Electron tomography and fractal aspects of MoS₂ and MoS₂/Co spheres

Abstract

A study was made by a combination of 3D electron tomography reconstruction methods and N₂ adsorption for determining the fractal dimension for nanometric MoS₂ and MoS₂/Co catalyst particles. DFT methods including Neimarke-Kiselev’s method allowed to determine the particle porosity and fractal arrays at the atomic scale for the S-Mo-S(Co) 2D- layers that conform the spherically shaped catalyst particles. A structural and textural correlation was sought by further characterization performed by x-ray Rietveld refinement and Radial Distribution Function (RDF) methods, electron density maps, computational density functional theory methods and nitrogen adsorption methods altogether, for studying the structural and textural features of spherical MoS₂ and MoS₂/Co particles. Neimark-Kiselev’s equations afforded the evaluation of a pore volume variation from 10 to 110 cm³/g by cobalt insertion in the MoS₂ crystallographic lattice, which induces the formation of cavities and throats in between of less than 29 nm, with a curvature radius r _k < 14.4 nm; typical large needle-like arrays having 20 2D layers units correspond to a model consisting of smooth surfaces within these cavities. Decreasing D _P, D _B, D _I and D _M values occur when Co atoms are present in the MoS₂ laminates, which promote the formation of smoother edges and denser surfaces that have an influence on the catalytic properties of the S-Mo-S(Co) system.

Introduction

Catalytic materials are the main pillars of liquid fuels production from hydrocarbons and its role is vital for supplying energy needs from petroleum natural resources. The layered transition metal sulfides (LTMS) such as molybdenum di-sulfide (MoS₂) were used extensively in the petroleum refining industry for more than five decades and these catalysts are referred by the catalysis research community as the “workhorses” of refining processes¹. From the industrial viewpoint cobalt and nickel are used as promoters of MoS₂ catalytic materials for enhancing deep hydrodesulfurization (HDS)^2–7 for clean fuels production containing ultra-low amounts of sulfur; however, from a basic viewpoint there is no a single model for explaining the promoter effects of Co and Ni. Previous research work by A.L. Farragher and P. Cossee⁸ proposed a model that explains the promoter effect of Co and Ni atoms in terms of a “pseudo-intercalation” effect, where Co atoms are located at octahedral sites of MoS₂ layered phase edges, i.e., (1010) type planes; also, B. Delmon et al. proposed a model based on the formation of a mix phase of MoS₂ and Co₉S₈, which could be formed by synergic interactions in the unsupported systems⁹; H. Topsøe et al. used Mössbauer spectroscopy for demonstrating that chemical bonding occurs at the edge planes of Cobalt-Sulfur-Molybdenum, thus coining the term “CoMoS” phase¹⁰; also, Chianelli et al. proposed a “Rim-Edge” model in an attempt for defining the seat of catalytic activity and specific sites within the MoS₂ stacking structure, which correlates with the activity and selectivity of unsupported systems¹¹. More recently, Lauritsen et al. reported a combined study using scanning tunneling microscopy (STM) and computer assisted numerical simulations involving plane wave density functional theory methods^12,13, which led them to conclude that metallic states in the cobalt-sulfur bonding play a key role¹⁴. Furthermore, MoS₂ layered packing structures produce diverse morphologies like nanotubes, needles, fullerenes and spheres, as described by Remškar et al.¹⁵, Camacho-Bragado et al.¹⁶, Blanco et al.¹⁷ and Ramos et al.¹⁸. The latter author used TEM and DFT simulations¹⁹ to show that electron donation of cobalt promoters occurs by synergic contact between Co₉S₈ and MoS₂ phases. Furthermore, non-conventional TEM sample holders allowed in-situ and operando experiments with these phases, as reported by Ramos et al., Helveg et al. and Casillas et al. These authors showed carburization effects on fresh MoS₂ and MoS₂/Co catalysts²⁰, crystal formation from molybdenum oxide precursors in the presence of H₂S and H₂ as well as variations of micromechanical properties^21,22. In other works, STEM 3D tomography was used, as reported by P.A Midgley and R.E. Dunin-Borkowski, to characterize low dimensional materials, proteins and organic specimens²³, while D.A. Muller resolved the atomic structure and chemical bonding of some crystallites²⁴. Ziese et al. implemented STEM-electron tomography techniques to determine the gold nanoparticles distribution over a SBA-15 type matrix²⁵, while Arslan et al. reported the use of this technique for locating gold particles supported over alumina oxide matrix²⁶. The present work afforded a multi-technique analysis of MoS₂ and Cobalt-promoted MoS₂ catalytic particles and a calculation was made of the surface fractal dimension at the molecular level for assessing better the textural and structural features promoted by Co insertion into the MoS₂ lattice. Surface fractal dimensionality is related to the roughness, steps and kinks at the molecular scale and it plays a key role for heterogeneous catalysts, as pointed out by several authors^27–30. We propose this parameter as an important one for gauging catalytic behavior of Co-promoted-MoS₂ catalysts and as a complement of “electronic effects” induced by insertion of the Co promoter, because it modifies both textural and structural properties of MoS₂; this is the first time that fractal dimensionality is shown as a result of Co-promoter insertion in spherical particles of MoS₂ and the profound effects on both texture and structure as verified in the case of MoS₂/Co system.

Results and Discussion

The crystallographic features of hydrothermally as-synthesized Cobalt promoted MoS₂ catalysts were determined by X-ray powder diffraction (Table 1); this comprised the use of Rietveld’s refinement method to verify the MoS₂ rhombohedral (R3m) symmetry, in agreement with recent work from Wang et al.³¹, from which a comparative analysis was performed as shown by Fig. 1, where one observes that a crystallographic variation occurs following cobalt addition during synthesis (Table 2), which can be explained in terms of Frenkel´s point defects³² (Table 3) caused by interstitial occluded cobalt atoms into the laminar MoS₂ structure, as described by Lauritsen et al.¹⁴. This explains the expansion of about 12.9% (from 0.7500 to 0.8465) of c-axis in the primitive lattice, as demonstrated by Radial Distribution Function results, which indicates interatomic distance variations of 11.7% for S····Mo and 24.5% for S—Mo—S, with respect to S···Mo···S distance of 3.56 Å (Table 4); these are consistent with displacements of Mo atoms to interstitial sites as confirmed on electron density maps in Figs 2a,b and 3a,b with face ab normalized to 1 and with c = 0.42 (slice 28) and c = 0.59 (slice 39); some specific data are reported in Tables 1-3). In fact, an increase of 10.4% (from 0.16667 to 0.18400) in occupancy position of sulfur O _S(2) at the MoS₂/Co lattice implies a stoichiometry variation for MoS₂ to MoS_(2+y), thus leading to a molecular increase of crystal density of about 2.14% (from 4.989 to 5.096 g/cm³) as reported in Table 1); also, the mean crystallites size of MoS₂ vary from 2 nm to 8 nm when cobalt is inserted, as discussed before¹⁸ and indicated in Table 2. The nitrogen adsorption profile of both MoS₂ and MoS₂/Co is consistent with type III isotherms, as shown in Fig. 4a,b with a pore size distribution with maxima at 29 and 38 nm for MoS₂ while these figures vary from 4 nm to 38 nm for MoS₂/Co as presented in Fig. 4c,d, thus indicating weak interactions between adsorbate and absorbent; also, a H3 type hysteresis loop (IUPAC standards) is observed in both cases, at the relative pressure (P/P°) interval between 0.4 and 0.45, thus leading to a model akin with slit-shaped pores, which was verified by electron tomography, as presented in Fig. 5a,b, thus indicating a higher N₂ uptake after comparing MoS₂ and MoS₂/Co (i.e., a variation of more than 727%); the adsorption isotherm at P/P°∼ 0.8 suggests the formation of condensate at the pores neck for P/P° > 0.9, i.e., a liquid–vapor menisci move towards the cavity of the particles, until pores filling with condensates occurs. With the purpose of understanding better this phenomena a series of DFT numerical simulations were completed to determine relevant pore structure parameters (i.e., S ^BET /S ^DFT, V _p ^DFT and Φ ^DFT)as shown in Table 5 ; We propose this parameter as an important one for gauging catalytic behavior of Co-promoted-MoS₂ catalysts and as a complement of “electronic effects” induced by insertion of the Co promoter, because it modifies both textural and structural properties of MoS₂; this is the first time that fractal dimensionality is shown as a result of Co-promoter insertion in spherical particles of MoS₂ and the profound effects on both texture and structure as verified in the case of MoS₂/Co system³². Thus, a summary of these results is presented in Table 5 where one observes an increase of 29% in S ^BET /S ^DF, with a further increase up to 110% for V _p ^DFT as a result of the overall increase of N₂ uptake upon insertion of cobalt atoms in the MoS₂ lattice. The calculation of Fractal dimension from transmission electron micrographs and the use of Neimark-Kiselev equation in D _{s(adsorption/desorption)} led to determine a decrease of 12% after insertion of cobalt (i.e., details are shown in Tables 6–7), thus implying a lower fractal dimension as exhibited in Fig. 5c,d for r _k values within the interval 6.05–40.44 nm for the MoS₂ spherically shaped particles while r _k values fall within the interval 4.95–20.08 nm for MoS₂/Co system that is spread on the surface, which is observed by STEM tomography (Table 7) as presented in Fig. 6a,b, from which the fractal dimension is obtained using D _P, D _B , D _I and D _M methods, i.e., 1.17 and 1.05 are the fractal dimensions for MoS₂ and MoS₂/Co, while D _B decreases from 1.71 to 1.57due to the surface topology associated with cobalt addition; D _I indicates dispersion of the surface due to the cobalt presence and finally D _M determines a dense surface on MoS₂/Co as observed by larger array of laminates revealed by high-resolution STEM (insets of Fig. 6a,b). Additionally, a second run of fractal calculations were done using TEM-2D images, from which fractal values show a decreasing trend with the cobalt presence, with values of D _P (25.0%), D _B (5.3%), D _I (17.0%) and D _M (16.0%) as well as when using scanning electron images with values of D _P (34.7%), D _B (28.0%), D _I (23.4%) and D _M (1.9%). See Tables 8–9.

Table 1.

Lattice parameters obtained by Rietveld refinement from x-ray powder diffraction for pure spherical shaped MoS₂ .

MoS2 R 3 m H (160)			Lattice: Rhombohedral			Occupancy
			Atomic fractional coordinates
Atom	Type	Site	x	y	z
Mo (1)	Mo4+	3a	0.0000	0.0000	1.0000	0.16667
S (1)	S2−	3a	0.0000	0.0000	0.2500	0.16667
S (2)	S2−	3a	0.0000	0.0000	0.7500	0.16667
Lattice parameters (Å)			Angles
a	b	c	α	β	γ	Density (g cm−3)
3.1710	3.1710	18.3445	90°	90°	120°	4.992

Figure 1.

Powder x-ray diffraction patterns and Rietveld refinement for (a) MoS₂ and (b) Co/MoS₂ samples, it is possible to observe a sharp peak at (003)-basal plane when cobalt atoms are present, compared to pure MoS₂ .

Table 2.

Lattice parameters obtained by Rietveld refinement from x-ray powder diffraction for cobalt promoted MoS₂ .

Material	Molybdenite crystallite size (nm)	Density (g cm−3)	Atomic fractional coordinates of S (2)			O S (2)
			x	y	z
MoS2	2 (0.4)	4.989	0.0000	0.0000	0.7500	0.16667
MoS2/Co	8 (0.8)	5.096	0.0000	0.0000	0.8465	0.18400

The number in parenthesis corresponds to the standard deviation.

O _{S (2)}: S (2) occupancy (see Table 1).

Table 3.

Statistical parameters after Rietveld refinement for both cases.

Material	R p	R wp	χ 2	R exp
MoS2	2.95	4.67	2.52	2.94
MoS2/Co	1.30	1.74	2.07	1.21

Table 4.

Radial distribution function peaks values of MoS₂ and Co/MoS₂ samples.

Material	Interatomic distances r (Å)
	Mo—Mo	S····Mo····S	S—Mo—S	S····Mo	Mo····Mo
MoS2 *	3.171	3.563	4.770	5.575	6.383
MoS2 #	3.170	3.560	4.720	5.710	6.360
MoS2/Co#	3.140			5.110	6.430

*Theoretical interatomic distances.

^#Obtained by XRD.

—Bond, ----Only distance.

Figure 2.

Radial distribution plots for (a) MoS₂ crystallographic lattice (a = b = 3.1710 and c = 18.3445 Å) (SG: R3mH). (b) Co/MoS₂ it is possible to observe a shifting of Mo-Mo and S-Mo-S peaks, as well the appearance of a new peak at 2.2 Å when cobalt atoms are present in the MoS₂ lattice.

Figure 3.

(a) Electron density maps to indicate cobalt atoms at the MoS₂ crystallographic lattice and (b) for Cobalt atoms into the MoS₂ lattice. (Data calculated using information from powder X-ray diffraction and DFT numerical simulations).

Figure 4.

(a and b) Nitrogen adsorption/desorption isotherms run at 77 K for both cases MoS₂ and Co/MoS₂. (c and d) Numerical simulation of pore diameter distribution for MoS₂ samples and (d) Co/MoS₂ samples.

Figure 5.

Scanning Transmission Electron Tomography for both MoS₂ and Co/MoS₂ samples. It is possible to determine surface dispersion and change of pore volume when cobalt atoms are present on the sample. Inset: High resolution image of specific section on both cases, one can observe large laminates growth due to addition of cobalt atoms into the MoS₂ lattice.

Table 5.

Specific surface area, pore volume and mean pore size for both cases.

Material	S BET / S DFT (m2g−1)	V P DFT (mm3 g−1)	Φ DFT (nm)
MoS2	20/21	10	29/38
MoS2/Co	26/27	110	4/7/12/21/29/38

Values were obtained from numerical DFT simulations and experimental isotherms.

Table 6.

Fractal dimension parameters as calculated by Neimark-Kiselev from isotherm curves for MoS₂ and Co/MoS₂ samples.

Method of analysis	Materials
	MoS2	MoS2/Co
D S (Adsorption)	2.47 (6.05–40.44)#	2.18 (4.95–20.08)#
D S (Desorption)	2.52 (6.05–49.40)#	2.25 (6.05–16.44)#

Ds scaling interval ∈ [2, 3]; ^#Radius of curvature (nm).

Table 7.

Fractal dimension parameters and porosity as calculated by different methods from STEM images.

Material	Method of analysis
	D p	D B	D I	D M	STEM-porosity (%)
MoS2	1.17 ± 0.01	1.71 ± 0.02	1.83 ± 0.01	1.86 ± 0.01	14.6
MoS2/Co	1.05 ± 0.01	1.57 ± 0.01	1.64 ± 0.01	2.21 ± 0.01	23.6

D _P, D _B, D _I and D _M are measured from STEM-images; D _p scaling interval ∈ [1, 2]; D _B scaling interval ∈ [1, 2]; D _I scaling interval ∈ [1, 2]; D _M ≥ 1.

Figure 6.

High resolution transmission electron microscopy images: (a and b) are TEM-images (scale bar 100 nm) corresponding to MoS₂ and Co/MoS₂ respectively. (c and d) are scanning electron microscopy images (scale bar 1.0 µm) of MoS₂ and Co MoS₂ using both techniques, to determine surface dispersion when cobalt atoms are added, as reported before¹⁸.

Table 8.

Fractal dimension parameters as calculated by different methods from high-resolution TEM images for MoS₂ and Co/MoS₂.

Method of analysis	TEM images scale bar at 100 nm
	MoS2	MoS2 /Co
D p	1.67 ± 0.25	1.25 ± 0.24
D B	1.69 ± 0.08	1.60 ± 0.06
D I	1.68 ± 0.37	1.40 ± 0.02
D M	2.00 ± 0.09	2.32 ± 0.17

D _P, D _B, D _I and D _M are measured from TEM-images; D _p scaling interval ∈ [1, 2]; D _B scaling interval ∈ [1, 2]; D _I scaling interval ∈ [1, 2]; D _M ≥ 1.

Table 9.

Fractal dimension parameters as calculated by different methods from SEM images for both MoS₂ and cobalt promoted MoS₂ samples.

Method of analysis	SEM-images at 1.0 µm
	MoS2	MoS2 /Co
D p	1.64 ± 0.03	1.07 ± 0.02
D B	1.90 ± 0.01	1.37 ± 0.01
D I	1.92 ± 0.01	1.47 ± 0.01
D M	1.98 ± 0.01	2.02 ± 0.02

D _P, D _B, D _I and D _M are measured from TEM-images; D _p scaling interval ∈ [1, 2]; D _B scaling interval ∈ [1, 2]; D _I scaling interval ∈ [1, 2]; D _M ≥ 1.

Conclusion

The abovementioned results led us to conclude that chemical state and geometric features together might play an important role, i.e., cobalt atom radius is about 20% larger than sulfur atoms while cobalt ions (Co⁺) are about 40% the size of sulfur ion S²⁻; also, the specific hydrothermal synthesis method could contribute too. It was found that Co tends to occupy MoS₂ edges, as determined by Rietveld’s refinement method, thus the “CoMoS phase” should be formed. Moreover, the use of Neimark-Kiselev set of equations led us to conclude that cobalt insertion into the MoS₂ crystalline arrays induce a pore volume increase from 10 to 110 cm³/g, which provokes an increase of the diameter of cavities as well as formation of throats with diameters smaller than 29 nm and r _k < 14.4 nm, which explains the higher N₂ consumption during the isotherm runs. Additionally, cobalt insertion promotes formation of large needle-like laminates with a stacking average of ~20 2D layers, as observed by high resolution STEM, with D _s values falling in a region where radii of curvature are smaller (14.4 nm), which means that smoother surfaces are formed inside the cavities. Also, a decreasing trend of D _P, D _B, D _I and D _M was found with insertion of cobalt in the MoS₂ laminates (Table 4b–d), which is interpreted as enhancing the crystallite edge smoothing and surface density. This fundamental approach allowed to understand better the behavior of “CoMoS” phase type catalysts. Further work using a similar approach for “spent” MoS₂/Co and MoS₂ catalytic phases is underway for studying the role of carbon in the catalytic properties of those phases.

Experimental Methods

Catalyst Preparation

A black powder precipitate was synthesized by mixing 3 mmol of sodium molybdate (Na₂MoO₄.2H₂O) and 9 mmol of thioacetamide (CH₃CSNH₂) when dissolved in 30 mL of deionized water, and then 0.5 g of sodium silicate (Na₂SiO₃.9H₂O) was added into the solution under violent stirring. The pH value of the solution was adjusted to 6.0 by dropping 12 M hydrochloric acid (HCl) solution. 0.50 g of cobalt chloride (CoCl₂) was added to the solution before the hydrothermal reaction at a precise temperature, i.e., 220 °C [inside reactor chamber] for 4 h, thus allowing a natural cooldown. The catalyst was washed using a 1 M of Sodium Hydroxide (NaOH) to remove possible residues, mainly silicic acid and this was dried at 200 °C in autoclave. The synthesis follows the stoichiometry reaction: 1) 6CoCl₂6H₂O + 12Na₂MoO₄ + Na₂SiO₃ + 26HCl → H₄SiCo₆Mo₁₂O₄₀ + 26NaCl + 47H₂O + 6Cl₂. 2) CH₃CSNH₂ + 2H₂O → CH₃COOH + NH_3 +H₂S. 3) H₄SiCo₆Mo₁₂O₄₀ + 27H₂S → 12Co_0:5MoS₂ + H₂SiO₃ + 3H₂SO₄ + 25H₂O (for more information see Ramos et al.¹⁸).

Powder XRD and Rietveld refinement

All diffraction patterns were obtained with a Bruker Advance D-8 diffractometer fitted with Bragg-Brentano geometry, using CuKα radiation and a Lynxeye type detector. The intensities were obtained in the 2-theta ranges between 10 and 100° with a step of 0.019447° and a measuring time of 10 s per point. The crystalline structures were refined by Rietveld’s method using TOPAS-Academic software³³. All theoretical crystal density was calculated by the following equation: ρ _crystal = (Z)(MM)(Avogadro’s number)⁻¹/Cell volume; where Z is the number of molecules per cell and MM is the molecular weight. Radial Distribution: The distance (r) between atoms in MoS₂ and MoS₂(Co) crystallites was obtained by Radial Distribution Function G(r) up to 6.5 Å, in a Siemens D500 diffractometer fitted with a molybdenum anode X-ray tube. The intensities were measured in a step-by-step mode of 0.01°, from 2 to 110° (2θ), using the Radiale program³⁴.

Adsorption/Desorption isotherms

All the measurements of N₂ sorption isotherms were obtained at 76 K using a Quantachrome Autosorb 3B instrument under N₂ and He gases (UHP grade) conditions. Prior to isotherms runs, all the samples were outgassed for 12 h at 473 K. The specific surface areas were calculated from desorption isotherms using BET equation, while the pore structure parameters were determined by non-local density functional theory.

Experimental HRTEM microanalysis and Electron Tomography

Imaging of ultra-high resolution TEM was performed in an FEI Tecnai F20 instrument operating at 200 kV in STEM mode. Images were acquired every 2°, from −70 to + 70, totaling 71 images for each tilt series. The HRTEM images were collected in a JEOL ARM (200 F) instrument at operational voltage of 200 kV, which was fitted with a Cs corrector (CEOS GmbH) and FEG-STEM/TEM unit; a HAADF probe size was set to 0.095 nm with a current of 23.2 pA for bright field imaging, the condenser lens aperture size was set to 40 µm. A camera length (CL) of 8 cm/6 cm and collection angle of 68–280 mrad/90–270 mrad was set for STEM images, to eliminate contributions from un-scattered beams. The specimens were prepared for electron microscopy by crushing the powder between two glass slides, and rubbing a holey carbon grid across the crushed powder to capture the material. All images were reconstructed using Gatan Digital Micrograph® computational software and these were aligned with respect to each other using the center of mass of the particle³⁵. These were reconstructed using total variation (TV) regularization, and visualized using the tomviz software³⁶.

Computational Software

Novawin 11.03 package was used for all the numerical simulations for porous size distribution and textural properties.

Author Contributions

M. Ramos was in charge of chemical synthesis and scanning electron imaging. F. Galindo-Hernández completed all computer assisted numerical simulations. I. Arslan and T. Sanders performed electron tomography measurements and computer assisted reconstruction. J.M. Domínguez is the principal investigator on this particular Energy project in charge of design and supervision of all experiments. This manuscript was mainly typed by M. Ramos, F. Galindo, I. Arlsan and J.M. Domínguez.

Competing Interests

The authors declare that they have no competing interests.