First-principles study of TiN/SiC/TiN interfaces in ... - APS Link Manager

PHYSICAL REVIEW B 86, 014110 (2012)

First-principles study of TiN/SiC/TiN interfaces in superhard nanocomposites V. I. Ivashchenko,1,* S. Veprek,2,† P. E. A. Turchi,3 and V. I. Shevchenko1 1

2

Institute of Problems of Material Science, NAS of Ukraine, Krzhyzhanosky str. 3, 03142 Kyiv, Ukraine Department of Chemistry, Technical University Munich, Lichtenbergstrasse 4, D-85747 Garching, Germany 3 Lawrence Livermore National Laboratory (L-352), P.O. Box 808, Livermore, CA 94551, USA (Received 20 April 2012; revised manuscript received 4 July 2012; published 16 July 2012)

Heterostructures with one monolayer of interfacial SiC inserted between several B1(NaCl)-TiN (001) and (111) slabs are investigated in the temperature range of 0–1400 K using first-principles quantum molecular dynamics (QMD) calculations. The temperature-dependent QMD calculations in combination with subsequent variable-cell structural relaxation reveal that the TiN(001)/B1-SiC/TiN(001) interface exists as a pseudomorphic B1-SiC layer at temperatures between 0 and 600 K. After heating to 900–1400 K and subsequent static relaxation, the interfacial layer corresponds to a strongly distorted 3C-SiC-like structure oriented in the (111) direction in which the Si and C atoms are located in the same interfacial plane. The Si atoms form fourfold coordinated Si-C3 N1 configurations, whereas the C atoms are located in C-Si3 Ti2 units. All (111) interfaces calculated at 0, 300, and 1400 K have the same atomic configurations. For these interfaces, the Si and C layers correspond to the Si-C network in the (111) direction of 3C-SiC. The Si and C atoms are located in Si-C3 N1 and C-Si3 Ti3 configurations, respectively. The ideal tensile strength of all the heterostructures is lower than that of TiN. A comparison with the results obtained from earlier “static” ab initio density functional theory calculations at 0 K for similar heterostructures shows the great advantage of QMD calculations that reveal the effects of thermal activation on structural reconstructions. DOI: 10.1103/PhysRevB.86.014110

PACS number(s): 71.20.Be, 68.35.Gy, 71.15.Pd, 62.25.−g

I. INTRODUCTION

Large experience in the design of superhard heterostructures, and understanding of their properties has been achieved during the last decade. Among them, TiN/SiN heterostructures and nanocomposites represent the most studied systems. They exhibit superhardness (35–100 GPa) combined with high thermal stability and oxidation resistance.1–5 The strong increase in hardness as compared with pure TiN coatings (20–21 GPa) has been attributed to the nanometer size randomly oriented TiN grains that prevent dislocation activity, and one monolayer (1 ML) thick SiNx interfacial layer.6 When the thickness of the SiNx layer increases above about 1 ML, the hardness enhancement decreases because of the weakening of the adjacent Ti-N bonds.7 The 1-ML-thick SiNx interfacial layer appears x-ray amorphous. The possibility of the formation of an epitaxial interface in TiN/SiNx heterostructures was considered in Refs. 8–13. The TiN/SiC heterostructures have been studied to a lesser extent. We carried out an extensive literature search on this system, and found only one paper that is devoted to the investigation of the structural and mechanical properties of TiN/SiC nanolayered coatings.14 Kong, Dai, and Lao et al. prepared thin TiN/SiC nanolayered coatings under different conditions of magnetron sputtering.14 They showed that the coherent 3C-SiC interfacial layers have been formed between TiN slabs with the (111) orientation when the thickness of the SiC layers was less than 0.8 nm. When the thickness of the SiC layer was about 0.6 nm, the hardness of the coatings reached the maximum value of about 60 GPa. Both coherent and incoherent TiN/SiNx interfaces were widely investigated in the framework of different firstprinciples procedures.6,7,15–21 It was shown that the epitaxial structure of the TiN(111)/B1-SiN and TiN(110)/B1-SiN interfaces was preserved after structural relaxation under periodic boundary conditions, whereas the TiN(001)/B1-SiN 1098-0121/2012/86(1)/014110(8)

became stable only after a distortion of the Si-atoms in the [110] direction by about 12 %.6,7,15 Marten, Alling, and Isaev et al. considered the B3-SiN-derived interface as a possible stable epitaxial layer in TiN/SiNx heterostructures.19 To the best of our knowledge, the TiN/SiC interfaces were not theoretically investigated so far. Therefore, given the remarkable experimental results achieved on the TiN/SiC nanolayered coatings,14 we carried out first-principles quantum molecular dynamics (QMD) simulations of the TiN/SiC heterostructures to understand the role of interfaces on the strength enhancement of the TiN/SiC nanolayered coatings. There are some important differences in the chemistry of the Ti-Si-N and Ti-C-N systems: whereas pure and stoichiometric TiN and Si3 N4 are immiscible,22 the Ti-C-N system forms a substitutional solid solution23 with hardness increasing from that of TiN (21–22 GPa) to that of TiC (40–41 GPa) following the rules of mixtures (see Fig. 8 in Ref. 24). It is therefore of great interest to study the TiN/SiC heterostructure where the carbon is bonded to silicon because the Gibbs free energies of formation at a typical deposition temperature of 800 K are −66.9 kJ/mol for SiC, −174.8 kJ/mol for TiC, and −261.2 kJ/mol for TiN (see Ref. 25, pages 634, 640, and 1542, respectively). Accordingly, the SiC interfacial layer is likely to be chemically stable.

II. COMPUTATIONAL METHODS

For the calculations of the TiN(001)/1 ML B1-SiC heterostructures, we considered the 96-atom (2 × 2 × 3) supercell constructed of the eight-atom B1(NaCl)-TiN cubic unit cells. The TiN(111)/1 ML B1-SiC heterostructures consisted of the 54-atom (3 × 3 × 1) supercell, derived from the 6-atom B1-TiN hexagonal unit cells with [1/2, 1/2, 0], [0, 1/2,−1/2], and [111] as the a, b, and c basis vectors, respectively. The interfacial B1-SiC monolayer has been introduced by

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©2012 American Physical Society

IVASHCHENKO, VEPREK, TURCHI, AND SHEVCHENKO


replacing Ti and N atoms with Si and C atoms, respectively, in the central lattice planes of the given supercell. Thus there are eight Si atoms and eight C atoms in the (001) interface, and nine Si atoms and nine C atoms in the (111) interface. (Note that the TiN(111)/1 ML B1-SiC heterostructure is “polar” in the c direction.) All the heterostructures consist of several parallel layers aligned perpendicularly to the c direction, and one of them is the Si-based interfacial layer. The present calculations are performed using the firstprinciples pseudopotential DFT QMD method as implemented in the quantum ESPRESSO code26 with periodic boundary conditions. The generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof27 has been used for the exchange-correlation energy and potential, and the Vanderbilt ultrasoft pseudopotentials were used to describe the electronion interaction.28 In this approach, the orbitals are allowed to be as soft as possible in the core regions so that their plane-wave expansion converges rapidly.28 The nonlinear core corrections were taken into account.26 The criterion of convergence for the total energy was 10−6 Ry/formula unit (1.36 × 10−5 eV). To speed up the convergence, each eigenvalue was convoluted with a Gaussian of a width of δ = 0.02 Ry (0.272 eV). All the initial structures were optimized by simultaneously relaxing the unit cell basis vectors and the atomic positions inside the unit cells using the Broyden-Fletcher-GoldfarbShanno (BFGS) algorithm.29 The QMD simulations of the initial relaxed heterostructures (called in the following “zero temperature” and denoted ZT) were carried out at 300, 600 (denoted LT), 900, and 1400 K (denoted HT) with fixed unit cell parameters and volume (NVT ensemble, i.e., constant number of particles, volume, and temperature) for ∼2.5 ps. In all the QMD calculations, the time step was 20 atomic units (a.u., about 10−15 s). The system temperature has been kept constant by rescaling the velocity. Only the point has been taken into account in the BZ integration, and the cutoff energy (Ecut ) for the plane-wave basis has been set to 24 Ry (∼326 eV). The variation of the total energy during each QMD time step was controlled. Figure 1 shows the change of the total energy during the simulation of the TiN(001)/B1-SiC heterostructure at 1400 K. During the initial 1 to 1.5 ps, all structures reached closely their equilibrium state and, at later times, the total energy of the equilibrated structures varied only slightly around the constant equilibrium value with a small amplitude of 0.025 eV/atom.

FIG. 1. Change of the total energy ET = ET (t) − ET (0) vs simulation time t during the simulation of the TiN(001)/SiC heterostructure at 1400 K.

After QMD equilibration, the geometry of all the heterostructures is optimized by variable-cell structural relaxation using the BFGS algorithm.29 The cutoff energy for the planewave basis Ecut = 30 Ry (408 eV) and the Monkhorst-Pack30 (2 × 2 × 2) mesh (four k points) were used. The relaxation of the atomic coordinates and of the unit cell was considered to be complete when the atomic forces were less than 1.0 mRy/Bohr ˚ the stresses were smaller than 0.05 GPa, and (25.7 meV/A), the total energy during the structural optimization iterative process has been changing by less than 0.1 mRy (1.36 meV). The heat of formation of the bulk materials is calculated as H f = Etot − ni Ei , where Etot is the total energy of the bulk phase with ni atoms of species i and Ei is the total energy of the bulk Si, C, and Ti atom, or half of the energy of N2 molecule. The conditions of the calculations for bulk Si, C, and Ti are summarized in Table I. The total energy and equilibrium bond length of N2 molecule have been calculated using an extended two-atom cubic cell. The bond length of N2 molecule is in ˚ within 1%. agreement with the experimental value (1.098 A) The interfacial formation energy E f that yields information about the relative stabilities of the SiC interfacial structures between the TiN slabs in the TiN/SiC heterostructures has been calculated as20 E f = S −1 [EH (NTiN ,NI ) − EL (NTiN ) − nSi ESi − nC EC ], NI = nSi + nC , where EH is the total energy of the heterostructure under consideration; NTiN and NI are the numbers of atoms in the TiN slab and SiC interface, respectively; EL (NTiN ) = NTiN ETiN , where ETiN is the total energy per atom of bulk TiN; S is the interfacial area; nSi and nC are the numbers of interfacial silicon and carbon atoms, respectively; ESi and EC are the energies (per atom) of bulk Si and C (cf. Table I). The structural and energetic parameters of B1-TiN, B1TiC, 3C-SiC, β-Si3 N4 , TiSi2 -C49, TiSi2 -54, Ti, Si, C, and N2 have been calculated by using the BFGS algorithm (Ecut = 30 Ry) to verify the reliability of our calculations. The computed structural and energy characteristics of the crystalline materials mentioned above are summarized in Table I. The calculated structural parameters of TiSi2 agree well with those obtained experimentally and from other DFT-based calculations.20 Also, our values of H f for the C49 and C54 phases of TiSi2 are consistent with H f determined experimentally.35 For TiC and β-Si3 N4 , the computed and experimental values also agree fairly well, whereas, the lattice parameter a and the heat of formation H f of 3C-SiC agrees within 4% and 17%, respectively. In the case of large-supercell calculations, the reduced energy cutoff and k-point mesh (in the case of QMD calculations, only the point is considered) are used to minimize computer time without compromising accuracy. An application of the reduced cutoff energy in large-scale QMD calculations was validated by Wang, Gudipati, and Rao et al.36 These authors have used a plane-wave energy cutoff of 348.1 eV for the pseudopotential calculations of elastic constants cij of TiN/Six Ny superlattices. We have chosen such conditions after having verified the accuracy of the lattice parameter a and bulk modulus B for TiN: For the 96-atom sample with Ecut = ˚ 24 Ry (∼326 eV) and one k point, we obtained a = 4.228 A

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FIRST-PRINCIPLES STUDY OF TiN/SiC/TiN . . .


TABLE I. Symmetry, number of atoms in the unit cell (N ), k mesh, lattice parameters (a, b, and c), and formation energy (H f ) of the computed phases in comparison to those of other experimental (in parentheses) and theoretical (in braces) investigations. Symmetry

N

˚ k mesh (A)

Lattice parameters a, b, and c (eV/f. u.)

Hf

TiN

¯ F m3m

2

(8 × 8 × 8)

4.249 (4.24)a {4.239–4.275}b

−3.47 (−3.46)a {−3.43, −3.56}a

TiC

¯ Fm3m

2

(8 × 8 × 8)

4.327 (4.318–4.330)b

−1.797 (−1.359 ÷ −1.973)g

3C-SiC

¯ F43m

2

(8 × 8 × 8)

4.379 (4.36)c

−0.547 (−0.663)h

β-Si3 N4

P63 /m

14

(4 × 4 × 12)

4.670, 4.670, 2.930 (7.607, 7.607, 2.911)a {7.652, 7.652, 2.927}a

−6.85 (−6.44 ± 0.83 ÷ −8.73 ± 0.03)a {−7.81}a , {−9.89}i

TiSi2 -C49

Cmcm

6

(4 × 4 × 4)

3.538, 13.418, 3.590 (3.62, 13.76, 3.60)a {3.571, 13.573, 3.556}a

−1.691 (−1.77 ± 0.09)j

TiSi2 -C54

Fddd

6

(4 × 4 × 4)

8.259, 4.795, 8.521 (8.269, 4.798, 8.553)a {8.270, 4.801, 8.553}a

−1.71

Ti

P63 /mmc

2

(8 × 8 × 6)

2.913, 2.913, 4.614 (2.951, 2.951, 4.683)d

—

Si

¯ Fd3m

2

(8 × 8 × 8)

5.465 (5.43)e

—

C

¯ Fd3m

2

(8 × 8 × 8)

3.573 (3.567)f

—

Phase

a

Reference 20. Reference 31. c X-ray powder diffraction file [074-2307]. d X-ray powder diffraction file [044-1294]. e X-ray powder diffraction file [089-2749]. f X-ray powder diffraction file [089-3439]. g Reference 32. h Reference 33. i Reference 34. j Experimental data for TiSi2 , see Ref. 35. b

and B = 276 GPa, whereas with Ecut = 30 Ry (∼408 eV) and the (2 × 2 × 2) mesh, the lattice constant and bulk modulus ˚ and 278 GPa, respectively. This is a very good were 4.248 A agreement. For the two-atom TiN cell with Ecut = 30 Ry (∼408 eV) and the (8 × 8 × 8) mesh, our calculated lattice ˚ and bulk modulus B = 273 GPa. constant a was 4.249 A The calculated lattice constants are close to the experimental ˚ and comparable to other theoretical results in value of 4.24 A, ˚ 31 (cf. Table I). Also the bulk moduli the range 4.239–4.275 A are consistent with the experimental and theoretical values in the range of 264–326 GPa.31 The calculated heat of formation for the two-atom TiN cell is in excellent agreement with the experimental value of H f (cf. Table I). We also compared the total energy of pure TiN obtained from a 96-atom unit cell with Ecut = 30 Ry (∼408 eV) and a (2 × 2 × 2) mesh with a two-atom cell, Ecut = 30 Ry and a (8 × 8 × 8) mesh. The total energy difference was only about 0.3 mRy/formula unit (∼4 meV/atom). The calculated surface energy (see Ref. 20 for details) for the five-layer (2 × 2) TiN(001) and ten-layer ˚ respectively. (3 × 3) TiN(111) slabs are 0.074 and 0.203 eV/A,

These values are consistent with those computed in Ref. 20 ˚ and for the nine-layer (1 × 1) TiN(001) slab (0.084 eV/A) ˚ eight-layer (1 × 1) TiN(111) slab (0.214 eV/A). Our surface energies are somewhat lower than those reported by Hao et al.,20 the probably reason being the larger dimensions for the x-y slab surface used in our calculations. The stress-strain curves were calculated with Ecut = 30 Ry and a (2 × 2 × 2) k mesh by incrementally deforming the 96and 54-atom supercells in the direction of applied strain (c direction), and simultaneously relaxing the atomic positions inside the supercells and the a and b basis supercell vectors at each step. The starting atomic configuration at each strain step was taken from the relaxed coordinates obtained from the previous step. A stress for a certain tensile strain was obtained from Hellmann-Feynman forces.26 III. RESULTS AND DISCUSSION

We investigated the TiN(001)/SiC heterostructures at 0, 300, 600, 900, and 1400 K as well as the TiN(111)/SiC

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FIG. 2. Total energy [ET = ET (T ) − ET (0)] and average bond lengths for the TiN(001)/SiC heterostructure as functions of simulation temperature (T ).

heterostructures at 0, 300, and 1400 K. Figure 2 shows the dependence of the total energy (ET ) and the structural parameters of the TiN(001)/SiC heterostructure on temperature. We note the pronounced changes of the energetic and structural properties that occur at T = 900 K. On the contrary, the initial TiN(111)/SiC heterostructure formed after static relaxation at 0 K remains practically unchanged with increasing temperature in this range (not shown). The total energies of 0.000, −0.079, and −0.098 meV/atom of the ZT(111), LT(111), and HT(111) heterostructures, respectively, are within the accuracy of the calculations, essentially the same, and significantly smaller than those seen in Fig. 2. In Fig. 3, we show the atomic configurations of the TiN(001)/SiC heterostructures equilibrated at 300 K [LT(001)] and at 1400 K [HT(001)] with subsequent relaxation, and present the structure of the initial unrelaxed TiN(111)/SiC heterostructure as well the HT(111) heterostructure equilibrated at 1400 K with subsequent relaxation. At first, let us consider the (001) heterostructures. One can see that the LT(001) heterostructure has an epitaxial B1-SiC interfacial layer preserved up to 600 K (cf. Fig. 2). A further increase of the temperature leads to a significant change of atomic arrangement caused by thermal motion of the atoms within and near the interface. The atomic redistribution occurs mostly within the interfacial SiC layer. We note the shift of the N atoms in the layer just above and below the (001) interface. The redistribution of the atoms results in the formation of the 3C-SiC-like units consisting of Si in tetrahedral Si-C3 N1 configurations. The C atoms form the five-fold coordinated C-Si3 Ti2 configurations. The atomic arrangement around the (001) interface in the LT(001) and HT(001) heterostructures is shown in Fig. 4. We can see the Si-C4 and C-Si4 B1-SiClike configurations in the LT(001) and the Si-C3 and C-Si3 3C-SiC-like configurations in the HT(001).

FIG. 3. (Color online) Atomic configuration of the LT(001) (a), HT(001) (b), initial unrelaxed TiN(111)/SiC (c), and HT(111) (d) heterostructures. In the initial unrelaxed heterostructure, the interface is represented with the B1-SiC epitaxial layer. Here and in other figures, Ti is big blue-grey, Si is medium dark blue, C is small greenblue, and N is small purple. The atomic configurations were computed ˚ using Si-C, Ti-C, and Ti-N bond length cutoffs of 2.5 A.

Figure 5 show the pair correlation function (PCF) for the LT(001), HT(001), and HT(111) heterostructures. The bond-angle distribution g(θ ) for these high-temperature heterostructures are shown in Fig. 6. The PCF of the LT(001) displays the peaks of the nearest neighbor (NN) Ti-C, Ti-N, ˚ and of the NN Ti-Si Si-C, and Si-N correlations at 2.1–2.2 A, ˚ that are very close to the and Si-Si correlations at 3.0 A corresponding lengths of the metal-nonmetal and metal-metal bonds (l) in TiN, respectively. The average Ti-C bond length of ˚ in the HT(001) heterostructure is larger than that in TiC 2.4 A ˚ whereas the Ti-N bond lengths are close to those in (2.164 A), ˚ TiN. The NN Si–Si correlations occur at the distance of ∼3 A. ˚ In contrast, the additional Ti-Si bonds with lTi-Si ∼ 2.7–2.9 A are formed around the interface of the HT(001) heterostructure. The peak of the NN Si–C correlations is located at a distance ˚ in 3C-SiC. The Si-N bonds that is equal to lSi-C = 1.89 A ˚ are elongated compared to those in β-Si3 N4 (lSi-N = 1.9 A) ˚ The bond angle distribution of the (lSi-N = 1.76–1.8 A). HT(001), g(θ ), in Fig. 6, shows a main peak at ∼109◦ , which means that the interfacial Si and C atoms form a Si-C network similar to that in 3C-SiC. The occurrence of the minor peak of g(θ ) at ∼140◦ indicates that this network is strongly distorted.

FIG. 4. (Color online) Si-C-N bond configurations in and around the interfacial planes for LT(001) and HT(001). The atomic configurations were computed using Si-N and Si-C bond length cutoffs of ˚ The two Ti atoms that are neighboring to the C atoms and site 2.5 A. above and below the interfaces are not shown.

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FIG. 7. (Color online) Atomic configuration for 3C-SiC (a) and Si-C-N bond configuration in and around the interfacial planes for HT(111) (b). The atomic configurations were computed using the ˚ The three Ti atoms that are Si-N and SiC bond length cutoffs of 2.5 A. neighboring to the C atoms and site below the C plane are not shown.

FIG. 5. Pair correlation functions for the low- and hightemperature 1-ML SiC interfaces: LT(001) (low curves), HT(001) (middle curves), and HT(111) (upper curves).

These findings show that the B1-SiC-like interfacial layer in the LT-TiN(001)/SiC heterostructures transforms into a 3C-SiC-like interface above 600 K. This interface can be viewed as two Si(111) and C(111) polar layers in 3C-SiC uniaxially deformed in the (111) direction. Let us now discuss the (111) heterostructure. The structure of the epitaxial layer, shown in Fig. 3(c), strongly differs from the interface structure presented in Fig. 3(d). For the relaxed TiN(111)/SiC interfaces, the Si atoms are tetrahedrally coordinated forming the Si-C3 N1 configurations like the Si-C4

FIG. 6. Bond angle distribution g(θ ) for the high-temperature 1-ML SiC interfaces. The bond angle distributions were computed ˚ using a Si-C bond length cutoff of 2.5 A.

configurations in 3C-SiC. The Si-C and Si-N bond lengths are ˚ respectively (cf. Fig. 5). The C atoms have six 1.89 and 1.77 A, neighbors forming the C-Si3 Ti3 configurations (cf. Fig. 3). The ˚ as compared Ti-C bonds are strongly elongated (lTiC = 2.4 A) ˚ to those in TiC (lTiC = 2.164 A). The Ti-N network is weakly distorted by the incorporation of the SiC interface into the ˚ and TiN(111). The Si-Si and Ti-Si correlations at 2.35 A ˚ which are present in Si and TiSi2 , respectively, are 2.7–2.8 A, absent in the (111) heterostructures (cf. Fig. 5). The main peak of g(θ ) in Fig. 6 is located at ∼109◦ , and a small maximum is observed at ∼120◦ . Accordingly, the Si-C interfacial layer in the (111) heterostructures is close to that of 3C-SiC, and the distortion of the interfacial layer gives rise to a small peak of g(θ ) around 120◦ . In Fig. 7, we compare the perfect 3C-SiC structure with a fragment of the Si-C-N network in the (111) interface. We see that three neighbor N(111), Si(111), and C(111) layers are similar to the corresponding layers in 3C-SiC, when one C layer is substituted by one N layer. This conclusion is consistent with the structural analysis of the (111) interface done above. To estimate the influence of the interfaces on the strength properties of the TiN(001)/SiC and TiN(111)/SiC heterostructures, the tensile strength of these heterostructures was calculated by applying a uniform strain throughout the system perpendicular to the plane of the interface. The results are shown in Fig. 8 in terms of stress-strain curves. The formation of the TiN(001)/SiC and TiN(111)/SiC interfaces in TiN leads to a drastic reduction of the ideal strength, i.e., the maximum stress after which the crystal becomes mechanically unstable, from 38 to 24 GPa, and from 102 to 44 GPa, respectively. The structural reconstruction of the TiN(001)/SiC interface above 600 K results in further decrease of the ideal tensile strength to 11 GPa. The strength decrease from LT-TiN(001)/SiC to LTTiN(111)/SiC can be understood as a geometrical factor, because the strength along various inequivalent crystallographic directions are different. The strength decrease between LTTiN(001)/SiC and HT-TiN(001)/SiC is due to the formation of the distorted 3C-SiC-like interface above 600 K that is accompanied by the elongation and weakening of the Ti-C bonds. This interpretation is supported by Fig. 9, which shows the atomic configurations of the low- and high-temperature

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FIG. 10. Partial local densities of states (PDOS) projected to the interfacial Si an C atoms for the HT(001) (solid line) and LT(001) (dashed line) heterostructures. The vertical line locates the Fermi level. FIG. 8. Stress-strain relation for the TiN and TiN/SiC heterostructures under tensile strain.

heterostructures just after the tensile instability. The failure is due to the breaking of the Ti-C bonds: the longer (and weaker) the Ti-C bonds, the easier the failure. Summarizing the latter data, one can say that the formation of one layer TiN(001)/SiC and TiN(111)/SiC interfaces in TiN strongly destabilizes titanium nitride. The observed strength enhancement in the TiN/SiC nanolayered coatings14 should be attributed to a combined effect of the SiC interfaces as barriers inhibiting dislocation motion and grain boundary shear. Future study, which have to include also the possible strengthening of the SiC interfacial layer and the investigation of the mechanism of plastic deformation which occurs in shear, will bring more understanding regarding possible analogy with the TiN/SiN system.6,7,15,16 We have also calculated the interfacial formation energy E f for the heterostructure under consideration. The values E f for the HT-TiN(001)/SiC and HT-TiN(111)/SiC heterostructures ˚ 2 ), respectively, which are 0.148 and 0.029 eV/(atom × A implies that, in the TiN/SiC nanocomposite and nanolayered coatings, the formation of the TiN(111)/3C-SiC-like interfaces will be preferable at any temperatures. This conclusion is

FIG. 9. (Color online) Atomic configurations of the heterostruc˚ tures under tensile strain, ε. The bond length cutoffs were 2.5 A.

supported by the fact that, in the TiN/SiC nanolayered coatings, the TiN(111)/3C-SiC-like interfaces have been predominantly observed.14 To gain more insight into the origin of the changes in electronic structure and stability of the SiC interfaces depending on their symmetry, let us analyze the partial densities of states (PDOS) projected to the interfacial atoms. There are several polytypes of SiC with the energy band gap in the range of 2.4–3.1 eV. The structural defects give rise to band gap states. Thus we can estimate the quality of the Si-C network of the interfaces by analyzing the local partial densities of states around the Fermi energy. Since GGA calculations underestimate experimentally measured band gaps, we will investigate the semiconductor properties of the interfaces in a comparative way. In Figs. 10 and 11, we show the PDOS of the silicon and carbon atoms sited at the interfaces of the LT(001), HT(001) and HT(111) heterostructures. For all the interfaces, the band gap states around the Fermi level are revealed, which points out that the interfaces consist of the distorted S-C fragments. In the

FIG. 11. Partial local densities of states (PDOS) projected to the interfacial Si an C atoms for the HT(001) (solid line) and HT(111) (dashed line) heterostructures. The vertical line locates the Fermi level.

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sequence LT(001)–HT(001)-HT(111), we observe an increase of the band gap. Judging from the evolution of the PDOS in this sequence, the most perfect Si–C network is expected to be for the TiN(111)/1-ML SiC heterostructure. This means that, in nanocomposites based on TiN/SiC, the formation of the crystalline SiC layer in TiN(111) is more favorable than in TiN(001), in agreement with the experiment.14 IV. CONCLUSIONS

We performed first-principles quantum molecular dynamics calculations of the TiN(001)/B1-derived SiC and TiN(111)/B1-derived SiC heterostructures at various temperatures. It is found that the B1-SiC(001) interfacial heteroepitaxial layers are preserved up to 600 K. Above 600 K, the B1-SiC-like interfacial layer in the TiN(001)/SiC heterostructures transforms into a distorted 3C-SiC-like interface. This interface consists of two Si(111) and C(111) polar layers that are uniaxially deformed in the (111) direction. The interface in the TiN(111)/SiC heterostructure is stable in the temperature range of 0–1400 K. Three neighbor N(111), Si(111), and C(111) layers in this heterostructure are identified as the corresponding layers in 3C-SiC, provided one C layer is substituted by one N layer.

*

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The calculations of stress-strain curves show that the formation of both the one layer TiN(001)/SiC and TiN(111)/SiC interfaces in TiN weakens titanium nitride. Future in-depth studies of the mechanism of plastic deformation in shear are needed to understand the experimentally observed strengthening of these heterostructures. For the TiN(001)/SiC heterostructures, the ideal strength decreases at temperatures above 600 K, which is explained by the formation of a new 3CSiC-like interface with elongation of the Ti-C bonds around this interface. The formation of the TiN(111)/3C-SiC-like interface is found to be more energetically favorable than the formation of the TiN(001)/3C-SiC-like interface in the temperature range of 0–1400 K. The analysis of both the atomic configurations and partial densities of states shows that the 3C-SiC structure of the TiN(111)/SiC interface is less distorted than that of the TiN(001)/SiC interface.

ACKNOWLEDGMENTS

This work was supported by the STCU contract No. 5539. The work of P.T. was performed under the auspices of the U. S. Department of Energy by the Lawrence Livermore National Laboratory under contract No. DE-AC52-07NA27344.

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