1 Introduction

1

Boron nitride (BN) is a well-known nonoxide ceramic and has extensive applications in engineering. BN may exist in various forms, including hexagonal BN (hBN), turbostratic BN (tBN), wurtzite BN (wBN), cubic BN (cBN), etc. Cubic boron nitride (cBN), which possesses the same lattice structure as diamond, is one of the most promising ultrahard materials due to its extraordinary properties, including ultrahigh strength and hardness, superior resistance against corrosion and wear, excellent thermal and chemical stabilities [1-3]. In the past decades, great efforts have been made in the theoretical [4] and experimental [5-7] investigations to the mechanical properties of the material. Li et al. [4] proposed an indentation strain-stiffening mechanism in nanotwinned cBN with first-principles calculations. Nistor et al. [7] studied the dislocations in cBN with a high resolution transmission electron microscopy (HRTEM), while Harris et al. [8] focused on the effect of temperature on the hardness of polycrystalline cBN. In addition, Natalia et al. [8] synthesized a kind of BN composite, which consists of nano-multilayered wBN and cBN and exhibits a distinct enhancement of hardness. Chen et al. [9] studied the mechanical properties of twinned c-BNs and found that the thickness of the twin layer has a direct impact on the mechanical behavior. Tian et al. [10], Guo et al. [11] and Hou et al. [12] synthesized BN at high pressure and high temperature, but they did not find that the hardness of the obtained materials is comparable with that of diamond. Recently, Tian et al. [5] synthesized a kind of nanotwinned cubic boron nitride (nt-cBN) that exhibits extraordinary strengthening as the twinning size is reduced to a few nanometers and the Vickers hardness of the nt-cBN can exceed the optimal hardness of synthetic diamond. It raises fundamental questions on new atomistic mechanisms governing the incipient plasticity in nanostructured strong covalent solids. It was thought that twin boundaries can serve as barriers against the glide of dislocations. However, Tian et al. did not elucidate this phenomenon in details. To get an insight into the hardening of nt-cBN, Nistor et al. [6] studied the dislocations in cBN with a HRTEM. Li et al. [4] studied the strain-stiffening mechanism during indentation with first-principles calculations. However, whether dislocations are generated in cBN and how they migrate, and the effects of temperature on the mechanical properties of cBN remain unclear.

2

Molecular dynamics (MD) simulation is a powerful tool for studying the deformation mechanism and mechanical properties of thin films [13, 14] and nano-multilayers [15]. For example, MD simulations were performed to investigate the slip system [16], anisotropy [17], temperature dependence of hardness [18] and plastic deformation [19-21] of materials under nano-indentation. Several empirical potentials have been suggested for the description of the interaction between boron and nitrogen atoms in boron nitride nanosystems, such as Tersoff [22-24] and Tersoff-Brenner (Tersoff-like) bond order potentials [25, 26], etc. Sekkal et al. [27] obtained the parameters in Tersoff potential based on that for carbon, and used them to describe the physical and mechanical behavior of cBN, where cBN was treated as a one-component system and the interactions between B and N was ignored. Matsunaga et al. [28] and Albe et al. [29, 30] obtained the Tersoff potential for BN by considering it as a real binary system. However, large differences can be found between the lattice constant, cohesive energy, elastic constants, surface energy and stacking fault energy obtained with these potential parameters and those obtained by experiments or first principles calculations (FPCs). Zhao et al. [31] recently optimized some parameters in the Tersoff potential by Albe et al. [29, 30] and used it to simulate the nano-indentation on the (111) surface of a cBN film. Zhao et al. found the shuffle-set dislocation in the initial stage of indentation, and calculated the general stacking fault energies to understand the possible slip systems in cBN under indentation, but how dislocations nucleate and migrate was not shown. More importantly, we found that the original potential may not be suitable for simulating the nanoindentation on the (001) surface of cBN, because the main slip system predicted is {001}110, which is different from {111}110 reported by Nistor et al. [6]. Their results are correct in the range mentioned in that paper, but there are some limitations, attributed to the complicated initiation and development of dislocations. They calculated the general stacking fault energy curves to understand the possible slip systems in cBN under indentation, and found that the potential can reasonably simulate some responses of cBN under indentation, for instance, in the initial stage the results predicted can match well with that obtained by experiment. However, it is not sufficiently suitable to reveal the nucleation and movement of dislocations in cBN as the indentation depth

3

is very large. Although it can well elucidate the deformation mechanism of plastic deformation of the material, its validity in more general cases needs to be further investigated. In the present article, the Tersoff potential for cBN is further optimized and applied in more general cases, and the deformation mechanisms of cBN under indentation is probed. The article is organized as follows: in Section 2, we further optimized some parameters in the Tersoff potential, which can not only well describe the geometrical, mechanical and physical properties of cBN, but also well reproduce the lattice constants and cohesive energy of hBN, wBN and rocksalt BN; in Section 3, the setup of nanoindentation on a cBN film for MD simulation and its identification are introduced; in the following section, the mechanisms of inelastic deformation during the nano-indentation and the effects of temperature on the mechanical properties of cBN are discussed; and the conclusions are drawn and given in Section 5.

2 Methods

2.1 Optimized Tersoff parameters for cBN We use a formulation of the Tersoff bond-order potential to investigate the mechanical response of cBN subjected to nanoindentation. The atomic interactions are described with a potential energy function in the form of an interactive empirical bond-order potential. The details of the empirical Tersoff potential have been given by Tersoff [22, 24]. In this work, the parameters in the Tersoff potential for N-N and those for B-B are optimized based on the parameters proposed by Albe et al. [29, 30], and those for B-N are optimized based on the parameters by Sekkal et al. [27]. The optimized parameters are listed in Table 1, in which the parameters d and h are slightly modified. They are related to the multi-body order parameters describing how the bond-formation energy is affected by the local atomic arrangement due to the presence of other neighboring atoms. The lattice constants, cohesive energy, bulk modulus and elastic constants of the cBN (B3 phase) calculated with MD simulations with the potential parameters in Table 1 are listed in Table 2, where some experimental results and the results obtained by FPC and by MD simulation using the Tersoff potentials with other sets of parameters are also given for comparison. In Table 2 the relative errors ERR_F and ERR_E are defined as 4

1

ERR _ F 

N

N

 i 1

 ai  ai  FPC  ai

FPC

2

  , 

ERR _ E 

1 N

N

 i 1

 ai  ai  E xp  ai

E xp

  

2

,

where ai (i =1, 2,…, 6) denotes a, Ec, B, C11, C12 and C44 obtained by MD simulation, respectively, and

FPC

ai

and

E xp

ai

are the reference values of ai obtained by FPC and

experiment, respectively. It can be seen by comparing the errors corresponding to different sets of parameters that the optimized potential can overall much better reproduce the results by experiment or FPC. We also calculate the lattice constant in a wide range of temperature, as shown in Fig. 1, for further verification of the validity of the optimized Tersoff potential. Since a nanoindentation process may inevitably involve plastic deformation, we calculate the surface energies (SE) and stacking fault energies (SFE) of different slip systems with the optimized potential, respectively, as shown in Table 3. The stacking fault energies are also calculated using the Vienna ab initio simulation program (VASP). The pseudopotential is adopted to describe the electron-ion interaction, and the generalized gradient approximation (GGA) by Perdew and Wang (PW91) [32] is used to address the exchange correlation functional. The maximum cut-off value of kinetic energy is set as 600 e V for the plane waves. The Monkhorst-Pack scheme is used for the k-point sampling in the first irreducible Brillouin zone (BZ) [33]. The 10×10×1 k points are adopted. We establish 13 layers atoms along 001, 110 and 111 orientations. The results of SEs and SFEs calculated with MD and FPC are shown in Table 3, where it can be seen that the sequence of SEs and that of SFEs are identical with that obtained by FPCs, indicating that slip first occurs along {111}110, and the slip along {110}110 and {001}110 may be activated as the energy is sufficiently large. We also examine the validity of the optimized potential in the other phases of BN by calculating the lattice constants and cohesive energies of the hBN, wBN and rocksalt BN, respectively, as listed in Table 4. It can be seen that the calculated results coincide well with the FPC values, indicating the transferability of the potential.

2.2 Simulation details We simulate with MD the mechanical responses of a cBN film subjected to indentation at different temperature with a dummy sphere diamond indenter. Fig. 2 shows the MD model for the simulation, where there are two kinds of atoms: boundary atoms and Newtonian atoms. The 5

three bottom layers of atoms are fixed as the boundary atoms to prevent the substrate from shifting during the nanoindentation. Periodic boundary conditions are imposed in both x and y directions, and the NVE ensemble is used. The atoms in the rest layers are kept at a constant temperature as thermostat atoms by a Langevin thermostat [34]. The time step is set as 1 fs. The sizes and some governing conditions of the nine cases are listed in Table 5. The orientations of the indentation surfaces of the cases A-H are [001], and that of the case I is [111]. Cases A and I are used to study the deformation process of cBN under indentation, which rule out the effects by the vibration of atoms. And cases B-H are used to discuss the effect of temperature on the mechanical properties of cBN.

2.3 Identification of local structure The Identify Diamond Structure (IDS) method is used to find the atoms arranged in cubic or hexagonal diamond lattice. To classify a central atom, this structure identification method takes into account the second nearest neighbors to discriminate between cubic and hexagonal diamond structures. The method can be considered as an extended version of the common neighbor analysis (CNA). It involves the characterization of the geometrical arrangement of the second nearest neighbors and can be used to identify and visualize the dislocations and stacking faults [35]. In order to display more clearly the defect region, the atoms with diamond structure are removed, and the local lattice structure is indicated by color: the cubic diamond structure (first neighbor) is in red, the cubic diamond structure (second neighbor) in blue, the hexagonal diamond structure in yellow, and the others in white.

3 Results and discussion

3.1 BN(001) film under indentation at 0 K To study the deformation mechanism without involving the effects of temperature, we first perform the indentation on BN(001) film at 0 K. Fig. 3(a) shows the indentation force-depth (P-h) curve obtained with MD simulation, where one can notice the difference between the loading and unloading curves, indicating the occurrence of inelastic deformation during indentation. Fig. 4 shows the atomic configuration and its evolution during the indentation, where the atoms in perfect diamond lattice structures have been removed for clarity. Fig. 4(a) shows the atomic configuration corresponding to Point a (h = 15.12 Å) in Fig. 3(a) when local 6

elastic deformation occurs beneath the indenter. One can notice that the atoms in this region are arranged with diamond lattice structure, as shown in Fig. 5(a), the reason why it is not identified by IDS may be attributed to the cutoff radius adopted. With the increase of h, a sudden pop in appears at Point b (h = 22.88 Å) in Fig. 3(a), along with a slight fluctuation, corresponding to the start of plastic deformation and the nucleation of dislocation, as shown in Fig. 4(b). With the further increase of h, defects grow and propagate in {111} planes, as shown in Fig. 4(c), where it can be seen that the slips of dislocations extend in the direction of about 45°. Fig. 4(d) shows the atomic configuration corresponding to Point d in Fig. 3(a), where it can be seen that the number of the atoms of non-diamond lattice increases, indicating the defects propagate in the {111} planes, and the new slips are observed in these planes. At h=30 Å (Point e in Fig. 3(a)), P tends to its maximum, and the defects develop extensively, as shown in Fig. 4(e). Figs. 4(f), (g) and (h) are the side, bottom and top views of the defect distribution at complete unloading, respectively. In these figures one can observe more clearly the defects distribution (eight {111} dislocations symmetrically distribute beneath the indenter). The activation of slip systems obtained in the simulation is in accordance with that assessed by SFEs. In order to examine the nucleation and slip of dislocations, a set of 011 planes are visually isolated from the bulk material. Figs. 5(a), (b) and (c) show the atomic configurations in the plane corresponding to Points a, b and c in Fig. 3(a), respectively. In Fig. 5(a), the atoms are arranged in almost perfect lattice, and no dislocation is observed. With the increase of h, some dislocations appear (shown in Fig. 5(c)), resulting in the release of stress in the zone beneath the indenter and a drop in force in the P-h curve (Point c in Fig. 3(a)). Analysis reveals that the resulting dislocation has the Burgers vector of a/2011 in the Burgers circuit (in the quadrangles in Fig. 5(c)). During the indentation, internal defects would be strongly affected by the stress field beneath the indenter. Fig. 6 shows the distributions of the local shear stress in xz, yz and xy slices of the specimen at different h. The stress is calculated simply with Thompson's method [36] embedded in LAMMPS, which compute the virial of individual atoms with either pairwise or manybody potential. This method is based on the virial theorem [37], which is equivalent to the continuum Cauchy stress if the velocity terms in the definition of virial stress is ignored (i.e. 7

T = 0 K) [38]. Note that the quantity computed is of units of pressure*volume, which would need to be divided by the volume of an atom to have the unit of stress (pressure). Since the volume of an individual atom is not well defined or easy to compute in a deformed solid, the units of pressure*volume would remain. However, it would not affect the decision regarded to whether the pressure is sufficiently large to induce a slip or twin deformation. It can be seen in Fig. 6 that the shear stress distributes in the direction of about 45ºbeneath the indenter, which is similar to the distribution of the defective atomic structures. As the shear stress approaches the theoretical shear strength of the crystal, geometrically necessary dislocations may nucleate. Therefore, stress-induced nucleation and development of dislocations should be the main mechanism of inelastic deformation in the cBN under nanoindentation.

3.2 Effects of surface orientation and temperature To further demonstrate the validity of the proposed approach, and rule out the effects by the vibration of atoms, we further perform the indentation on cBN(111) film at 0 K by Langevin thermostat [34]. Note that the temperature of the system would be a little higher than 0 K, which varies in a range between 0 K and 3 K. The size and governing conditions of which are the same as those listed in Table 5. Before indentation, the specimen is optimized using the conjugate gradient (CG) algorithm to achieve a stable configuration with minimum equilibrium energy. Fig. 3(b) shows the indentation P-h curve obtained with MD simulation. A coordination number is used to calculate the number of neighboring atoms from the central one within the specified cutoff distance, which can be used to distinguish different atomic structures and identify the location and type of different structural defects [17, 39]. Fig. 7 shows the atomic configurations in the BN(111) film at some typical h, where the atoms with coordination number of four have been removed for clarity. Fig. 7(a) shows the atomic configuration at Point a (h = 8.72 Å) in Fig. 3(b), where local elastic deformation occurs beneath the indenter. With the increase of h, a slight fluctuation appears at Point b (h = 12.08 Å) in Fig. 3(b), corresponding to the start of plastic deformation, where the nucleation of ( 1 1 1 ) dislocation can be observed, as shown in Fig. 7(b). With the further increase of h, another dislocation slips in the ( 1 1 1 ) planes, as shown in Figs. 7(c). At h=14.48 Å (point d in Fig. 3(d)), a slight platform appears in the P-h curve, corresponding to emerge of ( 1 1 1 ) dislocation. In this stage, the dislocations in the three 8

equivalent {111} planes slip along the 110 directions, forming a tetrahedron structure. At Point f (h = 20 Å in Fig. 3(b)), P approaches its maximum and the defects extend extensively, as shown in Fig. 7(f). The slip planes obtained is in accordance with that assessed with the GSF energies. To explore the effects of the temperature, we perform the nanoindentation on cBN(001) film at different temperatures ranging from 0 K to 2100 K, with 300 K for each interval. The size and governing conditions are listed in Table 5. The Langevin thermostat [34] is firstly applied to preheat the film to the prescribed temperature and then relax it at this temperature. The indentation P-h curves of the cBN(001) film at different temperatures are shown in Fig. 8(a), where the eight P-h curves almost coincide in the initial stage of indentation, indicating that temperature less affects the overall response of the cBN film in this stage. With the increase of h, marked differences can be observed between different curves. For a fixed h, P decreases with the increase of the temperature. The yield point (i.e., the point of initial dislocation nucleation) appears earlier at higher temperature. The hardness is defined as the load at a certain indentation depth over the projected contact area [40], where the projected contact area S is simply defined as S   (2 R  h )h

.

Small differences in the resulting hardness is expected but it would not be large enough to change the general picture and conclusion of this work. [41] To illustrate the effects intuitively, we calculate the hardness of cBN film at different temperatures, and show the results in Fig. 8(b), where the hardness decreases with the increase of temperature increases of temperature, which is in accordance with that reported by Harris et al. [7]. As the plastic deformation region beneath the indenter develops, pile-up occurs due to the extrusion of atoms by the indenter. We analyze the pile-up at different temperatures, aimed to shed light on the effect of temperature on the plastic properties of cBN. After unloading and removing the indenter, the top view of the indentation imprints in the surfaces are shown in Fig. 9, where Figs. 9(a), (b), ..., (h) correspond to the indentations at 0 K, 300 K, ..., 2100 K, respectively. When indentation is performed at T = 0 K, the number of the pile-up atoms is small and the height is low. With the increase of T, both the number of pile-up atoms and the 9

height of the pile-up increase, which indicates that temperature has a significant influence on the mechanical behavior of the cBN film, i.e., the capability of plastic deformation is enhanced with the increase of temperature. Conclusively, we firstly optimized the potential adopted, and demonstrated its validity based on its cohesive energy, lattice parameter, elastic constants, SE and SFE. The results are most close to the experimental data, as shown in Table 2, indicating the optimized potential can well elucidate the basic mechanical and thermal properties of cBN. And we also calculated the SE and SFE of different slip systems with the optimized potential, respectively, shown in Table 3. The results basically coincide with that by FPCs and the sequence of SEs and that of SFEs are identical with that obtained by FPCs. Then we clearly studied the deformation processes of indentation on cBN(001) and cBN(111) as shown in Fig. 4 and Fig. 7. Dislocations and Burgers vector shown in Fig. 5 and the atomic stress distribution shown in Fig. 6 may help us to better understand the deformation mechanisms. The slip system satisfactorily coincide with the experimental results by Nistor et al. [6]. We also discussed the effect of temperature on the mechanical properties of cBN, as shown in Fig. 8 and Fig. 9. The relationship between hardness and temperature is in accordance with that reported by Harris et al. [7].

4 Conclusions We optimized the parameters in the Tersoff potential for cBN based on the cohesive energy, lattice parameter, elastic constants, surface energy, and stacking fault energy. We found that the data obtained with the optimized potential is in good agreement with that obtained in experiment or with first principles calculation, and the modified potential is preferable for describing the physical and mechanical properties of cBN. We performed respectively the nanoindentations on the (001) and (111) surfaces of cBN films with molecular dynamics simulations, and found that the main plastic deformation mechanism is stress-induced slip of dislocations along the 110 orientations in the {111} planes. We also simulated the nanoindentations on cBN films at various temperatures ranging from 0 K to 2100 K with each interval of 300 K, and found strong temperature dependence of hardness, and the capability of plastic deformation is enhanced with the increase of temperature. Acknowledgements 10

The authors gratefully acknowledge the financial supports from National Natural Science Foundation of China (grant no. 11332013 and 11272364), the Graduate Scientific Research and Innovation Foundation of Chongqing (grant no. CYB16023), and the Chongqing Research Program of Basic Research and Frontier Technology (grant nos. cstc2015jcyjA50008). References [1] C. Walter, T. Komischke, E. Weingärtner, K. Wegener,;1; Structuring of CBN Grinding Tools by Ultrashort Pulse Laser Ablation, Procedia CIRP, 14 (2014) 31-36. [2] W.-F. Ding, J.-H. Xu, Z.-Z. Chen, Q. Miao, C.-Y. Yang,;1; Interface characteristics and fracture behavior of brazed polycrystalline CBN grains using Cu–Sn–Ti alloy, Materials Science and Engineering: A, 559 (2013) 629-634. [3] M.A. Umer, P.H. Sub, D.J. Lee, H.J. Ryu, S.H. Hong,;1; Polycrystalline cubic boron nitride sintered compacts prepared from nanocrystalline TiN coated cBN powder, Materials Science and Engineering: A, 552 (2012) 151-156. [4] B. Li, H. Sun, C. Chen,;1; Large indentation strain-stiffening in nanotwinned cubic boron nitride, Nature communications, 5 (2014) 4965. [5] Y. Tian, B. Xu, D. Yu, Y. Ma, Y. Wang, Y. Jiang, W. Hu, C. Tang, Y. Gao, K. Luo, Z. Zhao, L.M. Wang, B. Wen, J. He, Z. Liu,;1; Ultrahard nanotwinned cubic boron nitride, Nature, 493 (2013) 385-388. [6] L.C. Nistor, G. Van Tendeloo, G. Dinca,;1; HRTEM studies of dislocations in cubic BN, physica status solidi (a), 201 (2004) 2578-2582. [7] T.K. Harris, E.J. Brookes, C.J. Taylor,;1; The effect of temperature on the hardness of polycrystalline cubic boron nitride cutting tool materials, International Journal of Refractory Metals and Hard Materials, 22 (2004) 105-110. [8] N. Dubrovinskaia, V.L. Solozhenko, N. Miyajima, V. Dmitriev, O.O. Kurakevych, L. Dubrovinsky,;1; Superhard nanocomposite of dense polymorphs of boron nitride: Noncarbon material has reached diamond hardness, Applied Physics Letters, 90 (2007) 101912. [9] C. Chen, R. Huang, Z. Wang, N. Shibata, T. Taniguchi, Y. Ikuhara,;1; Microstructures and grain boundaries of cubic boron nitrides, Diamond and Related Materials, 32 (2013) 27-31. [10] Y. Tian, B. Xu, Z. Zhao,;1; Microscopic theory of hardness and design of novel superhard crystals, International Journal of Refractory Metals and Hard Materials, 33 (2012) 93-106. [11] X. Guo, B. Xu, W. Zhang, Z. Cai, Z. Wen,;1; XPS analysis for cubic boron nitride crystal synthesized under high pressure and high temperature using Li3N as catalysis, Applied Surface Science, 321 (2014) 94-97. [12] L. Hou, Z. Chen, X. Liu, Y. Gao, G. Jia,;1; X-ray photoelectron spectroscopy study of cubic boron nitride single crystals grown under high pressure and high temperature, Applied Surface Science, 258 (2012) 3800-3804. [13] T. Fu, X. Peng, C. Huang, D. Yin, Q. Li, Z. Wang,;1; Molecular dynamics simulation of VN thin films under indentation, Applied Surface Science, 357 (2015) 643-650.

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13

Fig. 1 Lattice constant versus temperature curve.

Fig. 2 Atomic model of MD simulation. The blue presents N atoms and the red for B atoms.

Fig. 3 Indentation force-depth (P-h) curves of (a) BN(001) film and (b) BN(111) film at 0 K.

Fig. 4 Deformation behavior of BN(001) film during the indentation process at 0 K. Only atoms in a local environment that does not correspond to a diamond lattice are represented. The indentation depths are (a) 15.12 Å, (b) 22.88 Å, (c) 23.52 Å, (d) 27.92 Å and (e) 30 Å in the loading stage and (f), (g) and (h) are the side, bottom and top views of the defect distribution at complete unloading, respectively.

Fig. 5 Atomic configurations in (111) plane at different h, N and B are colored green and red, respectively. (a) h = 15.12 Å, (b) h = 22.88 Å and (c) h = 23.52 Å.

Fig. 6 Local shear stress field σxz, σyz and σxy beneath the indenter, corresponding to the indentation depth of 15.12 Å, 22.88 Å and 30 Å, respectively.

Fig. 7 Deformation behavior of BN(111) film during the indentation process at 0 K. The atoms with coordination number of four are deleted for clarity. The indentation depths are (a) 8.72 Å, (b) 12.08 Å, (c) 12.88 Å, (d) 14.48 Å, (e) 18.08 Å and (f) 20.0 Å.

Fig. 8 (a) indentation P-h curves of cBN(001) film at different temperatures, and (b) hardness versus temperature curve.

Fig. 9 Formation of pile-up in indentation along 001: top view of the residual pile-up in BN surfaces after indenter removal. (a) - (h) are indented at different temperatures: (a) 0 K, (b) 300 K, (c) 600 K, (d) 900 K, (e) 1200 K, (f) 1500 K, (g) 1800 K, and (h) 2100 K. Color-scale indicates pile-up height in Å.

Tables Table 1 Optimized Tersoff interatomic potential parameters for cBN. m γ λ3 c d h n β λ2 B R

B-N [31] 3 1 0 38049 4.64704 -0.6048148 0.72751 1.5724×107 2.220 346.7 1.95

N-N[33, 34] 3 1 0 17.7959 5.9484 0 0.6184432 0.019251 2.627272104 2563.560342 2

B-B[33, 34] 3 1 0 0.52629 0.001587 0.5 3.9929061 0.0000016 2.077498242 1173.196962 2 14

D λ1 A

0.2 3.468 1393.6

0.1 2.829309329 2978.95279

0.1 2.237257857 1404.475204

Table 2 Experimental and predicted structure properties of cBN. a, Ec, B and Cij denote lattice constant, cohesive energy, buck modulus, and elastic constants, respectively Tersoff Properti es

Albe [33]

Sekkal [31]

Moon [37]

Matsunag a [32]

Zhao [35]

a (Å)

3.6346

3.592a

3.623c

3.658d

3.658e

3.619f

Ec (eV)

-6.68

-6.7117c

-6.70d

-6.63e

-6.309f

-6.47a

B (GPa)

382.2

-6.470a 402.41 b

365.3c

377d

385e

406f

402g

818.3

945.7b

951.3b

605d

497.7b

952f

838g

820

164.1

130.7b

101.6b

263d

331.4b

133f

184g

190

506.4

567.7b

571.3b

443d

177.3b

584f

489g

480

5.333

14.51

20.69

21.44

45.01

14.93

——

——

6.031

16.17

21.64

19.28

42.94

16.73

——

——

C11 (GPa) C12 (GPa) C44 (GPa) ERR_F (%) ERR_E (%) a

Exp. [35]

This work

FPC

3.604 g

3.615 -6.6 369-40 0

From [29]; b From [42]; c From [27]; d From [39]; e From [28]; f From [31]; g From [43]

Table 3 Stacking fault energy (Wstf) and surface energy (Wsurf) of cBN (001), (110) and (111)

Wstf(J/m2) Wsurf(J/m2) a

▓ (001) This work FPC 11.939 13.769a 5.948 3.2b

(110) This work FPC 8.573 8.074a 3.757 3.0b

(111) This work FPC 5.050 7.217a 2.511 2.6b

Calculated with VASP; b From [44]

Table 4 Lattice constants a and c, and cohesive energy Ec for hBN, wBN and rocksalt BN, predicted with Tersoff potential for cBN. Phase

Property

Tersoff

FPC 15

hexagonal

wurtzite

rocksalt a

a (Å)

2.584

c (Å)

6.66

Ec (eV)

6.649

a (Å)

2.566

c (Å)

4.190

Ec (eV) a (Å) Ec (eV)

6.734 3.546 4.448

2.489a, 2.510b, 2.496c 6.501a, 6.713b, 6.4896c 6.543c 2.525a, 2.552b, 2.532c 4.178a, 4.222b, 4.188c 6.589c 3.499b, 3.474c 4.842c

From [45]; b From [46]; c From [29]

Table 5 Sizes and governing conditions of nine cases. case Size(Å) Velocity(m/s) Temperature(K) A 144.6×144.6×108.45 40 0 B 144.6×144.6×108.45 40 300 C 144.6×144.6×108.45 40 600 D 144.6×144.6×108.45 40 900 E 144.6×144.6×108.45 40 1200 F 144.6×144.6×108.45 40 1500 G 144.6×144.6×108.45 40 1800 H 144.6×144.6×108.45 40 2100 I 127.81×123.97×106.43 40 0

TDENDOFDOCTD

16

Depth(Å) 30 30 30 30 30 30 30 30 20

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