Article pubs.acs.org/JPCC
Diffraction from Disordered Stacking Sequences in MoS2 and WS2 Fullerenes and Nanotubes L. Houben,*,† A. N. Enyashin,‡ Y. Feldman,§ R. Rosentsveig,∥ D. G. Stroppa,† and M. Bar-Sadan*,⊥ †
Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germany ‡ Physical Chemistry Department, Technical University Dresden, Bergstr. 66b, 01062 Dresden, Germany and Institute of Solid State Chemistry UB RAS, Pervomayskaya Str. 91, 620990 Ekaterinburg, Russia § Chemical Research Support, Weizmann Institute of Science, Rehovot 76100, Israel ∥ Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel ⊥ Department of Chemistry, Ben Gurion University of the Negev, Be’er Sheva, Israel S Supporting Information *
ABSTRACT: MoS2 and WS2 emerge as important materials due to their layered structure, either as molecular sheets or as onion-like inorganic fullerenes. The prominent anisotropy within the materials requires understanding of the layer stacking sequence in order to understand the difference of physical properties of these structures from the bulk materials. Traditional Rietveld refinement in this regime proves to be inadequate to describe the crystallographic structure of these fullerene particles and nanotubes since the results contradict the direct evidence by high-resolution transmission electron microscopy. Another direct method of structure analysis, known as Debye Function Analysis, is used to determine these special features in the X-ray powder diffraction. It is demonstrated that the experimental diffraction intensities are substantially distorted compared to bulk material and that line shapes and intensities are consistent with a random stacking of trigonal prismatic MS2 layers rather than a mixture of hexagonal and rhombohedral bulk phase. We compare experimental with simulated data for fullerenes of MoS2 and platelets and nanotubes of WS2 and discuss the results in relation to growth mechanisms.
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phases produced8,9 and possible structural modification by chemical functionalization. A remarkable example made possible by high-resolution electron microscopy is the deciphering of the registry relationship within the WS2 molecular layers of inorganic nanotubes (INT), in a way that shed light over the mechanical properties and electronic properties and could explain the excellent agreement between the calculated properties and the experimental data. The finding of a single chiral shell within the tube, which may serve as scaffolding for subsequent inner and outer armchair or zigzag layers to form, provided further insight into the reaction mechanism.2 In another example, MoS2 nanooctahedra were produced, and their atomic structure was compared with DFTB calculations that predicted their metallic nature due to lattice defects.10,11 The calculated model was awarded credibility by the atomic resolution images that coincided atom-by-atom with each other.2 This metallic-like structure suggests that the material may have enhanced catalytic properties, a question still open for further research.
INTRODUCTION Low dimensional nanostructures often possess unique properties with respect to the single crystal bulk material; thus, intensive attention is focused on their various applications in material sciences and nanoscale devices, where commercial applications are being explored.1,2 In particular, layered materials have attracted much attention because of the ability to produce either ultrathin films or closed-cage onion structures. Closed cage structures, namely, nanotubes and fullerenes, are an important subgroup of nanostructures. Multiwalled closed-cage, inorganic fullerene-like (IF), nanoparticles of WS2 and MoS2 and nanotubes thereof were discovered in 1992.3,4 They were shown to exhibit very good tribological behavior with numerous potential applications, and with advancements in the scale-up of the synthesis, they can be used as additives to lubricating fluids,5 as self-lubricating coatings,6 and for reinforcing nanocomposites.7 Products based on these new nanomaterials have already been commercialized recently. Chemical modifications, such as functionalization by molecules and by doping principally allow control over the desired properties of the nanoparticles. In order to achieve desirable properties, it is crucial to understand the relationship between a synthetic method and the atomic structures and © 2012 American Chemical Society
Received: August 12, 2012 Revised: October 16, 2012 Published: October 16, 2012 24350
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antiparallel, prismatic parallel, or octahedral parallel coordination, respectively. However, the terms 2H, 3R, and 1T will be used in some places in order to adhere to the terminology used previously in the literature. The techniques that were utilized so far in studying the structure, morphology, and the defects of INT and IF are transmission electron microscopy (TEM), high-resolution (HR)-TEM, and X-ray diffractometry (XRD). Raman spectroscopy has also been applied to detect and to quantify the morphological and structural properties as well as defects in IF and INT.16,18−20 The lack of structures containing the 1T phase in previous reports may be due to a small number of layers, which is under the sensitivity limit of XRD or Raman measurements, or due to the unstable nature of the 1T phase, preventing the formation of multiple 1T shells. It was theorized that the 1T phase may be the result of a transformation from the 3R to the 2H phase by an intermediate 1T phase that is trapped by fast quenching.21 These crystallographic features are the focus of the following experimental and theoretical research, where direct imaging by atomic-resolution transmission electron microscopy is correlated with the existing XRD data and simulations to explain in full the internal structure of the inorganic fullerene-like structures.
Although several synthetic methods have been reported for the production of IF-WS2 and IF-MoS2, reports on their atomic structure are scarce. The reason being that single particle analysis is complicated, and until recently, direct imaging by high-resolution electron microscopy was not available in the required resolution. The main issues of concern are the prevalence of the various phases of WS2 and MoS2, which differ in their coordination and stacking and therefore have different electronic and mechanical properties. In addition, the existence of stacking faults possibly alters the physical properties of the material in the same way as grain boundaries alter the bulk properties in 3D materials. There are three different bulk polytypes of WS2 and MoS2. The more common ones have a prismatic coordination of the sulfur atoms relative to the metal atom (see Figure 1): a
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RESULTS HRTEM Analysis and DFTB Calculations. Inorganic nanotubes of WS2 (INT-WS2),2 onion-like inorganic fullerenes of MoS2 (IF-MoS2),2,22 and hybrid MoS2 nanoparticles comprising octahedra within quasi-spherical shells22 were analyzed. Exemplary TEM images of IF-MoS2 and INT-WS2 samples are shown in Figure 2. Figure 2a,b depicts the closedcage structure of the multishell nanoparticles, whose sizes are typically in the range of a few tens of nanometers. Atomic resolution TEM images of these samples indicate a nearly random sequence of parallel and antiparallel stacking of the molecular layers. Examples for the atomic coordination between the outer shells in INT-WS2 are given in Figure 2c,d. Further examples are shown in the Supporting Information (Figure S1). The result of such direct measurements from HRTEM images of various structures shows that the probability for finding parallel stacking between two layers (such as in the 3R bulk phase) is about 30%, regardless of the morphology of the particle (Supporting Information, Table S1). Calculations based on density-functional tight-binding method with the correction on dispersion interaction23 as well as the calculations by DREIDING force-field method24 did not reveal a significant difference in the total energies of the bulk 2H- and 3R-MoS2 polytypes, i.e., in their relative stability. Depending on the calculation method, the values of the interfacial binding energy are found to be 0.036 eV/atom and 0.043 eV/atom, respectively, which is in agreement with other data.25,26 At the same time, the relative difference between the energies calculated for 2H- and 3R-MoS2 bulk polytypes does not exceed 10−3 eV/atom in both approaches, which is within calculation error. Therefore, the experimental observation of the preference of 2H-polytype in the pure bulk cannot be explained by the enthalpy factor. However, the identical finding for all fullerene-like morphologies may indicate a deeper explanation, which is not yet understood. Previous reports contain contradicting evidence, where some find even domination of the 3R stacking. For example, 3R
Figure 1. The 1T, 2H and 3R polytypes of MoS2 and WS2 viewed parallel to the c-axis. The prismatic sulfur coordination of the common 2H phase and the high pressure 3R phase is opposed to the octahedral coordination in the 1T coordination. Sulfur prisms are aligned antiparallel in the 2H and parallel in the 3R, showing characteristic chevron patterns of the central metal atoms and sulfur in side view.
hexagonal polytype 2Hb with two molecular layers (space group P63/mmc) and a rhombohedral polytype 3R with three molecular layers per unit cell (space group R3m), a high pressure polytype that is stable in plane geometry at pressures above 4 GPa.12 Less common is the octahedral polytype 1T with one molecular layer.13 The two prismatic phases are semiconducting, and the octahedral one is metallic-like. Therefore, the identification of the various configurations give direct evidence for electronic properties, and the boundaries between them may also explain some of the transport and mechanical properties. For example, an intrinsic hybrid metalsemiconductor superstructure can be produced by incorporation of a single 1T layer with dramatic effects on the electronic and optical properties. There is an ongoing discussion in the literature on which bulk phases are the prevalent ones in inorganic dichalcogenide nanoparticles. The high pressure phase (3R) was observed in INT and IF,14−16 which has been interpreted as indirect evidence for very large internal pressures, most likely due to the inherent strain. Another recent report shows that the generally unstable phase (1T) is produced to some minor extent by solar ablation.17 It should be mentioned that, in the INT and IF, the layers are slightly shifted or bent with respect to each other due to shape constraints and thus the stacking cannot be accurately described as pure phase 2H, 3R, or 1T with their perfect translational symmetry. We therefore prefer to characterize the coordination in terms of the principal symmetry of the coordination between the metal and chalcogenide atom, prismatic or octahedral, and the orientation change of this basic unit upon layer stacking. In this notation, the characteristics of the 2H, 3R, and 1T bulk phases are prismatic 24351
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Figure 2. TEM images of MoS2 inorganic fullerenes and WS2 nanotubes. (a) Low-resolution image of an onion-like IF-MoS2 nanoparticle and (b) multiwalled WS2 nanotubes. The atomic resolution images in (c) and (d) show the shell structure of multiwalled inorganic WS2 nanotubes. The atomic model is overlaid on the image to demonstrate the direct imaging of the stacking order within the material. Mo atoms are in red, S atoms in yellow. The chevron pattern points out the alignment of the layers with respect to the sulfur coordination. In image (c) mixed parallel and antiparallel alignments are visible; in image (d) antiparallel alignment is dominant.
stacking was found to be dominant on the outer part of microtubes27 and the 2H layer stacking and “radial disorder” was attributed to stacking faults in the outer layer of nanotubes grown from iodine chemical transport. Zink et. al15 report that for MOCVD grown IF-WS2 powder, Rietveld refinements indicate that the 3R variant predominates (about 60−80%), while the 2H variant is the minority component in as-grown samples. However, in annealed samples, the crystal structure was found to change to the 2H polytype since a crystallization process favored the thermodynamically more stable 2H polymorph. Deepak et al. conclude that 3R stacking is favored in the cap structure of MoS2 nanotubes grown by the sulphidization of as-synthesized MoO3 nanobelts.28 Reports from Tenne and co-workers point to a 2H stacking polytype according to the XRD measurements.29 We find the interpretation of the experimental data partially contradictive because the modeling on the basis of periodic bulk structures is insufficient. Therefore, it is important that a refined structure analysis is used to explain the contradictive experimental data and especially to correlate XRD powder diffraction data collected from an ensemble of particles with the direct images of single structures in the TEM. XRD Diffraction Simulation. One of the common uses of XRD data is to estimate the existence of certain phases within the sample and to estimate the ratio between them. This is usually done by comparing a diffractogram to that of the bulk phases. Each of the phases is assumed to contribute in a linear way to the overall signal, which is indeed a viable assumption for finely divided matter when each of the phases is represented by large blocks as is shown schematically in Figure 3a. Care has
Figure 3. Schematic representation of stacking disorder in layered materials: when the two phases are arranged in large blocks (a), the linear superposition of their bulk diffraction patterns is a viable procedure, but when the different phases are blended into each other (b), a Debye scattering model is better suited to describe the diffractogram.
to be taken, however, when interpreting diffraction from nanoparticles. Assumptions typically made for finely divided matter are not necessarily valid in the nanometer range.30 When a random, stochastic arrangement of layers is involved (see Figure 3b for a schematic example), the above-mentioned procedure is most likely to fail. The nanoparticles differ from bulk crystal structures: their layers do not necessarily form the thermodynamic stable phase, and stacking defects may occur, such as slight layer shifts and rotations. These small changes break the symmetry of the overall nanocrystal in such a way that the structure factor of a unit cell of the bulk crystal is not representative anymore for the nanoparticle. The corresponding diffraction pattern contains deviations from the bulk 24352
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Figure 4. Diffraction pattern simulation of MoS2 of various stacking arrangements. (a) Simulated pattern of pure 2H-MoS2 and of pure 3R-MoS2 compared to configurations with random stacking of MoS2 layers. The staggered lines present the random incorporation of parallel layers within an antiparallel lattice, in the probability p of 0.3, 0.5, and 0.7, respectively. (b) Result of the Debye scattering calculation for p = 0.3 compared to the conventional approach of a linear superposition of powder patterns calculated for a mix of 70% 2H and 30% 3R (which should be equivalent to the previous case of p = 0.3) bulk material with a corresponding size broadening.
shown in Figure 3. As explained above, the random stacking does not produce the same diffraction data as the linear sum of the two extreme cases of 2H and 3R stacking. Figure 4b compares between the diffractograms of the two models, the Debye approximation and the linear model of finely divided matter. In Figure 4a, different random mixtures of the 2H and 3R stacking are presented, showing the change of the diffractogram with the different composition of the sample. The most important feature to bear in mind is that the internal structure of each individual layer remains perfectly intact. The simulation only assumes different orientations between the layers: either by shifting or by placing them parallel/antiparallel, one relative to the other. Therefore, it is not surprising that the signal of reflections that express symmetry relationships between the layers is significantly altered when a random stacking model is assumed, contrary to the linear superposition model. For the interlayer reflections characteristic for the 3R parallel symmetry, we observe the following: while in the linear model, the {104}3R, {105}3R, {107}3R, and {108}3R reflections are preserved, in the more realistic Debye simulation they are eliminated completely due to the introduction of random stacking. Therefore, if the linear model is assumed, the absence of these symmetry peaks will be interpreted as an absence of the 3R phase altogether, while in fact the structure contains 30% of parallel alignment. In addition, there is a decrease in the relative intensity of 2H interlayer reflections peaks, i.e., peaks that correspond to mixed in-plane and out-of-plane components of the 2H symmetry ({102}2H, {103}2H, {105}2H, and {107}2H). This is simply due to the loss of a distinct symmetry relationship between the layers. There is also a considerable broadening of the {102}2H peak at 37° (2θ Cu Kα) and a pronounced increase of the intensity of the {006}2H and {009}3R peak at 44°. The latter is partially because of an increased scattering factor of the nearly forbidden {104}2H reflection in the 2H polytype. In accordance with literature, the disorder is also manifested in a broader background curve between 30−55°.33
diffraction that are not described accurately merely by shape or size broadening. Naturally, stacking disorder is also present in large crystals, but the signal mainly probes the bulk-like areas of the sample, and it is assumed that additional signal from stacking disorder is negligible. The alternative way to simulate powder diffraction patterns of MX2 nanoparticles, which is presented here, is in accordance with the earlier calculations for exfoliated MX2 layers by Yang et al.31 It is based on the Debye scattering equation,32 which predicts the scattered intensity in powder diffraction patterns to first order from gases, liquids, and randomly distributed nanoclusters in the solid state. The Debye equation is given by N
I (g ) =
N
∑ ∑ fi (g )f j (g ) i=1 j=1
sin(2πgrij) 2πgrij
(1)
where g is magnitude of the scattering vector in reciprocal lattice distance units, N is the number of atoms, f i(g) is the atomic scattering factor for atom i as a function of g, and rij is the spatial distance between atom i and atom j. The latter approach therefore allows us to calculate the diffraction pattern for a specific supercell, which is not periodic. The advantage is the ability to sum over a gallery of different supercells, which represent the different possible configurations, and obtain a representative diffractogram for the full gallery of cases. For the numerical computation, we chose a more efficient implementation based on pair distance histograms. The pair distances between atoms i and j were binned in a histogram to speed up computation. Thereby, supercell sizes of more than 10 × 10 × 10 nm3 containing about 90 000 atoms each could be implemented. Disorder was introduced by stochastic construction of a set of supercells with different atomic configurations. Convergence of the diffractogram was typically achieved after integration of about 40 supercells, corresponding to the summation of more than 1011 pairwise scattering amplitudes in the Debye scattering equation. As an example, we compare the two approaches for a situation where the parallel stacking may occur with 30% probability (p), in a similar way to the schematic structures 24353
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Figure 5. (a) Experimental X-ray diffraction pattern of a WS2 platelet sample (black solid line) and a matching simulated diffraction pattern of WS2 with 2H layer stacking (red dashed line). (b) Diffraction patterns simulated for WS2 with random stacking disorder. The probability p is a measure of the fraction of parallel layer stacking disorder. The layer stacking with p = 0 corresponding to a pure 2H crystal gives the best match with experiment.
of platelets. The simulated powder diffraction pattern for a pure 2H lattice configuration of WS2 is superimposed. The small differences in the peak broadening are most likely due to the limited number of atoms in the simulation compared to the physical dimensions of the platelets (the calculation was performed for a maximum particle volume of 1200 nm3). In the case of the platelets, the best match between simulation and experiment is achieved for a pure 2H phase. Figure 5b shows for a qualitative comparison the changes in the diffraction pattern of a WS2 platelet with the addition of random parallel stacking. The probability for random stacking is p, and as the value of p reaches 1, the structure transforms into the 3R stacking. Just like in the case of the MoS2 (Figure 4), the lattice reflections with indices {10k}2H, k > 0, are strongly broadened and dampened. None of these effects are seen in the experimental data of Figure 5a nor is there evidence for 3R stacking in the platelet experimental data. Therefore, it is obvious that the simulation should provide the capability of detecting the random parallel stacking of WS2 and MoS2, but it does not falsely detect parallel stacking when it is not present. Comparison with Experimental Data for IF-MoS2 and INT-WS2. Experimental diffraction data of IF-MoS2 grown in a sulfidization reaction from molybdenum oxide34 is shown in Figure 6a. The features in the spectrum can now be related to disorder: increased background signal between 30° and 50° in 2θ, the considerable broadening of the {103}2H peak and {105}2H peak with reference to a pure 2H phase, and the suppression of the {102}2H peak at 36°. These peculiarities are matched by the simulated data for a random stacking with ten layers and a probability for parallel stacking around 40%, which is presented in Figure 6a alongside the experimental data (solid line). In order to provide a quantitative matching of simulated data with a specific probability for parallel stacking, we compare the mean square difference between the experimental data and the simulated data, for different probabilities of parallel stacking (p). The mean square difference was calculated within the angular range between 2θ = 30° and 2θ = 64°, after normalization of the total diffraction intensity (Figure 6b). According to the simulation data, the diffraction signal is almost a constant in this angular range. The graph shows a distinct
Even the internal symmetry of the layers of such a random stacking sample may be reproduced with artifacts; although in the supercells, the internal parameters of the layers were kept intact at bulk values. In such a sample, there is an apparent shift of up to 1% of the a lattice parameter, due to a shift of the {100}2H reflection. It is clear that this artifact does not represent a physical change of the sample (i.e., a compressive in-plane strain). Such a shift was already predicted by Levy et al.33 Therefore, the simulation is extremely useful in differentiating between real phenomena and misinterpretation. Since neither peak shapes nor peak intensities of a diffraction pattern of disordered MX2 can be modeled by a linear superposition of bulk reference data, refinement approaches based on linear modeling like Rietveld refinement have to be interpreted with care with regards to physical parameters. Unrealistic size or strain broadening may be required to match experimental data with the insufficient model. The main features that may aid in the quantitative estimation of the stacking disorder are the vanishing of the {102}2H reflection together with the increased intensity of the {006}2H or {009}3R peak. In addition, the broadening of the {103}2H or {105}2H is also noted. Figure 4b presents the simulated Debye diffraction patterns of different mix ratios between the parallel and parallel alignments. For a probability of 30% to find parallel stacking (p = 0.3), the {102}2H reflection is still apparent, and the {006}2H or {009}3R peak is strongly enhanced. When there is an equal probability for a parallel and parallel stacking (p = 0.5), the {102}2H reflection vanishes completely. Only when p = 0.7, the typical 3R reflections ({104}3R, {105}3R, {107}3R, and {108}3R) are visible. Therefore, the matching of these features may allow for quantitative estimation of p. Comparison with Experimental Data for Platelets of WS2. The commercial material of WS2 consists of platelets (micrometer sized) with free open edges, in such a way that no restriction is made to translations of one molecular layer relative to the adjacent one. The case of the closed-cage structures is very different because of the seaming of the facets, one to the other, which produces strict boundary conditions. We have used the polycrystalline WS2 platelets as a control experiment, where we should only observe 2H features. Figure 5a shows an experimental X-ray diffraction pattern of a powder 24354
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Figure 6. (a) Experimental diffraction pattern of thermally annealed IF-MoS2 nanoparticles (black solid line) and a matching simulated diffraction pattern of MoS2 with random stacking disorder for p = 0.4 (red dashed line). (b) Residual square error for the optimization with the random stacking model (solid black curve) in the angular interval between 2θ = 30° and 2θ = 64°, χ2, as a function of the stacking disorder parameter p. For comparison, the red dashed line shows the residual square error, divided by a factor of 10, for the linear superposition of diffractograms for the 3R and 2H bulk phases where p is the volume fraction of the 3R phase.
compared to bulk values. These facets therefore contain negligible rotational disorder since they have the constraint of reaching the edge with a specific configuration to allow seaming; a constraint that is absent in restacked freely standing layers. A dominance of 3R phase as concluded in ref 22 is not in accordance with our data: 60−80% of 3R phase contribution would lead to a splitting of the {103} peak (see above), which is in contradiction to experiment. The broadening of the diffraction peaks is a pure consequence of stacking disorder. An important observation is that incommensuration of the layers, which is naturally more pronounced at small particles that are more curved, produces shifts of the layers relative to their adjacent layers and prevents the formation of a pure 2H or 3R symmetry. However, the small particles in the sooth contribute to the signal as weak background since the XRD pattern mainly probes the larger particles because of the proportionality between the scattering intensity and the number of atoms. In contrast to the inorganic fullerenes, nanotubes form bent layers, which introduce more disorder into the system. In the nanotubes case, stacking disorder is no longer sufficient to model the X-ray diffraction data, and bending has to be included in order to achieve satisfactory description of the experimental diffraction data of WS2 nanotubes with diameters of dozens of nanometers. This is probably because the diameter of the nanotubes is smaller than that of the IF, i.e., their curvature is larger. As mentioned above, smaller nanotubes have a high degree of disorder between the shells, so that the reflections that contain mixed in-plane and out-of-plane components (i.e., are dependent on the orientation of one layer relative to its adjacent one) get completely smeared. Figure 7a displays experimental X-ray diffraction data of inorganic nanotubes of WS2 (INT-WS2), with relatively large diameters.36 Comparing the INT-WS2 diffraction data with the data for the annealed IFMoS2 in Figure 6a, there is evidence for more substantial dampening and broadening of the {103}2H and {105}2H reflections. The simulation, which is superimposed on the
parabolic shape, with a minimum at 40% probability where the simulated pattern and the experimental pattern match the best. The match between simulation and experiment is significantly better for the random stacking model compared to the linear superposition: the residual square error when taking the linear superposition is an order of magnitude larger than that of the random stacking model we propose in the present article. In other words, the fit between the random stacking model and the experimental data is by far better than a superposition of the pure phases in their relative ratios. Another misfit of the linear superposition is the value of the parallel/antiparallel ratio that best matches the experimental data. Therefore, although a minimum can be reached by optimization, the linear superposition model provides the minimum at a much higher 3R content, which is essentially an artifact. The random stacking model does not reproduce the sharp {100}2H and {006}2H reflections in the experimental data, due to the limited number of atoms, i.e., layers in the supercell. However, the random stacking disorder model with the limited number of atoms in the supercell (81 000) is almost sufficient to describe the experimental data. In additional simulations, rotational disorder and layer bending were included, but we found that these disorder terms were small and negligible. Rotational disorder does not lead to the cancellation of the {102}2H reflection that we observe in experiment and can be explained by random stacking. This means that, in contrast to reported evidence for dry restacked MoS2 platelets where rotational disorder was found,35 in the present study we find that domains of nearly perfect alignment are present in the IF-MoS2. The experimental XRD data reflects a volume weighted average, and this is dominated by the larger MoS2 IF particles in the sample powder. The larger particles contain relatively large and flat facets. The bending energy of MoS2 is usually high enough to prefer morphology of flat facets, which are seamed at their edges to close the structure into an onion-like shape in large particles (>100 nm) or octahedral shape (
