Electronic characteristic, tensile cracking behavior and potential energy surface of TiC(111)/Ti(0001)interface: A first principles study

Silong ZHANG, Jio WANG, Lixing RAO, Qizhen HE, Xiolei XING,Yefei ZHOU, Qingxing YANG,*

a State Key Lab of Metastable Materials Science & Technology, Hebei Key Lab for Optimizing Metal Product Technology and Performance, College of Materials Science & Engineering, Yanshan University, Qinhuangdao 066004, China

b College of Physics and Mechanical & Electrical Engineering, Longyan University, Longyan 364012, China

c College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China

KEYWORDS

Abstract The preparation of TiC coating on Ti alloy surface to improve the wear resistance has attracted attention from researchers in aerospace field.The service life of TiC coating is related to the interfacial adhesion properties between TiC coating and Ti alloy substrate.However, it is difficult to explain its interfacial adhesion mechanism by experimental methods.Based on the termination of atoms on the TiC surface, two TiC/Ti interface models named as the C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interface were constructed by first-principles.The interfacial electronic characteristic of C—Ti bond is a mixture of polar covalent and metal bonds, and that of Ti—Ti bond is the metal bond.The tensile strains of both C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interface in the fracture stage are ranged from 12% to 14%.Their maximum tensile stresses are 16.201 GPa and 15.590 GPa, respectively.The sliding potential energy surface maximum of C-terminated-TiC(111)/Ti(0001)and Ti-terminated-TiC(111)/Ti(0001)interface are 5.387 J/m2 and 0.271 J/m2,respectively.And the sliding potential barriers on the minimum energy path are 2.094 J/m2 and 0.136 J/m2 with an ideal shear strength of 20.32 GPa and 1.61 GPa, respectively.In summary, the interfacial adhesion property of C-terminated-TiC(111)/Ti(0001) interface is better than that of Ti-terminated-TiC(111)/Ti(0001) interface.

1.Introduction

With the advantages of low density, high strength, low elastic modulus, good corrosion resistance and compatibility with composites, Ti alloys have shown great potential for use in the aerospace and military industries.1–3However, the low hardness and high friction coefficient of Ti alloys make them failure due to adhesive wear.4Therefore,it is important to prepare a wear resistant coating on the Ti alloy surface to improve its service life.

Due to its low density, high hardness, good thermal conductivity, excellent corrosion resistance and wear resistance,TiC coating has been widely applied on alloy surfaces.Wei et al.5synthesized TiC by mixing carbon nanotubes into Ti-6Al-4V matrix using discharge plasma sintering technique.It was found that with the increase of the Planetary Ball-Milling(PBM)speed,the grain size of TiC/Ti-6Al-4V composites is decreased, which leads to its hardness increase.Huang et al.6carburized the surface of Ti-6Al-4V alloy, and the carburized layer consisted mainly of C, TiC and Ti with a total thickness of about 104 μm.The vickers hardness of Ti-6Al-4V alloy surface is greatly improved by TiC coating after carburizing.Miyoshi et al.7investigated the tribological behavior of Ti-6Al-4V alloys containing 10wt%TiC particles with Multiwalled Carbon Nanotubes (MWNTs), Diamond-Like Carbon (DLC)/Cr, Graphite-Like Carbon (GLC)/Cr and MoS2/Ti coatings at different temperatures.It was shown that the wear rate of TiC/Ti-6Al-4V is increased with the increase of temperature.Oh and Lee8used high energy electron beam irradiation technology to prepare (TiC, SiC)/Ti-6Al-4V composites.TiC and Ti5Si3were formed in the composite layer,which improves its hardness.The service life of TiC coatings is related to the interfacial adhesion properties between TiC coatings and Ti alloy substrate.However, it is difficult to explain its interfacial adhesion mechanism by experimental methods.

Presently,the first-principles method have been a significant way to study the properties of material bulk phases, surfaces and interfaces.9,10Li et al.11investigated β-SiC(111)/TiC(111)interface with different terminations by first-principles.It was found that the covalent properties of Si—C and Ti—C bonds in the interface are much weaker than those in the interior.Fan et al.12studied the adhesion properties of TiC(111)/TiN(111) interface by first-principles.It was shown that the adhesion properties of the interface are very similar to those in bulk materials, showing ionic and covalent properties.Xiong et al.13calculated the interfacial properties of TiC(111)/TiB2(0001) interface by first-principles.The results showed that the C-HS-Ti interface consists of strong polar covalent bonding and weak metallic bonding, while the Ti-HS-B and the Ti-HS-Ti interface consists of primarily covalent and metallic bonding, respectively.Zhang et al.14,15investigated the atomic and electronic structures of Ag(111)/TiC(111) and Cu (111)/TiC(111) interfaces by first-principles.It was shown that the Ti terminal interface has the characteristics of metal bond, while the C terminal interface has the characteristics of ionic bond.Hu et al.16used the firstprinciples to study the interfacial properties and fracture behavior of Mg(1 1-01)/TiC(111) interface.It was found that the stacking sequence can optimize the interface structure,uniform charge density, and is the key factor for interfacial stability and strengthening.From research results,it is feasible to use the first-principles method to investigate the interfacial behavior of TiC/Ti interface and clarify the interfacial adhesion mechanism.

The first-principles method was used to establish the TiC/Ti interface models.Firstly, the interfacial adhesion work, interfacial energy and electronic structures of the TiC/Ti interface were calculated.Then, the tensile simulations of the interface models were also performed to analyze the tensile properties and material transfer of TiC/Ti interface.Finally,the potential energy surface of TiC/Ti interface was calculated,and the minimum energy path and the ideal shear strength of TiC/Ti interface was obtained.The first-principles method can provide a theoretical basis for revealing the TiC/Ti interfacial adhesion mechanism, and preparing high-performance Ti-based TiC coatings.

2.Computation methods

We use the Vienna Ab initio Simulation Package(VASP)software based on the Density Functional Theory(DFT).17–20The Generalized Gradient Approximation (GGA)21and the Projector Augmented-Wave Potential (PAW)22with Perdew-Burke-Ernzerhof (PBE) parameters were used to calculate the exchange–correlation potential function and to treat the interactions between ions and valence electrons separately.The grid of the Irreducible Brillouin Zone (IBZ) was sampled by the Monkhorst-Pack method.23Because the main phase in Ti alloy such as Ti-6Al-4 V is α-Ti phase, α-Ti phase was employed.The Cut-Off Energy (ENCUT) and K-Point(KPOINT) of TiC and Ti were tested respectively, and the details of the calculations were shown in Figs.1 and 2.According to Figs.1 and 2, the specific parameters for the cut-off energy and k-point selection in the calculation of the bulk phase models, surface models and interface models were listed in Table 1.Criterion for judging the convergence property was as follows:the convergence threshold of energy was 1.0×10–5eV/atom, and the convergence threshold of Hellmann-Feynman force was 0.02 eV/A?.

Fig.1 Variation curves of bulk phase energy with cut-off energy.

Fig.2 Variation curves of bulk phase energy with k-points.

3.Results and discussion

3.1.Determination of interfacial relationship between TiC and Ti

Before calculating the surface properties of TiC and Ti, the bulk phase structures of TiC and Ti must be fully relaxed to reach the most stable state.The crystal structures of TiC and Ti are shown in Fig.3.Fig.3(a) is the crystal structure ofTiC.It can be seen that TiC belongs to the Fm-3m(225)space group.After relaxation, its lattice constant is a = b = c =4.338 A?, which is close to that obtained by predecessors from experiments24and calculations.25Fig.3(b) is the crystal structure of Ti.Ti belongs to the P63/mmc(194)space group.After relaxation, its lattice constants are a = b = 2.919 A?, c =4.651 A?, which is close to that obtained by predecessors from experiments26and calculations.27

Table 1 Parameters of bulk,surface and interface of TiC and Ti for density functional calculation.

Fig.3 Diagrams of crystal structure.

According to Bramfitt two-dimensional lattice mismatch theory,28if the two-dimensional lattice mismatch between the substrate and the nucleating phase is less than 6%, the substrate can play a very effective heterogeneous nucleation role with respect to the nucleating phase,forming a coherent interface.If the two-dimensional lattice mismatch between the substrate and the nucleating phase is 6%–12%, the substrate can play a moderately effective heterogeneous nucleation role with respect to the nucleating phase,forming a semi-coherent interface.If the two-dimensional lattice mismatch between the substrate and the nucleating phase is larger than 12%, the substrate cannot be used as the heterogeneous nucleation core of the nucleating phase to form a non-coherent interface.Therefore, the Bramfitt two-dimensional lattice mismatch theory is used to filter out the combination of crystal surfaces with smaller mismatch to obtain a more stable interfacial structure.The Bramfitt two-dimensional lattice mismatch (δ) is calculated as

where(hkl)sis a low index crystal plane in the substrate phase;[uvw]sis a low index crystal direction in the low index crystal plane of substrate phase; (hkl)nis a low index crystal plane in the nucleation phase; [uvw]nis a low index crystal direction in the low index crystal plane of nucleation phase; d[uvw]sis the atomic distance along the [uvw]sdirection in (hkl)scrystal plane; θ is the angle between [uvw]sand [uvn]n; d[uvw]nis the atomic distance along the [uvw]ndirection in (hkl)ncrystal plane.

The two-dimensional lattice mismatches between different low-index crystal planes between TiC and Ti are listed in Table 2.The lattice mismatch of TiC(111)/Ti(0001) interface is the smallest(5.075%),which is in the range of very effective heterogeneous nucleation to form a coherent interface.Therefore, TiC(111) and Ti(0001) surface models are created on the basis of TiC and Ti bulk phase structures, as shown in Fig.4.Fig.4(a) is the TiC(111) surface model, where the C-terminated-TiC(111) and Ti-terminated-TiC(111) surface models represent that C and Ti atoms terminated at theTiC(111)surface models,respectively.Fig.4(b)is the Ti(0001)surface model.

Table 2 Lattice mismatch of TiC and Ti (normalize).

Fig.4 Schematic diagrams of surface model.

A 20 A? vacuum layer was added above the surface and interface models to counteract the interactions between the top and bottom atoms of the model due to the periodicity of model.The convergence test of surface model was carried out to determine the minimum number of the surface model layers with similar bulk energy.The equation for the surface energy of a polar surface is obtained from the definitions given in Refs.29,30 as

where Asis the surface area of surface model;Eslabis the total energy of surface model;Niand μiare the atomic number and chemical potential of i component, respectively; n is the total number of atoms; P is the ambient pressure; V is the volume of system;T and S are the temperature and entropy of system,respectively.The PV and TS terms can be neglected at 0 K and typical pressures.The TiC(111) surface is a polar surface and the surface energy equation is

where ATi(111)is the surface area of TiC(111) surface model;ETi(111)is the total energy of TiC(111) surface model; μbulkTiCis the chemical potentials of TiC bulk phase; NTiand NCare the atomic numbers of Ti and C atoms in the TiC(111)surface model, respectively; μTiand μCare the chemical potentials of Ti and C atoms in the TiC surface model,respectively.Synthesizing Eqs.(3) and (4):

Since the chemical formula of element in the compounds is lower than that in the elementary substances, there is

Synthesizing Eqs.(4), and (7)–(9):

Fig.5 Relationship between TiC(111) surface energy and difference of carbon chemical potential (μC – μbulkC ).

Table 4 TiC(111) surface energy range of other researchers.

The surface energies of Ti(0001) surface model with different number of layers are listed in Table 5.When the layer number of the model is larger than 5th layer, the surface energy of Ti(0001) surface model is converged to 2.027 J/m2.

3.2.Adhesion properties of TiC(111)/Ti(0001) interface

The interfacial adhesion work can be defined as the reversible work required to separate an interface into two free surfaces.The interfacial adhesion work represents the strength of interface structure.The formula for the interfacial adhesion work(Wad)32–34is

where ESurface(s)is the total energy of isolated substrate phase surface model; ESurface(n)is the total energy of isolated nucleation phase surface mode; EInterfaceis the total energy of the interface model; AInterfaceis the area at the interface.

The Ti(0001) surface was modeled as an interface with the C-terminated-TiC(111) surface and Ti-terminated-TiC(111)surface, respectively, as shown in Fig.6.The size of the two interface models in the x-y dimension is 5.173 A? × 2.987 A? and both contain 12 atomic layers.The C-terminated TiC(111)/Ti(0001) interface model contains 16 Ti atoms and 8 C atoms,while the Ti terminated TiC(111)/Ti(0001)interface model contains 18 Ti atoms and 6 C atoms.

The Wadcurves of the interface models with different interfacial distances are shown in Fig.7, where d is the interfacial distance, Fig.7(a) is the Wadcurve of C-terminated-TiC(111)/Ti(0001) interface.It can be seen that, when the interfacial distance is 1.900 A?, the Wadof C-terminated-TiC(111)/Ti(0001) interface is the largest, which is 6.301 J/m2.Fig.7(b) is the Wadcurve of Ti-terminated-TiC(111)/Ti(0001) interface.When the interfacial distance is 2.670 A?,the Wadof Ti-terminated-TiC(111)/Ti(0001) interface is the largest, which is 3.529 J/m2.

The two groups of interfaces with the largest interfacial adhesion work were sufficiently relaxed to obtain more accurate interfacial adhesion work, and the interfacial energy of the interface model was calculated according to the interfacial adhesion work.In general,the smaller the interfacial energy(γ)is,the more stable the interface is.The formula for the γ35,36is

Table 5 Surface energy of Ti(0001).

Fig.6 Schematic diagrams of interface model.

Fig.7 Curves of relationship between Wad and distance of interface.

where σSurface(s)is the surface energy of substrate phase;σSurface(n)is the surface energy of nucleation phase.

The Wadand γ of two interface models after sufficient relaxation are listed in Table 6.It can be seen that the Wadof C-terminated-TiC(111)/Ti(0001) interface is 9.509 J/m2and its γ is 0.405–2.203 J/m2after sufficient relaxation.And Wadof Ti-terminated-TiC(111)/Ti(0001) interface is 3.317 J/m2and its γ is 0.246–2.025 J/m2after sufficient relaxation.

The interfacial properties are related to the interfacial electronic structures and chemical bonding properties, which can be evaluated by differential charge density, electron localization function and density of states.The differential charge density can determine the charge transfer, and the differential charge density (Δρ) for the interface model is calculated as37

where ρtotalis the charge density of the interface model;ρSurface(s)is the charge density of substrate phase surface model; ρSurface(n)is the charge density of nucleation phase surface model.

When the Δρ is negative, it means that the charge of this part is transferred to other parts during the formation of interface.The Δρ diagram of TiC(111)/Ti(0001) interface is shown in Fig.8.In order to investigate the electronic structures and chemical bonding properties of interface in detail, the charge distribution at the two ends of interface was analyzed, and the atoms at the interface were numbered with Arabic numerals(substrate phase)and Roman numerals(nucleation phase),respectively.The location of dotted line is the interfacial position.

Fig.8(a) is the Δρ diagram of C-terminated-TiC(111)/Ti(0001) interface.It can be clearly seen that after sufficientrelaxation the Ti(1) atom moves to a position symmetrical to the Ti(II)atom around the horizontal line over the C(I)atom.A large amount of the Ti(1) atom charges are transferred around the C(I) atom, and part of the Ti(II) atom charges are transferred between the Ti(1) atom and the Ti(II) atom.Meanwhile, part of the second layer atoms charges in the Ti surface and the third layer C atoms in the TiC surface also are transferred to the interface.Fig.8(b) is the Δρ diagram of Ti-terminated-TiC(111)/Ti(0001) interface.A large amount of charges around the Ti(1) atom and the Ti(I) atom are transferred to the interface, and part of the second layer atoms charges in the Ti surface are also transferred to the interface.

Table 6 γ and Wad of TiC(111)/Ti(0001).

Fig.8 Charge density difference diagrams of TiC(111)/Ti(0001) interface.

Electron Localization Function(ELF)can be used to qualitatively characterize the local distribution of electrons and help to verify chemical bond types.The ELF calculation formula36is

where D(r)is the real electron gas density; Dh(r)is the uniform electron gas density.The ELF value varies from 0 to 1.When ELF = 1, the electron is completely localized; when ELF = 1/2, the electron is in a uniform electron gas state;and when ELF = 0, the electron is completely delocalized(or no electron).

The ELF diagram of TiC(111)/Ti(0001) interface is shown in Fig.9.Fig.9(a) is the ELF diagram of C-terminated-TiC(111)/Ti(0001) interface.It can be seen that the ELF between Ti(1) atom and C(I) atom is increased from 0.1 to 0.8, which indicates that polar covalent bonds are formed between Ti(1) atom and C(I) atom.The ELF between Ti(1) atom and Ti(II) atom is increased from 0.1 to 0.3 and then decreased to 0.1, which indicates that metal bonds are formed between Ti(1) atom and Ti(II) atom.Fig.9(b) is the ELF diagram of Ti-terminated-TiC(111)/Ti(0001) interface.The ELF between Ti(1)atom and Ti(I)atom is increased from 0.1 to 0.3 and then decreased to 0.1,which indicates that metal bonds are formed between Ti(1) atom and Ti(I) atom.

The Density of States (DOS) curve of TiC(111)/Ti(0001)interface is shown in Fig.10.Fig.10(a) is the DOS curve of C-terminated-TiC(111)/Ti(0001) interface.It can be seen that the total DOS at the interface is not zero too at the Fermi energy level (dotted line position), which indicates that the chemical bonds formed at the interface has some metallicity.Meanwhile, the s orbital and p orbital of C(I) atom has obvious hybridization phenomenon.When the energy is between–11 eV and–9 eV, Ti(1)-p,d and C(I)-s have obvious resonance.When the energy is between –5 eV and –1 eV,Ti(1)-d and C(I)-p have obvious resonance, which results in the formation of covalent bond between Ti(1) atom and C(I)atom.When the energy is between –5 eV and 2 eV, Ti(1)-d and Ti(II)-d have obvious resonance, which results in the formation of metallic bond between Ti(1) atom and Ti(II) atom.Fig.10(b) is the DOS curve of Ti-terminated-TiC(111)/Ti(0001) interface.The total DOS at the interface is not zero too at the Fermi energy level(dotted line position),which indicates that the chemical bonds formed at the interface has some metallicity.When the energy is between –3 eV and 2 eV,Ti(1)-d and Ti(I)-d have obvious resonance, which results in the formation of metallic bond between Ti(1) atom and Ti(II) atom.

Fig.10 DOS curves of TiC(111)/Ti(0001) interface.

3.3.Tensile cracking behavior of TiC(111)/Ti(0001) interface

In order to further analyze the interaction strength and material transfer of TiC(111)/Ti(0001) interface model, the tensile simulation of TiC(111)/Ti(0001) interface model was carried out.The tensile simulation was achieved by fixing the bottom and top atoms of interface model and increasing the height of interface model, i.e., the engineering strain was applied along the z-axis with a step size of 1%.During tensile simulation,the atoms can only relax in the z-axis direction, and Poisson contraction parallel to the interfacial direction was ignored.38–41The stress–strain curve of the interface model was calculated using the Nielsen-Martin formula:42

where σtensileand εtensileare the tensile stress and strain of interface model,respectively;l0and lInterfaceare the lengths of interface model before and after tensile simulation in the z-axis direction, respectively; V(ε) is the volume of interface model when the strain is ε; Etotal(ε) is the total energy of interface model when the strain is ε.

The strain energy and tensile stress curves with different strain at the TiC(111)/Ti(0001) interface are shown in Fig.11.Fig.11(a) is the variation curve of strain energy with tensile strain at the TiC(111)/Ti(0001) interface, where E and E0are the interfacial interaction energies of tensile process and initial state.It can be seen that the energy of the C-terminated-TiC(111)/Ti(0001) interface is higher than that of the Ti-terminated-TiC(111)/Ti(0001) interface during the tensile process.Fig.11(b)is the variation curve of tensile stress with tensile strain at the TiC(111)/Ti(0001) interface.The tensile stress at the C-terminated-TiC(111)/Ti(0001) interface is larger than that of the Ti-terminated-TiC(111)/Ti(0001) interface for the same tensile strain.When the strain is 12%, the tensile stresses at the C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interfaces are the largest,which are 16.201 GPa and 15.590 GPa, respectively.When the strain is larger than 20%, the tensile stress gradually approaches 0.Therefore, the interaction of the C-terminated-TiC(111)/Ti(0001) interface is stronger than that of the Ti-terminated-TiC(111)/Ti(0001) interface.

Fig.11 Strain energy and tensile stress of TiC(111)/Ti(0001) interface.

Fig.12 Charge density diagram of TiC(111)/Ti(0001) interface with different strains.

The charge density (ρ)diagram of TiC(111)/Ti(0001) interface with different strains is shown in Fig.12.The charge density around atoms is not zero, which indicates that there are interactions between atoms.It can be seen that both interface models fracture before the strain reach 15%.Fig.12(a) is the charge density diagram of the C-terminated-TiC(111)/Ti(0001) interface with different strains.It is found that the fracture occurs in the inner surface of Ti near the interface,and Ti(1) atom is transferred to the surface of TiC(111).Fig.12(b) is the charge density diagram of the Ti-terminated-TiC(111)/Ti(0001) interface with different strains.It is found that the fracture occurs at the interfacial position, and no atom is transferred.

The variation curves of bond length and bond angle at the TiC(111)/Ti(0001)interface with different strains are shown in Fig.13.Fig.13(a)is the change of bond length and bond angle at the C-terminated-TiC(111)/Ti(0001)interface.It can be seen that with the increase of strain, the Ti(1)—Ti(2) bond length and Ti(2)—Ti(1)—C(I) bond angle are gradually increased,and the Ti(1)—C(I) bond length, Ti(1)—Ti(II) bond length and C(I)—Ti(II) bond length are firstly increased and then decreased.These phenomena further reflect that the fracture location of C-terminated-TiC(111)/Ti(0001) interface in Fig.12(a)occurs in the inner part of the Ti(0001)surface close to the interface,and Ti(1)atom of Ti(0001)surface transfer to TiC(111) surface.Fig.13(b) is the change of bond length and bond angle at the Ti-terminated-TiC(111)/Ti(0001) interface.With the increase of strain, the Ti(1)—Ti(I) bond length is gradually increased, and the Ti(1)—Ti(2) bond length,Ti(I)—C(II) bond length and Ti(2)—Ti(1)—Ti(I) bond angle are firstly increased and then decreased.These phenomena further reflect that the fracture location of Ti-terminated-TiC(111)/Ti(0001) interface in Fig.12(b) occurs in interfacial position, and no atom is transferred.

Fig.13 Variation curves of bond length and bond angle with TiC(111)/Ti(0001) interface strains.

By observing the change in slope of the curves in Fig.13,it is found that the tensile process can be divided into three stages,namely the elastic deformation stage,the fracture stage and the complete failure stage.The curve slope of the fracture stage is significantly larger than those of the elastic deformation stage and complete failure stage, which indicates that the bond lengths and bond angles of the atoms are changed dramatically during the fracture stage.The fracture stage for both interface models appears when the strain is increased from 12% to 14%.

3.4.Potential energy surface of TiC(111)/Ti(0001) interface

The interfacial sliding potential energy surface can be used to reflect the shear sliding resistance and evaluate the relative sliding difficulty of two surfaces in interface model.The sliding barrier of the interface is represented by the energy difference between the two surfaces in different relative sliding states.In order to maintain the relative position of the sliding process,the atoms can only relax freely in the z-axis direction.The sliding potential energy calculation formula43,44is

where EIis the interaction energy of sliding interface at the current position;is the minimum interaction energy of sliding interface;ASlidingis the surface area of sliding interface.

11 × 11 mesh grid points were selected at the TiC(111)/Ti(0001) interface, and 121 interface models were constructed according to the relative positions of two surface models determined by mesh grid points.The mesh surface formed by the connection of all sliding potential energies at the TiC(111)/Ti(0001) interface is the Potential Energy Surface (PES).The red dotted line in Figs.14(a) and (b) is the Minimum Energy Path (MEP) required for the sliding process of TiC(111)/Ti(0001)interface,that is,the interface model require the least amount of energy to slide along this path.The Potential Energy Curve (PEC) of the TiC(111)/Ti(0001) interface can be obtained by connecting all the sliding potentials on this path.The PEC is differentiated to obtain dE/dlSliding, where E is the interaction energy of sliding interface,lSlidingis the sliding distance of interface, the maximum value of dE/dlSlidingis the ideal shear strength (τMEP) of TiC(111)/Ti(0001) interface on the MEP, as shown in Fig.14.

Fig.14 Potential Energy Surfaces(PES),Potential Energy Curves(PEC)and its differential along Minimum Energy Path(MEP)of TiC(111)/Ti(0001) interface.

Figs.14(a) and (b) are the PES of C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interfaces,respectively, where X and Y are two orthogonal directions when the interface model slides.It can be seen that the sliding potential energy maximum of C-terminated-TiC(111)/Ti(0001)and Ti-terminated-TiC(111)/Ti(0001) interface are 5.387 J/m2and 0.271 J/m2, respectively.Figs.14(c) and (d) are the PEC along the MEP of C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interfaces, respectively.The sliding potential barrier of C-terminated-TiC(111)/Ti(0001)and Ti-terminated-TiC(111)/Ti(0001) interfaces along the MEP are 2.094 J/m2and 0.136 J/m2, respectively.Figs.14(e)and (f) are the differential values (dE/dlSliding) for the PEC of C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001)interfaces along the MEP,respectively.It can be seen that the τMEPof C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interfaces are 20.32 GPa and 1.61 GPa, respectively.Therefore, it is more difficult to slip on the C-terminated (111)/Ti(0001) interface than on the Ti-terminated (111)/Ti(0001) interface.

4.Conclusions

(1) After sufficient relaxation,the interfacial adhesion work of C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interfaces are 9.509 J/m2and 3.317 J/m2, and their interfacial energy are 0.405–2.203 J/m2and 0.246–2.025 J/m2, respectively.The C—Ti bonds are a mixture of polar covalent bonds and metal bonds, and the Ti—Ti bonds at the interface are metal bonds.

(2) By the analysis of tensile simulations,the strains of both the C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001)interface in the fracture stage are ranged from 12%to 14%.The maximum tensile stresses are 16.201 GPa and 15.590 GPa, respectively.The fracture location of the C-terminated-TiC(111)/Ti(0001) interface model appears in the inner of the Ti surface model near the interface, while that of the Ti-terminated-TiC(111)/Ti(0001) interface model appears at the interface.Therefore, the interaction of the C-terminated-TiC(111)/Ti(0001) interfacial is stronger than that of the C-terminated-TiC(111)/Ti(0001) interface.

(3) By calculating the potential energy surface of interface model, the sliding potential energy maximum of the C-terminated-TiC(111)/Ti(0001) and Ti-terminated-TiC(111)/Ti(0001) interfaces are 5.387 J/m2and 0.271 J/m2, respectively.And the sliding potential barrier on the minimum energy path are 2.094 J/m2and 0.136 J/m2with an ideal shear strength (τMEP) of 20.32 GPa and 1.61 GPa,respectively.Therefore,it is more difficult to slip on the C-terminated(111)/Ti(0001)interface than on the Ti-terminated (111)/Ti(0001) interface.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by the National Natural Science Foundation of China (No.51771167), the Natural Science Foundation of Hebei Province, China (No.E2021203191),the Hebei Province Innovation Ability Promotion Project,China (No.22567609H), the Natural Science Foundation of Fujian Province, China (No.2020J05196), and the Innovative Funding Project for Doctoral Postgraduates of Hebei Province, China (No.CXZZBS2022147).