented on a ⟨110⟩ zone axis perpendicular to the ⟨111⟩ wire axis, an hcp structure was often found in a orientation, with the [0001] planes at a 60−65° angle to the interface. 9 This orientation relationship is {111} Ge // {101̅1}Au hcp; ⟨110⟩Ge//Au hcp. Since our initial report, we have found a broader range of angles, from about 40° to 75°, for the hcp ⟨0001⟩ planes and have also observed that this oblique orientation of the hcp planes to the nanowire interface occurs for the TEM in situ quenched hcp alloy structure (e.g., Figures 1 and 2). Examples of the angular orientation are also shown in Figure 4 for the occurrence of the hcp structure in differently sized nanocatalysts. The fact that we can use this approximate orientation relationship to find hcp Au particles (as distinct from fcc Au
Figure 2. Ge moves out of the quenched hcp structure while heating from 150 to 220 °C, and back in again as heating continues to 350 °C, as indicated by the position of the interface relative to the fixed dotted line. The nanoparticle remains crystalline throughout, as indicated by the presence of the stacking faults.
heating from 150 to 220 °C, the interface moves toward the end of the nanocatalyst, indicating that Ge is coming out of the metastable Au−Ge structure and lengthening the Ge nanowire. This process partially reverses between 220 and 350 °C, with the interface moving back and the nanowire shortening as Ge diffuses back into the nanocatalyst structure. The nanocatalyst maintains its metastable hcp structure throughout. As was observed for the nanoparticle in Figure 1, the images show the hcp {0001} planes at an oblique angle (42°) to the Ge {111} growth planes, and a number of stacking faults that also intersect the interface. The array of stacking faults propagate, continuing to intersect the moving interface, as the nanoparticle grows in the latter part of the process. The nanoparticle begins to melt at a temperature close to the bulk eutectic (361 °C). The increasing liquid phase volume and the shrinking β phase nanocrystal coexist for 10−20 s during this process. An interesting aspect of the results observed by TEM imaging (such as in Figure 2) and associated composition measurements (Figure 3) is that the Ge comes out of the metastable β
Figure 3. Compositional changes with heating and cooling. The melted value of 28 atom % Ge is used for calibration of the measurement as discussed in the text. The scatter in the heating data is due to repeated analysis of the same nanoparticle at a given temperature. The scatter in the as-grown data represents different nanoparticles. Dotted trend lines are meant to guide the eye.
phase and goes back in as a function of temperature, without inducing a phase transformation. This behavior is unusual for a metastable solid. Using EDS analysis in the TEM we measured the change in Ge content when a quenched β phase nanoparticle containing approximately 16 atom % Ge was heated on its nanowire pedestal. We note that this value is twice that of the C
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Figure 4. Typically the {0001} planes of the hcp phase are oriented at an oblique angle to the nanocatalyst/nanowire interface, shown here for several sizes of hcp nanocatalysts formed following nanowire growth. The angles are 59°, 43°, and 63° respectively. Figure 5. (a) A representiative XRD scan shows both the fcc and hcp phases occurring in the nanocatalysts. (b) The amount of the hcp phase increases when germane gas is present during catalyst solidification (in post-VLS cooling) and shows a dependence on germane (GeH4) precursor pressure.
particles) by tilting Ge nanowires to ⟨110⟩ zone axes confirms that there is a preferred orientation. However, its characteristics do not suggest that epitaxy is the cause. Even when the orientation angle is close to 60°, which corresponds to the hcp {101̅1} plane parallel to the {111} Ge nanowire growth plane, and with the nanowire viewed precisely along the ⟨110⟩ zone axis, the zone axis of the nanoparticle is observed to be tilted away from the viewing direction by a few degrees in random directions. This means that there is a small range of out-of-plane orientations of the β phase nanocatalyst relative to the nanowire as well as the in-plane variation in angles. The angular variations about this orientation relationship suggest that, if there is an epitaxial effect, it is weak and may be related to the nucleation event only, with the crystal able to rotate as it grows. It is possible that the orientation effect is related to the ability of Ge to move out of the metastable β-phase and achieve a more stable composition during crystallization and cooling. Literature results for both the Au−Ge eutectic liquid and the β phase structure indicate that Ge is randomly substituted for Au in a close-packed structure.15,16 Diffusion within the closepacked planes of the hcp structure may be somewhat faster than on other planes,28,29 so that an orientation with the closepacked planes intersecting the interface might facilitate outdiffusion of Ge. The rapid quenching and annealing results in the TEM suggest that the hcp alloy phase is a precursor to the almost pure hcp Au formed following nanowire growth. The question remains as to why the metastable phase forms during the nanowire growth process, but not during in situ TEM experiments using the furnace holder, when both processes have comparable (slow) cooling rates. We propose that Ge supersaturation also plays a role in the hcp phase formation following nanowire growth, and we used XRD to investigate this possibility. We use X-ray diffractometry scans to measure the amount of hcp vs fcc Au that occurs following a typical nanowire growth process, as a function of the presence of GeH4 precursor gas and its partial pressure in the chamber during the postgrowth cool-down. The results are shown in Figure 5, along with a representative scan showing the Au fcc (111) and the Au hcp (101) Bragg reflections. We note that most of the nanowires grow vertically in the ⟨111⟩ direction as a result of epitaxy on Ge (111) substrates. These observed reflections therefore indicate the orientation of the Au catalysts with respect to the vertical ⟨111⟩ nanowires. There are several considerations from the TEM observations to take into account in comparing the two Au peaks. First we note that the Au hcp (0002) peak has the same 2θ value as the fcc (111) peak, but our TEM results indicate that there is almost no hcp Au in this orientation. Therefore, we consider that the peak at 2θ = 38.18° results predominantly from diffraction from the fcc Au phase. Second, for the orientation relationship described in a previous paragraph for hcp Au, with the (0001) planes at about 60° to
the Ge (111) planes, the intensity of the hcp (101) peak in an X-ray diffractometry scan will be enhanced. We therefore consider that changes in the relative amounts of fcc and hcp Au can be determined, using the structure factors for the two peaks. We estimate the error in the XRD peak-fitting analysis to be ±5%. The results indicate that having GeH4 vapor present during the cool-down increases the amount of hcp Au phase formed at the tips of the nanowires, suggesting that Ge supersaturation plays a role in formation of the metastable structure. In considering the amount of hcp phase formed, we note that ex-situ TEM observations, while not having the averaging power of XRD, also give some indication of the degree of hcp Au formation when germane is present. Using the orientation effect described previously to find hcp structures, we estimated that approximately one in every 10 nanowires grown with GeH4 supersaturation during post-VLS cooling has an hcp Au catalyst nanoparticle. Given the 3-fold degeneracy of the {112̅0} orientations about each nanowire axis, we could expect three times that many hcp nanoparticles, i.e., at least 30% of the nanocatalysts form hcp structures, roughly consistent with the XRD results. Using in situ TEM and XRD, we have established two conditions that contribute to formation of the metastable alloy phase that is a precursor to hcp Au: Ge supersaturation and undercooling. Both of these effects can be considered in more detail in terms of thermodynamics and kinetics, as discussed in previous papers addressing the phenomenon of subeutectic temperature VLS Ge nanowire growth. Several authors have discussed Ge supersaturation of the liquid catalyst during growth, which is expected to occur as a result of the presence of GeH4 vapor and its influence in stabilizing the liquid phase below the eutectic temperature to allow for low temperature growth of the nanowires.9,24,26 Ge supersaturation shifts the composition of the liquid toward the Ge-rich side of the phase diagram thereby inhibiting the formation of fcc Au and promoting undercooling of the liquid. This can be understood in terms of both the metastable extension of the liquidus curve below the eutectic temperature in the phase diagram,26 and as an altered slope of the liquidus tie line when considering a metastable liquidus curve occurring below the eutectic temperature in a free energy diagram.9 These are different perspectives of the same phenomenon, i.e., a reduction of the free energy driving force for fcc nucleation, in a temperature range below the eutectic temperature, as a result of increased Ge concentration relative to the eutectic composition. D
DOI: 10.1021/acs.cgd.5b00803 Cryst. Growth Des. XXXX, XXX, XXX−XXX
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nonequilibrium conditions of Ge supersaturation and undercooling and (2) out-diffusion of Ge from the solidified alloy phase, while maintaining its hcp crystal structure.
With regard to undercooling, there will also be a kinetic barrier to fcc Au nucleation below the eutectic temperature, even at the eutectic composition, which is likely significant in the time frame of a typical nanowire growth process.9,24 Therefore, fast quench rates, such as those achieved in these in situ TEM studies, promote formation of the metastable phase, which is expected to have a lower kinetic barrier for nucleation than fcc Au. This lower kinetic barrier can be understood in terms of the liquid structure. As reported by Rivlin et al.,15 XRD studies of liquid Au−Ge show that the liquid structure resembles close-packing in the composition range between pure Au and the eutectic composition; i.e., it is much closer in atomic coordination and density to the metastable β alloy phase than it is to the two-phase equilibrium crystal system which includes the relatively open structure of diamond cubic Ge. Takeda et al.16 support Rivlin’s findings of a close-packed liquid and further show that the Ge atoms substitute randomly for Au atoms in the nearest neighbor and second neighbor configurations. Hoyer et al. report a prepeak in the structure factor of the Au-rich liquid alloy which they interpret as evidence of medium range order of Au4Ge tetrahedral clusters; such clusters would have Au−Au spacings that correlate with the position of the prepeak, as well as with the signature {0001} lattice spacing of the β phase.30 The structure and composition of the liquid alloy are, therefore, much more closely related to that of the solid metastable β phase than to that of the equilibrium phases. As a result, nucleation of the β phase does not require long-range diffusion and is promoted by fast quench rates and by undercooling below the eutectic temperature, where the viscosity of the liquid increases and the diffusion required to nucleate pure Au is inhibited. The preferred formation of the hcp β phase over the fcc Au phase occurs under nonequilibrium conditions under the combined effects of Ge supersaturation and undercooling, and, once formed, can approach a structure of pure hcp Au by out-diffusion of Ge.
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METHODS
Ge nanowires ⟨111⟩ were grown by the vapor−liquid−solid (VLS) method in a cold-wall CVD reactor on Ge (111) substrates using 40 nm nominal diameter Au colloids as the catalyst. Samples were heated to 375 °C for 2 min for the growth initiation, and then cooled down to 300 °C for 20 min for the nanowire growth. The germane partial pressure was varied systematically between 0.75 to 1.2 Torr. Details of the growth reactor and general growth procedures are given by Adhikari et al.31 Characterization and in situ experiments were carried in an FEI TF20 and an FEI aberration corrected Titan transmission electron microscope (TEM) and in a Philips X’Pert X-ray diffractometer. TEM samples were prepared by scraping the nanowires onto holey carbon support films. Heating and cooling in the TEM utilized both a standard furnace holder (Gatan) and a microfabricated resistive heating platform (Protochips Aduro). The latter holder uses a resistively heated ceramic substrate to heat a very small area of sample, providing for very fast heating and quenching rates and very little drift during heating. Figure 6 is an optical microscope image of the heating
Figure 6. Optical microscope images of the sample region of the Aduro heating holder: (a) shows the resistive leads that heat a 0.5 mm square ceramic substrate containing an array of 7 × 7 holes covered with a TEM support film. (b) Higher magnification shows nanowires visible (arrows) on the holey carbon support film.
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CONCLUSIONS In situ TEM results indicate that the Au−Ge β hcp alloy phase is the likely precursor to the formation of almost pure hcp Au in as-grown Ge nanowires, providing a unique pathway for this rarely seen form of Au. We demonstrate that the β phase can be accessed by rapid quenching in the TEM, and we use XRD measurements to show that Ge supersaturation also promotes formation of the metastable phase during the much slower cool-down of Au−Ge liquid catalysts after VLS nanowire growth. These nanoscale solidification results extend the range of occurrence of the beta phase in the metastable Au−Ge phase diagram observed in conventional melt quenching experiments. Germanium diffuses out of the rapidly quenched hcp alloy at temperatures in the range 175−250 °C, and then back into the structure near the melting point, suggesting facile Ge transport between β phase nanoparticles and their Ge nanowire pedestals as a function of temperature. The results further show that a preferred (approximate) orientation relationship of the hcp structure on the (111)-oriented Ge nanowire growth facet accompanies the formation of the metastable β phase on the tips of as-grown nanowires and on the nanowire pedestals after in situ TEM heating and quenching. Since this is not a strong epitaxial effect, we suggest that the oblique orientation of the planes may serve to stablilize the nucleation and growth of the β phase. We conclude that that the mechanism of formation of hcp Au nanocatalysts following Ge nanowire growth is (1) formation of the metastable hcp beta alloy phase under
chip showing the resistive leads contacting a ceramic substrate with an array of holes (a). The holes are covered by a holey carbon support film (b). Since 40 nm nanowires are below the optical resolution limit, it is interesting that they are visible on the carbon in (b). This is presumably a result of reflection from the wires. The wires are also sometimes found to be bunched, which adds to their visibility. We estimated the maximum cooling rate in the furnace holder for the relevant temperature range (200−400 °C) to be on the order of 3−4 °C/s. This is determined by monitoring the thermocouple readout as a function of time when the heater is turned off. The cooling rate in the reactor at the end of nanowire growth is estimated in a similar manner to be 2 °C/s. The maximum cooling rate for the Aduro holder is estimated by the manufactured to be 106 °C/s,27 where the temperature is measured by a high-speed optical camera. The higher cooling rate is a result of cooling a much smaller and more localized volume of material. In all cases, the maximum rate is achieved by turning off the heating element and allowing the sample to cool as quickly as possible in ambient conditions. We have calibrated the temperature of the furnace holder by observing the magnetic transition in a Ni thin film (363 °C), which is almost the same as the Au−Ge eutectic temperature (361 °C), and found it to be within ±3°. We also note that in situ TEM melting of the Au catalyst in Ge nanowires has been observed for many samples made by depositing on carbon films, or by cutting thin slices and observing them in cross-section. For 40 nm wires, melting typically occurs within ±3° of the eutectic temperature of 361 °C, indicating that the nanowires themselves may serve as an effective calibration standard to that degree of accuracy. We note that prior theoretical calculations by Adhikari et E
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al.24 indicate a small melting point depression of about 12 °C due to the Gibbs−Thomson (size) effect for 40 nm diameter wires, i.e., a melting point of 349 °C. Because we have calibrated the furnace holder thermocouple with a standard Ni film, and have also observed reproducible melting of the nanowire catalyst near a themocouple readout of 360 °C, we are reporting these measurement results in this paper. EDS analysis was performed using the Tecnai Image and Analysis (TIA) software. The accuracy of EDS analysis depends on the number of counts in the peaks, so it becomes less accurate as the composition of a given element goes to zero, hence the increased scatter in the EDS data of the low-Ge compositions. As reported previously, the Ge content in the Au particles of the as-grown nanowires is at or below 3 atom %. This is true regardless of the postgrowth cooling conditions, e.g., for the samples in Figure 5. For fcc catalysts this is expected, consistent with the Au−Ge phase diagram; for hcp catalysts, it was of great interest to find that the composition was almost pure Au.9 As also mentioned in the text, the melted state of the nanoparticles is expected to have the same initial eutectic composition, i.e., the same state for quenching experiments, regardless of the prior room temperature structure. We used the melted state as a calibration for the EDS k-factor determination, assuming that its composition was the eutectic composition, 28 atom % Ge. A theoretical analysis of the liquid composition for 40 nm catalysts suggested that a size-dependent deviation from the bulk eutectic value was negligible in this size range.24 Therefore, the assumption of the eutectic composition in the melt seemed reasonable. We use the Ge L and Au M peaks for quantification, since they do not overlap, and have a minimum of 7000−10000 counts in the Au M peak. The Ge L peak has a larger variation in counts, since it goes to zero as the Ge content goes to zero. The fact that the intensity goes to zero for some particles indicates that there is no significant stray signal from the attached nanowire. We did take care to measure well within the nanoparticle and away from the particle−wire interface to avoid any stray signal. We also performed the measurements in nanoprobe mode which reduces the presence of any stray signal from the illumination system. We calibrated the k-factor, kAB, for the Ge L to Au M peak using the CliffLorimer equation,32
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CA /CB = kAB(IA /IB) where CA, CB are the concentrations of elements A and B, kAB is a constant, and IA,IB are the intensities of the EDS peaks for elements A and B. We used the eutectic composition for CA (Ge) and CB (Au), 28 and 72 atom % respectively, and the measured EDS intensities of the melted nanoparticles. We averaged three measurements each on five different melted particles, averaged the five values, and determined the kGeL/kAuM factor to be 1.15 ± 3%. As noted for Figure 5, we used the calibration value of the composition, 28 atom % Ge for the melted value. XRD analysis was performed in a PANalytical X’Pert PRO X-ray diffraction system with a Cu Kα source (∼8 keV). Germanium nanowire samples were taped to the unpolished side of a Si wafer, which was then mounted on the circular stage of the diffractometer. Symmetric θ−2θ scans were performed on such samples in the range 2θ = 35° to 45° in order to avoid any strong signal as a result of X-ray scattering from the substrate or Ge nanowires.
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The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors acknowledge National Science Foundation Grant DMR-1206511 for financial support. Use of the facilities of the Stanford Nano Shared Facilities is appreciated. F
DOI: 10.1021/acs.cgd.5b00803 Cryst. Growth Des. XXXX, XXX, XXX−XXX
