Visualizing Structure Models and Patterson Densities in four WS 2 Polymorphs: Metastable (1 T ’, 4 M ) and Stable (2 H , 3 R ) Phases

3-dimensional atomic and electronic structures of four crystalline WS 2 phases are rendered using VESTA program. In this study, a comprehensive investigation for visualizing structure models and Patterson densities in metastable 1 T ’-and 4M-WS 2 phases and elucidate comparison to stable 2H-and 3R-WS 2 phases. Structure models are provided in Stick, Space-filling, Ball-and-stick and Polyhedral representations with size of atoms based on their atomic radii. Analysis on type of W-S coordination (WS 6 ) polyhedra reveals that metastable WS 2 phases are composed of distorted octahedra and for stable WS 2 phases it is perfect trigonal prisms. Moreover, evidence of different stacking sequences in WS 2 polymorphs is also visualized. Patterson densities are exploited from model-electron and -nuclear densities are demonstrated in Wireframe representation by optimizing the interatomic distances. These studies not only evidence the structural characteristics influencing the construction of four WS 2 polymorphs, but also provide an ideal platform for both fundamental and application-oriented research.

Among these WS 2 polymorphs, four are of tremendous attention for scientific and technological relevant applications, specifically the metastable phases 1T'-WS 2 , 4M-WS 2 and the thermodynamically stable 2H-WS 2 , 3R-WS 2 phases 28 .Additionally, the electronic configurations of WS 2 are classified into two categories according to the arrangement of S/W/S atomic planes: (i) metallic (1T'-WS 2 , 4M-WS 2 ) and (ii) semiconducting (2H-WS 2 , 3R-WS 2 ) phase.Owing to the most favorable phase-dependent electronic properties, WS 2 polymorphs have received much research interests for great potential in new generation technology including flat panel display, microwave absorption, energy storage, flexible nanoelectronic devices, biomedicine, lubrication, field effect transistors, superconductivity, photovoltaics, photoand electro-catalysis applications 13,[15][16][17]29  The ongoing experimental and theoretical efforts on visualizing the atomic and electronic characteristics are consistently devoted to optimize the structural features of either single or mixed WS2 polymorphs. Thestudy on atomic structure visualization of different WS 2 polymorphs has been carried out by various methods, e.g.X-ray and/or electron diffraction, atomic resolution microscopic (HRTEM, AFM, STM) and NMR as well as Mössbauer spectroscopic techniques, comparatively a little attention has been revealed up to now the electronic/nuclear structure analysis 19,21,26,[30][31] .However, no other reported studies have so far been carried out determining a comparative study on the 3D visualization of atomic structure analysis in particular unit cell parameters, atomic positions, stacking sequences and electron/ nuclear densities on distinctive WS 2 phases.These features, therefore, are of utmost important for understanding the fundamental properties and outstanding practical applications of both metastable and stable WS 2 polymorphs.In order to modify, thus, the structural properties of exciting WS 2 polymorphs, by necessity, it is important to visualize the constituents in WS 2 crystal from basic physics and/or chemistry concepts viewpoint.
In the present study we have carried out a detailed investigation on the visualization of 3D structural models of WS 2 polymorphs, including metastable 1T'-and 4M-as well as stable 2H-and 3R-WS 2 phases.Structural representations of WS 2 polymorphs are visualized in Stick, Space-filling, Ball-and-stick and Polyhedral models based on atomic radii type.Furthermore, we demonstrated the different type of WS 6 polyhedra and layer stacking in metastable and stable WS 2 phases.Patterson densities from model electron and nuclear densities are performed in wireframe representation for visualizing the components of bond lengths in WS 2 crystal.In a nutshell, this study paves a way towards the visualization of WS 2 constituents that can be explored the phase-dependent structural properties and technologically relevant applications of this polymorphs.

Theoretical modeling
An attempt to elucidate a variety of crystallography studies in 3D visualization of WS 2 polymorphs has been made through computational method via Visuaization for Electronic STructural Analysis (VESTA) program 32 .The distinct structure models of four different WS 2 polymorphs were obtained by optimizing the structural parameters including lattice parameters, atomic parameters and interatomic distances between metal and sulfur atoms, which then were used for an obvious visualization of WS 2 polymorphs.

Structure Models
Figure 1-4 demonstrate the unit structures of distinctive WS 2 polymorphs in different structure models.The structural characteristics in terms of space group, crystal structure, type of crystal system and lattice parameters of WS 2 polymorphs are summarized in Table 1.The 3D structure models of monoclinic crystal structure with one formula unit cell of 1T'-WS 2 phase are visualized in Fig. 1.A stick structure model is provided in Fig. 1  The 3D visualization of different structure models of 2H-WS 2 phase within a hexagonal crystal structure having two formula unit cells is evident in Fig. 3. Fig. 3(a) provides a structure model in stick representation and sticks in bicolour cylinder as bond of W and S atoms are elucidated.Fig. 3(b) exhibits the structure model in space-filling representation, the W and S atoms showed a tendency to fill the space of the corresponding hexagonal unit cell.The structure model in ball-and-stick illustration, as shown in Fig. 3(c), creates for a fascinating observation in terms of the atomic size present in the resultant unit cell.Interestingly it is found that the atomic size of W atom is bigger than the S atom, both W and S atoms are demonstrated in two different colours to distinguish each other.Fig. 3(d) illustrates the polyhedral structure model signifying the W atom is the innermost atom in all polyhedra structures.Compass with the direction of crystallography axis is shown independently in Figure 3.
Figure 2 displays the 3D structure models of 4M-WS 2 polymophs within a monoclinic unit cell containing four formula units.The structure model in stick representation is shown in Fig. 2(a) evidenced to adopt only stick as bond of W and S atoms in in Fig. 5(a)).The distortion in WS6 polyhedron of 4M-WS2 is also obtained, where the W-S distances vary as 2.434, 2.579, 2.3 and 2.469 Å for W1-S1, -S2, -S3 and -S4 and 2.534 and 2.435 Å for W2-S2 and -S4, respectively (as shown in Fig. 5(b)).While in 2H-and 3R-WS2, the single-layer is containing the perfect trigonal-prismatic (WS6) coordination and there is only a unique W-S distance of about 2.384 and 2.41 Å, respectively is exhibited (Fig. 5(c) and (d)).The variation in WS6 coordination polyhedra reveals the crystal symmetry difference between metastable phases and thermodynamically stable phases.The interatomic distances (Å) of W and S in various WS2 polymorphs are provided in Table 3.  4(d) showing the W atom is the central atom in the unit cell and the W atom that can form the most bonds.The direction of crystallography axis is illustrated by a compass in Fig. 4. In Table 2 we display the atomic parameters, which are used to generate the various structure models of different WS 2 polymorphs.

WS 6 Coordination Polyhedra
The most favourable atomic-scale information on the W-S coordination is crucial to understand the thermodynamic stability of WS 2 polymorphs.Crystalline WS2 structure is built up of layers and a single-layer of WS2 can be either octahedral (WS6) or trigonal-prismatic (WS6).The upper and lower panel of Fig. 5 provide the WS6 coordination polyhedra in the ball-and-stick representation for respectively metastable 1T'-and 4M-WS2 and stable 2H-and 3R-WS2 phases.The single-layer of 1T'-WS2 is composed of distorted octahedral (WS6) in which first neighbour W-S distances are observed 2.392 and 2.451 Å for W-S1 and W-S2, respectively (as shown

Stacking Arrangements
The stacking sequence of monolayer and multilayers in WS 2 polymorphs along z-axis is illustrated in Fig. 6.The stacking sequence is provided by a sequence of three alphabets elucidating the relative positions of S-W-S atoms in all layers.A monolayer in the 1T'-WS 2 phase consisting a sequence AbC Fig. 6(a).The 4M-WS 2 phase has stacking arrangement AbA of S atoms in the unit cell, as shown in Fig. 6(b).From Fig. 6(c), the stacking sequence AbA BaB with the S atoms overlying by the W atoms along Z-axis of the adjacent layer is obtained in 2H-WS 2 phase.The 3R-WS 2 phase has a stacking sequence AbA CaC BcB in the rhombohedral crystallographic unit cell, as shown in Figure 6(d).

Patterson Densities
The upper (lower) panel of Fig. 7 display the 3D distribution of Patterson densities from model electron (nuclear) densities in wireframe representation of WS 2 polymorphs.From Fig. 7, the wireframe structure model elucidating the visualization of charge carrier densities in only wire form and no obvious balls and sticks are evidenced.An electron density map is constructed for 1T'-, 4M-, 2H-and 3R-WS 2 phases and displayed in upper panel of Fig. 7((a), (b), (c) and (d), respectively).Green and red/orange shaded portion signifying the distribution of electron density of W and S atoms, respectively.The Patterson map indicates the strong electron density distribution at the corners of the unit cell and weak electron density is distributed in the central.In the lower panel of Fig. 7, WS 2 polymorphs display the Patterson map analysis of nuclear-densities.Owing to the strong nuclear force small shaded portions of Patterson densities from model nuclear densities are visualized authenticating the nucleons are confined in small region.In addition, the stable phases (2H-WS 2 and 3R-WS 2 ) have a higher density than metastable phases (1T'-WS 2 and 4M-WS 2 ).
(a) reveals that only stick is treated as bond of tungsten (W) and sulfur (S) atoms.The space-filling structure model is presented in Fig. 1(b) demonstrating the atoms filled space in resultant unit cell.Interestingly both the W and S atoms are in distinct colour to differentiate each other.Fig. 1(c) illustrates the ball-and-stick structure model resulting the atomic size of W is larger than the S. The polyhedral structure model is established in Fig. 1(d) suggesting improved 3D visualization of structure model.The compass shows the direction of crystallography axis separately.4M-WS 2 .Fig 2(b) reveals the space-filling structure model suggesting the W and S atoms packed the entire unit cell.The ball-and-stick representation of 4M-WS 2 phase is displayed in Fig. 2(c), giving out the atomic size of W atom is greater than S atom.The polyhedral structure model of this phase is represented in Fig. 2(d) indicating the W is central atom in all the polyhedral structures throughout the unit cell.The crystallography compass with axis labels is provided in Fig. 2 individually.

Fig. 3 .Figure 4
Fig. 3. Unit structures of stable 2H-WS 2 phase in (a) Stick, (b) Space-filling, (c) Ball-and-stick and (d) Polyhedral representation.Atom colors (sizes) are as follows: W, white (large); and S grey (small).The black solid lines indicate unit cell Figure 4 depicts the structure models in 3D visualization of 3R-WS 2 polymorphs for rhombohedral crystal structure containing three formula units.Fig. 4(a) shows the structure model in stick representation demonstrating the bicolour cylinder is evidenced as the bond of W and S atoms.Space-filling structure model is visualized in Fig. 4(b) indicating the space of entire unit cell is occupied by distinct W and S atoms.Fig. 4(c) displays the structure model in ball-and-stick representation based on atomic-radii establishing the greater size of W atom than the S atom.Polyhedral representation of structure model is elucidated in Fig.4(d)showing the W atom is the central atom in the unit cell and the W atom that can form the most bonds.The direction of crystallography axis is illustrated by a compass in Fig.4.In Table2we display the atomic parameters, which are used to generate the various structure models of different WS 2 polymorphs.