Computational investigation of mechanical properties and adsorption behavior of sulfur-doped h-BN nanosheets

Abstract

Doping h-BN surface with sulfur has been shown to enhance its efficiency in photocatalytic reactions. Here, using density functional theory calculations, the various configurations of S-doped h-BN were investigated in terms of their formation energy, mechanical properties, structural, thermodynamic, and electronic properties, as well as their ability to adsorb metal atoms and hydrogen molecule. The formation energy of S-doped h-BN surfaces is only slightly more positive compared to the pristine surface. The band gap energy experiences the most significant changes when an S atom replaces an N atom. At low temperatures, the pristine h-BN surface has a higher vibrational Gibbs free energy compared to S-doped h-BN surfaces, but at high temperatures, it exhibits a lower value. The bulk modulus of S-doped h-BN surfaces was found to range from 151.2 to 163.0 GPa. Additionally, the Poisson’s ratio of the S_N surface was found to be 0.237, which is slightly higher than that of the h-BN surface. The evaluated in-plane hardness of S-doped surfaces ranges from 221.8 to 196.1 GPa. Investigation into the adsorption of transition metals (Mo, Zn, Cd), post-transition metals (Ga), and metalloids (Ge, Se) on both pristine and S-doped h-BN surfaces revealed significantly enhanced binding energies on the S-doped surfaces. The strongest interactions occurred with the s-doped surface decorated with Mo and Ge metals. Hydrogen dissociatively adsorbs on the S_N surface. Also, the hydrogen molecule binds more strongly to metal-decorated surfaces. The results show that the S-doping of h-BN surface improves its electronic characteristics and adsorption capability without significantly altering its mechanical properties

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-17202-y.

Introduction

Crystalline hexagonal boron nitride is a synthetic material that was first successfully produced in the mid-nineteenth century¹. This structure is the most stable polymorphic form of boron nitride at room temperature², which has a structure similar to graphite. Strong covalent bonds bind boron and nitrogen atoms in each layer, whereas weak van der Waals interactions hold separate layers together³. Similar to graphene, a hexagonal boron nitride layer (h-BN) has a planar structure. The synthesis of high-quality h-BN thin films with excellent intrinsic characteristics remains an intriguing topic⁴. However, unlike graphene, this nanosheet has a wide band gap, which results in excellent chemical stability and oxidation resistance at high temperatures^5,6. Therefore, despite its similarities to graphene, h-BN’s unique features make it superior. These unique properties, along with its high surface area, low toxicity⁷, and adjustable band gap⁸, leading to the investigation of its various applications, including in quantum emitters⁹, electrochemical measurements¹⁰, molecular switching¹¹ as a solid-lubricating additive in self-lubricating composites¹², as a corrosion protective coating¹³ gas adsorption and detection^14,15, biosensing¹⁶, and in energy storage^17–19.

The mechanical properties of the h-BN surface have been of interest since the beginning due to potential applications in some fields, such as polymer nanocomposites²⁰. Depending on the method used, different computational studies have predicted different values in the range of 267.0–281.6 j/m² for the in-plane stiffness of this surface. Additionally, Poisson’s ratio of the h-BN surface has been reported in the range of 0.213–0.297^21–26. Examining the elastic properties of this surface through theoretical or experimental methods has also been done to estimate its bulk modulus^27–30.

Despite the high chemical and thermal stability of h-BN, its high band gap limits its usage in some applications. Therefore, efforts have been made to alter its electronic characteristics through methods such as doping or decorating the surface with metal atoms^31–33. Many computational and experimental studies have been reported on the h-BN surface, which have tried this method to improve catalytic activity^34,35, optical and magnetic properties^8,36,37, energy storage^38,39, sensing properties^40–42, and the adsorption or removal of pollutants by the surface^43–45.

The effect of sulfur atom replacement on the properties of the h-BN nanosheet has been experimentally investigated. S-doping generally results in an increase in the h-BN surface’s reactivity, hydrophilicity, charge transfer, and optical absorption. As a result, hydrogen is produced on this surface more efficiently than conventional visible-light photocatalysts⁴⁶. In addition, research has shown that the band gap and layer spacing of h-BN can be altered by regulating the amount of doped sulfur⁸. The structural and electronic properties of the S-doped h-BN have been studied through density functional theory (DFT) calculations⁴⁷. Furthermore, the computational approach has been utilized to demonstrate the impact of co-doping with Fe and S atoms on the stability and catalytic activity of the h-BN surface⁴⁸.

The fundamental understanding of S-doped h-BN surfaces, derived from a thorough characterization of their structural stability, electronic and optical properties, thermodynamic behavior, and mechanical characteristics, is critical for investigating their manifold applications. Although the S-doped h-BN surface has been studied concerning its optical properties, no research has been conducted on how S-substitution affects this surface’s mechanical properties or adsorption behavior. In the present study, a computational survey has been done on S-doped h-BN surface utilizing density functional theory. The mechanical and thermodynamic properties of various configurations of S-doped h-BN have been examined, as well as their structural and electronic characteristics. Furthermore, the effect of S substitution on the adsorption of some atoms on the surface was examined, as well as the hydrogen molecule interaction with the resultant surfaces. The investigated atoms in this study are Se, Ga, Ge, Mo, Cd, and Zn, whose adsorption on the h-BN surface has not been looked at. Density of states (DOS), partial density of states (PDOS), and band structure diagrams were used to investigate the effects of sulfur doping, metal decoration, and hydrogen adsorption on surface electronic properties. Charge transfers during these processes were investigated using Mulliken charge analysis and deformation charge density plots.

Computational methods

All DFT calculations were performed using the Dmol³ module in the Material Studio software package⁴⁹. The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof functional form was used to evaluate exchange–correlation energies⁵⁰. The basis set used in this study is the double numerical polarizing functions (DNP)⁵¹, which has comparable accuracy to the Pople 6-31G** basis set. This basis set is commonly used in the study of 2D surfaces^52–54. Grimme’s semi-empirical DFT-D2 method was utilized to take into account Van der Waals interactions⁵⁵. A vacuum distance of 20 Å was considered in the z-direction to avoid intercellular interaction. In relaxation calculations, the k-points of the Brillouin zone were sampled using a 5 × 5 × 1 grid produced by the Monkhorst–Pack scheme⁵⁶. This k-points grid was chosen based on its convergence with energy (Fig. S1). All calculations were performed using a global orbital cutoff radius of 4.9 Å. The values for the convergence threshold for maximum change in energy, force, and displacement were set to be 10^–5 Ha, 0.002 Ha.Å⁻¹, and 0.005 Å during geometry optimization, respectively.

To model S-doped h-BN surfaces, in line with experimental findings that confirm S–B and S–N bond presence in this surface^8,46 (thereby implying sulfur substitution for nitrogen and boron), three configurations were designed: S-substitution for a B atom, S-substitution for an N atom, or S-substitution for a pair of adjacent N and B atoms. The resulting surfaces were named S_B, S_N, and S_BN, respectively. The formation energy of these surfaces was calculated using the following equation:

1

In this equation, , , , and represent the total energy of the surface, the energy of an isolated N₂, molecule, the energy of a B atom in orthorhombic lattice, and the energy of a S atom in a rhombic lattice, respectively. The number of B, N, and S atoms in the supercell is indicated by i, j, and k, respectively. S-doped h-BN surfaces were investigated for their structural, electronic, mechanical, and thermodynamic properties in addition to their equation of state.

Birch–Murnaghan’s equation of state explicitly expresses the relationship between the volume of a substance and the pressure applied to it, which widely used for solids, especially in high-pressure conditions⁵⁷. Based on Birch-Murnaghan’s third-order equation of state,

2

where and are bulk modulus and its pressure derivative, and is the equilibrium volume at zero pressure. The bulk modulus is one of the elastic moduli that indicates the material’s resistance to volume changes and is a key factor in several equations of state for solids. An energy-based equation of state is obtained by integrating the P–V–T equation of state. This is very helpful when it comes to ab initio calculations. In this study, the bulk modulus and equation of state of surfaces were evaluated using the Gibbs2 program⁵⁸.

Closed-form expressions for necessary and sufficient elastic stability conditions have been found for two- and three-dimensional crystal systems^59,60. To investigate the impact of S-doping on the mechanical properties of the h-BN surface, the in-plane stiffness and Poisson’s ratio of the surfaces were calculated. The in-plane stiffness can be evaluated by the equation, , where is the strain energy and and are the uniaxial strain and equilibrium surface area. The strain energy is obtained by subtracting the total energy of the strained surface from the equilibrium surface’s total energy. To determine the elastic constants of each surface, compressive and tensile stresses up to 0.02 were applied along the x and y axes. After optimization calculations, strain energies were calculated. Results were fitted using the following formula;

3

where and denote the applied strains along the x and y axes, respectively, and and , with h representing the monolayer thickness. Using the coefficients of the above equation, Poisson’s ratio () and in-plane stiffness were obtained from the following formulas^22,61:

4

5

It should be mentioned that a rectangular cube supercell was used for these calculations (Fig. S2). In order to investigate the effect of S-doping on the adsorption properties of h-BN surfaces, the adsorption of Se, Ga, Ge, Mo, Cd, and Zn atoms was examined on h-BN and S-doped h-BN surfaces. The adsorption energy of a metal atom was evaluated using the following equation:

6

where surface denotes pristine or S-doped h-BN surface, and x denotes one of the Se, Ga, Ge, Mo, Cd, and Zn atoms. , and represent the total energy of the isolated x atom in a supercell, the total energy of the surface and the total energy of the adsorbed x surface, respectively. Subsequently, the adsorption of hydrogen molecule on the resulting surfaces was also investigated. The hydrogen adsorption energy was determined using the following equation:

7

In this equation, the term surface refers to either the pristine h-BN surface or the S-doped h-BN surface, which may be decorated with a metal atom, or left undecorated. , , and refer to the total energy of the surface, the total energy of the adsorbed H₂ surface, and the total energy of the isolated hydrogen molecule in the supercell, respectively. Charge transfers and changes in the electronic properties that occurred during the adsorption process were also investigated.

Results and discussion

S-doped h-BN

Variable-cell relaxation calculations were first carried out on h-BN and S-doped h-BN surfaces. The top and side perspectives of these surfaces are depicted in Fig. 1. The structural and electronic characteristics of the surfaces are reported in Table 1.

Fig. 1.

The optimized h-BN and S-doped h-BN surfaces from top and side views.

Table 1.

Formation energy, average distance of the S atom from the surface (h), cell constant (a), Mulliken charge of the sulfur atom (Q_S), and band gap energy () for h-BN and S-doped h-BN surfaces.

Structure	(Ha/unitcell)	h (Å)	a (Å)	QS (e)	Eg (eV)
h-BN	– 247.04	–	7.554	–	4.66
SB	– 246.81	1.06	7.660	0.53	0.85
SN	– 219.81	1.30	7.580	– 0.08	0.36
SBN	– 219.38	0.50	7.460	0.17	1.82

The supercell constants of h-BN were found to be a = b = 7.554 Å, and B-N bond length and B-N-B bond angle were found to be 1.454 Å and 120°, respectively, which are in agreement with previously published results^43,62,63. As Table 1 shows, substituting the S atom for B or N atoms increases the unit cell size, which is reasonable given the larger atomic radius of S compared to B or N atoms. In the S_B structure, the sulfur atom is closer to the surface, resulting in a larger cell parameter. The unit cell parameter for the S_BN structure shows a decrease compared to the h-BN structure. This decrease is anticipated and results from the substitution of one sulfur atom for two atoms of surface. The sulfur atom in S_BN and S_N has a completely symmetrical position relative to its neighboring atoms, but this is not true for S_B.

In the S_B and S_N structures, the neighboring atoms of the S atom have a small distance from the surface (up to 0.19 Å), but the other atoms remain on the surface. The S atom in the S_BN structure is located at an average distance of 0.50 Å from the surface. However, despite the slight distortion observed on the surface, the overall structure maintains its planar form.

A review of the reported formation energies in Table 1 reveals that all S-doped h-BN surfaces have a negative formation energy. Moreover, the S-doped h-BN surfaces’ formation energies are not significantly different from those of the h-BN surface, despite being more positive. So that the formation energy of the S_B structure is only 0.23 Ha higher than that of the h-BN surface. The formation energies of S_N and S_BN are close to each other and are more different from the h-BN formation energy. Nevertheless, experimental studies also support the substitution of sulfur atoms instead of nitrogen atoms⁴⁶.

In order to evaluate the electronic and magnetic characteristics of BN and S-doped surfaces, their band structures and PDOS plots were analyzed. Based on the band structure plot (Fig. S3), the h-BN surface is a p-type semiconductor with a large band gap energy of 4.66 eV, which matches the reported values^47,62,64. The h-BN surface’s down-spin bands completely overlap the up-spin bands and show no spin polarization (Fig. S3), indicating the nonmagnetic property of the surface. According to the PDOS diagram of the h-BN surface, the p orbitals around the Fermi level play the main and decisive role (Fig. 2). These orbitals strongly interact with s orbitals in a wide energy range.

Fig. 2.

PDOS diagrams of h-BN and S-doped h-BN surfaces. The Fermi level is set at zero energy.

The band structure diagrams show a significant change in surface electronic properties due to S-doping. The energy states formed around the Fermi level decreased the band gap energy to 0.36, 0.85, and 1.82 eV for the S_N, S_B, and S_BN surfaces, respectively. Research indicates that lattice distortion significantly influences the energy gap^65,66. Consequently, the observed reduction in the band gap of S-doped h-BN is likely attributable to structural distortions induced by sulfur substitution and the resultant alterations in the boron-nitrogen bonds within the unit cell. The replacement of the N atom with the S atom has turned the surface into an n-type semiconductor. Furthermore, the S_BN surface’s spin-down and spin-up bands fully overlap. On the other hand, the spin polarization is plainly seen in the band structure of the S_B and S_N surfaces. As a result, S_B and S_N surfaces are magnetic in contrast to h-BN and S_BN surfaces. The electronic properties of both S_N and S_B surfaces align with those reported by Asif et al.⁴⁷, exemplified by the resemblance in their respective band structure diagrams to our findings. However, discrepancies in band gap energies are evident, likely attributable to the considerably lower sulfur concentration utilized in their structures.

PDOS plots of S-doped h-BN surfaces are presented in Fig. 2 A comparison of the PDOS diagram of S-doped surfaces with that of the h-BN surface reveals that the addition of sulfur has caused a shift in the peaks toward negative energies. S-doped h-BN surfaces, similar to the pristine surface, exhibit high peaks near the Fermi level, primarily attributed to the p orbitals of surface atoms. The d orbital peaks of the S atom strongly resonate with the s and p orbitals of this atom, which confirms their hybridization. The d orbital peaks of the S atom in the valence region indicate electron transfer to these orbitals. However, the positive charge on the sulfur atom in the S_B and S_BN surfaces indicates that overall, a charge transfer from this atom occurs due to the bonding with the surface. Furthermore, the overlap of the S atom orbital peaks with the s and p orbital peaks of surface atoms over a wide energy range provides evidence of strong bonding between them.

In order to examine the impact of S-doping on the surface’s thermodynamic properties, frequency calculations were performed for all surfaces at the Gamma point. These calculations show that the optimized surfaces have no imaginary frequency, which indicates the stability of these structures. The frequency outputs were used to determine the zero-point energy and thermodynamic properties. Figure 3 shows the thermodynamic properties graphs for vibrational degrees of freedom vs. temperature. It can be observed that the h-BN surface has a higher entropy than S-doped h-BN surfaces at all temperatures (Fig. 3a), and the entropies of the S_B and S_N surfaces are extremely close to each other. However, the entropy of the S_BN surface is higher than that of the S_B and S_N surfaces up to 500 K, but S_BN shows lower entropy at higher temperatures.

Fig. 3.

Variation of (a) specific heat capacity (C_V), (b) entropy (S), (c) Gibbs free energy (G), and (d) enthalpy (H) with temperature for h-BN, S_B, S_N, and S_BN surfaces.

Although the heat capacities of all surfaces are very close to each other, the S_BN surface stands out with a lower heat capacity at temperatures above 400 K (Fig. 3b). However, all surfaces show a similar trend of heat capacity variation with temperature, ultimately converging in the high-temperature range. The overall trend of enthalpy changes with temperature is similar for both h-BN and S_BN surfaces (Fig. 3c). Furthermore, the S_B and S_N surfaces’ enthalpies are very close to each other and essentially coincide.

It is evident from Fig. 3d that the h-BN surface has the highest Gibbs free energy at low temperatures, whereas the S_BN surface has the lowest value. The pattern changes, though, and the h-BN surface has the lowest Gibbs free energy, while the S_BN surface has the highest at high temperatures.

Equations of state and mechanical properties

Biaxial compressive and tensile strains up to 25% were applied to the supercell of each surface. After optimization, the supercell energy and volume for different strains were used as input for the Gibbs2 program. Figure S4 shows the energy diagrams vs. supercell parameters for pristine and S-doped h-BN surfaces. Using the Debye model to incorporate the effect of temperature and Birch-Murnaghan polynomial averages, and were calculated for different pressures and temperatures using the aforementioned program.

Based on the results, the bulk moduli for h-BN, S_B, S_N, and S_BN surfaces are 171.8, 156.4, 151.2, and 163.0 GPa, respectively, at a temperature of 298 K and a pressure of 1 atm. No reports exist for the bulk modulus of S-doped h-BN surfaces. However, previous reports of the bulk modulus of pristine h-BN^25,27 surfaces support our calculated result. The diagrams in Fig. 4 display the changes in bulk modulus of the studied surfaces as temperature increases up to 350 K. All surfaces exhibit an expected drop in bulk modulus as temperature rises. In this temperature range, the bulk modulus for h-BN, S_B, S_N, and S_BN surfaces falls by 0.4, 0.6, 0.9, and 0.4 GPa, respectively. These plots demonstrate that B remains relatively constant for h-BN and S_BN surfaces up to 200 K, whereas B starts to experience changes for S_B and S_N surfaces at approximately 150 K and 100 K, respectively.

Fig. 4.

Variation of bulk modulus with temperature for h-BN, S_BN, S_N, and S_B surfaces.

In addition to bulk modulus, in-plane hardness and Poisson’s ratio were also calculated to investigate the effect of S-doping on the mechanical properties of the h-BN surface. For this purpose, compressive and tensile strains were applied along the x and y axes in the harmonic region, in the range of 0–0.02%, and each structure was completely optimized. The strain energy was calculated for each grid point, and the data were fitted to Eq. 3 using the least squares method.

In Fig. 5, strain energy is plotted against cell parameters for pristine and S-doped h-BN surfaces. As evident from the diagrams, the maximum strain energy corresponds to the condition where the compressive or tensile strain is the highest and is equal along both axes. In this condition, the strain energy of the pristine h-BN surface is higher compared to that of S-doped surfaces, and the strain energies of S-doped surfaces are very close. The strain energy of S-doped surfaces exhibits a larger difference when compressive strain is applied along one axis and tensile strain is applied along the other. The S_N surface has the lowest strain energy in this situation, and the S_B surface has the highest strain energy following the h-BN surface.

Fig. 5.

Strain energy variation with strain for h-BN, S_BN, S_N, and S_B surfaces from two views.

Using the obtained coefficients for Eq. 3, Poisson’s ratio and in-plane hardness were calculated for different surfaces with the help of Eqs. 4 and 5. The calculated in-plane hardness values for h-BN, S_B, S_N, and S_BN surfaces are 274.2, 221.8, 196.1, and 206.8 J/m2, respectively. Additionally, the evaluated Poisson’s ratio values for these surfaces are 0.224, 0.169, 0.237, and 0.216, respectively. For the pristine h-BN surface, the obtained values of Poisson’s ratio and in-plane hardness are in good agreement with previously published values^22,25,26. Comparing the in-plane hardness of nanosheets shows that S-doping of the h-BN surface increases its elasticity. Accordingly, the S_N nanosheet exhibits the highest elasticity compared to other surfaces. The comparison of Poisson’s ratio for the studied nanosheets shows that replacing a N atom or a pair of N and B atoms with an S atom (S_N and S_BN) does not cause much change in Poisson’s ratio. Replacing a B atom with an S atom decreases Poisson’s ratio, which means an increase in the resistance of the surface against deformation.

By elucidating the influence of S-doping on bulk modulus and in-plane stiffness, these findings offer fundamental guidance for the rational design of h-BN materials possessing tailored mechanical properties.

Metal atoms decoration

The impact of S-doping on the adsorption characteristics of the h-BN surface was examined in the next section of this work. In order to do this, different metal atoms’ adsorption on the pristine and S-doped h-BN surfaces was investigated. Furthermore, an H₂ molecule’s adsorption on every surface was investigated. In the study of metal adsorption on the pristine h-BN surface, all four adsorption sites were examined: the top of the N and B atoms (N and B sites), above the B-N bond (Br site), and above the hexagonal hole (H site). In the case of metal adsorption on S-doped surfaces, the S atom was taken into consideration as the adsorption site. Due to the protrusion of sulfur in S_B and S_N structures, the adsorption of metal atoms was examined on both sides of the surface, above the sulfur atom on the side where the sulfur atom protrudes from the surface (down site) and on the opposite side (up side). After optimization, the adsorption energies were calculated using Eq. 6. The most stable configuration for the adsorption of each metal on pristine and S-doped h-BN surfaces is depicted in Figures S5 to S8. Furthermore, the adsorption energies for the most stable configuration of adsorption of each metal atom on different surfaces are displayed in Table 2.

Table 2.

Metal adsorption energy on the pristine h-BN and S-doped h-BN surface.

Structure	(eV)	Structure	(eV)	Structure	(eV)	Structure	(eV)
h-BN-Mo	– 2.84	SB-Mo	– 7.43	SN-Mo	– 5.34	SBN-Mo	– 3.37
h-BN-Cd	– 0.36	SB-Cd	– 0.82	SN-Cd	– 0.75	SBN-Cd	– 0.11
h-BN-Ge	– 0.65	SB-Ge	– 4.57	SN-Ge	– 2.63	SBN-Ge	– 6.77
h-BN-Zn	– 0.26	SB-Zn	– 0.81	SN-Zn	– 0.54	SBN-Zn	– 0.33
h-BN-Ga	– 0.42	SB-Ga	– 3.23	SN-Ga	– 1.99	SBN-Ga	– 1.62
h-BN-Se	– 0.81	SB–Se	– 2.57	SN-Se	– 3.75	SBN-Se	– 1.86

Figure S5 illustrates that the adsorption of metal atoms does not alter the planar form of the h-BN surface. According to the data in Table S1, after optimization, no metal atom is placed at the Br site. Instead, the hexagonal cavity and N sites are generally preferred. So that all calculations led to the positioning of the metal atom on top of the N atom, in the case of the Ga and Ge atoms. The interaction between Zn, Ga, and Cd atoms and the surface is weak, which leads to a low binding energy. The most negative adsorption energy is associated with Mo adsorption, while the lowest is observed for Zn adsorption on the h-BN surface. Table S2 shows that the adsorption of the metal atom on the S_B and S_N surfaces, on the opposite side of the sulfur atom, results in a more negative adsorption energy.

A glance at Table 2 reveals that, except for Cd adsorption on the S_BN surface, the adsorption of metal atoms on S-doped h-BN surfaces consistently resulted in a higher binding energy compared to the pristine surface. The adsorption of Zn and Cd atoms on all surfaces exhibits a lower binding energy. This lower binding energy can be attributed to the electron configuration of 4s²3d¹⁰ and 5s²4d¹⁰ for these atoms. Metal atom adsorption on the S_B surface exhibits higher binding energy than on the S_N surface, except for Se atom adsorption. This is to be expected, as on the S_B surface, sulfur has replaced an atom with lower electronegativity (B), while on the S_N surface, sulfur has replaced an atom with higher electronegativity (N). Additionally, except for Ge atom adsorption, the S_N surface shows a higher binding energy for metal atom adsorption than the S_BN surface. The significantly enhanced binding energies of various metals on S-doped h-BN surfaces compared to the pristine h-BN highlight their promising potential for catalytic applications, gas sensing, and efficient hydrogen storage.

Table 3 presents the adsorption parameters for configurations showcasing the strongest metal-atom interactions. The calculated vibrational frequencies for the metal-decorated surfaces exhibited no imaginary components, providing strong evidence for their thermodynamic stability. Analyzing the metal-decorated surfaces reveals that the sulfur atom typically gets away from the surface along with the metal atom decoration in most situations. For example, the average distance of the sulfur atom from the surface, d_S, has increased from 1.06 and 0.50 Å to 1.95 and 1.38 Å, respectively, on S_B and S_BN surfaces due to the adsorption of MO and Ge atoms. But the Mo atom adsorption in the S_N surface does not have much effect on d_S. The data in Table 3 shows that the average distance of the metal atom to the surface, d_M, ranges from 1.24 to 1.62 Å. These distances, as well as high negative adsorption energies ranging from − 2.84 to − 7.43 eV, imply chemical adsorption.

Table 3.

Metal adsorption energy (), average distance of surface atoms to metal atom (d_M) and sulfur atom (d_S), Mulliken charge of metal atom (Q_M) and sulfur atom (Q_S), and band gap energy (E_g) for the strongest interaction between the metal atom and pristine and S-doped h-BN surfaces.

Structure	(eV)	dM (Å)	dS (Å)	QM (e)	QS (e)	Eg (eV)
h-BN-Mo	– 2.84	1.69	–	0.34	–	1.01
SB-Mo	– 7.43	1.32	1.95	1.12	– 0.09	1.02
SN-Mo	– 5.34	1.52	1.31	0.65	0.01	0.44
SBN-Ge	– 6.77	1.24	1.38	0.31	– 0.15	3.10

To elucidate the impact of sulfur doping and metal adsorption on the charge density distribution of the h-BN surface, the deformation charge density for configurations exhibiting the strongest metal-atom interactions was extracted and is presented in Figure S9, displaying both before and after metal adsorption. Deformation charge density is the difference between a surface’s electron density and that of its isolated constituent atoms. On the h-BN surface, blue regions on atoms, particularly boron, indicate decreased charge density. Adsorbing a Mo atom on the h-BN surface eliminates charge density reduction on adjacent boron atoms and induces charge density changes between the Mo atom and the surface. The plots show that sulfur atom substitution and metal adsorption directly impact the charge density of neighboring atoms and proximate bonds. Predictably, the specific substitutional site of the sulfur atom profoundly influences the surface’s electron density distribution.

The Mulliken charge analysis reveals that the adsorbed metal atom has transferred its charge to the surface. The highest and lowest values of the metal atom charge are 1.12 e and 0.31 e, associated with S_B-Mo and S_BN-Ge surfaces, respectively.

The PDOS diagram for the adsorption of metal atoms on each surface with the most negative adsorption energy is shown in Fig. 6, and the corresponding band structure diagram can be found in Fig. S10. The band structure diagrams for metal-decorated surfaces show that metal adsorption has caused many changes in the electronic properties of the surfaces. The adsorption of the Mo atom on h-BN, S_B, and S_N surfaces results in the creation of numerous impurity states near the Fermi level. The band structure diagram of S_BN-Ge clearly indicates that the adsorption of the Ge atom has transformed the surface into a p-type semiconductor. Decorating the h-BN surface with a Mo atom significantly decreases the band gap energy from 4.66 to 1.03 eV, while decorating the S_N and S_B surfaces with a Mo atom results in a slight increase of 0.17 and 0.08 eV in the band gap energy, respectively. However, decorating the S_BN surface with a Ge atom leads to an increase in the band gap energy from 1.82 to 3.10 eV.

Fig. 6.

PDOS diagrams of the metal-decorated h-BN and S-doped h-BN surfaces. The Fermi level is set at zero energy.

According to the PDOS diagrams of h-BN-Mo, S_B, Mo, and S_N-Mo, the Mo atoms’ s orbital peaks is entirely within the conduction region, indicating that its electrons has been transferred to the surface. The d orbital peak of h-BN-Mo is located close to the Fermi level and exhibits significant overlap with the surface atoms’ p orbital peaks up to the − 0.6 eV energy. Additionally, there are three distinct resonances at 1.04, − 0.34, and − 0.49 eV. This evidence supports the fact that there is a strong interaction between Mo and the surface. The overlap between the Mo atom’s d orbital peaks and the surface atoms’ p orbital peaks from the Fermi level energy to − 1.2 eV in the S_B-Mo surface is indicative of the strong adsorption of this metal onto the surface. As shown on the S_N-Mo surface’s PDOS diagrams, the overlap of the Mo atom’s d orbital peaks and surface atoms’ p orbital peaks is evident around the Fermi level. Strong resonance is also visible at specific energy levels, including − 0.83, and 1.75 eV. The p orbitals of the surface atoms near the Fermi level on the S_BN-Ge surface exhibit sharp and prominent peaks. These peaks overlap with the s and p orbital peaks of the Ge atom within the energy range of 0 to − 2.5 eV and − 5.4 to − 8.9 eV, indicating a strong interaction between the surface and the Ge atom.

Hydrogen adsorption

Given that efficient hydrogen storage and release are critical requirements in fuel cell technologies, investigating hydrogen adsorption serves as a crucial initial step in evaluating a surface’s viability for such applications. Therefore, the final stage of this study was the investigation of the impact of S-doping the h-BN surface and metal-decorating the resultant surfaces on the hydrogen molecule adsorption behavior.

To achieve this, on pristine or S-doped h-BN surfaces, a hydrogen molecule was placed roughly 1.5 to 2 Å above the hexagonal hole or on the opposite side on the S site, respectively. In the case of metal-decorated surfaces, the top of the adsorbed metal atom was examined as a potential H₂ adsorption site. The horizontal and vertical orientation of the hydrogen molecule was investigated for all the studied adsorption sites. After performing optimization calculations, the hydrogen adsorption energies were evaluated using Eq. 7. The most stable configurations for adsorbed H₂ on each surface are depicted in Fig. 7, and the corresponding adsorption parameters are listed in Table 4.

Fig. 7.

Top and side views of the H₂ adsorbed on pristine and S-doped h-BN surfaces.

Table 4.

Hydrogen adsorption energy (), hydrogen bond length (), average distance of the hydrogen molecule to the surface (), and to the metal atom (), Mulliken charge of metal atom (Q_M), and band gap energy (E_g) for the most stable configuration of the adsorbed H₂ on the pristine and S-doped h-BN surfaces.

Structure	Eads (eV)	(Å)	(Å)	(Å)	(e)	Eg (eV)
h-BN-H2	– 0.06	0.75	2.91	–	–	4.65
SB-H2	– 0.15	0.75	2.29	–	–	0.91
SN-H2	– 0.17	1.59	1.33	–	–	0.17
SBN-H2	– 0.14	0.75	2.45	–	–	1.81
h-BN-Mo-H2	– 1.49	1.04	2.37	0.61	0.54	1.22
SB-Mo-H2	– 0.85	1.72	2.32	0.92	1.23	1.02
SN-Mo-H2	– 0.28	0.82	3.40	1.88	0.61	0.91
SBN-Ge-H2	– 0.12	0.75	4.31	3.00	0.32	3.13

H₂ adsorption energy on the pristine and S-doped h-BN surfaces ranges from − 0.06 to − 0.017 eV, based on the data presented in Table 4. The h-BN surface has the lowest amount of H₂ binding energy, whereas the S_N surface has the highest amount. Although the H₂ adsorption energy is very close for the S-doped h-BN surfaces, examining the average distance of the hydrogen molecule to the surface () as well as the hydrogen bond length () demonstrates that the nature of hydrogen adsorption is not the same. A comparison of the H–H bond length indicates that the H₂ molecule dissociates during its adsorption on the S_N surface. Additionally, the average distance of the H₂ molecule to the surface in S_N-H₂ is 1.33 Å. This evidence strongly suggests the chemical adsorption of the H₂ molecule on the S_N surface. The relatively low binding energy can be related to the deformation of the structure during H₂ adsorption. The in S_B-H₂, S_BN-H_2, and h-BN-H₂ range from 2.29 to 2.45 Å, while the value remains constant at 0.75 Å after H₂ adsorption. These specific measurements, along with the low adsorption energy, indicate the physical adsorption of H₂ on these surfaces.

Figure S11 shows the most stable configurations for H₂ adsorbed on metal-decorated surfaces. The H₂ molecule exhibits a high binding energy on the h-BN-Mo-H₂ and S_B-Mo-H₂ surfaces, indicating a strong interaction with the surface. The short distance between the H₂ molecule and the Mo atom further supports this strong interaction. Additionally, the increase in H₂ bond length from 0.75 Å to 1.04 and 1.75 Å suggests the dissociation of the molecule during the adsorption process. Although hydrogen adsorption on the S_N-Mo surface does not have a high binding energy, it causes an increase of 0.07 Å in the H₂ bond length. The weakest interaction of H₂ is observed with the S_BN-Ge surface, with an adsorption energy of − 0.12 eV and no change in the H₂ bond length.

The H₂ adsorption on the h-BN-Mo and S_B-Mo surfaces resulted in a loss of 0.20 and 0.09 e charges of the metal atom, respectively, when comparing the amount of charge on the metal before and after the adsorption of the hydrogen molecule. However, the amount of charge on the metal does not change significantly in the cases of S_N-Mo and S_BN-Ge.

As shown in Fig. 7, the hydrogen molecule adopts a horizontal orientation when interacting with the h-BN, S_N, and S_N-Mo surfaces. However, in other cases, it exhibits a bent orientation. It is noteworthy that none of the surfaces change from their planar structure when hydrogen interacts with them. In summary, the H₂ adsorption energy does not change much by doping the h-BN surface with a sulfur atom, except in the S_N configuration. However, when a metal is added, the S-doped h-BN surfaces become better at adsorbing hydrogen molecules. Assessing a material’s suitability for fuel cell applications necessitates a comprehensive investigation into its hydrogen storage capabilities and thermal stability. This ensures the material possesses adequate storage capacity, maintains a suitable range of average hydrogen adsorption energy, and exhibits reversibility⁶⁷. The surfaces designed in this study present promising candidates for further investigation in hydrogen storage applications.

The band structure and PDOS diagrams of the adsorbed hydrogen surfaces were examined to look into their electronic characteristics. Due to the weak interaction between hydrogen molecules and h-BN, S_B, and S_BN surfaces, the band structure of these surfaces does not undergo significant changes upon hydrogen adsorption (Fig. S12). This weak interaction is confirmed by the high and sharp peaks of the s orbital of H atoms in the range of − 4.0 to − 6.0 eV in the PDOS diagrams of the h-BN-H₂, S_B-H₂, and S_BN-H₂ surfaces (Fig. 8). On the contrary, the chemical adsorption of H₂ molecule on the S_N surface has significantly altered the band structure of this surface. Additionally, the PDOS diagram of S_N-H₂ shows that the s orbital peaks of the H atoms overlap with the s and p orbital peaks of the surface in the broad energy range of 0.52 to − 9.76 eV.

Fig. 8.

PDOS diagrams of the H₂ adsorbed on metal-decorated h-BN and S-doped h-BN surfaces. The Fermi level is set at zero energy.

The PDOS diagram for h-BN-Mo-H₂ reveals that the s orbitals of the hydrogen atoms overlap with the s, p, and d orbital peaks of the surface atoms within the range of − 0.9 to − 1.1 eV. Additionally, there is an overlap with the s and p orbital peaks of the surface atoms within the range of − 5.4 to − 7.5 eV. Two strong resonances between the H atoms’ peaks and surface atoms peak at − 0.10 and − 6.46 affirm the chemisorption of H₂ on the surface. Two strong resonances between the H atoms’ orbital peaks and the surface atoms’ orbital peaks at − 0.10 and − 6.46 affirm the chemisorption of H₂ on the surface. The strong interaction between the H₂ molecule and the S_B-Mo surface has resulted in broadening the peaks of the s orbitals of H atoms, ranging from − 1.8 to − 6.3 eV. The peaks of the H atoms’ orbital overlap with the s and p orbital peaks of the surface atoms in the range of − 8.1 to − 8.9 eV, as shown in the PDOS diagram of the S_N-Mo-H₂ surface. Furthermore, from near the Fermi level to − 1.4 eV, the peaks of the p and d orbitals of the surface atoms overlap with the peak of the s orbitals of the H atom.

Conclusions

This research utilized DFT calculations to systematically examine the impact of S-doping on the electronic, thermodynamic, mechanical, and adsorption behavior of the h-BN surface. While the formation energy of the S-doped h-BN surfaces is more positive than the pristine surface, it is not much different from it. The impact of S-doping on the surface’s electronic properties is highly sensitive to the sulfur atom’s substitutional site. Replacing a single N atom with S reduces the band gap energy from 4.66 to 0.44 eV, whereas substitution for adjacent B and N atoms results in a band gap of 1.82 eV. The analysis of PDOS diagrams revealed that on S-doped surfaces, mainly the p orbitals of the surface atoms overlap with the p orbitals of the sulfur atom.

Across the entire temperature range, the vibrational entropy and enthalpy of pristine h-BN surfaces exceed those of S-doped h-BN surfaces. Regarding Gibbs free energy, the pristine surface exhibits higher values at low temperatures, yet demonstrates the lowest free energy at low temperatures. The bulk modulus of the h-BN surface decreases upon S-doping, most notably by 20.6 GPa for the S_N surface. Furthermore, the in-plane hardness is reduced by 19% when an S atom replaces a B atom and by 28% when it replaces an N atom. The Poisson’s ratio for S-doped h-BN surfaces falls within the range of 0.169 to 0.237.

Adsorption of Mo, Ge, Zn, Ga, Cd, and Se on h-BN, S_N, S_B, and S_BN surfaces shows significantly higher binding energy on S-doped surfaces compared to pristine h-BN, with one exception. Mo and Ge atoms exhibited the strongest interaction with the surfaces. PDOS diagrams of metal-decorated surfaces show electron loss from the Mo atom’s s orbital. The elongation of the H₂ bond length to 1.59 Å and its distance from the surface (1.33 Å) imply the chemisorption of H₂ on the S_N surface. Conversely, all adsorption parameters point to weak physisorption of hydrogen on the h-BN, S_B, and S_BN surfaces. The results indicate that there is a strong interaction between the H₂ molecule and h-BN-Mo, S_B-Mo, and S_N-MO surfaces, which causes the hydrogen to dissociate upon adsorption.

All findings demonstrate that sulfur doping of the h-BN surface enhances its electronic characteristics without appreciably changing its mechanical ones. Additionally, this enhances the surface’s ability to adsorb hydrogen molecules and metals. Future research could focus on elucidating the influence of sulfur doping concentration on their fundamental properties, a comprehensive investigation into their capacity for hydrogen storage, their potential as electrode materials in advanced metal-ion batteries, and exploring their catalytic properties in various reactions. Their efficacy in environmental remediation, particularly for pollutant gas adsorption and sensing, offers another promising direction.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Azadeh Ghahremani: Investigation, Data curation, Formal analysis, Software. Zahra Tavangar: Methodology, Supervision, Project administration, Validation, Writing-review and editing. Mohammad Reza zamani seyfikar: Formal analysis, Writing-original draft. All authors reviewed the manuscript.

Data availability

Data from this study is available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.