The Role of Valence Electron Concentration in Tuning the Structure

Using ab initio calculations, we demonstrate the strong influence of valence electron concentration (VEC) on the local atomic structure and electronic...
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The Role of Valence Electron Concentration in Tuning the Structure, Stability, and Electronic Properties of Mo6S9−xIx Nanowires J. Karthikeyan,† Vijay Kumar,‡,§ and P. Murugan*,† †

Functional Materials Division, CSIR-Central Electrochemical Research Institute, Karaikudi, Tamil Nadu 630003, India Dr. Vijay Kumar Foundation, 1969 Sector 4, Gurgaon, Haryana 122 001, India § Center for Informatics, School of Natural Sciences, Shiv Nadar University, NH91, Tehsil Dadri, Gautam Budh Nagar, Uttar Pradesh 201 314, India ‡

S Supporting Information *

ABSTRACT: Using ab initio calculations, we demonstrate the strong influence of valence electron concentration (VEC) on the local atomic structure and electronic properties of Mo6S9−xIx (x = 0−9) nanowires (NWs). We find new atomic models of the NWs with unique decoration of S/I atoms that are more stable than reported earlier. The electronic and mechanical properties of these NWs are in good agreement with experiments. Further we tuned VEC by either varying the number of I atoms or adding S/Li atoms to obtain semiconducting Mo6S3I6, Mo6S2I8, Li6Mo6S9, and Li3Mo6S6I3 NWs, all of which have VEC of 24 and isolated Mo6 octahedral units, as observed in bulk cluster compounds. These results suggest that VEC is the thumb rule to design and tune the atomic structure and electronic properties of Mo−S−I cluster based nanostructures.

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INTRODUCTION Nanostructures of Mo−S compounds are currently of great interest because of their potential in technological applications.1−6 A layer of MoS2 is a direct band gap semiconductor,7 and it is currently attracting much attention as an alternative to graphene which lacks a band gap required for applications in nanoelectronics and optoelectronics.8,9 In contrast, MoS2 nanoribbons are metallic and can be tuned to be half-metallic or semiconducting by applying either electric field or mechanical strain.10 On the other hand, subnanometer sized, air stable, and free-standing bundles of Mo6S9−xIx nanowires (NWs) have been formed by condensing S/I decorated Mo6 octahedra,11−13 and their electronic properties are tunable from metallic to semiconducting by controlling iodine doping.14−16 These NWs are candidates for designing interconnects and components of semiconductor nanodevices. Here we present the atomic structure and electronic properties of such NWs using ab initio calculations and demonstrate for the first time that their stability can be well understood and their properties can be tuned by using valence electron concentration (VEC). Bundles of NWs with 6.0 ≥ x ≥ 4.5 have been synthesized with good reproducibility11,12 while the structural stability of the NWs with low values of x has been shown to be weak.17 The NWs have unique structural, mechanical, and electronic properties17 in a given batch with a certain x value and are easily dispersible in many solvents.13 High-resolution transmission electron microscopy on these NWs18 suggests the presence of Mo6 octahedra, but the positions of I and S atoms are not clearly observed. Earlier theoretical studies19,20 on the atomic structure and electronic properties of these NWs © XXXX American Chemical Society

suggested them to be metallic, but it is not in agreement with experiments20,21 according to which NWs such as Mo6S3I6 are semiconducting with a band gap of about 1.2 eV. We have performed extensive ab initio calculations (refer to Table S1 of Supporting Information) and found new atomic structures of these NWs with unique decoration of S and I atoms that are lower in energy than the earlier models15,19,20 and have semiconducting behavior as well as large Young’s modulus in agreement with experiments. Earlier first-principles calculations15,19,20 suggested that two Mo6 octahedral units (O1 and O2 in Figure 1) are connected in such a way that one octahedron is rotated by 60° with respect

Figure 1. Ball and stick models of the optimized stable structures of Mo6S9‑xIx NWs for (a) x = 0, (b) x = 1.5, (c) x = 3, and (d) x = 9. Green, yellow, and dark red colored balls correspond to Mo, S, and I atoms, respectively. Received: May 15, 2015

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DOI: 10.1021/acs.jpcc.5b04663 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 2. Ball and stick models of the optimized lowest energy (right) and slightly higher energy isomer (left) of Mo6S9−xIx NWs for (a) x = 4.5, (b) x = 6.0, and (c) x = 7.5. The energy difference between the isomers is given.

Monkhorst−Pack k-points for ionic relaxation and 100 k-points along the z-axis to obtain the density of states (DOS) and band structure. For all the NWs, spin-polarized calculations were also carried out, but the results were the same as obtained from the non-spin-polarized calculations.

to another. Consequently, two elongated Mo6 prisms, P1 and P2, are formed in the unit cell. In this structure, I and S atoms were shown19 to occupy face capping positions of octahedra and bridge sites, respectively (see Supporting Information Figure S1). However, here we show that the I atoms prefer the bridge sites up to x = 3 and, subsequently, face capping positions on Mo6 octahedra for higher values of x. Moreover, we correlate the structural stability and electronic properties of the NWs with VEC that has been used to understand the stability of bulk cluster compounds such as (NH4)2Mo3S13 nH2O and Chevrel phase compounds in which the isolated Mo3 triangular and Mo6 octahedral units are present, respectively.22,23 In other cluster compounds, the clusters can be isolated or fused depending upon the value of VEC.24−26 According to the Hume−Rothery rule,27 the stability of complex structures of crystals can be understood using valence electron per atom concept. Mo6S8 cluster based Chevrel phase compounds, such as PbMo 6 S 8 containing isolated Mo 6 octahedra, have VEC = 24.28−30 The high stability of cluster compounds for a particular VEC is explained by touching of the Fermi sphere (FS) with the Brillouin zone (BZ) boundary when the electronic states are filled up to a (pseudo) band gap.31 Here we follow these ideas to understand the structural stability and electronic properties of Mo6S9−xIx NWs. We find that the structural stability of the NWs is strongly correlated with VEC, similar to bulk compounds. In order to further support that VEC is the thumb rule for the structural stability and electronic properties of Mo−S−I cluster based NWs, we added Li and varied the number of S/I atoms in the unit cell in such a way that the VEC becomes exactly 24. Our results show that in all such cases the converged structure contains isolated Mo6 octahedra and all of these NWs are semiconducting with a direct band gap.

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RESULTS AND DISCUSSION To begin with, we considered a pristine Mo6S9 NW with two Mo6S6 octahedra and placed three S atoms on the bridge positions of the prisms. In the optimized structure shown in Figure 1, one Mo6S6 octahedron is well bonded, but the other is separated into two Mo3S3 triangles that interact relatively weakly with each other (Mo−Mo distance between the triangles = 3.24 Å). The S atoms on the bridge positions are well bonded with the triangles (Mo−S = 2.19 Å), but they have a relatively long Mo−S bond (Mo−S = 2.43 Å) with the Mo atoms of the octahedron. It shows that one octahedron is not stable in this Mo6S9 stoichiometry. The obtained structure of this NW can be explained with VEC of the obtained local structures. The VEC/formula unit (fu) of this NW is 18. As the bridge S atoms are weakly bonded with the Mo atoms of the octahedron, we can treat the Mo6S6 octahedron to be effectively isolated with 24 valence electrons [(6 × 6) − (2 × 6) = 24] or slightly less (assuming partial charge transfer to bridge S atoms), and this can explain the stability of the octahedral structure.22,28−30 For the remaining Mo6S12 unit, the VEC is about 12, which is favored by the two triangular structures (VEC = 6 for each).23 The above description of the Mo6S9 NW shows that one of Mo6 octahedra does not have sufficient electrons to bind Mo atoms and the bridge S atoms. Therefore, we replaced three bridge S atoms with three I atoms that need only one electron each compared to two electrons for each S atom. Another way of substituting I atoms is on the faces of an octahedron symmetrically as it was also studied earlier.19 However, we find that the former is energetically more favorable than the latter by ≈83 meV/atom. The optimized structure with Mo6S7.5I1.5 configuration is shown in Figure 1. In this structure, an edge of one octahedron opens up while the two triangles found in Mo6S9 NW become octahedrally bonded with some distortions. Therefore, 3-fold symmetry of the NW is broken. Interestingly two octahedra also interact by forming direct Mo−Mo and Mo−S bonds. Accordingly, the doping of I atoms improves bonding in the NW. The lattice parameter (c) of this NW is 10.0 Å as compared to 11.0 Å obtained in the previous work.35 The VEC for this NW is in between that of isolated octahedral and triangular units thus the atomic structure forms distorted prisms. Further substitution of three more I atoms on the bridging positions of another prism leads to Mo6S6I3 configuration, and

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COMPUTATIONAL METHODS We use Vienna ab initio simulation package32 with projector augmented wave pseudopotentials33 and generalized gradient approximation (GGA)34 for the exchange-correlation energy. The electronic and ionic relaxations are performed using iterative conjugate gradient minimization method until the absolute value of the force on each ion becomes less than 0.01 eV/Å. The NW is kept in a large unit cell with 15 Å vacuum space in x and y directions between the surface atoms in successive cells. The optimization for the lattice constant (c) has been done by changing the lattice parameter along the NW axis (taken as the z-axis) successively in step of 0.1 Å. For understanding the structural stability with varying x we use a supercell approach with two (for x = 0, 3, and 9) and four (for x = 1.5, 4.5, 6, and 7.5) Mo6 octahedra. The BZ of the NW with four (two) Mo6 octahedra is sampled by 1 × 1 × 4 (1 × 1 × 8) B

DOI: 10.1021/acs.jpcc.5b04663 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Table 1. (a) Cohesive Energy per Atom (Ecoh), Optimized Lattice Constant (c), Band Gap (Eg), Valence Electron Concentration (VEC), and Young’s Modulus (Y) of Mo6S9−xIx NWsa x Ecoh (eV) c (Å) Eg (eV) VEC Y (GPa) YExpt (GPa) YTheory (GPa) a

0.0

1.5

3.0

4.5

6.0

7.5

9.0

4.91 13.19 0.46 18.0 158

4.74 20.0 0.24 19.5 429

4.55 9.30 metal 21.0 535

4.33 21.25 0.28 22.5 256 420

4.08 22.25 0.48 24.0 144 43038 82−9439 45−7038

3.84 23.65 0.41 25.5 119

3.57 12.65 0.53 27.0 105

For x = 1.5, 4.5, 6.0, and 7.5 there are four Mo6 octahedra in the supercell while for the others we use a unit cell with two octahedra.

Figure 3. (a) Cohesive energy per atom (Ecoh) and Young’s modulus and (b) formation energy per atom (FE) and its derivative for Mo6S9−xIx (x = 0−9) NWs. The VEC corresponding to each x is given in the top axis.

the prisms have I atoms and the octahedra with I or S atoms alternate. This is a unique and stable conf iguration, and the stability of NWs with this stoichiometry (Mo6S3I6) has also been suggested f rom experiments.11,12,20 Its VEC is 24, and all the Mo6 octahedra are isolated as in bulk cluster compounds. The calculated lattice constant (11.1 Å, which is half of the lattice constant of the supercell) is close to the experimental value of 11.92 Å.36 Note that experimentally the NWs have been synthesized for x = 4.5−6.0, and the EXAFS studies showed four Mo−Mo nearest-neighbor bonds for all the Mo atoms,37 suggesting the presence of Mo6 octahedra which agrees with our findings. For lower x values, Mo−Mo bonding is also possible between the octahedra in the NW via prism sites, and it will increase the number of Mo−Mo bonds. Around the composition of x = 4.5−6.0, Mo6 octahedra tend to be isolated, and good stability of NWs is expected. If we continue to substitute three more I atoms, we obtain Mo6S1.5I7.5 NW, and its optimized SIII structure is shown in Figure 2. In this stoichiometry we again find it energetically favorable to place six S atoms on one octahedron in the supercell rather than three S atoms on an octahedron in a unit cell. From the above discussion, it is evident that the stacking of S or I decorated Mo6 octahedra could vary in stacking sequence depending upon x, and there could be a possibility of coexistence of different polytypes in these NWs. In addition, the NWs with very low x ( 4.5, it is due to the small energy cost in bending the bridging Mo−I− Mo ionic bonds while applying stress. The deduced electronic density of states (DOS) of all the NWs are shown in Figure 4. The DOS of all the NWs except for x = 3 shows their semiconducting nature with an average energy band gap, Eg, of 0.4 eV which is supported by the experimental results.20,21 Note that the calculated gap is smaller due to the use of GGA. In contrast, the model proposed by the earlier theoretical studies with S on the bridge site shows the NWs to be metallic. We also performed calculations for the same model and indeed found similar results (Figure 4). One can observe strong hybridization between the Mo-4d and S-3p states in the occupied region. The population of the unoccupied Mo 4d states above the Fermi energy (Ef) comes down by increasing x. This supports the variation of VEC with

n[6E(Mo) + (9 − x)E(S) + xE(I)] − E((Mo6S9 − x Ix)n ) n × 15 n[6μ(Mo) + (9 − x)μ(S) + xμ(I)] − E((Mo6S9 − x Ix)n ) n × 15

and these are plotted in Figure 3. Here, n is the number of fu in the unit cell and E(Mo), E(S), and E(I) are the atomic energies of Mo, S, and I atoms, respectively. The chemical potentials (μ) Bulk of Mo, S, and I atoms are obtained from E(MoBCC ), Molecule E(SMolecule ), and E(I ), respectively. The E decreases 8 2 coh with increasing x value due to the relatively weak Mo−I bonds compared with Mo−S bonds. The calculated FE initially increases up to x = 3, and then it decreases gradually because of the fusion of octahedra by forming more Mo−Mo and Mo−S bonds in P1 and P2 sites, only for 0 < x < 4.5. Beyond this limit, the increase in the number of I atoms (increase of VEC) leads to isolation of the octahedral units in the structure of Mo6S3I6 NW. The derivative of the FE become almost constant beyond x = 6, which shows that no more Mo−Mo bonds are formed beyond this limit. The Young’s modulus (Y) of the NWs has been calculated from Y = kc/A, where A = π × R2 and k is deduced from the second-order energy derivative around the minimum energy by fitting the energy versus lattice parameter data with a parabolic curve. The radius of the NW (R) is calculated as R = R0 + RS2−/I− where R0 and RS2−/I− refer to distance between the D

DOI: 10.1021/acs.jpcc.5b04663 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C respect to x. Further the p states of I atoms get populated at higher binding energies (below −4 eV) only after x = 4.5 when octahedral faces get capped with I atoms. This shows that the octahedron sites bond more strongly than the bridging sites in prisms. Since S atoms bind more strongly, they prefer the octahedral sites while I atoms occupy the octahedron sites only after saturating the bridging sites. To further understand the electronic structure of these NWs near the Ef, we have shown the band structure in the energy range −1 to 1 eV from Ef in Figure 5. It is noted that in many

Figure 6. Ball and stick models of the optimized structures of (a) Li6Mo6S9, (b) Li3Mo6S6I3, and (c) Mo6S10I2 NWs. The top views of the respective structures are shown in the bottom. Here, green, yellow, dark red, and saffron color balls correspond to Mo, S, I, and Li atoms, respectively. Figure 5. Band structures of Mo6S9−xIx (x = 0−9) NWs. The respective x value is given. The horizontal dashed line shows Ef or the top of the valence band.

makes the VEC to be 24 electrons/fu, and the composition of the NW is Mo6I8S2. Interestingly, this Mo−S−I composition was also synthesized with good reproducibility and stability.29,40 Since the VEC matches for the local structure of Li6Mo6S9, Li3Mo6S6I3, and Mo6S2I8 NWs, they show semiconducting property with a direct band gap of 0.31, 0.14, and 1.56 eV, respectively (shown in Figure S3 of Supporting Information). This clearly proves that VEC is the thumb rule for understanding the structural stability and electronic properties of Mo−S cluster based nanostructures.

cases such as x = 0, 1.5, 4.5, and 7.5 the conduction bands (CB) have less dispersion, and the Mo6 units retain cluster-like behavior. Hence, the excitation of such NWs would be more a local phenomenon. From the DOS we find Mo-4d states in CB just above the Ef. In the case of NWs with x = 3, 6, and 9 we see good dispersion in the bands, which suggests good hybridization between the states of the Mo6 octahedra and the bridging atoms. The Mo6S7.5I1.5 NW is metallic since a band is crossing Ef at the middle of the BZ (Figure S2 in Supporting Information) so there is a possibility of Peierls instability. Accordingly, we doubled the unit cell and relaxed it further to obtain the electronic structure. It clearly shows a pseudogap of 0.24 eV. Also, the Mo6S6I3 NW is metallic due to the crossing of two bands at the Fermi level while the other NWs are semiconducting. For x = 4.5 and 6, the gap is direct with the value of 0.28 and 0.48 eV, respectively. Finally, we manipulated the local atomic structure of Mo clusters by changing the VEC by adding Li/S atoms in Mo6S9−xIx NWs. The optimized structures are shown in Figure 6. In Mo6S9 NW, we have two Mo3 triangles (VEC = 6 for each) and one Mo6 octahedron(VEC = 24) so the VEC/fu is 18, which can be complemented by adding 6 electrons/fu. Hence, we decorated three Li atoms on the bridging sites as discussed in ref 15 and three Li atoms on the octahedron. As a result, in the optimized structure, the two Mo3 triangles fuse together to form an isolated octahedron. Also, the decorated Li atoms in the NW bind with both Mo atoms as well as S atoms of both O1 and P1. Similarly, in Mo6S6I3 NW, we added three lithium (three electrons) per fu on the P1 (bridging) sites to complement the VEC, in order to form two isolated Mo6 octahedra. On the other hand, in Mo6I9 NW the VEC is 27/fu, which has excess of three electrons/fu. Accordingly, we added one S atom in the interstitial position between the three bridging I atoms of each prism in the unit cell to remove two electrons/fu. Further an I atom is replaced by S atom which

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CONCLUSIONS In summary, we have found new structures of Mo6S9−xIx NWs from ab initio calculations which are lower in energy than those reported earlier. In particular, we find new optimal distribution of S and I atoms that give close agreement with experimental findings with regard to stability, Young’s modulus, and semiconducting behavior. The local structural units in these NWs vary with x, and we have shown that this can be understood using VEC. Among the Mo−S−I NWs, Mo6S3I6 NW contains isolated stable octahedra due to the matching of VEC with 24. All the NWs we have studied except for x = 3.0 are semiconducting in agreement with the available experimental reports.20,21 Similar to a layer of MoS2 that is semiconducting with a direct band gap, such NWs and in particular those with VEC = 24 are interesting for optical and electronic applications. For intermediate x values the NWs may have polytypes which differ in S and I decoration either in prism site (with low x < 3) or in octahedral sites (with x > 3). There is a strong influence of VEC on the atomic and electronic structure, and it is the thumb rule in deciding the stability of Mo−S cluster based nanostructures as also demonstrated by adjusting the VEC value via the method of doping. We hope that our work will provide a new ground to explore and predict new Mo−S cluster based nanostructures with desired properties. E

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ASSOCIATED CONTENT

S Supporting Information *

(1)Various models of Mo6S9−xIx NWs and their physical properties; (2) properties of NW isomers studied with a single unit cell; (3) properties of NW isomers studied by doubling the unit cell; (4) atomic structure of Mo6S3I6 NW proposed in previous reports; (5) electronic structure of Mo6S7.5I1.5 with single unit cell; (6) band structure of Li6Mo6S9, Li3Mo6S6I3, and Mo6S2I8 NWs. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.jpcc.5b04663.

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AUTHOR INFORMATION

Corresponding Author

*Ph +91-4565-241443; Fax +91-4565-227779; e-mail [email protected] (P.M.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by the Department of Science and Technology (DST), India, through Fast Track Scheme. The authors acknowledge the use of the CDAC(NPSF), CSIR-CECRI, CSIR-NCL, and CSIR-CMMACS high performance computing facilities. J.K. acknowledges kind support from Dr. Vijay Kumar Foundation and Shiv Nadar University.

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REFERENCES

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DOI: 10.1021/acs.jpcc.5b04663 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.5b04663 J. Phys. Chem. C XXXX, XXX, XXX−XXX