Strain-induced phonon shifts in tungsten disulfide nanoplatelets and nanotubes

The relationship between structure and properties has been followed for different nanoscale forms of tungsten disulfide (2H-WS2) namely exfoliated monolayer and few-layer nanoplatelets, and nanotubes. The similarities and differences between these nanostructured materials have been examined using a combination of optical microscopy, scanning and high-resolution transmission electron microscopy and atomic force microscopy. Photoluminescence and Raman spectroscopy have also been used to distinguish between monolayer and few-layer material. Strain induced phonon shifts have been followed from the changes in the positions of the A1g and E 2 g 1 Raman bands during uniaxial deformation. This has been modelled for monolayer using density functional theory with excellent agreement between the measured and predicted behaviour. It has been found that as the number of WS2 layers increases for few-layer crystals or nanotubes, the A1g mode hardens whereas the E 2 g 1 mode softens. This is believed to be due to the A1g mode, which involves out of plane atomic movements, being constrained by the increasing number of WS2 layers whereas easy sliding reduces stress transfer to the individual layers for the E 2 g 1 mode, involving only in-plane vibrations. This finding has enabled the anomalous phonon shift behaviour in earlier pressure measurements on WS2 to be resolved, as well as similar effects in other transition metal dichalcogenides, such as molybdenum disulfide, to be explained.


Introduction
Tungsten disulfide (WS 2 ) Transition metal dichalcogenides (TMDs) have been used widely as solid lubricants [1] and chemical catalysts [2] for many years. Interest in them has, however, grown rapidly over recent years with the explosion of research into 2D materials. This is because TMDs, unlike graphene, have a tuneable bandgap, a transition from an indirect to a direct bandgap with a reducing number of layers [3,4] and strong spin-orbit coupling arising from broken inversion symmetry [5]. These particular properties have made TMDs very promising candidates for optoelectronic and electro-mechanical applications. The class of materials is usually expressed as MX 2 , where M is a transition metal atom, such as Mo, W, Nb, etc and X represents a chalcogen atom, for instance S, Se, etc. Although the number of known combinations of MX 2 has exceeded 40 species, not all of them are of particular interest. Some are unstable under ambient conditions, react rapidly with the atmosphere and thus lose their special properties [6]. Hence, most research has focused upon the limited number of stable materials that includes WS 2 , molybdenum disulfide (MoS 2 ), WSe 2 and MoSe 2 . Among this group of materials, WS 2 has drawn particular attention as a result of its unique optical [7], thermal [8] and electronic [9] properties.
The crystal structure of WS 2 involves the stacking of sheets consisting of W atoms sandwiched by two planes of S atoms packed into an individual layer of WS 2 . In contrast to graphene, WS 2 exhibits a variety of polymorphs where tungsten atoms are covalently bonded to six adjacent sulfur atoms with their coordination as either trigonal prismatic or octahedral (sometimes referred to as trigonal-antiprismatic). In terms of the stacking sequence, the most extensively studied polymorphs are 2H-and 3R-WS 2 where H and R represent hexagonal and rhombohedral forms respectively and the digits denote the numbers of layers in the unit cell. The individual layers are held together through weak van de Waals forces that result in the application of TMDs as solid lubricants, similar to graphite. As the result of thermodynamic factors, the 2H stacking sequence is the most commonly-encountered crystalline form of WS 2 [10]. It belongs to the P6 3 /mmc space group with lattice parameters of a=0.31532 nm and c=1.2323 nm measured by x-ray diffraction [11].
Analogous to graphene, which is considered to be the building block of other sp 2 carbon allotropes, WS 2 is also found in different morphological forms such as inorganic fullerene-like nanoparticles and inorganic WS 2 nanotubes. The WS 2 nanotubes are generally considered to consist of a number of layers of WS 2 nanosheets wrapped into a 1D tubular form. They are found mostly as multiwall nanotubes, similar to those of MoS 2 , with the number of sheets in the shells normally greater than four [12]. It was not until 2001 that Whitby et al [13] managed to synthesize single-wall WS 2 nanotubes by employing multiwall carbon nanotubes as a template. Recently single-to three-wall nanotubes of WS 2 were synthesized by high power plasma irradiation of multiwall nanotubes [14]. The difficulty of producing single-wall WS 2 nanotubes was attributed to the poor stability of single-wall materials [12] and the need for highly exergonic conditions during the reaction [14]. The inter-shell distance of multiwall WS 2 nanotubes is found to be constant throughout the walls and similar to or slightly higher [15] that of multi-layered WS 2 (c/2). Regardless of the number of layers, the inner diameter varies over the range ∼6 to ∼12 nm. It has a value close to 7 nm for shell numbers less than 10 and a value of the order of 10-12 nm for shell numbers above 10, as the result of strain energy effects resulting from curvature of the WS 2 layers [12].

Preparation methods
As the result of the layer-dependent properties of WS 2 , a number of different techniques have been employed to prepare exfoliated WS 2 . The 'Scotch tape' mechanical exfoliation technique developed initially for the preparation of graphene is still exploited extensively in TMD research. It is the most efficient and straightforward preparation method and the specimens produced via this method possess a pristine structure that is ideal for fundamental studies of their intrinsic properties [16]. Monolayer WS 2 flakes can usually be identified and located using optical microscopy [17]. Despite the high efficiency and viability of the technique, it is difficult to scale up. Consequently this limits its use for the preparation of large quantities of material. Additionally, compared to MoS 2 , crystals of WS 2 seem to be more difficult to exfoliate with this approach [18].
Another top-down preparation method is liquid phase exfoliation, where monolayer WS 2 can be obtained through sonication treatment in appropriate organic solvents [19] or aqueous solvent with aid of various surfactants [19]. This is a promising way to produce a large quantity of exfoliated WS 2 nanosheets and the resulting suspension is convenient for producing nanocomposites, thin films and coatings. Nevertheless, some applications of such products may be limited because the typical lateral size of monolayers produced by this method is only a few hundred nm [19] and larger flake sizes (typically>1 μm) are needed some applications, such as nanocomposites. A more viable method is intercalation that reduces the exfoliation barrier by intercalating ionic species into the interlayer spaces [19,20]. This was firstly demonstrated on TMDs using lithium by Danis et al in 1972 [21] and later, was used to obtain monolayer of MoS 2 by Morrison et al in 1986 [22].

Electronic properties
The electronic structures of TMD materials have been studied extensively using first principles calculations or tight-binding approximations and characterised with a variety of spectroscopic tools [23][24][25]. WS 2 , a typical member of the TMDs MS 2 family, shows semiconducting behaviour under ambient conditions similar to MoS 2 . There is strong interlayer coupling in WS 2 and it undergoes a significant transition from an indirect band gap to a direct one with a decreasing numbers of layers [23]. Similar to graphene and other semiconductors, the mobility of the carriers in 2D TMDs including WS 2 is governed mainly by the following scattering processes: (1) acoustic and optical phonon scattering; (2) Coulomb scattering at charged impurities; (3) surface interface phonon scattering and roughness scattering [26][27][28][29].
Due to its superb electrical mobility and massless carrier properties people have sought to use graphene in different electronic devices, especially in transistors. However, the absence of a bandgap essentially makes graphene unsuitable for applications such as digital logic transistors. Semiconducting TMDs materials, including WS 2 , with a sizable bandgap and high carrier mobility have therefore become very attractive for use in transistors. Since the electronic properties of WS 2 are very layer dependent, people have examined the properties of WS 2 over a range of layer thicknesses. The transition from an indirect to a direct bandgap found on reducing the number of layers of WS 2 leads to an intense single peak profile observed in the photoluminescence (PL) spectrum of monolayer WS 2 [3,30,31]. This strong PL is a characteristic feature of monolayer WS 2 and has been used widely to determine the layer number, quality and uniformity of WS 2 materials.

Raman spectroscopy
Raman spectroscopy is a powerful and versatile tool to study 2D materials such as graphene and 2D TMDs. It has been used widely in probing structural information such as the number of layers, defects, doping levels, strain effects and other factors. Similar to MoS 2 , bulk WS 2 belongs to the D6h point group, exhibiting A 1g , 2A 2u , 2B 2g , B 1u , E 1g , 2E 1u , 2E 2g and E 2u vibrational modes, where only the A 1g , E 1g and 2E 2g modes are Raman active [32,33]. In monolayer WS 2 , the unit cell is composed of three atoms with nine vibrational modes at the Γ-point based on D 3h symmetry, which are namely  2A , 2 A 1 ′, 2E′ and E″. Among these modes, the A 2 ″ mode is infrared active, A 1 ′ and E″ are Raman active and E' is both Raman and infrared active. In this work, the same terminology will be used for these in monolayer and in the bulk as is commonly done in the literature [5,7,[34][35][36]. In the back scattering configuration of Raman spectroscopy, the E 1g mode is forbidden. The E 2g 2 mode, also referred to as a shear mode, is found at very low frequency and usually blocked by the notch filter [37]. Therefore, E 2g 1 and A 1g are the most significant modes found in WS 2 Raman spectra.
The Raman spectrum of bulk WS 2 , using a 514 nm laser excitation, comprises two major bands corresponding to E 2g 1 at ∼351 cm −1 and A 1g at ∼420 cm −1 . Due to the heavier mass of the W atom, the phonon bands in WS 2 are shifted to lower frequencies in comparison to MoS 2 [35]. Together with the major bands, a rich spectrum of second order bands is also observed. These second-order Raman features are seldom studied due to band overlap. For example, the longitudinal acoustic phonon mode (2LA) is very close to the E 2g 1 band (within ∼5 cm −1 ), causing ambiguity in investigations of the E 2g 1 mode [38]. Only recently, studies were conducted focusing on the 2LA mode in terms of its polarisation dependence and the effect of layer number [36,38]. Regarding WS 2 nanotubes, the spectra show no significant differences or additional peaks when compared with the bulk materials. Only minor shifts in the position of the E 2g 1 and A 1g bands have been found due to strain effects [39]. Staiger et al [40] also pointed out the presence of an emerging B 1u mode in WS 2 nanotubes, that is silent in bulk crystals, and explored its relationship with the nanotube geometry and excitation energy.
As bulk WS 2 is thinned down to monolayer, the phonon modes are expected to soften due to the decreasing number of layers weakening the interlayer interactions [38,41]. This indeed is the case for the A 1g mode where, from bulk to monolayer, a red-shift of ∼3 cm −1 occurs. In contrast, an anomalous phenomenon has been found for the E 2g 1 band, where a minor blue-shift (∼0.5 cm −1 ) is observed for monolayer [41]. Similar behaviour is also observed in MoS 2 and other TMDs [41,42]. Such anomalous behaviour allows Raman spectroscopy to be utilized as a characterisation method for the number of layers in WS 2 [36,38]. In addition to the band shifts discussed above, the intensity ratio of the modes E 2g 1 /A 1g shows a layer dependence which varies slightly with laser excitation. Molina-Sánchez et al calibrated the number of layers using vibrational frequency differences, mostly between A 1g and E 2g 1 bands [35]. It should be noted, however, that none of these methods alone is absolutely reliable due to subtle shifts of the E 2g 1 and A 1g peaks and interferences brought about by adjacent second-order bands in WS 2 . Overall, it is better to use them in conjunction with other characterisation methods such as atomic force microscopy (AFM) and TEM.
The Raman spectra of TMDs are very sensitive to external perturbations such as temperature, strain and magnetic fields. Several groups have undertaken research into the effects of these factors, particularly strain, on the electronic structure, phonon vibrational modes and interaction of phonons and electrons in TMDs using Raman spectroscopy [43][44][45][46][47][48][49]. The majority of the studies have been undertaken on MoS 2 which gives well-defined band shifts under strain. Rice et al [46] reported uniaxial strain induced phonon softening in monolayer and few-layer MoS 2 . They found shift rates of −0.4 cm −1 /% strain for the A 1g mode in both mono-and few-layer crystals and −2.1 cm −1 /% strain, −1.7 cm −1 /% strain for the E 2g 1 mode in monolayer and few-layer crystals respectively. The E 2g 1 mode is believed to be more sensitive to uniaxial strain since its corresponding in-plane vibrations whereas the A 1g mode is perpendicular to the crystal plane. Moreover, a splitting of the E 2g 1 mode was observed in a similar experiment when strained up to 0.8%, indicating the removal of degeneracy arising from the breaking of symmetry by strain [45,47]. In addition, Nayak et al demonstrated a pressure-induced semiconducting-to-metallic transition in few-layer MoS 2 using ultra-high hydrostatic pressure (35 GPa) indicating the successful modulation of electronic structure with strain [43]. A similar pressure-induced transition was later achieved in few-layer WS 2 , showing similar behaviour to MoS 2 [44]. Similar levels of stress-induced Raman band shifts were predicted for both MoS 2 and WS 2 nanotubes by Ghorbani-Asl and coworkers [49]. Recently, a detailed study has been undertaken of the high-pressure vibrational properties of WS 2 nanotubes using synchrotron-based infrared and Raman spectroscopies [48]. It was found that most of the vibrational modes showed a similar hardening trend with their vibrational frequencies increasing with pressure, with the exception of the A 1g mode which exhibited strong pressure sensitivity.

Mechanical properties
The number of investigations that have been undertaken upon the intrinsic mechanical properties of WS 2 is very limited. Initial experiments were undertaken upon WS 2 nanotubes using a very delicate methodology developed for the study of carbon nanotubes where AFM and in situ scanning electron microscopy (SEM) were used synchronously to determine stress and strain, as well as to gain an insight into the deformation process [50][51][52]. It is found that WS 2 exhibits a high value of Young's modulus in range of 150-170 GPa, a shear modulus of 2 GPa, a high strength of ∼16 GPa and an impressive fracture strain at 14%. This value of Young's modulus is in good agreement with theoretical predictions, implying a low level of defects [51]. The good performance of WS 2 nanotubes is comparable to that of strong conventional materials such as steel, aramid fibres and some classes of carbon fibres. In particular, however, the 14% strain to failure is a feature unique to all nanotube materials [50]. People have also conducted pressure studies on bulk WS 2 using x-ray diffraction to monitor changes in the a and c lattice parameters [53]. The bulk modulus was determined to be K 0T =61 ± 1 GPa with K′ 0T =9.0 ± 0.3 GPa. Furthermore, the c-direction of the hexagonal crystal structure was found to be much more compressible than the a-direction. With research interest sparked into 2D TMDs, their intrinsic mechanical properties have been investigated more recently [54,55]. Liu et al [54] studied the elastic properties of WS 2 , MoS 2 , graphene and their bilayer heterostructures(in the a-b plane). It was found that the 2D moduli of MoS 2 and WS 2 are very close, giving values of 171±11 N m −1 and 177±12 N m −1 respectively, half of that of graphene (349±12 N m −1 ).
The present study aims to understand the structure-property relationships in the different forms of WS 2 . This has been undertaken by firstly characterising the structural similarities and differences between the structure and properties of exfoliated monolayer and few-layer WS 2 nanoplatelets, and WS 2 nanotubes using a combination of high-resolution TEM and Raman spectroscopy. The effect of deformation upon these materials has then been followed from straininduced Raman bands shifts that have been related to change in the phonon modes of WS 2 crystals with deformation predicted using density functional theory.

Materials
The few-layer WS 2 nanoplatelets were prepared on a Si/SiO 2 substrate by tape exfoliation from WS 2 crystals with an average grain size of 200 μm supplied by HQ Graphene, Groningen, the Netherlands. An AFM (Bruker Dimension 3100) operated in the tapping mode was used to determine the thickness of the exfoliated WS 2 nanoplatelets on the Si/SiO 2 substrate. The WS 2 nanoplatelets were also examined by SEM (Philip XL30 FEG-SEM) using an accelerating voltage of 8 kV on the Si/SiO 2 substrate after coating with gold to reduce charging.
The WS 2 nanotube samples were synthesized by a bottom-up solid-gas reaction for which the detailed growth reaction is given in another publication [56]. In this processs, tungsten oxide nanoparticles of ∼100 nm in diameter were used as a precursor to react with hydrogen (H 2 ) and hydrogen sulfide (H 2 S) gases at a temperature of 750°C-840°C. The reaction proceeds in a one pot mode from the growth of suboxide nanowhiskers to beyond full oxide-to-sulfide conversion and the formation of hollow WS 2 nanotubes. The technique can produce nanotubes with different dimensions but in this study we have confined our investigations to thick (50-150 nm) and long (micron dimensions) nanotubes consisting of many (>20) layers.
Similar characterisation techniques as those used for the WS 2 nanoplatelets (SEM and AFM using the same instruments) were employed to characterise the morphology of the nanotubes. A nanotube/acetone suspension was prepared using a 30 min sonication bath to break the bundles and achieve a homogenous suspension. The SEM and AFM specimens were then produced by drop casting the nanotube/acetone suspension on to a Si/SiO 2 substrate and characterised in the same way as the WS 2 nanoplatelets described above.

Transmission electron microscopy
The WS 2 nanoplatelets were exfoliated onto a Si/SiO 2 substrate as described above. The deposited flakes were then transferred to a lacey carbon Cu TEM grid via a polymer-free technique. The nanotubes were prepared by sonication in de-ionised water for 15 min before being dropped via a micropipette onto a Cu quantifoil TEM grid. The solution was left to dry on a hot plate for 5 min at 100°C. The TEM used during this project was a JEOL 2100 field emission TEM, operated at an accelerating voltage of 200 kV. All TEM images were taken using phase contrast imaging in a bright field detector, with acquisition times between 0.5 and 2.5 s.

Raman and PL spectroscopy
Raman spectroscopy employing a laser excitation of 514 nm was used initially to characterise the structure of the WS 2 nanoplatelets and nanotubes on Si/SiO 2 substrates. The specimens that were employed in the Raman experiments were also used for the AFM studies. Spectra were obtained using a Renishaw 1000 Raman spectrometer with a 50x objective lens giving a laser spot size of the order of 1-2 μm. To prevent radiation damage and undue specimen heating the power of the laser beam kept below 1 mW. PL spectroscopy was employed in order to identify monolayer regions in thin exfoliated crystals using a Horiba LabRAM HR Evolution spectrometer with the 488 nm line of an argon ion laser.
In situ deformation studies were undertaken in the same Raman spectrometer. In this case the WS 2 nanoplatelets and nanotubes were deformed on the surfaces of a poly(methyl methacrylate) PMMA beams. The WS 2 nanoplatelets were transferred to the PMMA beam surface after mechanical tape exfoliation from the WS 2 crystals and deformed without the application of any further coating. In the case of the WS 2 nanotubes, they were drop casted onto the PMMA beam surface from a nanotube/ethanol suspension and then first deformed on the beam with no top coat of resin. Subsequently, a WS 2 -nanotube/epoxy solution with a nanotube loading of 0.5 wt% (relative to the epoxy resin) was prepared and spin coated onto a PMMA beam coating and then allowed to cure for 24 h at room temperature. The three different types of specimen used in the deformation studies are shown schematically in figure 1 and the experimental set-up is illustrated in figure S1 of the supporting information.
The PMMA beams were deformed using the fourpoint bending rig on the specimen stage of the Raman spectrometer with the direction of laser polarisation parallel to the tensile axis. The position of different WS 2 Raman bands from the nanoplatelets and nanotubes was determined as a function of strain. Spectra were obtained from the centre of the nanoplatelets and from individual nanotubes lying in a direction parallel to the tensile axis. A resistance strain gauge linked to a multimeter was attached to the tensile surface of the beams to monitor the strain on the beam surface. As the thickness of the WS 2 nanomaterials was several orders of magnitude thinner than the PMMA beam, bending the beam led essentially to the application of uniaxial strain through the PMMA substrate using the bending rig. The strain was capped at around 0.5% to avoid damage to the polymer-WS 2 interface. Similar band shift behaviour was observed after several strain cycles, indicating an intact interface.
Density functional theory Ab initio methods have been very successful at reproducing the measured phonon dispersion of MoS 2 [57] hence we used first-principles plane-wave calculations based on density functional perturbation theory (DFPT) [58] to calculate the frequencies of the phonon modes at the Brillouin zone centre as a function of in-plane strain. We used DFPT as implemented in the QUANTUM ESPRESSO package [59] with ultrasoft pseudopotentials [60]; the 5s 2 , 5p 6 , 5d 4 and 6s 2 electrons of W were treated as valence electrons, giving a total valence of 14 for W. The local density approximation (LDA) was used with a Perdew-Zunger exchange-correlation functional [61], as the LDA was found satisfactory in earlier studies [62]. Layers in the three-dimensional supercell were spaced by about 1 nm to ensure there was no interaction between them and so no van der Waals corrections were required. Convergence of the total energy was checked with respect to the kinetic energy cutoff (60 Ry) and Brillouin zone sampling (an 18×18×1 Monkhorst-Pack grid was used) [63]. The optimized lattice parameter a was found to be 0.3122 nm, which agrees to better than 1% with the experimental value of 0.315 32 nm [11].
Two types of distortion of the planar lattice were applied; a symmetry-preserving isotropic expansion ('hydrostatic') and a shear distortion ('shear'), which preserves area [64]. In both cases, the positions of the W atoms were fixed to obtain the required unit cell parameters but the S atoms were allowed to relax in the direction normal to the layer plane to minimize the vertical forces on them before calculation of the lattice modes (these forces were always less than 10 −4 eV Å -1 ). The maximum strains used were of the order of 0.5% and so no adjustment to the density of k-point sampling was necessary.

Results
Structure and morphology Nanoplatelets produced by the tape exfoliation normally have a range of number of layers and require the aid of optical microscopy and AFM to locate and identify them [65,66]. Monolayer WS 2 was more difficult to locate using optical microscopy and AFM and so PL spectroscopy [3] was also employed. Figure 2(a) shows an optical micrograph of flakes with regions of different thickness and the positions where PL spectra were obtained are marked. It can be seen from figure 2(b) that a very strong PL peak at 2 eV is obtained from position 1 indicating that this is an area of monolayer WS 2 [3].
Analysis of a number of SEM images shows the resulting flake size ranges ranging from a few microns to tens of microns ( figure 3(a)), with some evidence of folding. In contrast to graphene, this is considerably smaller after mechanical exfoliation than the original crystal size in the starting materials (∼1 mm), probably due to the poorer mechanical properties of WS 2 compared to graphene [52,54]. The optical micrograph of a flake in figure 3(b) illustrates a small nanoplatelet (highlighted) that had a characteristic blue colouration which is a fingerprint for a thin WS 2 nanoplatelet in the optical microscope [67] with AFM confirming its height as a ∼5.6 nm step corresponding to a few-layer nanoplatelet with around 9 WS 2 layers (figure 3(c)). Figure 4(a) shows the WS 2 nanotubes dispersed on a Si/SiO 2 substrate, where the NTs are oriented randomly and can be seen to stack together to form bundles. A high magnification image of an individual NT is shown in figure 4(b) and the open-tip nature of this WS 2 NT is evident as reported earlier [68]. The outer diameter given by the AFM measurement of the NT in figure 4(b) was measured as 43 nm. It was found that the outer diameter of NTs was in the range 20-200 nm consistent with the reported values [56]. Further analysis of the length of the NTs in figure 4(a) using image analysis software is given figure 4(c). It shows that the length distribution of the NTs is in the range 0.3 -10 μm with the majority being shorter than 2 μm, again consistent with the reported values [56]. However, no careful analysis of the influence of the ultrasonic (US) treatment on the length of the nanotubes was undertaken. Typically, a mild US treatment leads to breakage of the nanotubes and to an average shortening by a factor of 2. Figure 5(a) shows a low magnification bright field TEM image of an exfoliated WS 2 nanoplatelet on a lacey carbon Cu grid. The flake is folded and a number of few-layer regions were located at the edges. One such region is presented in figure 5(b). The number of layers decreases from left to right, as indicated in the intensity profile taken along the arrow. We estimate the thinnest region contains 2-3 WS 2 layers. This thin region is displayed in a fast Fourier transform (FFT) filtered high-resolution image in figure 5(c) (masked FFT inset). Contrast appears to change throughout the image, caused by undulations in the atomic lattice. These result in peaks and troughs which are highlighted in areas (i), (ii) and (iii). Area (i) shows a typical under-focused hexagonal bright field lattice (trough), indicating that area (i) is perpendicular to the zone axis. Area (ii) shows an over-focused area (peak) wherein the hexagonal structure appears white rather than black. The hexagonal structure in the top left section of (ii) and the under-focused area (iii) appear stretched, which is due to a slight tilt in the lattice, i.e. in the location between a peak and a trough.

Transmission electron microscopy
The structure of the WS 2 nanotubes was also investigated using TEM. A low magnifcation image of the NTs is shown in figure 6(a) along with measurements of their lengths. It can be see that they are consistent with the sizes of the NTs determined in figure 4. The micrographs in figures 6(b) and (c) shows the nanotube tips and confirms that they can either be closed or open-ended. The closed tip consists of ∼23 atomic layers, while the open-ended tip changes from ∼22 in the body to ∼10 atomic layers near the tip. A high resolution micrograph of the wall of a nanotube is shown in figure 6(d) along with an intensity scan (inset) across ∼23 atomic layers. The average spacing between the peaks in the scan in of the order of 0.634 nm, slightly larger than c/2 in the unit cell of the bulk material [11] but comparable to the value of 0.631 nm observed in our earlier study [15]. Figure 7(a) shows typical Raman spectra of WS 2 NTs, a WS 2 single crystal, a WS 2 nanoplatelet and a WS 2 monolayer. As shown in figure 7(b), the E 2g 1 mode involves an in-phase vibration of the W atoms with respect to the S atoms vibrating in the opposite direction in-phase, while the A 1g mode arises from the S atoms moving in in-phase and in out-of-plane directions [45,46]. In addition to the first-order modes, WS 2 gives a rich spectrum of second-order and multi-phonon bands with the laser excitation of 514 nm, due to strong electron-phonon coupling [38]. The 2LA mode overlaps with the E 2g 1 mode as the result of a very minor frequency difference (∼5 cm −1 ). The individual components can, however, be separated by curve-fitting with a Lorenzian function [38,69]. It is noteworthy that the ratio between the two major bands is different for the single crystal, few layer and monolayer specimens. This is consistent with the report of Berkdemir et al [38] who showed an increase of the I I E A 2g 1 1g ratio in WS 2 with a decreasing number of layers. Additionally, the A 1g mode undergoes a very subtle red shift as the number of layers is reduced. This trend is expected due to the decrease in the interlayer van der Waals interaction, causing weaker restoring forces in the vibration as the number of layers decreases. A blue-shift was, however, found for the E 2g 1 mode. Such behaviour have been widely observed among TMDs (MoS 2 , TaSe 2 , WSe 2 ) and is attributed to the reduced long-range Coulomb interaction  between the effective charges caused by an increase in the dielectric screening or stacking-induced changes in the intra-layer bonding [31,46,70]. This trend was also evident upon the thinning down of the WS 2 nanoplatelets during the exfoliation process.

Deformation
Deformation of the WS 2 nanoplatelets and nanotubes on the surface of the PMMA beam substrate was undertaken as shown schematically in figure 1 with Raman spectra being obtained in situ. The results of in situ Raman deformation measurements of the WS 2 monolayer shown in figure 2 are presented in figure 8. It is clearly seen that there is a significant red-shift in the 2LA, E 2g 1 and A 1g modes. This indicates good stress transfer as a result of a strong van der Waals interaction between the exfoliated nanoplatelets and the substrate aided by the large contact area. Similar strain-induced phonon softening has been observed in uncoated graphene nanoplatelets using the similar preparation method with uncoated specimens [71]. The band shift rates for the A 1g , E 2g 1 and 2LA Raman bands for the monolayer were −0.58±0.07 cm −1 /% strain, −2.05±0.14 cm −1 /% strain and −2.07±0.19 cm −1 /% strain, respectively and they are listed in table 1.
The strain induced band shifts for the few-layer nanoplatelet shown in figure 3 are presented in figure 9 and the shift rates of the A 1g , E 2g 1 and 2LA Raman bands are listed in table 1. The lower shift rates for the E 2g 1 and 2LA Raman bands are an indication of slippage between the WS 2 layers. This is due to difficulties in stress transfer as the result of the weak van der Waal bonding between the layers as has been found in fewlayer graphene [72]. On the other hand the shift rate is higher than in the monolayer for the A 1g band; this anomalous behaviour will be discussed later.
The results of the in situ Raman measurement on the uncoated WS 2 NT specimen are shown in figure 10(a). In this case there is no measureable shift in any of the three Raman bands as the result of the absence of stress transfer due to poor contact between the nanotubes and substrate. Their cylindrical nature (figure 4) means that the contact area is minimal and, moreover, the fact that the nanotubes have steps in their walls and are not completely straight (figure 6) makes the contact with the substrate even more difficult. Figure 10(b) shows that the behaviour is completely different for the WS 2 NTs in the epoxy resin. In this case large band shifts are found for all  In particular the shift rates of the bands are similar to those for the monolayer with the exception of the A 1g mode which is the highest of all materials studied. The is reason for this phenomenon will be discussed later.
The Raman band shifts for monolayer WS 2 were also calculated using DFPT using an identical approach to that used for monolayer MoS 2 in our earlier publication [46]. Two types of distortions of the planar lattice were applied; a symmetry-preserving isotropic expansion and a shear distortion that preserves area [64]. In each case, the positions of the W atoms were fixed to obtain the required unit cell parameters but the S atoms were allowed to relax in the z (hydrostatic) and x, y, z (shear) directions to minimize the forces on them before calculation prior to calculating the lattice modes. The maximum strains used were the order of 0.5% so that no adjustment to the density of the k-point sampling was necessary. We followed the method of Mohiuddin et al [73] to derive the phonon shift for uniaxial strain. For the hydrostatic case, the symmetry modes of type E (in-plane displacements) and type A (out-of-plane displacements) shift to lower frequency ω as the lattice expands at a rate that is given by the Grüneisen parameter γ m for a particular phonon mode m as: where the strain ε=ε x +ε y . Further details of the analysis are given in our earlier publication [46]. The frequency values calculated by DFPT for the A 1g and E 2g 1 modes are compared to the experimentally measured values of in table 1 and it can be seen that there is a good agreement between the calculated and measured frequencies for the monolayer and few-layer nanoplatelets, and nanotubes giving confidence in our DFPT calculations. Our values of the Grüneisen    parameters g A 1g and g E 2g 1 calculated for the WS 2 monolayer were 0.18 and 0.50 respectively.

Discussion
The calculated values of the Raman band shift rates determined from the Grüneisen parameters for the A 1g and E 2g 1 modes in the monolayer are also listed in table 1. It can be seen that good agreement is obtained between the measured and calculated values for the monolayer. Significant discrepancies between the measured and calculated values of Raman band shift rates and Grüneisen parameters are found, however, for the few-layer nanoplatelets and nanotubes. In particular the value of ∂ω( ) A 1g /∂ε is found to be higher and the value of ∂ω( ) E g 2 1 /∂ε lower, respectively, for the few-layer nanoplatelets and nanotubes than for the monolayer. This is shown more clearly in figure 11 where the ratio of the two shift rates plotted against the number of layers in the WS 2 nanostructures. It can be seen that there is a large and systematic change for the WS 2 crystals with different morphologies. The reasons for this behaviour will now be considered. Firstly, there is a significant increase in the value of ∂ω( ) A 1g /∂ε as the number of layers increases indicating hardening of the mode. This mode involves out-of-plane atomic motion ( figure 7(b)) and is therefore sensitive to the number of layer present in the crystal. Secondly, the E 2g 1 mode involves only in plane atomic motion and is not hardened by the increase in the number of layers. The value of ∂ω( ) E g 2 1 /∂ε actually decreases as the number of layers increases due probably to poor stress transfer from the substrate through the crystal, due to easy shear, as has been found for few-layer graphene [72,74]. These findings are consistent with recent studies upon multilayer WS 2 [44] and WS 2 nanotubes [48] deformed under pressure where in both cases significantly higher Raman band shift rates with pressure were found for the A 1g mode than for the E 2g 1 mode.
It is known from the behaviour of graphene [74] that stress-induced Raman band shifts can be used to estimate the effective Young's modulus of forms of graphene with different numbers of layers. The measured value of ∂ω( ) E g 2 1 /∂ε enables the relative inplane Young's modulus of the different WS 2 nanomaterials to be estimated in a similar way. Since the measured value for the WS 2 monolayer predicted is similar to that predicted using DFTP theory, it is likely that the monolayer has the theoretical modulus value of 150-170 GPa. The value of ∂ω( ) E g 2 1 /∂ε for the fewlayer material is around half that of the monolayer material, hence it would be expect that its Young's modulus would be half the theoretical value due to easy shear between the van der Waals bonded layers [74]. On the other hand the value of ∂ω( ) E g 2 1 /∂ε for the nanotubes is around 80% of that of the monolayer, implying a reduction in Young's modulus of around 20% compared to the monolayer.
Our present studies also enable similar observations to be explained for stress-induced phonon shifts in MoS 2 nanoplatelets. Rice et al [46] undertook an experimental study of phonon shifts during the uniaxial deformation of MoS 2 monolayer and few layer crystals. They found that the shift rate of the A 1g mode per unit strain was significantly lower than that for the E 2g 1 mode, an observation confirmed by their DFPT calculations for MoS 2 monolayer. In contrast, studies upon the deformation of multi-layered [43] and bulk [75] MoS 2 crystals under pressure have shown significantly higher Raman band shift rates with pressure for the A 1g mode as compared with the E 2g 1 mode. This hardening of the A 1g mode with the increase in crystal thickness seem therefore to be a characteristic of crystals of 2D TMD materials showing that care must be taken in comparing and correlating the behaviour of materials with different crystal morphologies.
A related study by Conley et al [76] showed that PL spectroscopy could be used to follow the change in the optical band gap in monolayer and bilayer MoS 2 with strain from shifts of peak positions and intensity changes. In view of the similarities of the structure and properties of these two TMD materials it is highly likely that the PL in WS 2 will undergo similar changes with strain. Hence a combination of Raman spectroscopy and PL spectroscopy on these materials can give a unique insight into both their structure and physical properties.

Conclusions
A detailed investigation has been undertaken of straininduced phonon shifts in tungsten disulfide monolayer and a few-layer nanoplatelet, and nanotubes. The materials were fully characterised and in all cases signficant Raman band shifts have been found for both the A 1g and E 2g 1 modes. This behaviour has been modelled using DFPT theory and good agreement between theory and experiment has been obtained for monolayers. For thicker crystals, however, the A 1g mode has been found to harden and the E 2g 1 mode to soften as the number of layers in increased. Similar behaviour is found for both few-layer material and nanotubes showing consistency between the different morphological forms of WS 2 . In addition, this study has also enabled anomalous phonon shift behaviour during the deformation for MoS 2 to be explained.