First-principles calculation of atomic structure, stability and electronic structure of TaB2/SiC interface

The atomic structure, interface stability and electronic interaction of TaB2(0001)/SiC(111) interfaces were investigated by first principles calculation. The study found that the termination atom and stacking position are the key factors affecting the bonding strength and stability of the interface. On the basis of considering work of adhesion (W ad) and interfacial energy (γ int), the Ta–TaB2/C–SiC center-site stacked (Ta–CS–C) and B–TaB2/C–SiC center-site stacked (B–CS–C) configurations are recognized as the most stable structures from ten TaB2/SiC interface models. Electronic interaction of the two most stable interfaces were revealed by analyzing the charge density distribution, charge density difference and partial density of states, and found that ionic and metallic bond coexisted in Ta–CS–C interface, while covalent bond played a dominant role in B–CS–C interface.


Introduction
Carbon materials, especially carbon fiber reinforced carbon matrix (C/C) composite materials, with unique advantages of low density, low thermal expansion coefficient (CTE), high strength, high thermal conductivity and structural stability, are considered as the most promising thermal structure material and have aroused special interests in aeronautic and aerospace fields [1][2][3][4][5], such as hypersonic vehicles and rocket propulsion systems. However, the application of C/C composites facing huge challenges due to its sensitivity to the oxidants at a temperature higher than ∼723 K [6,7]. Considering the superiority of C/C composites as thermal structural material, it is necessary to address the problem of easy oxidation, to extend its service life. High-temperature anti-oxidation protective coating was considered as an effective measure.
With low oxygen permeability, high chemical stability, excellent self-healing ability, and a similar CTE with C/C substrate, SiC-based coatings have become the preferred oxidationresistant coating material for C/C composites [8][9][10]. Among the coating components, SiC combined with the ultra-high temperature ceramics (UHTCs), including ZrB 2 , ZrC, HfB 2 , TaB 2 etc, exhibits unparalleled oxidation resistance, good chemical and thermo-physical compatibility. Wang et al [11] examined the anti-oxidation performance of the C/C composite coated with the gradient HfB 2 modified SiC coating at 1773, 1873 and 1973 K. The results suggested that the HfB 2 -SiC coating with good crystallization exhibits excellent oxidation resistance at 1773 K, with a mass loss of 0.17% after 800 h, and the hafnium compound could consume the crack formation energy and block the crack propagation during the oxidation process. Ren et al [12] investigated the anti-oxidation ability of ZrB 2 -SiC coating and indicated that the excellent oxidation protective ability of the ZrB 2 -SiC gradient coating can be maintained for more than 207 h at 1773 K. Zirconium compound played a role of pinning phase, which not only improves the oxidation resistance of the coating, but also consumes the crack energy and prevents the propagation of the crack. Li et al [13] studied the anti-ablation properties of the ZrC-SiC coating prepared by solid-phase infiltration, and proposed that the dense ZrC-SiC coating is composed of ZrC and SiC phases. The coating and the matrix are chemically bonded and have a good bonding strength. The ablation resistance of the ZrC-SiC coating enhanced with the increase of ZrC content, this is due to the fact that zirconium compound absorbs a large amount of heat during the melting process, thereby reducing the temperature of the coating surface, in addition, the formed Zr-Si-O glass phase could also prevent the permeation of oxygen. Jiang et al [14] examined the anti-oxidation and anti-ablation performance of TaB 2 -SiC-Si coating and proved that the TaB 2 -SiC-Si coating could protect graphite from oxidation for 321 h and 168 h at 1020 • C and 1550 • C, respectively. This is mainly because the Ta 2 O 5 -SiO 2 barrier layer prevents the oxidizing gas from diffusing into the coating. Researches on SiC-UHTCs coatings suggested that the excellent coating performance largely comes from the following two aspects: UHTC bonded well with the SiC, consuming the crack propagation energy and deflecting the crack; Glass phase on the coating surface blocks the oxygen penetration. Obviously, the interface between UHTCs and SiC in UHTCs-SiC coatings has a significant impact on its performance. Therefore, it is therefore of great importance to obtaining the detailed heterointerface information between UHTCs and SiC, which is beneficial for us to have a good understanding of the properties of the UHTCs-SiC coatings. Taking into account the difficulty of exploring the interface with experimental methods, a first-principles calculation based on density functional theory (DFT) has been employed to reveal the interface characteristics at atomic and electronic scales, and has been successfully applied to SiC/ZrB 2 [15][16][17] HfB 2 /SiC [18], and ZrC/SiC [19] systems. However, up to now, the interface characteristics between TaB 2 and SiC in TaB 2 -SiC coating are still mysterious, although there are many practical applications of the TaB 2 -SiC coating as anti-oxidation and anti-ablation materials. Therefore, the purpose of this paper is to bring to light the interface characteristics between TaB 2 and SiC, and find the most possible interface configurations by analyzing the atomic structures, bonding strength, stability, and electronic structure within the framework of the first-principles study.

Calculation methods
In this work, a first-principles study was applied to the TaB 2 /SiC interface, using Cambridge Serial Total Energy Package (CASTEP) software [20], which is based on DFT. The Perdew-Burke-Ernzerhof functional of generalized gradient approximation was selected to describe the exchange-correlation energy [21,22]. The ion-electron interactions of Ta, B, Si and C atoms were described by the plane-wave ultrasoft pseudopotential [23]. The convergence test of the kinetic energy cut-off value and K-point meshing were conducted based on the method reported in our previous study [18], consequently, the plane wave cut-off energy for bulk TaB 2 and SiC was set to 350 eV, and grid meshing of 9 × 9 × 8 and 8 × 8 × 8 was applied to TaB 2 and SiC, respectively. For the slabs and interfaces, a cut-off energy of 350 eV and a k-point grid of 9 × 9 × 1 was adopted. Periodic boundary conditions applied for slabs and interfaces, and a vacuum layer of 15 Å was inserted between the above and below surfaces to minimize their interaction. Geometric optimization was imposed on all calculations through the Broyden-Fletcher-Goldfarb-Shanno algorithm to keep the atomic coordinates fully relaxed and reach the ground state [24,25]. Geometric optimization was considered complete when the following convergence criteria are satisfied: 5 × 10 −6 eV/atom for energy, 0.01 eV Å −1 for maximum force, and 5 × 10 −4 Å for maximum displacement.

Bulk properties
Inspecting the table 1 that our calculated lattice constant 'a' and 'c' of TaB 2 are: a = 3.102 Å, c = 3.261 Å, which is good in line with the theoretical and experiment results [26][27][28][29]. For SiC, the calculated lattice constant 'a' of 4.361 Å, is also very consistent with the experimental and theoretical values in references [15,[30][31][32]. Therefore, the consistency between our calculated lattice constant and reference values provides evidence that our calculation method and subsequent calculation results are credible (figure 1).

Slab thickness and surface energy
The (0001) plane of TaB 2 was chosen for the fact that TaB 2 is a hexagonal crystal, the (0001) plane has the highest density of atomic packing with better stability, and has been investigated extensively [27,33,34]. Considering the polar characteristics of the TaB 2 (0001) plane, it well be terminated by one kind of atom at one side, thence, the TaB 2 (0001) slab with the same terminal atom at two sides should be adopted to prevent the dipole effect, as presented in  figures 2(a) and (b). Researches on SiC have shown that the (111) plane of SiC tends to be exposed to the outside [35,36]. Theoretically, SiC(111) slab should also consider the dipole effect caused by the difference between upper and lower surface terminal atoms. However, the study by Li et al [37] confirmed that the number of dangling bonds has a greater impact on the stability of SiC(111) surface than the dipole effect. Therefore, as presented in figures 2(c) and (d), an even atomic layer SiC(111) slab with fewer dangling bonds is adopted in this work, ignoring the dipole effect.
The TaB 2 (0001) and SiC(111) slabs should have sufficient thickness to achieve a bulklike interior and ensure the accuracy of the subsequent calculations. Undoubtedly, a slab with more atom layers could improve the accuracy of calculation results, but it will cost additional computational resources. The minimum number of the atomic layers essential for the Ta or B terminated TaB 2 (0001) slabs can be determined by observing the changing trend of the distance between adjacent atomic layers with respect to the number of atomic layers after relaxation. The alteration in atomic spacing is calculated by equation (1): where d 0 i j and d i j are the distances between adjacent i and j atomic layers before and after relaxation.
As shown in table 2, the variation of the distance between adjacent atomic layers in Ta-and B-terminated TaB 2 (0001) surfaces are different. For the Ta terminated surface, the changes of the layer spacing mainly occur between the first and the second layer, and the variation in all slabs basically follows the contraction-expansion cycle. While for the surface ends with B atom, the change of the atomic layer spacing are mainly concentrated in 2/3. Overall, the variation of the interlayer distance in the interior of the Ta-and B-terminated TaB 2 (0001) slabs can be ignored as the number of atomic layers greater than 11, so the 11-layered Taand B-terminated TaB 2 (0001) slabs are selected. For SiC(111) slab, numerous studies have demonstrated that SiC(111) slab with 12 atomic layers is sufficient to show the interior feature of the bulk SiC [11,13].

Surface energy
The stability of a surface is closely related to the type of termination atom. Surface energy (γ surf ) can be used to describe which kind of atomic-terminated surface is more stable. γ surf can be given by equation (2): where E slab is the total energy of the slab after relaxation, N and μ represent the number and chemical potential of i atom, respectively, and A is the surface area.
Since the atom types on the above and below surfaces of the TaB 2 (0001) slab are the same, the ratio of Ta to B in TaB 2 (0001) slab is not 1:2, which is a non-stoichiometric structure. Thus, the chemical potential of each atom must be considered. Theoretically, the fully relaxed TaB 2 (0001) slab will be balanced with the bulk TaB 2 , then the following equations (3) and (4) will exist: where μ bulk TaB 2 is the total energy of bulk TaB  According to equations (2)-(4), equation (5) will exist: Given that TaB Consequently, the chemical potential range of the tantalum is as follows: In this work, the calculated formation energy of ΔH TaB2 = −2.067 eV, is very close to the experimental value of 2.0 eV [38] and calculation result of −2.08 eV [27]. Thus, the surface energy of the Ta and B terminated TaB 2 (0001) surfaces can be determined, as shown in figure 3. It is evident that the surface energy of the Ta-TaB 2 (0001) and B-TaB 2 (0001) as a function of Δμ Ta . B-TaB 2 (0001) surface has smaller surface energy than that of Ta-TaB 2 (0001) in the Ta-poor side, and the γ surf of B-TaB 2 (0001) surface raised with the increase of Δμ Ta , while the Ta-termination one declined, consequently, the B-TaB 2 (0001) surface turns into the one with larger surface energy at Ta-rich side. Smaller surface energy means a better stability, so we believe that the B-TaB 2 (0001) surface has a better stability than Ta-TaB 2 (0001). The higher stability of the B-TaB 2 (0001) surface may have a weaker interaction with other surfaces, which will be verified in the subsequent adhesion energy calculation. As presented in figure 2, for SiC(111), the atom types on the above and below surfaces are different, so the γ surf of the SiC(111) surface are calculated using the method reported in reference [30]. Our calculated γ surf of 4.22 J m −2 is close to the other given results of 4.16 J m −2 and 4.33 J m −2 [15,39].

Work of adhesion
As presented in figure 4, TaB 2 (0001)/SiC(111) interfaces are constructed by placing SiC(111) surface on the TaB 2 (0001) surface and adding a 15 Å vacuum layer. Considering the difference between lattice length of the TaB 2 (0001) (d Ta-TaB2(0001) = 3.1322 Å, d B-TaB2(0001) = 3.1334 Å) and the SiC(111) (d Si-or C-SiC(111) = 3.0745 Å), a slight tensile strain is applied to SiC(111) surface to match the TaB 2 (0001) surface according to the method of Trivedi [40]. Then, we further assume that the interface strain can be ignored in such a coherent interface and the energetics of the interfacial bonding will not be affected.
The interface atom at SiC side have different stacking positions on TaB 2 (0001) surface. As exhibited in figure 5, taking the interface atoms at SiC side being C atoms as an example to describe the stacking positions. Interfacial C atoms have three (top, center and hollow) or two (top and center) possible stacking sites on Ta-terminated and B-terminated TaB 2 (0001) surface, respectively. The top site (TS) indicates that interfacial C atoms are situated on the top of the interfacial atoms of TaB 2 side (figures 5(a) and (d)); the center site (CS) indicates For different TaB 2 /SiC configurations, bonding strength is the primary factor that must be considered. Bonding strength can be evaluated by the work of adhesion (W ad ), which can be defined as the difference in energy between the system in which the surfaces are free to another in which they are in contact, forming the interface. W ad can be determined according to equation (9) [41]: where E SiC slab and E TaB 2 slab denote the energies of the separated 12-layer SiC(111) and 11-layer TaB 2 (0001) slabs with the same lattice parameter as TaB 2 /SiC interface, respectively. E TaB 2 /SiC interface is the energy of TaB 2 /SiC interface system, and A refers to the interfacial area.
To determine the appropriate spacing distance (d 0 ) between TaB 2 (0001) and SiC(111) slabs, the interface distance between two slabs is manually adjusted from 0.8 Å to 3.0 Å, and then the relationship between separate distance (d 0 ) and work of adhesion (W ad ) is obtained. As it can be seen from figure 6, for all unrelaxed interfaces, W ad is a function of separation distance (d 0 ) with parabolic-like. The optimal d 0 is the abscissa corresponding to the maximum value of the ordinate in each W ad versus d 0 profile. Generally, a larger W ad means higher bonding strength and better stability of the interface, so the configurations of Ta-CS-C, Ta-HS-Si, B-CS-C and B-TS-Si have better stability than other structures.
The equilibrium states of the ten TaB 2 /SiC interfaces are also calculated by fully relaxing the interface geometries. The W ad and d 0 of the ten TaB 2 /SiC interfaces before and after relaxation are summarized in table 3 for comparison. The difference in bonding strength of the interfaces with different stacking positions and terminal atoms can be noticed. Besides, the larger W ad always appears in the interface with the smaller spacing distance. All of these demonstrate that the termination atom and stacking position are the key factors affecting the bonding strength. Comparing with the unrelaxed configurations, the interface spacing becomes shorter and the bonding strength becomes larger after optimization, the reduced distance between TaB 2 and SiC slabs thereby enhancing their interaction, this is the reason why the W ad of all interfaces becomes larger after relaxation. It is worth noting that the W ad of the interfaces with B termination at TaB 2 side is smaller than the Ta-terminated ones, which is consistent with the B-TaB 2 (0001) surface energy analysis result. Among them, the relaxed Ta-CS-C, Ta-HS-Si, B-CS-C and B-TS-Si configurations exhibit the largest W ad of 6.04 J m −2 , 5.84 J m −2 , 4.73 J m −2 and 4.47 J m −2 , respectively.

Interfacial energy
Interfacial energy (γ int ) is always employed to describe the thermodynamic stability of an interface, and can be regarded as the difference between surface energies of two slabs, and the work of adhesion. The lower interfacial energy implies the interface is energetically more favorable. γ int can be computed by [42]: where γ surf TaB 2 and γ surf SiC denote the TaB 2 (0001) and SiC(111) slab surface energy, respectively, and W ad is the work of adhesion.
The relationship between interfacial energy and μ slab Ta − μ bulk Ta of the ten TaB 2 /SiC interfaces were shown in figure 7, and the γ int values of each configuration are summarized in table 4. Clearly, the interfacial energies as a function of μ slab Ta − μ bulk Ta : within the range of Δμ Ta , the interfacial energies of the interfaces with Ta termination at TaB 2 side decrease monotonously, which is opposite to that of B terminated interfaces. The Ta-CS-C and B-CS-C interfaces have the lowest interfacial energies of 0.323-2.272 J m −2 and 0.313-2.612 J m −2 , respectively. Combined with the calculation results of W ad , it can be determined that Ta-CS-C and B-CS-C are the most preferred and stable configurations due to their smallest interfacial energy and largest adhesion energy.

Electronic structure
The stability and mechanical properties of the Ta-CS-C and B-CS-C structures are closely related to the interfacial electronic interaction. Therefore, the calculation about the charge density distribution, charge density difference and partial density of states (PDOS) are performed. Figure 8 shows the charge density distribution [(a) and (b)] and charge density differences [(c) and (d)] of the Ta-CS-C and B-CS-C interfaces, respectively.
It can be seen from figure 8(a) that the charge distribution between interfacial C and Ta atoms in Ta-CS-C is not obvious. On the contrary, the charge in B-CS-C has a clear distribution in the triangular area formed by the interfacial B and C atoms, as shown in figure 8(b). To further explore the charge distribution, the charge density difference of Ta-CS-C and B-CS-C interfaces is calculated according to the following formula: where ρ TaB 2 /SiC , ρ TaB 2 (0001) and ρ SiC(111) are the charge densities of the TaB 2 /SiC, TaB 2 (0001) and SiC(111) system, respectively.  Inspecting figure 8(c) that the electron density between C and Ta is small, and the partial valence electrons of the interfacial Ta in the direction C and Ta have a certain degree of loss, in addition, there is a small amount of transferred charge accumulation in the interface area. These features are similar to the characteristic of ionic/metal bonds. For the B-CS-C interface (figure 8(d)), the charge transfer characteristics are completely different from the Ta-CS-C, a significant charge accumulated at the interstitial region between interfacial C and B atoms, considering that B and C are non-metallic elements, it is likely that a covalent bond is formed between B and C in the B-CS-C interface. These speculations will be confirmed in the density of states analysis.
For the purpose of further illustrating the electronic interaction and bonding feature of the Ta-CS-C and B-CS-C interfaces, the layer-projected partial density of states (LPDOS) is performed, as shown in figure 9. A grid meshing of 21 × 21 × 1 was applied to improve the accuracy. Noting that the total density of states (TDOS) curves of the Ta-CS-C and B-CS-C interfaces are very similar, which means that they have similar electronic structures. Besides, both Ta-CS-C and B-CS-C interfaces have metallic properties, this can be proved by the peak of TDOS curve at Fermi level. For the Ta-CS-C interface (figure 9(a)), the orbital hybridization of the interfacial C-p and Ta-d orbits was observed in the range of −10 eV to −0 eV, the density of states peaks of interfacial C-p in this range are sharper than that of inner atoms, while Ta-d are flatter, which means that the ionic bonds exist between interfacial Ta and C atoms. Compared with the third C and Ta atoms, the interfacial C-s have a higher state at −12 eV, while the interfacial Ta-d have a lower state at here, which also confirms the existence of ionic bond. In addition, the interfacial C-p and Ta-d have the larger DOS values than those of inner atoms in the range from −1.5 eV to Fermi level, which indicates that they also have certain metallic bond component. Therefore, the ionic and metallic bonds coexist in Ta-CS-C interface. As for the B-CS-C interface ( figure 9(b)), due to the interaction of interfacial atoms, the partial density state curve of the atoms near the interface is different from that of internal atoms, especially the interfacial C and B atoms. The obvious overlapping state of interfacial C and B atoms can be found in the range of −12 eV to 0 eV, and the identical peaks appear at −10.5 eV, −6.7 eV, −4 eV and −1 eV, indicating that covalent bonds formed between interfacial C and B atoms. Meanwhile, it is also noticed that the first layer B-p and second layer Ta-d orbital of TaB 2 side is significantly different from the third layer B-p and fourth layer Ta-d in the vicinity of Fermi level, respectively, and a new peak appeared at −1 V for both first layer B-p and the second layer Ta-d orbitals of TaB 2 side, which are obviously affected by the interfacial C-p orbital of SiC side. The new peak of second layer Ta-d orbital at −1 eV corresponds to the peak of the interfacial C-p at SiC side, which means that the covalent interaction between interfacial C-p orbital of SiC side and second layer Ta-d orbital of TaB 2 side. In all, the covalent bond played a dominant role in B-CS-C interface.

Conclusions
In this present work, ten TaB 2 /SiC interfaces were constructed in the consideration of different terminations and stacking sites. The atomic structure, bonding strength, stability and electronic feature of the TaB 2 (0001)/SiC(111) interfaces were analyzed by examining the adhesion energy, interfacial energy, and bonding nature. With the help of the first-principles study, it is found that termination atom and stacking position are the key factors affecting the bonding strength and stability of an interface, the Ta-TaB 2 /C-SiC center-site stacked (Ta-CS-C) and B-TaB 2 /C-SiC center-site stacked (B-CS-C) configurations are significantly more stable than any others, which are the most preferred interface structures. By performing the charge density difference and PDOS analysis, electronic interactions in Ta-CS-C and B-CS-C interfaces were revealed, and confirming that ionic and metallic bonds coexisted in Ta-CS-C interface, while covalent bond played a dominant role in B-CS-C interface. In all, comparing the bonding strength and stability of each interface, we believe that Ta-CS-C and B-CS-C interfaces are more likely to appear in the TaB 2 -SiC coating.