High-Pressure Structural Stability and Elasticity of Supercrystals Self

Dec 22, 2010 - Diamond anvil cell (DAC) SAXS experiments in the pressure range from ambient to 12.5 GPa revealed nearly perfect structural stability o...
0 downloads 0 Views 5MB Size
Download PDF
LETTER pubs.acs.org/NanoLett

High-Pressure Structural Stability and Elasticity of Supercrystals Self-Assembled from Nanocrystals )

Paul Podsiadlo,*,† Byeongdu Lee,‡ Vitali B. Prakapenka,§ Galyna V. Krylova,† Richard D. Schaller,†, Arnaud Demortiere,† and Elena V. Shevchenko*,† †

Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, United States § Center of Advanced Radiation Sources, University of Chicago, Argonne, Illinois 60439, United States Chemistry Department, Northwestern University, Evanston, Illinois 60208, United States

)

‡

bS Supporting Information ABSTRACT: We report here combined quasi-hydrostatic highpressure small-angle X-ray scattering (SAXS) and X-ray diffraction (XRD) studies on faceted 3D supercrystals (SCs) self-assembled from colloidal 7.0 nm spherical PbS nanocrystals (NCs). Diamond anvil cell (DAC) SAXS experiments in the pressure range from ambient to 12.5 GPa revealed nearly perfect structural stability of the SCs, with face-centered cubic organization of the NCs. Pressureinduced ordering (annealing effect) of the superstructure was observed. The ambient pressure bulk modulus of the SCs was calculated to be ∼5 GPa for compression and ∼14.5 GPa for decompression from fitting of Vinet and Birch-Murnaghan equations of state. XRD measurements revealed strong preferential crystallographic orientation of the NCs through all phase transformations to as high as 55 GPa without any indication of NC sintering. The first phase transition pressure of the NCs was found between 8.1 and 9.2 GPa and proceeds through homogeneous nucleation. Bulk modulus of PbS NCs was calculated to be ∼51 GPa based on fitting to the equations of state (KPbS,bulk ∼ 51-57 GPa). Closest surface-to-surface distance between the NCs in the SCs was calculated based on combined XRD and SAXS data, to reversibly tune from ∼1.56 nm to ∼0.9-0.92 nm and back to ∼1.36 nm in the ambient-12.5 GPa-ambient pressure cycle. The bulk modulus of the ligand matrix was extrapolated to be ∼2.2-2.95 GPa. These results show a general method of tuning NC interactions in packed nanoparticle solids. KEYWORDS: Self-assembly, nanocrystals, superlattices, SAXS, XRD, bulk modulus, diamond anvil cell, DAC, high pressure

superlattices (SLs)2,14 with primary (NCSLs, single type of NC),14 binary (BNSLs, two types of NCs),15-17 ternary (TNSLs, three types of NCs),18,19 and even dodecagonal quasi-crystalline (DDQC, from two types of NCs)20 internal organization. Precise ordering in SLs offers a unique opportunity to control the magnetic, optical, and electronic coupling between the individual NCs which can lead to collective properties such as vibrational coherence,21 reversible metal-to-insulator transitions,22 enhanced p-type conductivity,23 spin-dependent electron transport,24 enhanced ferro- and ferrimagnetism,25,26 tunable magnetotransport,27 and efficient charge transport in 2D and 3D superstructures.4-7,28-32 Due to precise positioning of the NCs within the 3D SLs, such systems are frequently referred to as “supercrystals” (SCs). Recently we showed through systematic nanoindentation studies that the mechanical properties of single-component SCs are unique to this material and they have more similarities with

T

he development of efficient methods for preparation of highly monodisperse nanocrystals (NCs) has led to the discovery of a wide range of novel phenomena at the nanoscale. As such, noble metal NCs revealed strong size-dependent plasmon resonances,1 semiconductor NCs were discovered to possess size-dependent optical properties,2 and magnetic NCs revealed size-dependent magnetic properties, including transitions from superparamagnetism to ferromagnetism.3 With these discoveries a number of potential applications have been envisioned for electronic, magnetic, and optical devices.4 Some of the most promising are related to the densely packed solids of NCs, with potential applications in field-effect transistors,5-7 light-emitting devices,8 photodetectors,9 photoconductors,10 and solar cells.11 As a result the current scope of nanoscience is shifting from the fundamental synthesis of the building blocks to the studies of collective properties of NC ensembles and their hierarchical architectures,12,13 including the NC solids. There is a broad range of examples of self-organization of NCs into highly periodic two- (2D) and three-dimensional (3D) r 2010 American Chemical Society

Received: October 12, 2010 Revised: December 3, 2010 Published: December 22, 2010 579

dx.doi.org/10.1021/nl103587u | Nano Lett. 2011, 11, 579–588

Nano Letters

LETTER

polymer nanocomposites rather than with their microscale counterparts, i.e., colloidal crystals, with moduli of elasticity (E) and hardnesses (H) in ranges of ∼0.2-6 GPa and 10-450 MPa, respectively.33,34 However, unlike polymers, the SCs are brittle with fracture toughness (Kc) of only 40 kPa/m1/2. On the other hand, unlike atomic crystals, the SCs also offer flexibility of tuning interparticle distance due to presence of the “soft” shell of organic ligands. Tuning of the interparticle distance in SLs has been previously shown through applying external pressure to a 2D Langmuir monolayer,22,31 pre- or postdeposition replacement of the surface ligands,5-7,35 and postassembly thermal annealing,36 and it is of paramount importance for controlling the magnetic and electronic coupling between the NCs, as was revealed in the reversible insulator-to-metal transitions for 2D monolayers of Ag NCs.22 The nanoindentation results on 3D solids with different degrees of ordering33,34,37-39 of NCs showed significant differences when compared to results obtained for 2D NCSLs.22,40,41 The 2D NCSLs revealed unusually high stiffness40 (E of the order of several gigapascals) and elasticity,22,40,41 which leads to questions regarding the role and structural organization of the organic ligands matrix that interconnect the inorganic cores in the different solids. Furthermore, our previous experiments with thermal annealing of facecentered cubic (fcc) organized SLs composed of 7 nm PbS NCs showed the possibility of irreversible modification of the surface-to-surface distance from ∼14 to ∼9 Å without losing the structural organization.36 The same study showed that such isotropic thermally induced structural compaction was not accompanied by loss of the organic ligands. In light of these results in this study we investigated in situ structural stability and mechanical properties of fcc-organized SCs composed of 7 nm PbS NCs stabilized with oleic acid (OA) under quasi-hydrostatic pressure conditions using a diamond anvil cell (DAC), X-ray diffraction (XRD), and small-angle X-ray scattering (SAXS) techniques. The focus of previous high-pressure XRD and optical studies was directed at phase transformation of individual NCs such as CdSe,42-44 CdSe/CdS,45 Si,46,47 Ag,48 and Fe2O3.49 It was shown, for example, that in contrast to extended solids, NCs can convert from one structure to another by a single nucleation event and the phase transformation pressure onset strongly depends on the NC size.44 In addition to that, the band gap energy shift in NCs upon compression can be very large50,51 which makes NCs excellent candidates for application as pressure-tunable lasers or optical pressure sensing devices in a broad energy range. The DAC technique was also used to probe optical properties of CdSe NC solids.52,53 Recently this method was applied to study structural transformations of the Au NC solids with a high degree of ordering.54,55 However, these studies demonstrated contradicting results: both preferential54 and random55 sintering of Au NCs were observed under similar experimental conditions. Here we report combined results for elastic structural transformations of both the atomic lattices of inorganic PbS cores as well as those of the fcc-organized NC superlattices upon external pressure variation, which allowed us to elucidate their mechanical properties. Experimental Section. Toluene, isopropanol (i-PrOH), ethanol, n-hexane, 1-octadecene (ODE), oleic acid (OA), and bis(trimethylsilyl) sulfide ((TMS)2S), were all purchased from Sigma-Aldrich and were at least of ACS purity. PbAc2 3 3H2O was purchased from Across Chemicals. Polished Si(100) wafers used for growing the SCs were obtained from Silicon Quest International (Santa Clara, CA). The wafers were diced into 4 mm by 1 cm strips with a wafer dicing saw and further cleaned by sonication in pure toluene. Glass test tubes

(0.8 cm i.d. by 10 cm long) used for SCs growth were obtained from Fisher Scientific. Rhenium foil used for preparation of DAC chamber was purchased from Sigma-Aldrich. The foil was subsequently diced into 4 mm  4 mm squares for further use as gasket chambers. The diamonds used in this study were obtained from Almax Industries. PbS NCs (7 nm) were synthesized according to the method of Hines and Scholes.56 SCs were grown on Si substrates by the slow destabilization of NCs with a nonosolvent.57 In a typical preparation, a single Si strip was placed vertically in a glass test tube and 0.5 mL of a moderately concentrated NC solution (∼1  1012 NCs/mL) in toluene was added to the bottom with a micropipet. Subsequently, 0.8 mL of i-PrOH was gently added on top of the NC solution avoiding disturbance and intermixing of the two solutions. The tubes were then sealed with Parafilm and allowed to sit undisturbed for approximately 1 week. Upon complete diffusional intermixing of the solvents and precipitation of the NCs, the solvents were carefully withdrawn with Pasteur pipets and discarded. The substrates were removed, air-dried, and stored for subsequent studies. High-resolution SEM images were obtained with an FIB FEI Nova 600 NanoLab SEM operated at 18 keV accelerating voltage. Optical images were obtained with a Zeiss Axio Imager and Leica MZ16 and MZ6 microscopes. In each high-pressure experiment, an individual SC (∼20 μm in size) was extracted from the Si substrate and loaded into a ∼150 μm diameter hole in a preindented Re gasket (chamber thickness of ∼40 μm). Together with the SC, a small ruby fluorescent ball was loaded alongside for in situ pressure determination.58 Neon (Ne) was loaded to the DAC using a pressurized gas loading system59 as a pressure-transmitting medium. Each SC was compressed using beveled diamond anvils with 300 μm diameter culets. SAXS measurements that reveal the structure of SC were performed at beamline 12ID-C of the Advanced Photon Source (APS) at the Argonne National Laboratory. For SAXS, a monochromatic X-ray beam (energy, 18 keV corresponding to X-ray wavelength λ = 0.688 Å) was focused onto an area of 100 μm  50 μm on the sample at a sample-to-detector distance of ∼2 m. The detector for the SAXS experiment was an APS-built CCD detector. Measured 2D images were converted into 1D curves in the form of intensity versus the scattering vector: Q = 4π sin(2θ)/λ. In SAXS experiments samples were compressed up to 12.5 GPa. X-ray diffraction that reveals the structure of NC was performed at beamline 13-ID-D of the GSECARS sector. The X-ray beam (37 keV energy, corresponding to X-ray wavelength of λ = 0.3344 Å) was focused to a 2 μm diameter spot with a Kirkpatrick-Baez mirror system. In XRD experiments, DACs with both 400 and 300 μm diameter culets were used. In addition to ruby, a small flake of gold was also loaded as an additional internal pressure standard.60 The distance and tilting of the MAR165-CCD detector were calibrated using a CeO2 standard. In XRD experiments samples were compressed up to 32 and 55.5 GPa, with the maximum pressure set by the culet size and degree of alignment of the diamonds. Results and Discussion. With the goal of better understanding the properties of self-assembled structures at high pressures, we have prepared SCs composed of 7.0 nm PbS NCs stabilized with OA, similar to those that were previously used in time-resolved SAXS studies of the thermal annealing of SCs and nanoindentation studies on NCs SCs.33,34,36 The typical size of the SCs was in a range of approximately a few to 100 μm (Figure 1A) which allowed us to easily choose SCs with appropriate dimensions, matching the size of the DAC chamber (Figure 1B). SAXS diffraction spectra of an individual SC revealed primarily fcc organization of the NCs (Figure 1C and Figure S.1 in the Supporting Information). 580

dx.doi.org/10.1021/nl103587u |Nano Lett. 2011, 11, 579–588

Nano Letters

LETTER

Figure 1. (A) SEM overview of SCs grown on Si substrate. Inset shows the high-resolution scanning electrom microscopy image of NCs on the surface of a SC. The inset scale bar corresponds to 30 nm. (B) Optical image of a DAC chamber loaded with a single PbS SC and a ruby pressure standard. (C) Integrated SAXS diffraction spectrum of a single SC at 1.86 GPa along with simulated diffraction spectra for fcc and hcp packing of NCs. (D) Integrated XRD spectrum of a single SC at 1.82 GPa (black) along with a simulated powder diffraction spectrum for PbS (red). (E) Comparison of integrated XRD spectra at the beginning of the experiment (1.82 GPa, black) and after complete decompression from 55 GPa (0.08 GPa, red).

length, trans conformation, of a single OA chain is ∼18 Å, the surface ligands cannot be fully interdigitated in the extended form and must adopt other conformations. Poor interdigitation of the ligands was also elucidated from the low value of the fracture toughness, and a glasslike state of the NCs was proposed.33 Despite the brittle character, the SCs were easily manipulated and loaded intact into a DAC (Figure 1B). In comparison to the majority of previous studies, we chose to work with Ne as a pressure-transmitting medium because it has been reported to have nearly hydrostatic response up to 15 GPa and deviations of less than 1% have been shown for pressures up to 50 GPa.61 Previous studies on pressure-dependent transformations and optical properties of individual semiconductor NCs primarily utilized liquid solvent media, e.g., 4-ethylpyridine or 4:1 methanol/ethanol mixture42,44 which have good hydrostatic response to

On the basis of the SAXS pattern, the center-to-center distance between √ closest neighboring NCs can be calculated as d = d111 6/2 = 85.6 Å ((1 Å), where d111 is the d-spacing of {111} plane of the fcc lattice. This corresponds to 15.6 Å of interparticle spacing (d - 7.0 nm core diameter) as compared to 14 Å for the 7.0 nm PbS NC SCs used in thermal annealing experiements36 and 19 Å for the 7.1 nm PbS NC SCs synthesized for the nanoindentation study.34 The variation in the interparticle spacings in SCs can be attributed to a number of factors, such as the rate of formation of SCs, slight variations in the concentration of capping ligands, and difference in the drying of the samples. Furthermore, the variations can result from the fact that NCs might not be perfectly spherical. The NCs can have a different degree of faceting in different synthetic runs which can also lead to the different concentration of the capping ligand. As we pointed out previously, since the extended 581

dx.doi.org/10.1021/nl103587u |Nano Lett. 2011, 11, 579–588

Nano Letters

LETTER

Figure 2. (A) Evolution of SAXS diffraction spectra as a function of pressure in the range of ambient f 12.5 GPa f ambient. The acquisition of compression data starts at 1.86 GPa, and the data are compared to the diffraction spectrum of SCs on Si substrate. (B) Diffraction pattern from a single SC at 11.45 GPa.

peaks is mainly due to the finite size of single crystalline domain in the SC that is not infinitely large. SAXS studies on individual SCs showed that the width of the peaks in SAXS spectra of individual SCs is comparable to the widths of the peaks in spectra obtained on a number of SCs (Figure S.2 in the Supporting Information). Analysis of SAXS data on individual SCs indicated that some SCs may have domains even with different crystallographic organization. For example, the SC used in high-pressure studies exhibited fcc organization of NCs with a trace amount of hexagonally organized (hcp) domains (Figures 1C and 2 and Figure S.1 in the Supporting Information); however, the amount of hcp is minor when compared to fcc. The dimensions of SC domain are inversely proportional to the width of the peak. A plot of full widths at halfmaxima (FWHM) of the d(111) peak as a function of pressure (Figure S.2B in the Supporting Information) shows little relative change, indicating that the size of domains is relatively constant. The remnant increased compaction (and slight densification) of the SCs upon decompression is to some extent analogous to densification of amorphous glasses.62,63 Evaluation of structural SAXS data (Figure 3) indeed shows substantial compressibility and elasticity of the SCs. The unit cell parameter, a, was reversibly changed from 121 to 107.05 Å during compression and back to 118.2 Å during the release cycle without any hysteresis, except for the initial densification that is likely due to lower density of packing in the as-prepared SCs. The corresponding volume change of an fcc unit cell is ∼30.8% during compression and 25.7% during release. The nearest neighbor center-to-center NC distance (Figure 3C) changes between ∼85.6 and ∼75.7 Å and back to ∼83.6 Å, resulting in nearly 10 Å of spacing change upon compression. Recently, Wu et al.54 also reported reversible, ∼13 Å center-to-center spacing change during compression up to 9 GPa of an fcc superlattice composed of 5.2 nm Au NCs stabilized with dodecanethiol. Further compression resulted in sintering of the Au NCs along [110] planes to form either a dense packed array of nanowires or a 3D mesophase.54,55 The structural SAXS information allowed us to extract the effective bulk modulus of the SC. We used the Vinet and Birch-Murnaghan equations of state60 (V-EOS (eq 1) and B-M

about 8-10 GPa. Accordingly, recent studies on structures selfassembled from 5.2 nm Au NCs showed that nonhydrostatic conditions in silicon oil above ∼8 GPa can lead to fusion of the NCs along a preferential crystallographic direction and formation of densely packed arrays of nanowires54 or 3D mesoporous architectures.55 By using Ne, as opposed to organic solvents, we also avoid potential leaching of ligands and structural destabilization of the SCs at higher pressures. Similarly to ambient pressure measurements,36 individual SCs loaded into the DAC exhibited well-resolved diffraction patterns (Figures 1C and 2). The SCs showed well-defined diffraction spots analogous to single atomic crystals, thus suggesting a highly crystalline character of the superstructure (Figure 2B), although not ideal given the number of spots from hexagonal close packed (hcp) ordering (Figure 1C). Bragg spots in the SAXS pattern in Figure 2B also suggest that the SC in the DAC is a twined crystal, where 111 is the twin plane. The complete evolution of the SAXS patterns is shown in Figure 2A. The diffraction patterns show that the organization of NCs within the SC is nearly perfectly preserved up to 12.5 GPa and back to ambient pressure. Peak positions shifted to higher Q values with pressure increases and generally exhibited reversible behavior upon pressure decreases (Figure 2A). This is contrary to the high-pressure observations made by Wu et al. on Au NCs structures which showed irreversible change in SAXS diffraction upon formation of nanowire or 3D mesoporous architectures from the fcc lattices of spherical NCs.54,55 Our observations also indicate some flexibility of the ligands either to plastic deformation or rearrangement of ligands at the surface of the NCs. It is noteworthy that the width of all long-range order peaks became narrower and more intense after decompression, which suggests a higher degree of NC order in the decompressed SC (Figure S.2 in the Supporting Information). The position of the peaks after release of the pressure is slightly shifted to higher Q values in comparison to the original peak position of SC loaded into DAC and SCs on Si substrate (ΔQ(111) ∼ þ0.0022 A-1), suggesting that the final structure is slightly compacted (Figure 3). For a perfect and infinite crystal, the Bragg diffraction would be substantially narrow (excluding instrumental width) resulting in singularities at the different peak positions. The width of our 582

dx.doi.org/10.1021/nl103587u |Nano Lett. 2011, 11, 579–588

Nano Letters

LETTER

Figure 3. Structural parameters of PbS SCs under pressure calculated based on SAXS and XRD data: (A) Graphical representation of a single unit cell of fcc organized NPs depicting structural transformations of both the SC and the inorganic cores. The characteristic dimensions are directly proportional to the experimentally established parameters. (B) fcc unit cell parameter of SC. (C) Closest neighbor (center-to-center) NC distance in SC. (D) Closest interparticle spacing based on fcc structure of the PbS NC SCs and pressure-dependent volume changes of individual PbS NCs. The volume change of PbS NCs was calculated assuming either no phase change of the B1 (NaCl, Fm3) structure (black and red) or complete phase transformation (blue and olive) and reduction of volume of the NaCl structure to a new phase at 8.5 GPa based on parameters from refs 64 and 65. (E) Calculation of bulk modulus from fitting of Birch-Murnaghan and Vinet's equations of state to the SAXS data.

as-prepared SCs might not have an equilibrium structure, which is likely related to the nonequilibrium conformation of ligands. For this reason, fitting of the compression data gave divergent results for the two models with B0-Vinet = 5.5 GPa and B00 -Vinet = 10.5; and B0-B-M = 4.5 GPa and B00 -B-M = 17.0 (Figure 3E). The decompression data, however, gave a much better fit (Figure 3E) with B0 = 14.5 GPa and B00 = 7.5 for both Vinet and B-M EOSs. We should also point out that using a commonly accepted value of B00 = 4.0 gave poor fits for both EOSs as can be seen in Figure S.3 in the Supporting Information. While the compression fits are within the same order of magnitude when compared to our nanoindentation results (E ∼ 1.7 GPa33,34), the decompression results are nearly an order of magnitude greater. The bulk and elastic moduli for homogeneous and isotropic materials can be related by the following formula: E = B0(1 - 2ν), where ν is Poisson's ratio. For fcc-organized noninteracting, hard spheres, ν was reported by Frenkel and Ladd to be ∼1/3,66 and further successfully used for calculations of mechanical properties of dense films of CdSe NCs.37,39 Using the reported Poisson's ratio

EOS (eq 2), respectively) to calculate the ambient pressure bulk modulus (Figure 3D): P300 ¼ ( "   - 2=3 "  1=3 #  1=3 #) V V V 13B0 exp 1:5ðB0 0 - 1Þ 1 V0 V0 V0

ð1Þ P300

3 ¼ B0 2

"  "  #)  5=3 #( V0 7=3 V0 3 0 V0 2=3 1 þ ðB0 - 4Þ -1 4 V V V

ð2Þ In these equations P300 is the pressure at 300 K, B0 is the ambient pressure bulk modulus, B00 is the pressure derivative of the bulk modulus (B00 = dB0/dP), V is the unit cell volume, and V0 is the initial unit cell volume. Some densification of the SC during compression, most likely resulting from plastic deformation modifies the mechanical properties of initial SC. This is because 583

dx.doi.org/10.1021/nl103587u |Nano Lett. 2011, 11, 579–588

Nano Letters

LETTER

In similarity to CdSe NCs42,43 the first transformation in PbS NCs appears to proceed through a single nucleation event, while the transformation from the intermediate phase to CsCl structure stretches from ∼41.6 GPa to above 55.5 GPa (Figure S.5A in the Supporting Information). Although the reported GeS and TlI phases have been quoted extensively,64,71,74-76 in our analysis we found that none of the suggested structures yield satisfying fits to the experimental data (Figure S.5B in the Supporting Information). The accurate assignment of the intermediate PbS NC phase cannot be made at present without single-crystal XRD measurements. These measurements are the subject of an ongoing study. In direct analogy to the bulk modulus calculations for the SCs, we have applied fitting of the Vinet and B-M EOSs to the XRD data for the NaCl structure (Figure 4C). The results revealed unchanged bulk modulus in comparison to the reported values for bulk PbS, with B0 = 51 GPa and B00 = 4.0 for both EOSs. Extrapolating the P-V relationship for the NaCl over the entire experimental range of SAXS, we can establish a lower bound limit for the fundamental unit cell size change of the PbS NCs. With this approach, in the range of the experimental pressure (up to 12.5 GPa) the diameter of the NCs has reversibly changed by 4.7% from 7.0 to 6.67 nm, corresponding to a 13.4 vol % change of initial PbS NCs (Figure S.6 in the Supporting Information). Combining the SAXS and XRD data, based on the NaCl structure, we found that the interparticle distance nearly reversibly changed from 15.6 to 9.0 Å and back to 13.6 Å (Figure 3D). According to the literature data, transformation of the NaCl to the new phase results in a -2 to -5 vol % change of the PbS lattice64,65,71,74 at the transformation pressure. Two recent reports gave contradicting parameters for B-M EOS for this new phase, revealing either softening (CrB-like structure) or stiffening (TlI-like structure) when compared to the NaCl phase. The EOS elastic parameters for CrB-like intermediate phase have been reported to be B0-tr = 30.9 GPa and B0 0-tr = 4.0,65 while for TlI-like phase they have been reported to be B0-tr = 134 GPa, B0 0-tr = 4.0, and V0-tr = 192.1 Å3.64 A volume change of -2 vol % was measured directly by optical observation.74 On the other hand, -3, -3.3, and -5 vol % changes were reported based on XRD experiments when the new phase was identified as SnS,71 TlI,64 or CrB,65 respectively. Using these available parameters for bulk modulus, B0-tr-CrB = 30.9 GPa or B0-tr-TlI = 134 GPa, and the derivative, B0 0-tr = 4.0, with largest, -3.3 and -5 vol.% changes, respectively, reported in refs 64 and 65, we have extrapolated new V0-tr-CrB = 187.3 Å3 and V0-tr-TlI = 166.5 Å3 (accounting for elevation of the phase transformation pressure to above 8 GPa for the NCs) and we have further extrapolated our calculations of the NC size (Figure S.6 in the Supporting Information) and the interparticle spacing to include complete phase transformation of the NaCl to the new phase above 8 GPa (Figure 3D), allowing us to establish the upper limit for the interparticle spacing. The calculations show sudden increase in the interparticle distance and subsequently gradual descent to a distance of either ∼9.2 or 10.3 Å, for TlI and CrB calculations, respectively. We should note that the report suggesting CrB-like structure as an intermediate phase of PbS also suggested coexistence of the NaCl and CrB phases above the phase transition pressure, thus suggesting that the actual result of our calculation should be in between that of the pure NaCl extrapolation and the CrB phase. Experimentally we do not observe a sudden change of the unit cell size of the superlattice, possibly suggesting a simultaneous slow relaxation of the ligand matrix (buffering/sponge effect). The substantial

the relationship between the moduli reduces to E = B0, suggesting that nanoindentation may underestimate the mechanical properties of the SCs. In comparison to other materials, we should point out that recent high-pressure studies on ultrahigh molecular weight crystalline polyethylene revealed modulus and its derivative: B0 = 4.3-5.2 GPa and B00 = 8.0-8.9, respectively.67 In direct analogy, the elastic moduli of 2D suspended monolayers of Au and CoO NCs were reported with values of ∼6 GPa40 and ∼14 GPa,41 respectively, and elastic moduli of electrophoretically deposited films of CdSe NCs were reported as high as ∼12 GPa.39 Hence our high-pressure results still fall within the general trend for these types of materials. In order to further understand the role of ligands in the deformation of the SCs, we need to account for pressure-induced volume and phase changes in individual PbS NCs. It is wellknown that nanosized structures often exhibit increased mechanical properties when compared to their bulk counterparts. For example studies of Ag,68,69 Pb,68 and ZnO70 structures revealed increasing mechanical properties with decreasing size in the nanometer regime. Simultaneously, the crystalline solids can undergo pressure-induced phase transformations and kinetics of phase transformations in nanomaterials have been shown to be strongly size-dependent. This phenomenon has been especially well characterized for colloidal CdSe NCs.42,43 Pressure-induced structural transformations of PbS have been studied extensively for bulk material.64,71,72 The bulk modulus and pressure derivative of PbS obtained from the high-pressure experiments were reported to be B0 ∼ 51-57 GPa and B00 ∼ 4.0-4.3, respectively.64,65,72 The high-pressure results obtained for PbS NCs revealed elevated first-order phase transition pressure when compared to the bulk phase, although no definitive calculations have established the size-dependent mechanical properties of the NCs. Qadri et al. revealed decreasing slopes of the room temperature P-V data for decreasing NCs sizes, suggesting that the mechanical properties in fact decrease with decreasing NC size.73 Given the lack of accurate data, we have performed synchrotron X-ray diffraction (XRD) experiments on our NCs in the SCs. The ambient pressure integrated XRD spectrum for PbS NCs is shown in Figure 1D along with a simulated powder diffraction pattern. The structure and unit cell parameters fit well with the reported NaCl-like (Fm3) structure. The ambient pressure unit cell parameter, a, for PbS has been reported at 5.936 Å while our results show slightly larger unit cell size of ∼5.96 Å. A compilation of the high-pressure results up to 14.7 GPa is shown in Figure 4A along with unit cell parameter change of the NaCl-like phase in Figure 4B (for comparison, molar density pressure dependence is presented in Figure S.4 in the Supporting Information). These results clearly show that the PbS NCs undergo a phase transformation above ∼8 GPa, which is still in the pressure range of our SAXS experiments. The transformation produces sudden intensity change of (111) and (200) diffraction peaks (Figure 4A), suggesting that at 9.2 GPa the structure is no longer that of the NaCl phase. The (111) and (200) peaks, while at first glance appear to belong to the NaCl phase, in fact they display saddle positional changes suggesting that they already belong to a new phase. Similarly to previous results, the phase transformation pressure is substantially elevated above that of bulk PbS, which reportedly transforms from the NaCl structure to SnS,71,74 GeS (Pnma),75 CrB (Cmcm),65 or a TlI tetragonal (Cmcm)64,76 structure starting at ∼2.2-2.86 GPa, and further to CsCl (Pm3m) structure above 22.0 GPa. 584

dx.doi.org/10.1021/nl103587u |Nano Lett. 2011, 11, 579–588

Nano Letters

LETTER

Figure 4. (A) XRD data for 7 nm PbS NCs under quasi-hydrostatic pressure (curves in red indicate appearance of a new phase). (B) Unit cell parameter, a, for NaCl-like and CsCl-like structures calculated based on the XRD data. (C) Calculation of bulk modulus from fitting of Birch-Murnaghan and Vinet's EOSs to the compression XRD data.

differences between the bounds based on the two different intermediate structures urges more detailed study of the transformations in PbS. Nevertheless, in contrast to structures assembled from Au,54,55 even though PbS NCs have preferential orientation within the superlattices (Figure 5) and orientated attachment phenomena has been previously reported for PbS nanostructures,77 neither isotropic nor directional sintering of individual NCs was observed at 12.5 GPa as it is followed from SAXS data. It is likely that even compression up to 55 GPa does not cause the sintering of individual NCs; thus we have been able to observe regular fringes of superlattice in TEM along Æ111æ oriented thin edge of SC recovered from compression up to 56 GPa (Figure S.7 in the Supporting Information). It is also worth mentioning that the surface of SC was covered by a layer of material, presumably by a fraction of ligands extruded from the SC during the compression cycle, and due to the poorly conductive nature of this layer, it was difficult to obtain a high-resolution SEM image. Combining this information together with SAXS results, we can conclude with confidence that the superlattice nature of the SCs is preserved even up to very high pressures when using Ne as a pressure transmitting medium. The combination of SAXS and XRD results suggests that the shrinking of NCs due to pressure in fact helps in accommodating

such a large change in SC's unit cell size and, to some extent, prevents sintering of the NCs. The interparticle distance of 9.0-10.3 Å upon maximum compression in this study is comparable to the change observed upon thermal annealing of the SCs. Previously, based on thermogravimetric analysis, we found that in the SCs the OA molecules not only coat the surface of the NCs but also fill the empty voids of the fcc structure.34,36 Since all of the space not occupied by inorganic PbS cores is filled with the organic OA, we can calculate the total volume of OA by simply subtracting the volume occupied by individual NCs in the fcc lattice (four NCs) from the volume of the SCs unit cell obtained from SAXS. The resulting data for compression and decompression are plotted in Figure 6 along with B-M and Vinet EOS fits results. The calculated volume of the OA changes by -42 vol % upon compression and þ34 vol % upon decompression. For compression data, we can calculate the change of the ligands matrix volume accounting for total phase transformation of the NCs to TlI- or the CrB-like phases. We obtained the following constants for the EOS parameters for compression: B0-Vinet = 2.2-2.4 GPa and B00 -Vinet = 9.0; B0-B-M = 2.7-2.95 GPa and B00 -B-M = 9.0; for calculations without phase change and with change to TlI phase. The results of EOS fit to data based on phase change to CrB-like structure gave unrealistic B00 = 32 due to the 585

dx.doi.org/10.1021/nl103587u |Nano Lett. 2011, 11, 579–588

Nano Letters

LETTER

Figure 5. High-pressure, 2D XRD patterns showing preferential orientation of NCs in the SC: (A-F) compression; (G, H) release. The pattern (H) after complete decompression was acquired 24 h after depressurization. Dark intense spots are diffraction peaks of crystalline Ne.

Figure 6. Calculated ligand volume response as a function of pressure during compression (A) and decompression (B) and associated fits of the Birch-Murnaghan and Vinet's EOSs.

suggested large volume change of PbS upon phase transition (-5 vol %) and hence large discontinuity in the data. For decompression we have been only able to fit results to data based on NaCllike structure only. This is because NCs typically show substantial hysteresis in the phase transformation pressure which we cannot ascertain at this point. For decompression, the parameters were quite close to the compression results: B0-Vinet = 2.2 GPa and B00 -Vinet = 9.0; B0-B-M = 2.7 GPa and B00 -B-M = 9.0. Overall, the B00 once again deviates greatly from the commonly used value of 4.0 because of the soft nature of the organic ligands and possibly due to the initial compaction of the SC structure. For comparison, compressibility measurements on a family of 18 different solids of low molecular weight organic compounds incorporating sixmembered carbon rings (benzene and cyclohexane derivatives) showed B0 in a range of 5.9-12.5 from fitting the experimental data to modified Murnaghan EOS,78 which is comparable to our results. Our results are also an order of magnitude greater from those previously calculated based on nanoindentation study, E = 0.15 GPa, for 7.1 nm PbS NCs. However, we have to consider that nanoindentation is a directional method whereas the present study utilizes nearly isotropic compression (quasi-hydrostatic conditions). Interestingly though, high elastic modulus (on the

order of several GPa) has been previously reported for ligand matrix in freely suspended monolayers of NCs.40,41 In light of the variety and complexity of the interacting forces in the SC (including strong dipolar interactions resulting in preferential alignment of the NCs), we speculate that the large modulus of the ligand matrix and the superlattice as a whole represent a combination of the actual modulus and strong repulsive interactions between the NCs, thus resulting in nearly perfect recovery of the structure with slight compaction. Conclusions. In conclusion, we presented the first combined in situ quasi-hydrostatic high-pressure SAXS and XRD structural studies on faceted, 3D SCs self-assembled from 7 nm PbS NCs. The results revealed high structural stability and elasticity of the SCs even at high pressures. A preferential orientation of NCs is observed in the SCs and it is preserved to as high as 55 GPa. Ambient pressure bulk modulus of the SCs was calculated to be ∼5 GPa during compression and ∼14.5 GPa during release from standard equations of state. NCs were found to undergo firstorder phase transition above 8 GPa, and the transformation proceeds through a single nucleation event (within a pressure range of 8.1-9.2 GPa) during the first transition and heterogeneous nucleation during the second transformation from the 586

dx.doi.org/10.1021/nl103587u |Nano Lett. 2011, 11, 579–588

Nano Letters

LETTER

intermediate to CsCl structure. Bulk modulus of PbS NCs was calculated to be ∼51 GPa based on fitting of the XRD data to equations of state and it is unchanged in comparison to the reported values of bulk PbS. We obtained a bulk modulus for the ligand matrix of ∼2.2-2.95 GPa, which is an order of magnitude greater than that observed from nanoindentation study. High structural stability of the SCs and the ability to tune the interparticle spacing seem to offer promise for further manipulation of the collective properties of self-organized artificial solids including the structures that consisted of NCs transformed at high pressures into a different phase. Combining high-pressure XRD and SAXS provides unique opportunities to obtain direct information about mechanical properties of individual building blocks and their hierarchical architectures.

(7) Yu, D.; Wang, C. J.; Guyot-Sionnest, P. Science 2003, 300, 1277– 1280. (8) Caruge, J. M.; Halpert, J. E.; Wood, V.; Bulovic, V.; Bawendi, M. G. Nat. Photonics 2008, 2, 247–250. (9) Konstantatos, G.; Howard, I.; Fischer, A.; Hoogland, S.; Clifford, J.; Klem, E.; Levina, L.; Sargent, E. H. Nature 2006, 442, 180–183. (10) Nakanishi, H.; Bishop, K. J. M.; Kowalczyk, B.; Nitzan, A.; Weiss, E. A.; Tretiakov, K. V.; Apodaca, M. M.; Klajn, R.; Stoddart, J. F.; Grzybowski, B. A. Nature 2009, 460, 371–375. (11) Gur, I.; Fromer, N. A.; Geier, M. L.; Alivisatos, A. P. Science 2005, 310, 462–465. (12) Nie, Z. H.; Petukhova, A.; Kumacheva, E. Nat. Nanotechnol. 2010, 5, 15–25. (13) Choi, C. L.; Alivisatos, A. P. Annu. Rev. Phys. Chem. 2010, 61, 369–389. (14) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Science 1995, 270, 1335–1338. (15) Redl, F. X.; Cho, K. S.; Murray, C. B.; O'Brien, S. Nature 2003, 423, 968–971. (16) Shevchenko, E. V.; Talapin, D. V.; Kotov, N. A.; O'Brien, S.; Murray, C. B. Nature 2006, 439, 55–59. (17) Kalsin, A. M.; Fialkowski, M.; Paszewski, M.; Smoukov, S. K.; Bishop, K. J. M.; Grzybowski, B. A. Science 2006, 312, 420–424. (18) Shevchenko, E. V.; Kortright, J. B.; Talapin, D. V.; Aloni, S.; Alivisatos, A. P. Adv. Mater. 2007, 19, 4183–4188. (19) Evers, W. H.; Friedrich, H.; Filion, L.; Dijkstra, M.; Vanmaekelbergh, D. Angew. Chem., Int. Ed. 2009, 48, 9655–9657. (20) Talapin, D. V.; Shevchenko, E. V.; Bodnarchuk, M. I.; Ye, X. C.; Chen, J.; Murray, C. B. Nature 2009, 461, 964–967. (21) Courty, A.; Mermet, A.; Albouy, P. A.; Duval, E.; Pileni, M. P. Nat. Mater. 2005, 4, 395–398. (22) Collier, C. P.; Saykally, R. J.; Shiang, J. J.; Henrichs, S. E.; Heath, J. R. Science 1997, 277, 1978–1981. (23) Urban, J. J.; Talapin, D. V.; Shevchenko, E. V.; Kagan, C. R.; Murray, C. B. Nat. Mater. 2007, 6, 115–121. (24) Black, C. T.; Murray, C. B.; Sandstrom, R. L.; Sun, S. H. Science 2000, 290, 1131–1134. (25) Sun, S. H.; Murray, C. B.; Weller, D.; Folks, L.; Moser, A. Science 2000, 287, 1989–1992. (26) Cheon, J.; Park, J. I.; Choi, J. S.; Jun, Y. W.; Kim, S.; Kim, M. G.; Kim, Y. M.; Kim, Y. J. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 3023–3027. (27) Dong, A. G.; Chen, J.; Vora, P. M.; Kikkawa, J. M.; Murray, C. B. Nature 2010, 466, 474–477. (28) Tran, T. B.; Beloborodov, I. S.; Lin, X. M.; Bigioni, T. P.; Vinokur, V. M.; Jaeger, H. M. Phys. Rev. Lett. 2005, 95, No. 076806-1-4. (29) Parthasarathy, R.; Lin, X. M.; Jaeger, H. M. Phys. Rev. Lett. 2001, 87, No. 186807/1-4. (30) Yu, D.; Wehrenberg, B. L.; Jha, P.; Ma, J.; Guyot-Sionnest, P. J. Appl. Phys. 2006, 99, No. 104315-1-7. (31) Liljeroth, P.; Vanmaekelbergh, D.; Ruiz, V.; Kontturi, K.; Jiang, H.; Kauppinen, E.; Quinn, B. M. J. Am. Chem. Soc. 2004, 126, 7126– 7132. (32) Vanmaekelbergh, D.; Liljeroth, P. Chem. Soc. Rev. 2005, 34, 299–312. (33) Tam, E.; Podsiadlo, P.; Shevchenko, E. V.; Ogletree, D. F.; Delplancke-Ogletree, M.-P.; Ashby, P. D. Nano Lett. 2010, 10, 2363– 2367. (34) Podsiadlo, P.; Krylova, G.; Lee, B.; Critchley, K.; Gosztola, D. J.; Talapin, D. V.; Ashby, P. D.; Shevchenko, E. V. J. Am. Chem. Soc. 2010, 132, 8953–8960. (35) Tangirala, R.; Baker, J. L.; Alivisatos, A. P.; Milliron, D. J. Angew. Chem., Int. Ed. 2010, 49, 2878–2882. (36) Lee, B.; Podsiadlo, P.; Rupich, S.; Talapin, D. V.; Rajh, T.; Shevchenko, E. V. J. Am. Chem. Soc. 2009, 131, 16386–16389. (37) Banerjee, S.; Jia, S. G.; Kim, D. I.; Robinson, R. D.; Kysar, J. W.; Bevk, J.; Herman, I. P. Nano Lett. 2006, 6, 175–180. (38) Jia, S. G.; Banerjee, S.; Lee, D.; Bevk, J.; Kysar, J. W.; Herman, I. P. J. Appl. Phys. 2009, 105, No. 103513-1-9.

’ ASSOCIATED CONTENT

bS

Supporting Information. Comparison of SAXS longrange order diffraction peaks for SCs on Si substrate and individual SC at the beginning of and after compression, plot of full width halfmaxima for (111) peak of SAXS spectra, 2D SAXS diffraction spectrum indexing with hcp and fcc peak positions, calculation of bulk modulus for SC based on fiting of EOSs to compression data, evolution of molar density for NaCl and CsCl phases of PbS NCs, evolution of compression XRD spectra for the PbS NCs up to 55 GPa of pressure, optimized fitting of the GeS and TlI XRD spectra to the intermediate phase of PbS NCs, plot of pressure-dependent PbS NC diameter with and without phase transformation from NaCl to TlI, and electron microscopy images of SC recovered from compression up to 55 GPa of maximum pressure. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] and [email protected].

’ ACKNOWLEDGMENT Work at the Center for Nanoscale Materials was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-06CH11357. P.P. acknowledges the support of Willard Frank Libby postdoctoral fellowship from Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation;Earth Sciences (EAR-0622171) and Department of Energy;Geosciences (DE-FG02-94ER14466). Use of the Advanced Photon Source was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357 ’ REFERENCES (1) Burda, C.; Chen, X. B.; Narayanan, R.; El-Sayed, M. A. Chem. Rev. 2005, 105, 1025–1102. (2) Murray, C. B.; Kagan, C. R.; Bawendi, M. G. Annu. Rev. Mater. Sci. 2000, 30, 545–610. (3) Leslie-Pelecky, D. L.; Rieke, R. D. Chem. Mater. 1996, 8, 1770– 1783. (4) Talapin, D. V.; Lee, J. S.; Kovalenko, M. V.; Shevchenko, E. V. Chem. Rev. 2010, 110, 389–458. (5) Talapin, D. V.; Murray, C. B. Science 2005, 310, 86–89. (6) Kovalenko, M. V.; Scheele, M.; Talapin, D. V. Science 2009, 324, 1417–1420. 587

dx.doi.org/10.1021/nl103587u |Nano Lett. 2011, 11, 579–588

Nano Letters

LETTER

(75) Maclean, J.; Hatton, P. D.; Piltz, R. O.; Crain, J.; Cernik, R. J. Nucl. Instrum. Methods Phys. Res., Sect. B 1995, 97, 354–357. (76) Chattopadhay, T.; Schnering, H. G.; Grosshaus, W. A.; Holzapfel., W. B. Physica B & C 1986, 139, 356–360. (77) Cho, K. S.; Talapin, D. V.; Gaschler, W.; Murray, C. B. J. Am. Chem. Soc. 2005, 127, 7140–7147. (78) Vaidya, S. N.; Kennedy, G. C. J. Chem. Phys. 1971, 55, 987–992.

(39) Lee, D.; Jia, S. G.; Banerjee, S.; Bevk, J.; Herman, I. P.; Kysar, J. W. Phys. Rev. Lett. 2007, 98, No. 026103-1-4. (40) Mueggenburg, K. E.; Lin, X. M.; Goldsmith, R. H.; Jaeger, H. M. Nat. Mater. 2007, 6, 656–660. (41) He, J.; Kanjanaboos, P.; Laszlo Frazer, N.; Weis, A.; Lin, X.-M.; Jaeger, H. M. Small 2010, 6, 1449–1456. (42) Chen, C. C.; Herhold, A. B.; Johnson, C. S.; Alivisatos, A. P. Science 1997, 276, 398–401. (43) Jacobs, K.; Zaziski, D.; Scher, E. C.; Herhold, A. B.; Alivisatos, A. P. Science 2001, 293, 1803–1806. (44) Tolbert, S. H.; Alivisatos, A. P. Science 1994, 265, 373–376. (45) Choi, C. L.; Koski, K. J.; Sivasankar, S.; Alivisatos, A. P. Nano Lett. 2009, 9, 3544–3549. (46) Tolbert, S. H.; Alivisatos, A. P. Annu. Rev. Phys. Chem. 1995, 46, 595–625. (47) Tolbert, S. H.; Herhold, A. B.; Brus, L. E.; Alivisatos, A. P. Phys. Rev. Lett. 1996, 76, 4384–4387. (48) Koski, K. J.; Kamp, N. M.; Smith, R. K.; Kunz, M.; Knight, J. K.; Alivisatos, A. P. Phys. Rev. B 2008, 78, No. 165410-1-10. (49) Clark, S. M.; Prilliman, S. G.; Erdonmez, C. K.; Alivisatos, A. P. Nanotechnology 2005, 16, 2813–2818. (50) Pietryga, J. M.; Zhuravlev, K. K.; Whitehead, M.; Klimov, V. I.; Schaller, R. D. Phys. Rev. Lett. 2008, 101, No. 217401-1-4. (51) Zhuravlev, K. K.; Pietryga, J. M.; Sander, R. K.; Schaller, R. D. Appl. Phys. Lett. 2007, 90, No. 043110-1-3. (52) Kim, B. S.; Islam, M. A.; Brus, L. E.; Herman, I. P. J. Appl. Phys. 2001, 89, 8127–8140. (53) Grant, C. D.; Crowhurst, J. C.; Hamel, S.; Williamson, A. J.; Zaitseva, N. Small 2008, 4, 788–794. (54) Wu, H.; Bai, F.; Sun, Z.; Haddad, R. E.; Boye, D. M.; Wang, Z.; Fan, H. Angew. Chem., Int. Ed. 2010, 49, 8431–8434. (55) Wu, H.; Bai, F.; Sun, Z.; Haddad, R. E.; Boye, D. M.; Wang, Z.; Huang, J. Y.; Fan, H. J. Am. Chem. Soc. 2010, 132, 12826–12828. (56) Hines, M. A.; Scholes, G. D. Adv. Mater. 2003, 15, 1844–1849. (57) Talapin, D. V.; Shevchenko, E. V.; Kornowski, A.; Gaponik, N.; Haase, M.; Rogach, A. L.; Weller, H. Adv. Mater. 2001, 13, 1868–1871. (58) Mao, H. K.; Xu, J.; Bell, P. M. J. Geophys. Res., [Solid Earth Planets] 1986, 91, 4673–4676. (59) Rivers, M.; Prakapenka, V. B.; Kubo, A.; Pullins, C.; Holl, C. M.; Jacobsen, S. D. High Pressure Res. 2008, 28, 273–292. (60) Fei, Y. W.; Ricolleau, A.; Frank, M.; Mibe, K.; Shen, G. Y.; Prakapenka, V. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 9182–9186. (61) Klotz, S.; Chervin, J. C.; Munsch, P.; Le Marchand, G. J. Phys. D: Appl. Phys. 2009, 42, No. 075413-1-7. (62) Lee, S. K.; Eng, P. J.; Mao, H. K.; Meng, Y.; Newville, M.; Hu, M. Y.; Shu, J. F. Nat. Mater. 2005, 4, 851–854. (63) Tsiok, O. B.; Brazhkin, V. V.; Lyapin, A. G.; Khvostantsev, L. G. Phys. Rev. Lett. 1998, 80, 999–1002. (64) Grzechnik, A.; Friese, K. J. Phys.: Condens. Matter 2010, 22, No. 095402-1-6. (65) Knorr, K.; Ehm, L.; Hytha, M.; Winkler, B.; Depmeier, W. Eur. Phys. J. B 2003, 31, 297–303. (66) Frenkel, D.; Ladd, A. J. C. Phys. Rev. Lett. 1987, 59, 1169–1169. (67) Fontana, L.; Vinh, D. Q.; Santoro, M.; Scandolo, S.; Gorelli, F. A.; Bini, R.; Hanfland, M. Phys. Rev. B 2007, 75, No. 174112 -1-11. (68) Cuenot, S.; Fretigny, C.; Demoustier-Champagne, S.; Nysten, B. Phys. Rev. B 2004, 69, No. 165410-1-5. (69) Jing, G. Y.; Duan, H. L.; Sun, X. M.; Zhang, Z. S.; Xu, J.; Li, Y. D.; Wang, J. X.; Yu, D. P. Phys. Rev. B 2006, 73, No. 235409-1-6. (70) Chen, C. Q.; Shi, Y.; Zhang, Y. S.; Zhu, J.; Yan, Y. J. Phys. Rev. Lett. 2006, 96, No. 075505-1-4. (71) Wakabayashi, I.; Kobayashi, H.; Nagasaki, H.; Minomura, S. J. Phys. Soc. Jpn. 1968, 25, 227–233. (72) Wei, L.; Jun-fang, C.; Teng, W. Physica B 2010, 405, 1279–1282. (73) Qadri, S. B.; Yang, J.; Ratna, B. R.; Skelton, E. F.; Hu, J. Z. Appl. Phys. Lett. 1996, 69, 2205–2207. (74) Bassett, W. A.; Takahashi, T.; Stook, P. W. Rev. Sci. Instrum. 1967, 38, 37–42. 588

dx.doi.org/10.1021/nl103587u |Nano Lett. 2011, 11, 579–588