Atom by atom: HRTEM insights into inorganicnanotubes and fullerene-like structuresMaya Bar Sadan*†, Lothar Houben*‡, Andrey N. Enyashin§, Gotthard Seifert§, and Reshef Tenne†‡

*Institute of Solid State Research and Ernst Ruska Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Julich GmbH,52425 Julich, Germany; †Materials and Interfaces Department, Weizmann Institute of Science, Rehovot 76100, Israel; and §Physikalische Chemie,Technische Universitat Dresden, 01062 Dresden, Germany

This Feature Article is part of a series identified by the Editorial Board as reporting findings of exceptional significance.

Edited by Steven G. Louie, University of California, Berkeley, CA, and approved August 14, 2008 (received for review June 5, 2008)

The characterization of nanostructures down to the atomic scale isessential to understand some physical properties. Such a charac-terization is possible today using direct imaging methods such asaberration-corrected high-resolution transmission electron micros-copy (HRTEM), when iteratively backed by advanced modelingproduced by theoretical structure calculations and image calcula-tions. Aberration-corrected HRTEM is therefore extremely usefulfor investigating low-dimensional structures, such as inorganicfullerene-like particles and inorganic nanotubes. The atomic ar-rangement in these nanostructures can lead to new insights intothe growth mechanism or physical properties, where imminentcommercial applications are unfolding. This article will focus ontwo structures that are symmetric and reproducible. The firststructure that will be dealt with is the smallest stable symmetricclosed-cage structure in the inorganic system, a MoS2 nanoocta-hedron. It is investigated by means of aberration-corrected micros-copy which allowed validating the suggested DFTB-MD model. Itwill be shown that structures diverging from the energeticallymost stable structures are present in the laser ablated soot and thatthe alignment of the different shells is parallel, unlike the bulkmaterial where the alignment is antiparallel. These findings cor-respond well with the high-energy synthetic route and theyprovide more insight into the growth mechanism. The secondstructure studied is WS2 nanotubes, which have already been shownto have a unique structure with very desirable mechanical properties.The joint HRTEM study combined with modeling reveals new infor-mation regarding the chirality of the different shells and provides abetter understanding of their growth mechanism.

aberration-corrected high-resolution transmission electron microscopy �inorganic closed-cage structures

Nanoscience today is concerned with producing continuouslynew structures of increased complexity. Nanotubes, nano-

wires, and nanoparticles, such as quantum dots (QDs), are reportedin the literature as both building blocks for nano-architectures, suchas molecular transistors, and as the constituents of macroscopicmaterials (nanocomposites) that are used for variety of applica-tions. In the latter case, macroscale measurements become relevant,e.g., x-ray diffraction (XRD), because they determine the ensem-ble-averaged lattice spacing of nanoparticles. In other cases, forexample when the nanoparticles are used as an additive for high-performance lubricants or self-lubricating coatings, knowledge isrequired of the mechanical properties of the nanocomposite as awhole. However, to understand the structure-functionality relation-ship from first principles, the characteristics of individual nanopar-ticles are needed. Such characterization can then be compared withab initio calculations, which provide an invaluable insight into thestructure and properties of specific kinds of nanoparticles. Someproperties in particular, for example electrical conductivity, dependclosely on the interface between different phases or compoundsinside the particle, or they correlate sensitively with the atomicconfiguration of the nanoparticle.

Inorganic fullerene-like nanoparticles (IF) and inorganic nano-tubes (INT) (1) represent special cases in this context for a numberof reasons. First, these unique phases are only stable in thenano-regime, i.e., up to 100 nm or so (2). Second, the IF areubiquitous among layered compounds, and their discovery led tothe birth of a new field in inorganic chemistry (1, 2). Moreover,these structures already hold perspectives for current and futureapplications, such as solid lubricants (3), additives in high-strengthand high-toughness nanocomposites (4, 5), and a variety of otherpotential applications. Building on this potential, ApNano Mate-rials started pilot industrial production of IF-WS2.

Advanced transmission electron microscopes (TEM) provide amultitude of complementary diffraction, imaging, and spectro-scopic techniques—all available in a single instrument—that enablequantitative, structural, and chemical information to be gained overscales ranging from 1 �m to �1 Å. Within this field, high-resolutiontransmission electron microscopy (HRTEM) is a fast growingdomain. Recent advancements in aberration-corrected TEM havedemonstrated single atom sensitivity for light elements at sub-ångstrom resolutions (6–8). HRTEM studies rely closely on struc-tural models to verify and establish the findings extracted from theimages. This relationship may be used iteratively with other theo-retical and experimental techniques to gain more informationabout the location of individual atoms within nanostructures, whichare not fully periodic. Indeed, the exploitation of atomic-scaleHRTEM for the elucidation of closed-cage structures, such as IFand INT, is a perfect example. Coupled with first-principle com-putational methods, the atomic-scale analysis of IF is most attrac-tive because it makes the analysis of inorganic nanotubes andfullerene-like structures possible, enabling the prediction of newproperties, some of which have yet to be verified by experiment.

The inorganic analogue of the C60, the smallest stable symmetricclosed-cage structure in the inorganic system, is most-probably ananooctahedron. It is produced by high-energy far-from-equilibrium methods, such as laser ablation. This structure revealsthe basic symmetry prevalent in the inorganic system, which essen-tially stems from the tendency to produce a square-like latticedefect instead of the pentagonal or heptagonal defects typical forcarbon systems. Early indications for this idea were suggested backin 1993 (9). A good example of this divergence from carbonchemistry is the boron nitride system. Boron nitride is isoelectronicand structurally analogous to carbon (10). Furthermore, in analogyto the carbon system, boron nitride exists in two phases: thehexagonal (graphite-like) and the cubic (diamond-like) form, with

Author contributions: M.B.S., L.H., G.S., and R.T. designed research; M.B.S., L.H., and A.N.E.performed research; A.N.E. and G.S. contributed new reagents/analytic tools; M.B.S. ana-lyzed data; and M.B.S., L.H., and R.T. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

‡To whom correspondence may be addressed. E-mail: reshef.tenne@weizmann.ac.il orl.houben@fz-juelich.de.

© 2008 by The National Academy of Sciences of the USA

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the former being the stable form in ambient conditions. Nonethe-less, unlike the almost perfectly spherical carbon onions, medium-size (�20 nm in diameter) BN IF structures were found to bestrongly facetted (11). When produced in smaller sizes by electronirradiation, the basic structure of the BN particles exhibits rectan-gular shapes, attributed to a 3D octahedral structure (10, 12), whichis obtained by placing (B-N)2 squares in the six corners.

Symmetric nanooctahedra of MoS2 and MoSe2 were produced bylaser ablation for the first time in 1999 (13, 14). In analogy to carbonfullerenes, and to the BN system, closed inorganic cages producedby energetic techniques are also expected to be highly symmetricand to occur in a specific size range (13). In a previous study, densityfunctional tight binding calculations (DFTB) proceeded by molec-ular dynamics (MD) annealing were used to elucidate the structureand electronic properties of octahedral MoS2 fullerenes (15, 16).These octahedral particles manifest the strong relation betweenshape and properties, even among structures of the same size andcomposition. In contrast to bulk and nanotubular MoS2, which aresemiconductors, the Fermi level of the nanooctahedra is situatedwithin Mo d-bands, endowing the nanoparticles with a metallic-likecharacter. According to the DFTB-MD calculations, the occur-rence of metallic-like d-band conductivity correlates sensitivelywith defect formation at the apices and the seaming of the trian-gular faces at their edges.

The theoretical calculations resulted in 15 suggested structuremodels of the nanooctahedra, which differed in their constructionprinciples (arrangement of facets, edges, and vertices) (15, 16). Byestimating energetic properties of these structure models, a stabilitycurve was constructed from the model calculations, which could becompared with size statistics extracted from the experimentalimages. The favorable agreement between the two establishes thevalidity of the model. In particular, nanooctahedra 3–6 nm in size(�103–105 atoms in total) consisting of 3–5 MoS2 shells were foundto be the most stable species.

Another low-dimensional structure of great interest is the nano-tube. WS2 nanotubes were discovered in the early 1990s, and sincethen they have been the subject of intensive study (2, 17–20). Thisstructure is fascinating, because it also exhibits properties that differfrom the bulk 2H material. For example, theory predicts that,although the bulk 2H-MoS2 (WS2) material has an indirect bandgap, and in analogy so would the armchair MoS2 (WS2) nanotubes,the zigzag MoS2 (WS2) nanotubes should have a direct band gap(21, 22). Another feature discovered was that the band gap de-creases with diameter size, because of the change in curvature of theS–W–S triple layer. This contrasts with carbon nanotubes and QDs(23), where the bandgap increases with the shrinking size of thenanoparticles because of quantum confinement of the electron(hole). Furthermore, the mechanical behavior of the nanotubesconsiderably outweighs that of the bulk material (17).

Previous studies provided some information on the structure andgrowth mechanisms of WS2 nanotubes (18–20). They concludedthat the reaction starts by a reduction of the WO3 particle and theformation of a volatile phase within it, encapsulated by the first WS2layers. When the appropriate conditions are introduced into thefluidized bed reactor (FBR), a volatile WOx phase forms in the coreof the nanoparticle. The pressure within the particle is strongenough to allow the WOx volatile phase to break through andbecome the root of the nanotube. The volatile phase serves as afeeding source for the growth of the tube, because, upon reachingthe growth front, it promptly reacts with the H2S gas to produceWS2 (20). Previous studies could only detect chiral WS2 nanotubeswith a chiral angle of 7 � 3°. With one exception, only one chiralangle was observed in the diffraction patterns for all tubes (19). Itwas therefore assumed that the chiral growth mode was energeti-cally and kinetically favorable, because it provided a continuousgrowth front. Because the growth process is continuous, the helicityangle does not change during growth and the nanotube continuesto grow with the same chiral angle (20). However, as was the case

for nanooctahedra, there is still a need for a detailed understandingof the structure, which could affect our knowledge of its properties.

The present study summarizes the progress of experiment andmodeling, with the aim of providing a new understanding of theatomic arrangement of inorganic fullerene-like structures.

The imaging process in the TEM only allows for the detection andlocalization of single atoms in rare, specific cases. In the case ofcrystalline samples, the atomic structure of a sample represented byatomic columns at certain viewing directions is usually exploited,because it facilitates the structural interpretation. In nonperiodicstructures, the alignment to such viewing directions with a simplestructure projection is naturally impossible. The misalignmentresults in both a lower signal-to-noise ratio and an increasedcomplexity for the structural interpretation.

Both the nanotubes and nanooctahedra in this study are non-periodic in the transmittance direction with a changing atomicstructure and thickness. Therefore, calculations of model structures(sometimes supercell data with �100,000 atoms) and correspond-ing calculated microscopy images, are used to deduce details of theatomic arrangements on the ångstrom scale. The calculation of thestructures serves as the basis for atomic-scale simulations of TEMand STEM data, which must then be verified by matching them withthe experimental data. Aberration-corrected high-resolution TEMand STEM are also used to gain a more in-depth understanding ofthe atomic structure of the nanotubes and nanooctahedra, whichallows the signal-to-noise ratio to be optimized at sub-ångstromresolution with insignificant point spread.

Results and DiscussionMoS2 Nanooctahedra. Nested MoS2 structures are formed by severalMoS2 molecular layers closing in on themselves to produce acage-like structure, where the smallest stable nested structure beingan octahedron (a rectangular bipyramid). Each molecular layerconsists of three atom layers: a central molybdenum layer sand-wiched between an outer sulfur layer and an inner sulfur layer. Eachmolybdenum atom is bonded to six sulfur atoms. The shells are heldtogether by van der Waals forces.

Sub-ångstrom resolution and direct atomic imaging allowed thesuggested atomic structure and stability range of the nanooctahedrato be validated. Because of the large sizes of the nanooctahedra, thenanoparticle structure could not be calculated using full DFT code.Nevertheless, using an approximate DFT model based on DFTBcalculations and MD annealing, a striking correspondence betweenthe experimental images and suggested models was established.

Fig. 1 presents atomic models of MoS2 nanooctahedra alongsidethe projection of their calculated electrostatic potential. The imagecalculations were based on calculated and partially relaxed model

A B C

D E F

Fig. 1. A ball model of a three-shell nanooctahedron envisioned by theoreticalcalculation (15, 16) in the �110� (A) and �100� (D) projections. Mo atoms aredisplayed in red, S atoms in yellow. (B and E) The corresponding calculatedprojected electrostatic potential and (C and F, respectively) HAADF-STEM imageof the structure taken in a probe-side aberration-corrected FEI Titan 80-300electron microscope. The HAADF image approximately represents a projectedmass density map, which is dominated by the Mo skeleton.

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structures using the EMS HRTEM image calculation software (24).In Fig. 1 C and F, corresponding high-angle annular dark-field(HAADF) STEM images show the Mo atoms at the shell edge ofthe structure resolved. The STEM images confirm the hollow shellstructure of the nanooctahedra; in some images the inner partappears opaque, meaning that the nanooctahedra are potentiallyfilled with amorphous Mo-S soot. However, the projected potentialmaps show a difference in brightness in two orthogonal viewingdirections of the octahedron (Fig. 1 A–C and D–F, respectively). Itappears that the signal density inside the particle stems from thedifferent number of vertices and edges that the beam passes in thecentral part; therefore the viewing direction in Fig. 1F shows highersignal in the central part. A large signal in the central part does notnecessarily mean the existence of material inside the particle as itwould be the case for strictly spherical nanoparticles.

Phase contrast imaging was done in an aberration-corrected FEITitan 80-300 microscope with an information limit of 0.8 Å at anoperating voltage of 300 kV to enhance the sensitivity and to imagelight atoms (S). These high-resolution TEM images, taken in thenegative spherical-aberration imaging (NCSI) mode, successfullyreveal details of the atomic structure, including the sulfur coordi-nation. An example is shown in Fig. 2, which presents a comparisonbetween suggested structures calculated by the DFTB method andexperimental images. The structures in Fig. 2 B and E fit very wellwith the apex structure of a calculated model for an octahedralcoordination of the light sulfur atoms, which is characteristic of oneof the most energetically stable structures calculated by the DFTBmethod.

By imaging nanooctahedra structures that lack mirror symmetryrelative to the basal plane of the structure, the existence of lessstable structures from the energetic point of view could also beproven. The existence of structures that are predicted to be ofhigher energy by the DFTB calculations is not surprising in thisexperimental system. The synthetic conditions of laser ablationset-ups are far from equilibrium: the short high-power strikes; thehigh rate of temperature cooling (�10�9 s), and the turbulences inthe reactor impose different environments in its inner space.Therefore, the exact reaction mechanism that leads to the forma-tion of the nanooctahedra remains still an open issue. Recentlyseveral papers were published concerning triangular monolayers ofMoS2 and WS2, which presented both experimental and theoreticalgrounds for the relative stability of such structures (25–28). Ap-parently, these structures are stabilized by the addition of excess Satoms in the form of S2 pairs at the edges. It could be speculatedthat these triangular MoS2�x nanostructures are the building blocksof the system as they are seamed together to form a 3D hollowoctahedron in most cases. In some cases, pentagonal projections

and triangular projections of MoS2 were also detected in the soot,possibly representing a pentagonal bi-pyramid and a triangularprism, respectively, or a distorted version of them also constructedby triangular faces. Moreover, experiments and DFT calculationsindicated that the WS2 (MoS2) triangular monolayers were metal-lic-like as a result of the sulfur pairs at the structure rims (25). Theabsence of the triangular faces in the soot produced by the laserablation experiments may be attributed to the difficulty in detectingthese minute monolayers even with advanced microscopes.

Holographic data of the exit-plane wave function of the electronwave in TEM were retrieved by focal series reconstruction (FSR)(29, 30). For high-resolution TEM, the combination of a spherical-aberration correction in the microscope with the numerical FSRimproved the control and correction of residual parasitic lensaberrations (31). It also increased the signal-to-noise ratio, turningthe electron microscope into a quantitative measurement tool ofhigh precision on the atomic scale (32, 33). These advantages applyto the thin objects studied here because the phase of the exit planewavefunction is linearly related to the projected electrostaticpotential.

Fig. 3A shows a single image of a nanooctahedron from a focalseries and Fig. 3B presents the reconstructed phase from a set of 15images in the series. The enhancement of the signal-to-noise-ratiocan be clearly seen. A slight parasitic twofold astigmatism wascorrected. Unlike the case of a single image, the four shells wereclearly resolved by the FSR. At the edge, the layer structure isresolved; bright atom rows correspond to Mo rows. The neighbor-ing rows of lighter contrast correspond mainly to a densification ofS atoms in the projection. However, in contrast to the 2H bulkmaterial, the parallel alignment of the two inner shells was observedhere.

In summary, the HRTEM study verified the calculated atomicstructure model on an atomic level. It enabled the identification ofa specific model from the proposed 15 models (15). The imaging inan aberration-corrected technique provided a unique opportunityto study the nonperiodic nanooctahedron structure because itallows the light elements and the heavier ones to be imaged in anunmatched resolution. Direct comparison with the atomic structurepredicted by ab initio models was possible mostly in the apices andat the edges of the nanooctahedra, where the overlap was minimalbetween the exit waves scattered from different atoms.

The HRTEM study also provided insights into the generalsymmetric relations of the structures, and revealed the presence ofstructures of higher energy, which are unfavorable by the energeticcalculation. Therefore, it is evident that kinetics plays a major rolein the synthetic process, supported by the presence of several othernanostructures in the soot. The reaction mechanism is still un-known. However, it can be assumed that one of the building blocksof the nanooctahedra are the MoS2 triangular monolayers. Otherfeatures show a deviation from the 2H bulk lattice arrangement.

A B

D

C

E

Fig. 2. Atomic resolution image of a MoS2 nanooctahedron taken in animage-side aberration-corrected FEI Titan 80-300 under NCSI conditions. Fullstructure (A). A magnified part of the tip of the octahedron revealing the sulfuratoms is shown in B and D, with a superposition of the models presented in C andE. The models in C and E correspond to two of the 15 hypothetical structuresproposed in ref. 15. Mo atoms are displayed in red; S atoms are displayed inyellow. In B, one of the most stable structures (no. 5 of ref. 15) coincides, whereasthe less stable structure fails to match (in D).

A B

Fig. 3. Focal series reconstruction of a MoS2 nanooctahedron. (A) NCSI imageof an octahedron taken from a focal series of images recorded using an aberra-tion-corrected FEI Titan 80-300. (B) Image of the phase of the exit-plane wave-function retrieved by focal series reconstruction. The red angles are a schematicrepresentation of the S-Mo-S units.

Bar Sadan et al. PNAS � October 14, 2008 � vol. 105 � no. 41 � 15645

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WS2 Nanotubes. The folding of sheets of WS2 into single- ormultiwalled tubes may result in a multitude of hypothetical atomiccoordinations, similar to their carbon counterparts. A basic ques-tion, which was raised in the past but has yet to be addressed,concerns the chirality of different shells in a single nanotube: Do thenanotubes consist of a single chirality (all of the shells possess asingle chiral angle), or could there be a situation where each shellacquires a different chiral angle? Advanced high-resolution TEMand STEM provide additional information into the real-spacestructure of individual nanotubes, complementing diffraction dataand Moire-based techniques. In particular, this aids real-spaceanalyses of the chirality and registry of the shells.

Already in the first article on CNT by Iijima (34) diffractionpatterns were used to shed light on the chirality of the newlydiscovered structures. Since then, diffraction patterns have beenused extensively in studies on carbon nanotubes (34–36). Diffrac-tion methods were also applied in the past for the elucidation of thestructure of inorganic nanotubes (18, 19, 37, 38). It has been shownbefore that the chirality of the tube can be identified by means ofcertain diffraction spots on the pattern. The relevant spots areproduced by the top and bottom parts of the tube: nonchiral tubesare expected to show the same pattern for the top and bottom parts;therefore, the {hk0} diffraction spots would be superimposed oneach other. However, in chiral tubes where the chiral angle dictatesan opposite orientation in the top and bottom parts there are twosets of {hk0} diffraction spots. This splitting of the {hk0} spotsallows the chiral angle to be estimated, with some measurementerror. If real-space images of the same tube exist, one may also tryto match the diameter of the tube with the chiral angle to uniquelyidentify the tube by its roll-up vector.

Alternatively, the Moire pattern produced by the hexagonallattice in the top and bottom part of a tube (38) could bequalitatively interpreted when combined with the features in real-space images. Fig. 4 shows representative bright-field images of thetwo basic classes of WS2 nanotubes observed in the present study.Armchair and zigzag Moire patterns are visible. When the hexag-onal pattern is oriented in such a way that the edge of the hexagonfaces the tube axis, the pattern represents a zigzag configuration(Fig. 4A Inset). When the pattern is oriented so that the apex of thehexagon faces the tube axis, the pattern represents an armchair tube(Fig. 4B Inset).

Simulation studies have shown that the shifting of the differentshells relative to each other or a slight tilt of the tube relative to thetransmission direction has little influence on the pattern. When achiral shell is introduced into the tube, a rotational Moire patternis formed, and a periodical superstructure can be seen along thetube axis. As the number of chiral shells in the nanotube increases,the Moire pattern becomes less clear and the basic hexagonalpattern eventually disappears. Fig. 5 presents the gradual impactthat the introduction of a chiral shell into the tube has on the

hexagonal pattern. Examining Fig. 4 again, it can be concluded that,because the hexagonal pattern is well preserved, the majority of thenanotubes in the present study consisted mostly of armchair orzigzag shells, with the addition of probably no more than one or twochiral shells. If the chiral shells had different chiral angles, it couldhave been possible to identify two split pairs in the {hk0} spots whenexamining the FFT of the images, but no such splitting was observedin the present study. The bright-field (BF) high-resolution imagesobtained in the present study contribute valuable information thatwas not available before. Using the information from the diffractionpattern alone to determine the number of chiral/nonchiral shells inthe nanotube is not adequate. Fig. 5 shows a few basic features,aiding in the identification of the chiral shells from the nonchiralones. The dotted pattern along the edge represents W atomic‘‘rings,’’ which is typical to nonchiral tubes, where all of the atomsat the ring lie in the same plane normal to the tube axis. A chiraltube produces a bow-like structure at the projected edge, which isimaged at finite resolution as an almost continuous line. The innerhexagonal structure is uniform and perpendicular to the tube axisin the nonchiral tube. In the chiral structure, the inner hexagonalstructure creates undulating rows of high contrast dots that are notperpendicular to the tube axis, forming the Moire pattern. Theover-all appearance changes into a patch-like pattern with alter-nating contrast in the chiral structure.

Fig. 6 shows a single image of a WS2 nanotube from a focal seriesand the reconstructed phase from a set of 15 images in the series.

A B

Fig. 4. HRTEM image of WS2 nanotubes taken under NCSI conditions in anaberration-corrected FEI Titan 80-300. (Insets) An enlarged frame of the Moirepattern formed in the inner of the tube. The schematic drawn hexagons identifyzigzag (A) and armchair (B) tubes.

A

B

C

Fig. 5. High-resolution TEM images of WS2 nanotubes simulated for optimizedphase contrast at negative spherical aberration in an image-side corrected FEITitan 80-300 microscope at an accelerating voltage of 80 kV. Bright contrastcorresponds to projected atom positions. The corresponding W skeleton model isoverlaid on the right-hand side of the images. (A) A WS2 nanotube with fourzigzag shells [roll-up vectors (0, 146) (0, 158) (0, 170) (0, 182)]. (B) A four-shell WS2

nanotube,wherethesecondinnershell is chiral,withachiralangleof6.6° [roll-upvectors (0, 146) (21, 147) (0, 170) (0, 182)]. (C) A four-shell WS2 nanotube, wherethe second inner shell and the outer shell are chiral, with a chiral angle of 6.6°[roll-up vectors (0, 146) (21, 147) (0, 170) (24, 168)].

A B C

Fig. 6. Focal series reconstruction of a WS2 nanotube. (A) NCSI image of WS2

nanotube taken from a focal series of images recorded in an image corrected FEITitan 80-300 microscope operated at 80 kV and (B) the phase of the exit-planewavefunctionretrievedbyfocal series reconstruction.The informationregardingthe chirality and diameter of the shells was used to construct and simulate (C) theHRTEM image of a five-shell tube [roll-up vectors (0, 98) (8, 107) (0, 123) (0, 134)(0, 146)], which is overlaid (B) on part of the exit-plane wavefunction. The chiralangle of the second inner shell is 3.6°. The relative shift of the shells against eachother is depicted by the schematic lines, marking W atom positions at the edge ofthe shells.

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The neighboring rows of lighter contrast correspond mainly to adensification of S atoms in the projection. The FFT of the wave-function presented in Fig. 6B was used to retrieve information aboutthe chiral angle in a manner analogous to the processing of thediffraction patterns. The retrieved chiral angle was calculatedwithin the range of 3–6°. The high-resolution images were used tomeasure the diameters of the concentric shells, and the comparisonof the hexagonal pattern with the calculated nanotubes clearlyindicates that the majority of the shells are zigzag. The fingerprintof nonchiral shells, the dotted pattern along the edge of the shells,was identified and used to determine the chirality of the shells. Itwas concluded that this particular tube consists of three zigzag outershells, followed by a chiral shell and later by at least one inner zigzagshell. A set of several possible nanotubes was suggested, combiningdiameter-matching nonchiral zigzag shells with a chiral shell froma range of possible chiral angles and matching diameter. Thesimulated tubes were compared with the experimental images, andthe best fit is presented in Fig. 6C. The construction of an embeddedchiral shell within several nonchiral shells was found to be repeatingin the observed tubes, regardless of whether the shells were mainlyzigzag or armchair.

The findings in the present study were used to refine the growthmechanism of the tubes: They suggest that, although the growthfront of the nanotubes is probably dictated by the chiral shell, itserves as a template to the inner and outer walls, which are eitherof armchair or zigzag symmetry. The reason for this is the need tolower the energy and maintain the van der Waals distance of 0.62nm between shells, which complicates the matching of chiralitybetween shells. Note that the template chiral wall grows continu-ously, whereas the armchair and zigzag tubes grow stepwise. Thearmchair or zigzag tubes can be more easily adjusted to the requireddiameter because their roll-up vector lies along the lattice basevectors. A refined growth mechanism for the nanotubes wouldinclude the growth of a chiral shell on which rings of WS2 arethreaded, producing concentric shells that form the multiwallnanotubes. This insight is of great importance, because it confirmsthe fact that the outer shells are most likely either armchair or zigzagand not chiral. Therefore, theoretical calculations can be used tounderstand various measurements [e.g., mechanical measurementsof a tensile stress-strain test on individual nanotubes (17)]. Thesecalculations are facilitated using a nonchiral tube because of thecomputation time and complexity. The good correspondence be-tween the model and experimental work can be attributed to thefact that the tensile force is applied on the outermost shell, whichis, in most cases, a nonchiral one and therefore matches thecalculated models, and allows one to conclude that the shell is mostlikely defect free. Furthermore, the destruction mode of thenanotube under critical stress can vary quite dramatically betweenchiral and nonchiral nanotubes. In nonchiral tubes, if a bond in themidpoint between the two edges of the nanotube collapses, thestress is transferred to the neighboring bonds and leads to theirimmediate unzipping. In analogy to the lengthening mode of aspring under tensile stress, the failure mode of the chiral tube doesnot necessarily involve immediate failure of a chemical bond.Instead, it may involve a mechanism whereby the pitch and collapseof the hollow core is lengthened. In the experiments in ref. 15, thefailure mode was associated with the unzipping of nanotube bonds,which strongly suggests that the outermost layer is indeed nonchiral.

Moreover, the difference in chirality inside the tubes, i.e., theexistence of a tube containing adjacent chiral and nonchiral shells,could explain the mediocre electrical performance of the nano-tubes, which were found to be much less conductive than the bulkmaterial (39). This can in turn be attributed to the mobility ofelectrons within the different shells in the tube. The scattering of thedrifted electrons due to the symmetry mismatch between the layerscould explain the reduction in their mobility in the nanotubes.

Regarding quantitative measurements of intershell separations,a large number of HRTEM simulations were performed with

nanooctahedra and nanotubes structures. When these structureswere projected onto a HRTEM image, the measured distances onthe image appeared to be continuously increasing or decreasing,although the structures have evenly spaced shells. Therefore, bulkmeasurements of powder diffraction would lead to more accurateand unambiguous results, as performed previously for onion-likenanoparticles (40). The synthesis process is continuously beingimproved, and it produces bulk quantities of high yield WS2-NT,which enables bulk characterization.

It is worth mentioning that the analysis of diffraction patterns inprevious studies, led to the conclusion that no zigzag or armchairtubes were observed (18, 19, 37, 38). In contrast, most of the tubesin the present study have a majority of nonchiral shells, which couldbe attributed to the merging of diffraction spots into almostcontinuous lines because of the large roll-up vectors of the WS2nanotubes. Therefore, fine details in the principal lines of thediffraction pattern could be hidden, which would make the iden-tification of nonchiral shells complicated. Nonetheless, real-spaceimages can be used to gather more information by examiningindividual nanotubes of interest.

Fig. 7 shows the high-angle annular dark-field (HAADF) STEMimage of the atypical case of a tube with all shells being chiral. Theaberration-corrected HAADF STEM was used because of theclose relation between the images produced and the projectedpotential of the structures. In these images, the signal of a singleatom is strongly dependent on the atomic number Z. The sensitivityto the light elements is lost, in this case with the advantage that theW sublattice is revealed more clearly and directly. The depth of fieldis strongly limited in HAADF, so that the image in Fig. 7 illustratesjust the upper part of the tube. All shells in the tube seem to behelical, with a similar chiral angle that can be retrieved from theFFT using the same procedure described before. The adjacentshells cannot be of exactly the same chiral angle, because this wouldproduce shells with varying distances, some of them much largerthan the bulk value in WS2. Calculations show that some roll-upvectors produce subsequent shells with a shell distance twice aslarge as the bulk value of 0.62 nm. To produce concentric shells inthe right spacing that would match the diameters measured fromthe images, close chiral angles of 2.1° to 2.8° were chosen. Theatomic model was constructed with a left-handed and a right-handed helicity, allowing the helicity to be directly determined. Incorrespondence with previous reports a right-handed helicity wasfound here (37). Very few measurements have been performed onthe handedness of inorganic nanotubes, because they are verydemanding both in terms of imaging and simulation.

In conclusion, this study revealed new information as a result ofthe advanced instrumentation combined with ab initio calculations,

Fig. 7. HAADF-STEM image of a WS2 nanotube taken in a probe-side correctedFEI Titan 80-300 microscope operated at 300 kV. The projected potential of afour-shell tube isoverlaid [roll-upvectorsandchiralangles (4,92,2.1°) (6,103,2.8°)(5,115, 2.1°) (7,123, 2.7°)]. The correspondence between the two in the atomicscale is apparent and the helicity can be clearly seen.

Bar Sadan et al. PNAS � October 14, 2008 � vol. 105 � no. 41 � 15647

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which was then used to refine the established growth mechanism.Furthermore, the study provided new insights into observationsthat remained unexplained until now. In the future, these newmethodologies could be exploited in a generic fashion to examinesamples in simpler, routinely used instruments. Because aberration-corrected microscopy becomes increasingly wide-spread, it is pre-dicted that more of this iterative work between sophisticatedmodeling and atomic resolution will be performed, providing newinsights into the nanoparticle world.

Materials and MethodsWS2 nanotubes were synthesized in a one-step reaction, which is described indetail in refs. 1, 18, 19, and 41. The black soot produced can be directlyattached to a Quantifoil TEM grid or sonicated in ethanol and spread onthe grid.

MoS2 nanooctahedra were prepared by laser ablation using a Nd:YAG laser.The details of the synthesis of MoS2 nanooctahedra are presented in refs. 15and 16.

TEM data of WS2/MoS2 nanoparticles were acquired using a FEI Titan 80-300transmission electron microscope equipped with a double-hexapole aberration-corrector (42) for the objective lens. For single images, negative spherical-aberration imaging (NCSI) conditions were adjusted. At an acceleration voltageof 80 kV, NCSI conditions were achieved at a negative spherical aberration of �52�mbalancedbyanoverfocusof�17nm.Atanaccelerationvoltageof300kV,therespective values were �12 �m and �5 nm.

Focal series reconstruction (FSR) was used to retrieve the phase of the electronexit plane wavefunction (29, 30). Experimental focal series were taken with an

equidistantfocal stepcorrespondingtohalf thedefocusspreadofthemicroscopeat the respective acceleration voltage. Fifteen images were recorded around theNCSI defocus for the phase retrieval, using the Brite/Euram FSR algorithms basedon maximum-likelihood algorithms for nonlinear reconstruction (29, 30).

High-angle annular dark field (HAADF) STEM images were taken using a FEITitan 80-300 electron microscope equipped with a probe-side double-hexapoleaberrationcorrectoratanaccelerationvoltageof300kV.Theprobe-forming lensaberration was corrected to a beam semiangle of 25 mrad, corresponding to aprobe size �0.8 Å. An inner collection angle of 70 mrad of the HAADF detectorassured that the recorded electrons were scattered close to atomic nuclei.

For the simulation study, MoS2 nanooctahedra (up to �103 atoms) werecalculated by the DFTB-MD method. To calculate the structure of larger nanooc-tahedra a phenomenological model based on the DFTB-MD method was devel-oped. Further details on the calculation and construction principles are given inreferences (15, 16). The multislice iteration and the electron optical imaging werecalculated using EMS image simulation software (24). NCSI conditions (43) wereapplied.

Models of WS2 nanotubes were produced by geometrically cutting and rollingan appropriate single monolayer of hexagonal WS2 into a tube. Bulk bondlengths were assumed for the unrolled layer, whereas it was assumed that thesulfur shells were slightly homogeneously strained upon rolling.

ACKNOWLEDGMENTS. M.B.S. thanks Dr. R. Rosentsveig for nanotube samples.R.T. holds the Drake Family Chair in Nanotechnology and acknowledges thesupport of the Harold Perlman Foundation and the Irving and Cherna MoskowitzCenter for Nano and Bio-Nano Imaging. M.B.S. is grateful for the support of theG.M.J. Schmidt Minerva Center for Supramolecular Chemistry. L.H. thanks theGerman Science Foundation (DFG) for their support of sub-ångstrom microscopyat the Ernst Ruska Centre.

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