Nourdine Zibouche, Agnieszka Kuc, Pere Miró and Thomas Heine

Abstract: We explore the stability and the electronic properties of hypothetical noble-metal chalcogenide nanotubes PtS2, PtSe2, PdS<sup>2</sup> and PdSe<sup>2</sup> by means of density functional theory calculations. Our findings show that the strain energy decreases inverse quadratically with the tube diameter, as is typical for other nanotubes. Moreover, the strain energy is independent of the tube chirality and converges towards the same value for large diameters. The band-structure calculations show that all noble-metal chalcogenide nanotubes are indirect band gap semiconductors. The corresponding band gaps increase with the nanotube diameter rapidly approaching the respective pristine 2D monolayer limit.

Reprinted from *Inorganics*. Cite as: Zibouche, N.; Kuc, A.; Miró, P.; Heine, T. Noble-Metal Chalcogenide Nanotubes. *Inorganics* 2014, *2*, 556–564.

### 1. Introduction

Inorganic nanotubes (INTs) are a class of materials that are very attractive for many applications in nanotechnology due to their interesting physical and chemical properties, which arise from their low dimensionality. In 1930, Pauling had already stated that mismatched layered materials may form cylindrical shapes [1]. However, the first carbon-based tubular forms, namely carbon nanotubes (CNTs) have been observed by Iijima in 1991 [2]. At the same time, the synthesis of WS<sup>2</sup> NTs by Tenne and co-workers [3], has demonstrated that these tubular systems are not limited to carbon, but can also be obtained from any other layered compound. Later on, several INTs have been prepared and produced such as transition-metal sulfides [3,4]. boron-nitrides [5,6], metal oxides [7,8], rare earth oxide [9] and more recently misfit layered compounds [10].

WS<sup>2</sup> and MoS<sup>2</sup> NTs, being the first synthesised INTs, are semiconductors. They have demonstrated excellent mechanical properties [11–16] and are known to be good solid lubricants [17]. They have also been suggested as scanning probe tips [18], catalysts [19], reinforcements for composite materials [20], photo-transistors [21], gas storage and host materials [22,23], *etc*. Later, other transition-metal chalcogenide (TMC) NTs have been reported such as TiS2, NbS2, ReS2, TiSe<sup>2</sup> and TaS<sup>2</sup> [24–28]. Subsequently, many more TMC NTs can be expected due to the large manifold of the layered TMC materials [29,30]. Nowadays, different techniques and strategies have been employed and developed for the synthesis and growth of large amount of NTs such as chemical transport technique [31], thermochemical decomposition [32] and *in situ* heating [33]. For example, WS<sup>2</sup> and MoS<sup>2</sup> NTs were produced using gas-solids reactions at high temperatures by the reduction of WO<sup>3</sup> (MoO3) in the atmosphere of a mixture of H2, N<sup>2</sup> and H2S gases [3,4,34].

In this work, we aim to extend the scope of inorganic nanotubular materials by investigating noble-metal chalcogenide MX<sup>2</sup> single wall nanotubes, where M = Pt, Pd and X = S, Se. Tubular forms based on these materials have not yet been experimentally observed, however, considering that PtS2, PtSe2, PdS2, PdSe<sup>2</sup> belong to the family of layered TMCs, one can expect that such compounds may also form nanotubes. Structure and electronic structure of these noble metal chalcogenides have been subject to controversial debate in the 1950s and 1960s. Two possible phases of the Pd- and Pt-based TMCs were suggested, namely orthorhombic (pyrite) and 1T. [35–38]. We have calculated the relative stability of bulk and monolayered forms of these TMCs. While the orthorhombic phase is preferable for the bulk PdS<sup>2</sup> material (energy difference of 56 meV - all energies are given per MX<sup>2</sup> formula unit), the monolayers (MLs) favor the 1T arrangement (energy difference of 68 meV). For the heavier PdSe2, we have found similar trends for the MLs, where the 1T form is by 0.6 eV more stable than the orthorhombic one. Bulk PdSe<sup>2</sup> is unstable in the orthorhombic form, forbidding comparison with the 1T structure. Therefore, the choice of the 1T polytype to simulate the single-wall NTs is justified. In view of the renaissance of layered materials and the advance of experimental technology it is important to reexamine these phases and attempt exfoliation.

A recent study of bi- and monolayered noble-metal materials have shown interesting quantum confinement effects and electromechanical properties, suggesting them for applications in optoelectronics and flexible devices [39]. Therefore we have investigated, using density functional theory (DFT), the stability of the MX<sup>2</sup> NTs and their structural and electronic properties. The strain energy is found to be chirality independent and exhibits the characteristic dependence on the tube diameter <sup>d</sup> (∼1/d<sup>2</sup>). The band structure analysis shows that noble-metal chalcogenide NTs are all semiconducting in a similar way to their ML counterparts. Unlike MoS<sup>2</sup> and WS<sup>2</sup> NTs, where the band gap is direct and indirect for zigzag and armchair, respectively, PtX<sup>2</sup> and PdX<sup>2</sup> NTs have indirect band gaps which increase with the diameter.
