Computational study of bulk and surface properties on ruthenium oxide (RuO 2 )

. Metal oxides are widely used in lithium-air batteries to improve the formation of stable discharge products and improve lifespan and electrochemical performance. Despite the intense studies on metal oxides catalysts, ruthenium oxide attracted the most attention since it doesn’t only catalyse the redox processes but reduces the over-potential and stabilizes the Li cyclability. Hence, in this work we discuss the bulk and low Miler index surfaces of RuO 2 using the first principle density functional theory calculations. It was found that the lattice parameters are in good agreement with the reported results, with less than 1.4% difference. Furthermore, RuO 2 was also found to be mechanically stable with all positive independent elastic constants ( C ij ) obeying the mechanical stability criteria and a positive tetragonal shear modulus (C’> 0). The bulk to shear ratio indicates that the structure is ductile. The density of states shows a slight pseudo gap for RuO 2 at the Fermi energy, which suggests that the structure is stable. Finally, low Miller index surfaces ( i.e. (110), (010), (001), (111), and (101)) were modelled using METADISE code, and the most stable facet was in agreement with the reported literature.


Introduction
The whole world is moving away from the reliance on fossil fuels and the quest of finding alternative energy sources which are environmentally friendly, clean and affordable continues. Various alternative energy sources are considered, which includes solar energy [1], biomass [2], hydropower [3], geothermal energy [4] and etc. Among the listed energy sources, lithium-ion battery continues to grow and advance for use in electronic devices, electric cars, and large-scale stationary storage systems. However, their output capacity is limited to 150 mAh/g which is due to the cathode-electrolyte interactions, resulting in transitional-metal dissolution and irreversible structural transformation upon cycling [5,6].
Lithium-air batteries (LABs) appeared as an alternative next-generation energy source with high energy density value of 3505 Wh/kg, which is close to that of a gasoline engine and 10 times greater than that of lithium-ion batteries [7,8]. Unlike Li-ion batteries, the LABs have its positive electrode as metal (i.e. lithium) and a negative porous electrode that allows oxygen in from the surrounding (hence it's called the breathing battery). During discharge processes, the oxygen drawn from the atmosphere through the porous cathode is reduced by the lithium ions to form discharge products such as Li2O2 and Li2O, then the oxides produced further decompose to form back the lithium ions and oxygen during the charging process [9,10]. Several studies demonstrated that the performance of the battery depends on which oxide is produced as a discharge product [11,12,13].
However, the fundamental challenge that limits the use of metal-air battery technology is the production of unstable discharge products which further interact with other components of the battery resulting in capacity fading. Several catalysts have been proposed to promote the formation and decomposition of stable discharge products during charge/discharge cycle, which are the transitional metal-oxides [14,15], noble metal/metal oxides [16] and carbon-based materials [17,18,19]. Among all, metal oxide catalyst gave an improved capacity retention and improved electrochemical performance [20]. These metal oxide catalysts include manganese dioxide (MnO2) [21], cobalt oxide (Co3O4) [22], ruthenium dioxide (RuO2) [23], and titanium dioxide (TiO2) [24], which can significantly reduce charge over-potential and increase the cycling performance [25].
Metal oxides are widely considered for catalysis in various applications, such as carbon conversion/energy conversion [26], water splitting [27], etc. In lithium-air batteries, the use of metal oxides nanostructure showed an improved formation and decomposition of stable Li2O2 discharge product [28]. Subsequently, Maenetja et al [29] studied the formation of both Li2O2 [30] and NaO2 [31]stable discharge products on the MO2 (M = Mn, Ti, V), where it was indicated that the formation of Li2O2 gas-phase is more favored in the presence of -MnO2 catalyst.
One other catalyst is the ruthenium dioxide, which resulted in low charge overpotentials due to its high catalytic activity during cycling, hence long-term cycle stability [32]. O'Dwyer et al. [33] indicated that the RuO2 catalyst can still decompose Li2O2, implying that RuO2 has strong OER activity. Liao et al [34] RuO2 was designed and studied as a 2D nanosheet structure, which had a high surface-to-mass ratio and low weight, allowing the material to have a higher electrolyte-electrode interaction and enhance O2 diffusion. Additionally, because most solid-state catalyst materials are metal-based and have a high density, the porous structure and large surface area of the carbon material may help reduce the catalyst material's loading mass and raise the battery's specific energy.
Here, we discuss the density functional theory calculations of ruthenium dioxide bulk and surfaces. We analyze the bulk structural properties, elasticity, density of states, low Miller index surface and particle morphology with reference to the reported literature.

Method
Spin-polarised density functional theory (DFT) calculations were performed with the Vienna Ab-initio Simulation Package (VASP) program [35], using the generalized gradient approximation (GGA) in the form of the Perdew-Burke-Ernzerhof (PBE) exchangecorrelation functional [36]. The cut-off energy was fixed at 500 eV and the k-mesh of 6×6×8 and 6×6×1 was set for the bulk and surfaces, respectively. The semi-empirical method of Grimme with the Becke-Johnson damping [D3-(BJ)] [37,38] was included to model the longrange dispersion interactions and describe the surfaces properly [39,40,41,42]. To model the Ru 3d electrons, the effective parameter, Ueff = 3.9 eV was used, which was consistent with our previous studies [43]. Gaussian smearing with a width of 0.05 eV was included [38] to improve the convergence of the Brillouin zone integrations during geometry optimizations.

Equilibrium lattice parameters
The crystal structure of ruthenium oxide (RuO2)rutile phase has a tetragonal symmetry with a space group P42/mnm (no. 136). It has a body-centred structure with geometry coordination of octahedral tetravalent ruthenium (Ru 4+ ) ions and trigonal planar oxygen coordinated (O 2-) ions. Upon full optimization, the predicted lattice parameters were a = b = 4.49 Å and c = 3.11 Å, which are in agreement with the listed literature data within <1.4% [44,45,46,47]. The heat of formation of this structure is -380.66 kJ/mol which indicate that RuO2 is thermodynamically stable and the calculated ∆Hf was in agreement with the reported literature.  Table 2 summarises the calculated elastic constants, moduli, and the Pugh's ratio at the strain of 0.005 for RuO2. The elastic constants can be used to gain insight on the mechanical stability of solids. A crystal structure is said to be mechanically stable if strain energy is positive (which implies that all the elastic constants should be positive) and it should satisfy the stability criteria for its respective crystal. For tetragonal phases, there are six independent elastic constants, which are C11, C12, C13, C33, C44, C66. The stability following are the tetragonal system's mechanical stability requirements [50]:  Table 2 summarizes the calculated and their respective reference elastic constants obtained from different reported data. The elastic constants in table 2 comply with the above mentioned mechanical stability requirements, proving that they are mechanically stable since they are all positive. We observed a major difference with the listed available reference data since we have included the U-parameter of 3.9 eV to model the localized 3d Ru electrons. RuO2 is mechanically stable as shown by our structure's expected tetragonal shear modulus (C'), which is positive and equal to 33.5. The B/G ratio of 1.94, which is higher than 1.75, indicates that the structure is ductile.

Density of states
In order to correlate the structural and mechanical stability of the RuO2 system, we compare their total density of states (tDOS) plots in Figure 1. It is noted from literature that the DOS of structures of the same composition can be used to mimic the stability trend with respect to their behaviour at the Ef (Fermi level), in which the structure with the highest and lowest density of states at Ef is considered the least and most stable, respectively [53,54]. The total DOS and partial DOS obtained from bulk RuO2 oxide are plotted in figure 1. The valence band width in the previous work was -8.1 eV, while the overall valance band width in this study is -8 eV. Additionally, there is a partially filled electronic band located right at the Fermi level [55]. The partial DOS shape demonstrates that the O-2p state dominates the valence band at lower energy (O atoms adopt the sp 2 hybridization), but the top section predominantly arises from the Ru-4d state, with the Ru 4+ peak occurring at -1 eV. The conduction band began with greater Ru-4d than O-2p states [56]. These PDOS features are in qualitative agreement with results from previous studies [57,58]. We observe a sight pseudo-gap at the Fermi energy (Ef), indicating that our structure is electrically stable.

Surface models
All the surface terminations were generated by cutting the geometry-optimized (2×2) supercell bulk structure [59], using the Tasker [60] dipole method, as implemented in the Minimum Energy Techniques Applied to Dislocations, Interfaces and Surface Energies (METADISE) code [61]. When cleaving the surfaces, symmetry and stoichiometry were preserved, thus no electric dipole moments. When constructing the surface terminations, we considered the stacking sequence for low Miller index facets. We have modelled the two possible terminations for each surface orientation using stoichiometric, non-polar, and symmetric slabs along the z-direction. We then considered the stabilities of five low-index surface orientations ((110), (010), (001), (111) and (101)) by performing periodic calculations of slabs with stoichiometric composition, and vacuum gaps (see Figure 2). The total number of layers and surface areas of each surface are showed in Table 3 Table 3 summarizes the calculated surface energies of RuO2 using the expression:

Surface energies and particle morphology
where and are the total energy of the slab and relaxed bulk, and A is the area of the slab. The (110) surface with the lowest surface energy of = 0.045 eV/Å 2 was found to be the most stable facet, which is in agreement with the reported literature data of 0.0645 eV/Å 2 , [62]. and 0.078 eV/Å 2 [56]. Similar to other rutile phases, such as IrO2 [63] and TiO2 [64], the (110) surface was previously observed to be the most stable facet. As compared to other modelled facets, we observed an increasing surface energy, and decreasing stability, i.e. (110) < (101) < (111) < (001) < (100). These calculated surface energies were utilized to determine the equilibrium RuO2 particle morphology using Wulff's method [65]. Similarly to isostructural transition metal oxides like TiO2 [66], MnO2 [67]and VO2 [68], the most enhance plane is for (110) surface. The (001), (101) and (111) surface does not appear in the Wulff morphology because of its higher surface free energy with respect to the (110) and (011) planes.

Conclusion
The ruthenium dioxide bulk and surfaces stability were successfully evaluated using density functional theory (DFT). It was found that the lattice parameters are in good agreement with the reported results, with less than 5% difference. Furthermore, RuO2 was also found to be mechanically stable with all positive independent elastic constants (Cij) obeying the mechanical stability criteria and a positive tetragonal shear modulus (C'> 0). The bulk to shear ratio indicates that the structure is ductile. The density of states shows a slight pseudo gap for RuO2 at the Fermi energy, which suggests that the structure is stable. The electrical conductivity of RuO2 bulk can therefore be correlated with the number of free d-electrons of the metal ion, confirming that RuO2 to be a metallic-like conductor. The most stable surface was found to be the (110) surface and we observed the surface stability trend of (110) < (101) < (111) < (011) < (100). The morphology of RuO2 is strongly consistent with previous studies and other rutile phase structures, like MnO2.