The characteristics and mechanical properties of Mo/VC interface structures via first-principles calculations

Hard coatings play an important role in modern industry due to their exceptional strength, making them widely used as tool coatings and high-temperature protective coatings.¹ Previous studies have primarily focused on enhancing the hardness and wear resistance of these coatings; however, it is increasingly recognized that coatings possessing both high strength and toughness are more valuable for practical industrial applications. The metal/ceramic multilayer structure, which represents a typical tough/hard system, has been demonstrated to exhibit remarkable strength and toughness in ceramic composites, providing novel insights into the toughening of hard coatings.^2,3

Molybdenum/Vanadium carbide (Mo/VC) nano-multilayers exhibit great potential as a coating system. VC is widely utilized in the manufacturing of cutting tools, drills, and abrasives due to its exceptional hardness and wear resistance. The incorporation of tough metals into VC can effectively enhance its mechanical properties. Wang et al.⁴ investigated the hardness and toughness of Mo/VC coatings and observed that the multilayers maintained a high hardness level of ∼22 GPa, while the toughness increased from 2.91 to 4.70 MPa m^1/2 with varying Mo ratios ranging from 60% to 90%. He et al.^5–7 reported that Mo, which acts as a mild carbide-forming element, is often employed as an independent phase additive in transition metal carbides (TMCs) to improve impact toughness without compromising hardness at higher levels. This phenomenon arises from interfacial effects between Mo and TMC phases, including high specific surface area and strain hardening, which significantly influence the mechanical properties of composites.

There has yet to be a unified conclusion on the toughening mechanism for the nano-multilayer coatings, and most of the studies have focused on the effect of the modulation parameters of the coatings on their hardness and toughness. In fact, complex interfaces in nano-multilayers are also crucial for toughening hard coatings, which has been demonstrated in numerous research studies on multiphase materials.^8–12 For instance, Wei et al.¹² investigated the interfacial characteristics and toughening phenomena of an ultrafine crystalline WC–Co system, revealing a co-lattice interface between WC and Co with a high mismatch degree of up to 14%. This co-lattice interface strengthens bonding at the interface, reduces grain boundary fracture, and improves toughness. Nevertheless, further exploration is needed to understand the microscopic mechanisms in detail. Consequently, first-principles simulations have been employed to investigate interface structure and properties.^13–19 In terms of metal–ceramic interfaces,^20–28 researchers mainly focused on studying the effects of interfacial dopant atoms, stacking order, bonding strength, and other factors. Mikula et al.²⁵ used density functional theory to examine the mechanical behavior of magnetron-sputtered Ti–Al–Ta–N hard coatings and reported that Ta enhances metal–metal bonding while maintaining strong metal-N bonds; this leads to reduced shear resistance and improved coating toughness. Yang²⁶ studied Fe/WC interfaces and found that the C-terminated MT-stacking Fe(100)/WC(110) interface exhibited significant adhesion work (8.76 J/m²), along with strong covalent bonding at the interface. Jin et al.²⁷ demonstrated that among different termination structures for W(110)/WC(0001) interfaces, C-terminated W(110)/WC(0001) showed superior stability with an adhesion energy (W_ad) value as high as 11.98 J/m². The analysis of the Ag/BaTiO₃ interface²⁸ also revealed that TiO₂-terminated Ag(001)/BaTiO₃(001) interfaces exhibit relatively high adhesion work and interface fracture toughness, attributed to the formation of Ag–O bonds resulting from the hybridization between Ag-5s orbitals and O-2s orbitals.

This paper aims to identify the optimal interface structure of the Mo/VC interface in order to guide subsequent experiments. A total of 15 interface models for Mo/VC were constructed using Density Functional Theory (DFT)-based first-principles simulation calculations, considering various interfacial orientations, atomic terminations, and stacking modes. Subsequently, a systematic investigation was conducted on the adhesion strength and interfacial energy of these interfaces. Furthermore, an in-depth analysis was performed on the electronic structure and tensile mechanical properties of two specific interfaces: C-terminated hollow-site Mo(110)/VC(111) and V-terminated central-site Mo(211)/VC(220). The obtained results provide valuable insights into the interfacial properties of Mo/VC interfaces and offer physical support for further enhancements in novel Mo/VC nano-multilayer coatings.

The first-principles calculations were performed using the Cambridge Serial Total Energy Package (CASTEP), employing the plane-wave ultrasoft pseudopotential method based on Density Functional Theory (DFT).²⁹ To optimize the geometry of bulk Mo and VC unit cells, we employed generalized gradient approximation (GGA)³⁰ of the Perdew–Wang 91(PW91)³¹ as an exchange–correlation function. Additionally, the atomic structure was relaxed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm.

The electronic configurations for Mo, C, and V were Mo 4s² 4p⁶ 4d⁵ 5s¹, C 2s² 2p², and V 3s² 3p⁶ 3d³ 4s², respectively. A plane wave cutoff energy of 550 eV was used in all calculations. For constructing the Mo/VC interface, a supercell approach with periodic boundary conditions was utilized, while a vacuum layer of thickness 10 Å along the z axis was included to eliminate periodic interaction between free surfaces of Mo and VC. K-points were set as 12 × 12 × 1 for modeling the Mo/VC interface. Convergence tolerances were defined as follows: energy: 5.0 × 10⁻⁶ eV/atom; maximum force: 0.01 eV/Å; and maximum displacement: 0.005 Å.

The tensile deformation process is applied in the z-direction (i.e., perpendicular to the interface) with a uniform 2% strain increment for each iteration. The model employed for each step of tensile strain is based on the relaxed interface model from the previous step, ensuring more accurate and controlled investigation of strain effects. The relationship between stress and strain during this process is determined using formula (A1) in the  Appendix.

The XRD and TEM results from previous research have indicated that Mo exhibits a body-centered cubic (bcc) structure, while VC adopts a NaCl B1 structure.⁴ Specifically, the space group of Mo is Im-3m, whereas VC belongs to the Fm $3̄$m space group. Table I presents the calculated values for lattice constants (α), bulk modulus (B), Young’s modulus (E), and elastic constants (C_ij) of both bulk Mo and VC, alongside corresponding calculation and experimental data obtained from other studies. These comparable results serve to validate the reasonableness and validity of the employed calculation parameters in this study.

The surface properties are significantly influenced by the atomic layer number of the surface slab. Therefore, a convergence test of the surface energy was conducted to determine the appropriate layer number for Mo and VC slabs in the interface models, which can be calculated using formula (A2) in the  Appendix. The results indicate that stable values of surface energy were achieved with nine layers for Mo slab models and 12 layers for VC slab models. Hence, interface models were constructed using a 9-layer Mo slab and a 12-layer VC slab. Table II presents the obtained surface energies and lattice constants for various Mo and VC slab models. It is noteworthy that all Mo slab models exhibit similar surface energies, while there is relatively different variation observed among VC slab models. Specifically, the VC(111) slab model demonstrates the highest surface energy at 3.98 J·m⁻².

Considering four types of interface orientations (Mo(110)/VC(220), Mo(200)/VC(200), Mo(211)/VC(220), and Mo(110)/VC(111)), two terminations (V- and C-termination), and three stacking sequences (top-, central-, and hollow-site), a total of 15 Mo/VC interface geometries were constructed by placing a 9-layer Mo slab on top of the 12-layer VC slab. The top, central, and hollow sites refer to the positions of the Mo atoms on the top of surface, second-layer, and third-layer atoms of the VC slab, respectively. The lattice constant of VC (4.18 Å) is much greater than Mo (3.15 Å). Therefore, a supercell approach with periodic boundary conditions was employed to obtain a perfect lattice match between Mo and VC. Table III presents the lattice mismatch degrees for different interfaces; although there is an interfacial mismatch degree of ∼7%, co-lattice stacking at the interface is still possible. Therefore, this study mainly focuses on coherent interfaces. The optimal interface structures were obtained using the Uber method,³⁹ as shown in Fig. 1 where fully relaxed interface models are presented. During the relaxation process, three atomic layers at the top of the Mo slab and two atomic layers at the bottom of the VC slab were fixed in their respective positions. As depicted in Fig. 1, no significant atom displacement occurs at the interface after structure relaxation, indicating that all interface models are stable.

The bonding strength of the interface model is assessed based on the work of adhesion (W_ad). Formula (A3) in the  Appendix was utilized for calculating the Mo(110)/VC(220), Mo(200)/VC(200), Mo(211)/VC(220), and Mo(110)/VC(111) interface models.

Table III presents the optimal interfacial spacing (d₀) and adhesion work (W_ad) obtained from the relaxation models depicted in Fig. 1. It is evident that most interfaces exhibit adhesion work values ranging from 4 to 6 J m⁻², while C-terminated Mo(110)/VC(111) interfaces display prominent W_ad values around 10 J m⁻². Notably, among all 15 interface models, the C-terminated hollow-site Mo(110)/VC(111) interface exhibits both the highest adhesion work W_ad (10.64 J m⁻²) and smallest interfacial spacing d₀ (1.2 Å) owing to strong bonds formed between C and Mo atoms. Based on W_ad, it can be concluded that the C-terminated hollow-site Mo(110)/VC(111) interface represents an optimal configuration, followed by the C-terminated central-site Mo(110)/VC(111) interface and V-terminated central-site Mo(211)/VC(220) interface. The comparative results further demonstrate that surface termination plays a predominant role in determining W_ad values, whereas stacking order and interface orientation have relatively minor influences.

The interfacial energy E_int essentially arises from changes in the chemical bonding of atoms at the interface and structural strains. It refers to the excess energy per unit area of the system after the formation of an interface. Experimental values of the interfacial energy E_int are rarely found in the literature due to the difficulty in experimental measurements. For solid/solid interfaces, if the two solid phases are similar, the interfacial energy E_int is minimal and can be considered as E_int = 0. If the two solid phase materials are entirely different, such as Mo and VC, the interfacial energy should be positive, which is caused by the interfacial mismatch strain generated by the structural mismatch. The interfacial energy E_int can be calculated using formula (A4) in the  Appendix. The results are listed in Table III. The relatively low values of E_int (2.98 and 3.02 J m⁻²) were obtained in the C-terminated hollow-site Mo(110)/VC(111) interface and V-terminated central-site Mo(211)/VC(220) interface, respectively. In general, the interface stability increases with the decrease of E_int. Thus, it is indicated that the C-terminated hollow-site Mo(110)/VC(111) interface and V-terminated central-site Mo(211)/VC(220) interface are more stable than other interfaces. It is consistent with the results of the adhesion work W_ad.

Thermodynamically, the C-terminated hollow-site Mo(110)/VC(111) interface and V-terminated central-site Mo(211)/VC(220) interface are more favorable during the coating preparation process due to their higher adhesion work and lower interfacial energy. Therefore, in order to gain a deeper understanding of the bonding nature at these interfaces, we have performed electronic structure calculations. As displayed in Fig. 2, charge density differences reveal electron transfer phenomena. Negative values or blue color indicate charge loss, while positive values or red color indicate charge gain. At the C-terminated hollow-site Mo(110)/VC(111) interface, electrons are transferred from Mo atoms to C atoms near the interface, resulting in an accumulation of electrons around the interface C atoms. On the other hand, at the V-terminated central-site Mo(211)/VC(220) interface, electrons accumulate around the interface V atoms with a more pronounced electron loss observed. These findings confirm that chemical bonds with polar covalent properties form at these interfaces, which enhance interaction between interfacial atoms and subsequently improve strength and toughness.

The partial density of states (PDOS) for these two interfaces is illustrated in Figs. 3 and 4, respectively. Obviously, the PDOS curves of the interfacial layers exhibit distinct characteristics compared to those of the interior layers. In Fig. 3, the interfacial Mo layer within the Mo(110) slab exhibits novel peaks at approximately −5 eV, −6.5 eV, and −11.7 eV, which align with the peaks observed in both the interfacial C layer and second V layer within the VC(111) slab. These resonant peaks arise from a hybridization between interfacial C-s orbitals, C-p orbitals, and Mo-d orbitals, thus indicating a strong interaction between Mo and C at the interface as well as formation of robust covalent bonds. Additionally, the PDOS curve of the interfacial C layer exhibits a downward shift in energy, indicating electron transfer between the Mo and C atoms at the interface. A similar trend is observed in the PDOS curves for the V-terminated central-site Mo(211)/VC(220) interface. New peaks emerge around −2, −4.5, and −11.7 in the interfacial Mo layer of the Mo(211) slab, corresponding to resonating peaks found in the interfacial V layer of the VC(220) slab. Furthermore, charge interactions occur not only between Mo and V atoms at the interface but also between Mo atoms and C atoms in the second layer.

In order to further investigate the stability of the C-terminated hollow-site Mo(110)/VC(111) interface and V-terminated central-site Mo(211)/VC(220) interface, we conducted a study on the tensile fracture process of these two interfaces. The relationship between tensile strain and stress for the C-terminated hollow-site Mo(110)/VC(111) interface is presented in Fig. 5. The fracture mode exhibits typical ductile characteristics. Initially, when the strain is below 4%, there is a linear increase in stress due to the reasonable elastic modulus of both Mo(110) and VC(111) surfaces. The calculated value of elastic modulus for this interface was found to be as high as 300 GPa, which aligns with experimental data.⁴ As the strain increases from 4% to 22%, although stress continues to rise, it no longer maintains a linear relationship with strain. No significant fluctuation appears in the stress–strain curve, indicating that the C-terminated hollow-site Mo(110)/VC(111) interface remains stable. At a maximum applied strain of 22%, an ideal tensile strength of ∼26.01 GPa is achieved before fracture occurs at a maximum strain of 40%. The atom positions within the interface structures are visualized in insets of Fig. 5. It can be observed that even at a strain level reaching up to 22%, an excellent interface structure between Mo and C is maintained without any significant changes in atom positions compared to V and C atoms.

The tensile stress–strain curve of the V-terminated central-site Mo(211)/VC(220) interface is depicted in Fig. 6. This interface exhibits significant strengthening under stretching conditions, with an ideal tensile strength of 35.53 GPa and a corresponding strain of 32%, demonstrating excellent deformation resistance. Moreover, the area beneath the stress–strain curve serves as a measure of toughness, confirming that the V-terminated central-site Mo(211)/VC(220) interface possesses notable fracture resistance. In particular, this interface maintains its structural integrity throughout the stretching process. A comparison between Figs. 5 and 6 reveals that the V-terminated central-site Mo(211)/VC(220) interface displays a good relationship between tensile strength and toughness although the C-terminated hollow-site Mo(110)/VC(111) interface presents higher adhesion work. Hence, it is evident that mechanical properties cannot be solely explained by adhesion work.

The atomic structures (layer 1′-1 represents the interface) and charge density distribution of the C-terminated hollow-site Mo(110)/VC(111) interface and V-terminated central-site Mo(211)/VC(220) interface under different strains are represented in Figs. 7 and 8, respectively. In Fig. 7(a), it is evident that covalent chemical bonds form between the interfacial Mo and C atoms due to a significant electron accumulation at the interface. From Figs. 7(b)–7(f), as external tensile strain is applied, an increase in atom-to-atom distance along the z direction leads to reduced atom-to-atom constraint and enhanced atomic migration ability. When the strain exceeds 22%, substantial positional changes occur for Mo atoms in the interface model, indicating fracture of chemical bonds and formation of initial cracks in the Mo slab. The charge density distribution during stretching process at the C-terminated hollow-site Mo(110)/VC(111) interface also suggests slight changes near the interface, while there is a significant decrease in charge between Mo atomic layers. The odd-numbered layers of the Mo slab (1′–2′, 3–4′, 5′–6′, and 7′–8′ layers) are identified as the most probable fracture areas for the C-terminated hollow-site Mo(110)/VC(111) interface. In comparison, the atomic structures and charge density distribution of the V-terminated central-site Mo(211)/VC(220) interface (Fig. 8) differ from those of the C-terminated hollow-site Mo(110)/VC(111) interface. During the stretching process, there is a uniform increase in interatomic distance along the z direction without significant atom migration. According to Griffith’s fracture theory,⁴⁰ G∼2γ represents the fracture work of an interfacial constituent phase at a specific crystallographic surface, where γ denotes surface energy. If G > W_ad, fracture occurs at the interface; if G < W_ad, fracture takes place within the interfacial constituent phase. As shown in Tables II and III, Mo(110) and VC(111) slabs exhibit fracture works of 5.80 and 7.96 J/m², respectively, which are lower than W_ad = 10.64 J/m² representing interfacial adhesion work. Similarly, Mo(211) and VC(220) slabs have respective fracture works of 5.86 and 4.08 J/m² that are comparable to V-terminated central-site Mo(211)/VC(220)’s interfacial adhesion work W_ad (6.92 J/m²). Therefore, it is more likely for fractures to occur within the Mo slab at C-terminated hollow-site Mo(l10)/VC(111), while further analysis is required to determine precise location(s) of fractures at V-terminated central-site Mo(211)/VC(220).

The local strain, which represents the ratio of the change in spacing perpendicular to the interface before and after applied strain to the initial spacing, was also calculated. Figure 9 illustrates the variation of local strain under different strains for two interfaces: C-terminated hollow-site Mo(110)/VC(111) and V-terminated central-site Mo(211)/VC(220). In Fig. 9(a), the local strain is uniformly distributed on each layer of the VC(111) slab due to equal extension of layer spacing. Conversely, the Mo (110) slab exhibits a strong sensitivity to applied strain, resulting in concentrated local strain. At applied strains of 4%, 16%, 22%, 30% and 40%, corresponding local strains are observed as follows: in Mo (110) slab: 2.2%, 11.3%, 20.8%, 30.6%, and 40.3%; in VC(111) slab: maximum values reach up to 12.3%, 25.4%, 41.4%, 73.8%, and 95.1%. Meanwhile, at the interface (layer 1′–1), the local strain remains relatively less than 8.7%. This can be attributed to stronger covalent characteristics at this interface region. Yang et al. concluded that interfacial fracture failure can be recognized when exceeding a value of 80% for local strain.^14,41 The tolerable applied strain of the Mo(110)/VC(111) interface is ∼30%, shown as the maximum local strain close to but not more than 80%. Fracture occurs when the applied strain reaches 40%. In Fig. 9(b), the local strain in both Mo(211) and VC(200) slabs is more uniform, as their fracture work closely resembles the adhesion work of the interface.

In this paper, the adhesion work and interfacial energy of 15 Mo/VC interfaces with various interface orientations, terminations, and stacking sites were analyzed using first-principles calculations. The results of the adhesion work indicated that the C-terminated hollow-site Mo(110)/VC(111) interface and V-terminated central-site Mo(211)/VC(220) interface are more favorable for formation during the coating preparation process. Stable covalent bonds were observed at these interfaces. Under tensile fracture conditions, the C-terminated hollow-site Mo(110)/VC(111) interface exhibited an ideal tensile strength of ∼26.01 GPa at a strain of 22%, while the V-terminated central-site Mo(211)/VC(220) interface showed a tensile strength of about 35.53 GPa at a strain of 32%. Both interfaces could tolerate strains exceeding 30%. For the C-terminated hollow-site Mo(110)/VC(111) interface, the fracture work of the Mo(110) and VC(111) slabs is 5.80 J/m² and 7.96 J/m², respectively, which is lower than the interfacial adhesion work W_ad = 10.64 J/m², resulting in localized strain concentration and fracture within the Mo slab. However, for the V-terminated central-site Mo(211)/VC(220) interface, the fracture work of the Mo(211) and VC(220) slabs is 5.86 and 4.08 J/m², respectively, which is comparable to the interfacial adhesion work W_ad (6.92 J/m²), indicating a more uniform local strain distribution. The V-terminated central-site Mo(211)/VC(220) interface shows the apparent advantages in the tensile strength and toughness and reaches a trade-off between adhesion work and mechanical properties. It is implied that if more V-terminated central-site Mo(211)/VC(220) interface can be obtained in the sputtering deposition process, then the performance of Mo/VC nano-multilayers may be further improved.

This work was supported by the National Natural Science Foundation of China (NSFC) (Contract Nos. 51902254 and 51902252), the Natural Science Foundation of Shaanxi Province (Grant No. 2018JM5108), the Natural Science Basic Research Program of Shaanxi (Grant Nos. 2022JM-261, 2022JQ-371), the Xi’an Science and Technology Planning Project (Grant No. 22GXFW0099), the Xi'an Association for Science and Technology Youth Talent Support Program (Grant No. 095920221361), the Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant No. 22JK0512), and the Qin Chuangyuan Originally Cited High-level Innovation and Entrepreneurship Talent Program (Grant No. QCYRCXM-2022-138).

The authors have no conflicts to disclose.

Wenya Xu: Investigation (equal); Software (equal); Writing – original draft (equal). Chen Wang: Supervision (equal); Writing – original draft (equal). Zhi Li: Investigation (equal); Methodology (equal). Yanjie Shi: Methodology (equal); Validation (equal). Hongfu Li: Validation (equal). Jian Li: Methodology (equal). Yanming Liu: Investigation (equal). Pan Dai: Funding acquisition (equal); Software (equal). Yu Meng: Data curation (equal). Wenting Liu: Funding acquisition (equal); Software (equal). Xianghong Lv: Funding acquisition (equal); Software (equal). Na Jin: Writing – review & editing (equal).

The data that support the findings of this study are available within the article