Calculation on surface energy and electronic properties of CoS2

Density functional theory was employed to investigate the (111), (200), (210), (211) and (220) surfaces of CoS2. The surface energies were calculated with a sulfur environment using first-principle-based thermodynamics. It is founded that surfaces with metal atoms at their outermost layer have higher energy. The stoichiometric (220) surface terminated by two layer of sulfur atoms is most stable under the sulfur-rich condition, while the non-stoichiometric (211) surface terminated by a layer of Co atoms has the lower energy under the sulfur-poor environment. The electric structure results show that the front valence electrons of (200) surface are active, indicating that there may be some active sites on this face. There is an energy gap between the stoichiometric (220) and (211), which has low Fermi energy, indicating that their electronic structures are dynamically stable. Spin-polarized bands are calculated on the stoichiometric surfaces, and these two (200) and (210) surfaces are predicted to be noticeably spin-polarized. The Bravais–Friedel–Donnay–Harker (BFDH) method is adopted to predict crystal growth habit. The results show that the most important crystal planes for the CoS2 crystal growth are (111) and (200) planes, and the macroscopic morphology of CoS2 crystal may be spherical, cubic, octahedral, prismatic or plate-shaped, which have been verified by experiments.


Y-lZ, 0000-0003-2581-2067
Density functional theory was employed to investigate the (111), (200), (210), (211) and (220) surfaces of CoS 2 . The surface energies were calculated with a sulfur environment using first-principlebased thermodynamics. It is founded that surfaces with metal atoms at their outermost layer have higher energy. The stoichiometric (220) surface terminated by two layer of sulfur atoms is most stable under the sulfur-rich condition, while the non-stoichiometric (211) surface terminated by a layer of Co atoms has the lower energy under the sulfur-poor environment. The electric structure results show that the front valence electrons of (200) surface are active, indicating that there may be some active sites on this face. There is an energy gap between the stoichiometric (220) and (211), which has low Fermi energy, indicating that their electronic structures are dynamically stable. Spin-polarized bands are calculated on the stoichiometric surfaces, and these two (200) and (210) surfaces are predicted to be noticeably spin-polarized. The Bravais-Friedel-Donnay-Harker (BFDH) method is adopted to predict crystal growth habit. The results show that the most important crystal planes for the CoS 2 crystal growth are (111) and (200) planes, and the macroscopic morphology of CoS 2 crystal may be spherical, cubic, octahedral, prismatic or plate-shaped, which have been verified by experiments.

Computational approach
The standard powder diffraction pattern of CoS 2 in Joint Committee on Powder Diffraction Standards (JCPDS) showed that the major diffraction peaks can be ascribed to the (111), (200), (210), (211) and (220) surfaces of CoS 2 , which were selected to be discussed in this paper.
The total energy calculations were carried out using first-principles spin-polarized DFT with the Cambridge Sequential Total Energy Package (CASTEP) program [22]. The spin-polarized effect was considered since the system was magnetic. The GGA formulation of Perdew, Burke and Ernzerhoff (PBE) were used to calculate the exchange-correlation energy [23]. The electron-ion interaction was described by the ultra-soft pseudo potential [24]. Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm was employed to optimize the model geometry.
For the bulk cell of CoS 2 (containing four formula units of CoS 2 ), Brillouin-zone sampling was performed on a dense Monkhorst-Pack k-point mesh of 6 × 6 × 6 points and cut-off energy was set as 450 eV. To simulate the various terminations of (111), (200), (210), (211) and (220) CoS 2 surfaces, we used slab technique with periodic boundary conditions imposed in the two directions parallel to the slab. To ensure the decoupling of the adjacent slabs, a 12 Å thick vacuum region along the surface normal was employed. The slab thickness was between 10 and 16 atomic layers based on the restriction of computational ability. All the atoms of the slab were relaxed with the eight bottom layers fixed to their bulk values. The lattice constants were fixed at bulk optimized conditions. For the various surface slab model, Brillouin-zone sampling was performed on a dense Monkhorst-Pack k-point mesh of 4 × 4 × 1 points and cut-off energy was set as 280 eV. It was found that there was little change if a higher cut-off parameter was used (i.e. less than 5 meV Å −2 ).
The stability of the various considered surfaces were investigated by associating DFT results with thermodynamic concepts [25][26][27][28]. The surface free energy in equilibrium with particle reservoirs at temperature T and pressure p is defined as Here, G surf denotes the Gibbs free energy of a periodic repeated slab, which exposes a surface with area A. Since the two exposed faces of the slab are not symmetrically equivalent, the factor of A is 1. The terms N i and μ i are the number and the chemical potential of species i, respectively, presented in the system, i = Co or S. The two chemical potentials, μ Co and μ S, are related via the Gibbs free energy of the bulk under the equilibrium condition, that is, m Co þ 2m S ¼ g bulk CoS2 , where g bulk CoS2 denotes the Gibbs free energy per formula unit. Combination with equation (2.1), a surface free energy as a function of the chemical potential of S is obtained as The term μ S is restricted by the following conditions: (i) no Co metal or sulfur from CoS 2 decomposition, and (ii) no condensation of bulk sulfur on the surface. So the following relationship is obtained: The term DH bulk f,CoS2 (T ¼ 0,p ¼ 0) is the low-temperature limit for the formation heat of CoS 2 , while E bulk S is the total energy of S atom in the α phase of bulk sulfur.

Bulk CoS 2
CoS 2 crystallizes in a rock-salt structure with space group symmetry of PA3 [29]. There are four formula units of CoS 2 in the face-centred cubic cell, as shown in figure 1. The Co atoms are situated at all corners and face centre positions, and the S 2 dimers are at the centre and midpoints of the twelve edges of the unit cell. Table 1 shows the comparison of the geometrically optimized lattice parameters with the experimental values, and the difference was small, indicating that the established model is acceptable.

CoS 2 surface models
The (

Surface energy
The calculated surface energy of different termination surfaces varying with S chemical potential (μ S ) is displayed in figure 7. The vertical dashed lines represent the upper and lower bounds of S specified by equation (2.3). The lower limit labelled as S-poor condition is defined as the equilibrium state achieved by decomposition of CoS 2 into Co and S, and the upper limit is S-rich, which corresponds to the state of accumulation and deposition of gaseous sulfur on the surface. Since there is no coefficient including μ S in equation (2.2), it is speculated that the surface free energy of the stoichiometric surfaces is independent of μ S , which is confirmed by the straight lines in the figure 7. These lines correspond to the surfaces of (111)-4S, (200)-2S, (210)-2S, (211)-3S, (220)-2S and (210)-2S. The order of surface energy increase is E Surf (220)- As seen in figure 8, the highest surface energy (200)-2S surface has the highest Fermi energy, followed by (111)-4S surface, and the Fermi energy of (211)-3S surface is slightly higher than that of (210)-2S surface, which is the lowest. The thermodynamic stability of (200)-2S surface is supposed to be stable  royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 7: 191653 due to its high surface energy, leading to the fast growth rate of this surface. However, the high Fermi energy of this surface indicates that its front valence electrons are active, resulting in transferring electrons with the lowest non-occupied band of the matched reactant easily. There may be 'active points' that bond with ions, molecules or crystal growth units in solution. Once adsorption occurs, the surface energy of the surface will be changed, resulting in the change of the growth rate of the surface, and then the crystal morphology. On the other hand, the other surface slabs have the lower Fermi energy, implying that their front valence electrons are less active and have fewer 'active points'. Especially for the (211)-3S with a very low surface energy, this surface is relatively stable in terms of thermodynamics and dynamics of electronic structure. Figure 9 shows that there are some differences in the energy distribution range, peak number and peak value on (111)    royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 7: 191653 sub-peak on (111)-4S at Fermi level is wider than that of other facets, and the difference between the subpeak and the peak at the lower energy region on (210)-2S is smaller than that of other facets, indicating that the number of energy bands with higher energy on these two surfaces is larger. On the other hand, there is no secondary peak near the Fermi energy for (211)-3S, which indicates that the thermodynamic properties of (211) surface are stable. The band structures ( figure 10) show that the band fluctuation near Fermi level at (200)-2S surface is large, which indicates that the effective mass of the electron is small, the degree of non-locality is large and the atomic orbital expansion of the band is strong. Figure 10 also shows that there are energy gaps on (211)-3S and (220)-2S slabs, which are 0.035 and 0.128 eV, respectively, indicating that their inner electrons are stable and (220)-2S surface is more stable than (211)-3S. Therefore, we can say that the dynamic stability of the electronic structure of (220)-2S in the system is better than those of other surfaces.
From the band structure diagram, the Fermi levels on (111)

Morphology prediction by Bravais-Friedel-Donnay-Harker method
In order to learn about the importance of the surfaces on growth morphology, Bravais-Friedel-Donnay-Harker (BFDH) method was employed to simulate and predict the macroscopic morphology of CoS 2 . As is shown in figure 11a, (200) and (111) are the important surfaces with the importance order of (111) > (200). These results successfully predict the exposed faces (111) and (200), and (111) is more thermodynamically stable than (200), which is consistent with the results obtained from the above surface energy calculation. Moreover, it can be inferred from the crystal morphology that CoS 2 crystal will tend to octahedron if (111) is the main exposed surface, the crystal will tend to cube if (200) is the main exposed surface, and it will tend to quasi-spherical if (200) and (111) are both exposed surfaces. The growth habit of the selected surface slab models was predicted using the same method, and the results are shown in figure 11b-f. The (111) surface tends to grow into hexagonal or hexagonal plate-like crystals, (200), (211) and (220) surfaces tend to grow into quadrangular -like crystals, while (210) tends to grow into plate-like crystals. Therefore, it can be inferred that there may be spherical, cubic, octahedral, prismatic and plate-like CoS 2 crystals in the growth of CoS 2 . CoS 2 octahedron can be prepared by hydrothermal synthesis according to our previous results [8,32]. Other CoS 2 crystals with different morphologies were also confirmed by experiments, the spherical by Wang's group [33], flakes obtained by a simple chemical bath deposition (CBD) method [34] and prisms by prismatic Co-precursors [35].

Conclusion
The various terminations of (111), (200), (210), (211) and (220) surfaces using the first-principle and the slab technique were investigated. The stability on thermodynamic of the various terminations in the arbitrary sulfur environment was examined by surface energy. The stoichiometric surfaces (220)-2S royalsocietypublishing.org/journal/rsos R. Soc. Open Sci. 7: 191653 and (211)-3S are more stable under S-rich condition, while (210)-Co and (111)-S become more stable surfaces under S-poor conditions. The electronic structure of five stoichiometric surfaces were calculated, and the results show that the front valence electrons of (200)-2S with the highest Fermi energy are active, indicating that there may be 'active points' on this surface and easy to bond with ions, molecules or crystal growth units in solution. The Fermi energies of (220)-2S and (211)-3S are low, and their inner electrons are stable, showing that the dynamic stability of electronic structure is good. Moreover, the high energy occupying bands are less, which again shows that they have good thermodynamic stability when they are the main exposed surfaces. The spin polarization of (200)-2S and (210)-2S surfaces is high. The calculated results by BFDH method showed that the important crystal planes of CoS 2 crystal growth were (111) and (200). The macroscopic morphology of CoS 2 crystal may be spherical, cubic, octahedral, prismatic and plate, which is confirmed by experiments.
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