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Pressure Driven Enhancement of Ideal Shear Strength in bc8-Carbon and Diamond Weiguang Gong, Menglong Wang, Chang Liu, Zhen Qin, Yanhui Liu, Xinxin Zhang, Quan Li, and Weitao Zheng J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09089 • Publication Date (Web): 03 Nov 2017 Downloaded from http://pubs.acs.org on November 11, 2017

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The Journal of Physical Chemistry

Pressure Driven Enhancement of Ideal Shear Strength in bc8-Carbon and Diamond Weiguang Gong,† Menglong Wang,† Chang Liu,† Zhen Qin,† Yanhui Liu,*,‡ Xinxin Zhang,§ Quan Li,*,† and Weitao Zheng† †

State Key Laboratory of Superhard Materials, Key Laboratory of Automobile Materials of MOE, and

Department of Materials Science, Jilin University, Changchun 130012, China ‡

Department of Physics, College of Science, Yanbian University, Yanji 133002, China

§

Department of Science, Shenyang University of Chemical Technology, Shenyang 110142, China

ABSTRACT Superhard materials with strong covalent 3D networks have been the focus of intense research over the past decades. In the current work, the ideal shear strength and deformation mechanism at ambient and high pressure for bc8-carbon (bc8-C) and diamond are systematically investigated by first-principles calculation. Our results demonstrate that the ideal shear strength of bc8-C phase is much lower than that of diamond at ambient pressure. By introducing pressure effect, the ideal shear strength in both bc8-C and diamond increases with increasing pressure. Interestingly, the ideal shear strength for bc8-C exceeds that of diamond above 200 GPa due to the restriction effect by pressure. We have examined the origin of this phenomenon in terms of energy, volume, bond length, local bond deformation and breaking mechanisms.

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1. INTRODUCTION Carbon is one of the most abundant chemical elements in the Earth's crust, which can be stabilized in various allotropes with varied physical properties and wide applications in science and technology, such as graphite, diamonds, lonsdaleite, cold-compressed superhard graphite,1-4 graphene, etc.5 Graphite is the most stable allotrope and soft enough to form a streak on paper due to the weak interaction between the neighboring layers, while diamond is the hardest known substance in nature with the Vickers hardness of 100–160 GPa, though extensive experimental and theoretical efforts have been devoted to exploring new candidates.6-7 However, the shortcomings of diamond (e.g., low thermal and chemical stability) severely limit the application fields. With the development of science and technology, an intensive task is to search for alternative superhard materials. The high hardness for covalent compounds are achieved by the strong and short 3-dimensional chemical bonding network and thus hardness can be integrated control of the type and the density of the covalent bonding. The higher density and stronger of the chemical bonding, the compounds possess the higher the hardness and strength. The crystal structures and the corresponding physical and chemical properties are very sensitive to changes of external pressure conditions.8-15 In principle, the high-pressure phase forms stronger and denser chemical bonding network and thus exhibits better mechanical properties (e.g., higher bulk modulus and shear modulus as well as superior mechanical properties) than those of the corresponding low-pressure phase.7 Previous first-principle calculations show that diamond undergoes a structural transition to another fourfold coordinated convert phase, bc8-carbon (bc8-C).16-19 This phase has been experimentally obtained as a metastable allotrope of Si20 and Ge21. Recent experiment of shock-wave exploration for the high-pressure allotropes of carbon provides direct evidence for the existence of a diamond-bc8-liquid triple point on the melt boundary at ∼850 GPa.22 Based on the previous calculations, it is found that bc8-C has very high Vickers hardness (89 GPa), bulk modulus (427 GPa) and shear modulus (559 GPa), which are comparable to these of diamond at atmospheric pressure. It is widely accepted that the ideal shear strength can be considered as a 2


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good approximation of hardness, and thus it is an important indicator for evaluating the strength and hardness of materials.23 During the process of hardness measurement, the chemical bonding networks effectively resist the external shear stress near the indenter24-25 when the indenter pressed into covalent crystal. Therefore, it is essential to understand the detailed atomistic structural deformation modes and the evolution of the corresponding electron localization distributed in the bonding region for superhard materials. In this paper, we carry out the calculations on the stress-strain relations of bc8-C and diamond in the main symmetry directions at high pressure and large shear deformation. Our calculations further demonstrate that the ideal shear strength of bc8-C phase is much lower compared to diamond at ambient pressure. By introducing pressure effect, the calculated ideal shear strength in both bc8-C and diamond increases with the increasing pressure. Interestingly, the lowest ideal shear strength for bc8-C exceeds that of diamond above 200 GPa, which stems from the constraint effect on structure evolution by pressure. We have examined the origin of this phenomenon in terms of energy, volume, bond length, local bond deformation and breaking mechanisms.

2. COMPUTATIONAL METHOD In the present work, the stress-strain relations were carried out using the density functional theory with the projector augmented wave (PAW) potentials26 and Ceperley and Alder (CA) local-density approximation (LDA) pseudopotential scheme27, as implemented in the VASP code28. The Perdew−Burke−Ernzerh (PBE) generalized gradient approximation (GGA) functional29 and the Heyd−Scuseria−Ernzerhof (HSE) hybrid functional30-31 has been used to estimate the accuracy of different choices of the exchange–correlation functionals. The total energy was minimized by relaxing the structural parameters using a conjugate gradient optimization method32. We used an 11 × 11 × 11 Monkhorst-Pack33 k-point grid and 600 eV energy cutoff to achieve an energy convergence, residual forces and stresses within 1 meV/atom, 0.005 eV/Å and 0.1 GPa, respectively. The relaxed loading path and ideal shear strength were 3



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determined using a previously established method34-35 with modifications with the consideration of compressive effect. At zero pressure, the lattice vectors were re-deformed in the direction of the applied shear strain, and the applied shear strain is fixed to obtain the shear stress at each quasistatic step, while the other five independent tensors were simultaneously relaxed. At high pressure conditions, structures of the selected materials are optimized to a specific pressure. Then, the normal components (σxx, σyy, σzz) of the stress tensor equal to specific pressure and the two independent shear components (σxy , σyz) of the stress tensor are negligibly small. The atomic positions, cell shape, and strain-stress relationship are determined at each quasistatic step by the corresponding relaxation process. The dynamical properties were calculated by the direct supercell calculation method as implemented in the Phonopy program36. Elastic constants were calculated by the strain-stress method, and the bulk, and shear modulus were derived from the Voigt–Reuss–Hill averaging scheme.37 3. RESULTS AND DISCUSSION Both bc8-C and diamond are crystallized in cubic lattices with the space group of Ia-3 (16 atoms per unit cell) and Fd-3m (8 atoms per unit cell), respectively. The equilibrium lattice parameters for bc8-C are a = b = c = 4.424 Å and a = b = c = 4.476 Å by LDA and GGA, respectively, with carbon atoms occupying 16c (0.84395, 0.65605, 0.34395) sites in the unit cell. To test the different choices of the exchange–correlation functionals, the Heyd−Scuseria−Ernzerh of (HSE) hybrid functional is used to calculate the equilibrium lattice parameters with the equilibrium lattice parameters for bc8-C and diamond are 4.441 Å and 3.546 Å, respectively. As listed in Table 1, the optimized lattice parameters for bc8-C and diamond using the above three functionals are all in excellent agreement with the available theoretical and experimental data.38-41 As shown by the previous results,42-45 LDA is good to describe the mechanical and electronic properties for light-element covalent compounds, and thus we employed the LDA for the rest of the study. To basically realize the mechanical properties, the elastic constants of bc8-C and diamond are 4


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calculated. It is well-known that the elastic constants of the crystals should satisfy the generalized elastic stability criteria,46 i.e., C11 > 0, C44 > 0, C11 > |C12|, (C11 + 2C12) > 0 for cubic lattice. Clearly, these calculated elastic constants Cij of bc8-C and diamond satisfy criteria, suggesting that they are mechanically stable at ambient conditions. Dynamical stability for bc8-C and diamond at ambient and high-pressure conditions have been checked by the calculation of phonon spectra as shown in Figure 1. Our results show that there are no imaginary phonon frequencies for both phases in the wide pressure range of 0-1200 GPa, indicating they are dynamically stable.

Table 1. Calculated elastic constants Cij (GPa), equilibrium lattice parameters a (Å), isotropic bulk modulus B0 (GPa), shear modulus G0 (GPa), ratio of G0/B0, Young’s modulus E0 (GPa), and Poisson’s ratio ν for bc8-C and diamond at ambient pressure. Phases

Diamond

bc8-C

Method

C11

C12

C44

a

B0

G0

G0/B0

E0

v

This work (LDA)

1101.5

148.7

598.3

3.534

466.3

546.2

1.171

1178.4

0.079

This work (GGA)

1052.9

126.4

565.4

3.571

435.2

522.1

1.199

1118.8

0.07

Cal. (LDA)

1105.8c

140.5c

607.3c

3.525c

462.3c

545.0c

1.18c

1173.8c

0.08c

Cal. (GGA)

1053.3c

119.5c

569.1c

3.566c

430.7c

518.0c

1.203c

1109.3c

0.07c

Expt.

1079a

124a

578a

3.567b

443a

538a

This work (LDA)

1247.8

69.3

598.3

4.424

462.2

594.7

1.287

1248.6

0.050

This work (GGA)

1169.0

53.4

558.0

4.476

425.3

557.9

1.312

1164.5

0.043

1172d

54d

559d

4.477d

427d

559d

1.316d

Cal. (GGA)

a

Reference 38. Reference 39. c Reference 40. d Reference 41. b

5



(b) Frequency (THz)

Frequency (THz)

(a) 40 30

20

10

0

diamond X

M

40

20

R

Γ

diamond X

Frequency (THz)

30

20

10 bc8-C

X

60

0 R

(d)

0

80

0GPa

(c) 40 Frequency (THz)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Γ

Γ

R

M

Γ

R

40

20 bc8-C X

R

M

60

0 M

1200GPa R

80

0GPa

R

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1200GPa R

Figure 1. Phonon spectra of bc8-C and diamond at ambient and high-pressure conditions. The bulk, shear, and Young’s moduli of bc8-C are calculated with the Voigt–Reuss–Hill method. Our results demonstrate that the theoretical shear and Young's moduli for bc8-C are higher than these of diamond, indicating the bc8-C is a low compressible and potential superhard material. We also check the pressure effect on the bulk modulus, shear modulus, Young's modulus for the two phases, as shown in Figure 2. With increasing pressure, these shear and Young's muduli for bc8-C increase more quickly than these of diamond, while the theoretical trend of bulk modulus for bc8-C are almost identical to diamond with slight higher value at above 10 GPa. It is known that the bulk modulus and shear modulus reflect the mechanical resistant to compressibility, and shape change under the external conditions, respectively, and G0/B0 represents the relative directionality of the bonding.47 The calculated ratio of G0/B0 for bc8-C (1.287) is similar with that of diamond (1.171), which indicates that the directionality of the bonding of bc8-C is strong. Brittleness and ductility are intrinsically related to the mechanical properties of materials, which are associated with the value of B0/G0, where, the ratio above the threshold of 1.75 is corresponding to ductility, while the value below the threshold is related to brittleness.48 Based on the criteria proposed by Pugh49, bc8-C has a B0/G0 ratio of 0.777, similar with that of diamond (0.848), below the critical value 1.75, which 6


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means that bc8-C is brittleness. In terms of rigidity, the bc8-C is very close to diamond. 6000

5000

Elastic Modulus (GPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


4000

3000

E0

Diamond

B0

Diamond

G0

Diamond

E0

bc8-C

B0

bc8-C

G0

bc8-C

2000

1000

0 0

200

400

600

800

1000

1200

Pressure (GPa)

Figure 2. Elastic modulus of bc8-C and diamond as a function of pressure.

In previous studies, the theoretical hardness of bc8-C has been predicted based on semi-empirical microhardness model with a simulated Vickers hardness of ~89 GPa.50-51 This hardness value is extremely high, which is only 7.3% lower than that of diamond (96 GPa), indicating bc8-C is indeed a superhard solid, although it does not exceed that of diamond in hardness as originally proposed. The predicted hardness are based on the structural and electronic properties at equilibrium. There is still a need to evaluate the ideal shear strength at large strains of bc8-C to examine the bond deformation and breaking mechanisms under normal and high pressure conditions.

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160

(111)[11-2] (111)[10-1] (111)[-1-12]

140 120

120

(a) Diamond

(001)[100] (001)[110] (001)[450] (110)[001] (110)[1-10] (110)[-111] (111)[01-1] (111)[-1-12] (111)[-321]

100 A2

100

Stress (GPa)

Stress (GPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

80 60

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80 60 40

(b) bc8-C

B2

40 20

20 0 0.0

A1

0

A3

0.1

0.2

0.3

0.4

B3

B1

0.00

0.05

0.10

0.15

0.20

Strain

Strain

Figure 3. The calculated stress-strain curves on various shear sliding planes in different directions under pure shear deformation for bc8-C under ambient pressure compared to diamond in various symmetry directions.

Here, we perform an overall study on the stress-strain relations of bc8-C and diamond in various symmetry directions under shear deformation. The calculated stress-strain curves along several shear paths for diamond and bc8-C are shown in Figure 3(a) and 3(b), respectively. The peak stresses for diamond are 140.0, 106.8, and 97.5 GPa in (111)[-1-12], (111)[10-1], (111)[11-2] directions, respectively, which are in excellent agreement with previous calculations52-53. At small strains, the shear stresses versus strain in three directions for diamond exhibit a steep and almost linear rise, as shown in the stress-strain curves, indicating its large elastic constants. It should be noted that the rising slopes of bc8-C and diamond are almost the same. At the critical shear strain (τ = 0.12, B2), the stress has only declined slightly from the peak value for bc8-C and its deformation range before bond softening is especially shorter compared to diamond from the overall perspective. The structural failure occurs at τ = 0.36 and 0.13 for diamond and bc8-C, respectively. Both of the peak stress have a sharp drop behavior in the shear stress near the critical strain for diamond and bc8-C. The peak stress in the weakest shear direction for diamond is the largest one, while bc8-C is the exact opposite, and often the higher the peak value is, 8


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the greater strain is. It is noticed, the highest peak stress of 93.4 GPa is found under the (110)[1-10] shear loading for bc8-C, which remains below the minimum stress peak of diamond. The lowest peak stress (i.e., the ideal shear strength) of 46.1 GPa at a strain of 0.1 is predicted under the (001)[100] shear loading, which is places bc8-C well above the threshold (40 GPa) for a superhard material, but far below the weakest shear stress peak of diamond. In other words, the ideal shear strength of bc8-C is only 47.3% of the value for diamond at ambient conditions and is much lower than the simulated hardness.

Figure 4. The ‘‘snapshots’’ of the strained structures right before (A2, B2) and after (A3, B3) the bond-breaking points as well as equilibrium structures (A1, B1) corresponding to the filled symbols in the stress-strain plot at 0 GPa for diamond and bc8-C, respectively. To explain the disparity, we now turn to a detailed analysis of the atomistic structural deformation modes to understand the shear deformation process at atmospheric pressure in two allotropes. We have shown in Figure 4 the equilibrium structure (A1, B1), strained structures right before (A2, B2) and after (A3, B3) the 9



(b)

-9.0

0GPa -9.5

Energy (eV/atom)

Energy (eV/atom)

(a)

A2

B2 B1

-10.0

A3

B3 A1 -10.5

Volume (Å3)

Volume (Å3)

120 90 60

Bond length (Å)

2.4 2.0

d1

d3

d2

1.6

bc8-C (001)[100] Diamond (111)[11-2]

1.2 0.00

-7.8

200GPa

M2

N2

-8.4

N3 -9.0 N1

M3

-9.6 M1 75 60 45 30

30

Bond length (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

2.4

d4 2.0

d1

1.6

d2

1.2 0.0

d3 bc8-C (001)[100] Diamond (111)[11-2]

0.1

Shear Strain

0.2

0.3

0.4

0.5

0.6

Shear Strain

Figure 5. Calculated energy (upper panel), unit cell volume (middle panel), and bond length (lower panel) of bc8-C versus strain in the (001)[100] shear directions compared to diamond in the (111)[11-2] shear direction at 0GPa (left) and 200 GPa (right).

bond-breaking points, corresponding to the filled symbols in the stress-strain relationship [Figure 3] and plotted in Figure 5 the corresponding changes of the enthalpy, unit cell volume and bond length as functions of strain. The results show that despite their distinct differences in ideal shear strength, both of diamond and bc8-C undergo a cubic-to-graphitic transformation with a dramatic volume expansion, energy decline sharply and the remarkable reduction in bonding strength related to their structural deformation modes at before and after critical points. Bc8-C is a metastable phase at ambient conditions with 638.3 meV/atom higher than that of graphite, while diamond has nearly degenerate energy with graphite. As a result, the relative energy difference for the cubic-to-graphitic (layered) transformation is much higher for bc8-C, in comparison with that of diamond. Moreover, the energies of diamond and bc8-C at the critical points are nearly identical [Figure 5 top panel] at large shear conditions. These intriguing behaviors lead to a much higher kinetic 10


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barrier (774.6 meV/atom) for the transformation from diamond to graphite, and thus possesses a much higher peak strength. In the process of the equilibrium to the fracture state, the volume expansion ratio of bc8-C is 46.9%, which is well above the 36.2% of diamond, stemming from the higher density of bc8-C than that of diamond. This is different from the bond breaking mode of diamond. These provide an explanation for the low strength of bc8-C despite its high elastic moduli and simulated Vickers hardness at equilibrium.

(a)

500

(b) 250

(111)[10-1] Diamond (111)[11-2] Diamond (111)[11-2] Diamond (001)[100] bc8-C (111)[-321] bc8-C (110)[-111] bc8-C

bc8-C (001)[100] Diamond (111)[11-2]

200

300

200

M2

100 50

N1

0

100

200GPa

N2

150

Stress (GPa)

400

Stress (GPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


N3

M1 -50

M3

0 0

200

400

600

800

1000

1200

0.0

0.1

0.2

Pressure (GPa)

0.3

0.4

0.5

0.6

Strain

Figure 6. (a) Calculated the shear peak stress versus pressure (0~1200GPa) for bc8-C in the weakest direction of shear stress of the inequivalent (001), (011), and (111) planes compared to diamond in principal symmetry directions of cleavage plane. (b) Calculated stress of bc8-C versus strain in the (001)[100] shear directions at 200 GPa compared to diamond in the (111)[11-2] shear direction.

In principle, the high-pressure phase of covalent material forms with both higher volumetric mass density and bond density stronger bonding network and thus exhibiting superior mechanical properties compared to the low-pressure phase. Hereby, we continued to carry out a systemic investigation of shear deformation and strength of bc8-C by performing stress-strain calculations in the inequivalent (001), (110), and (111) planes along the weakest direction of shear stress at selected hydrostatic pressures. The results are summarized in Figure 6(a) and compared to the 11



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peak stress of diamond in its three shear directions. The peak curve of the weakest stress direction with the change of pressure at different planes shows a state of winding upward for bc8-C, while the weakest stress peak curve of diamond does not always rise, especially, it shows a trend of rising firstly and then decreasing slowly in (111)[11-2] directions. Remarkably, as pressure approaches 200 GPa, the lowest shear peak stresses of bc8-C in (001)[100] directions becomes higher than that of diamond in (111)[11-2] directions. We show the calculated shear stress-strain relation for bc8-C and diamond in the weakest shear directions at the same pressure (200GPa), as presented in Figure 6(b). It is clear to see that the upward trend of bc8-C is apparently higher than that of diamond, which is obviously different from that at atmospheric pressure.

Figure 7. The ‘‘snapshots’’ of the strained structures right before (M2, N2) and after (M3, N3) the bond-breaking points as well as equilibrium structures (M1, N1) corresponding to the filled symbols in the stress-strain plot at 200 GPa for diamond and bc8-C, respectively.

12


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Figure 8. Calculated 3D electron localization function (ELF) plots at key structural snapshots for diamond (a) and bc8-C (b), respectively.

In order to explore specific effect of pressure, we examine in Figure 5(b) the corresponding changes of the enthalpy, unit cell volume and bond length as functions of strain. The equilibrium structure (N1, M1), strained structures right before (N2, M2) and after (N3, M3) the bond-breaking points, corresponding to the filled symbols in the stress-strain plot are shown in Figure 7. We have provided the calculated electronic local functions (ELF) to further understand the bond change and bonding characteristics of diamond and bc8-C at key structural snapshots, as shown in Figure 8. The typical isosurfaces with ELF of 0.75 is chosen to show the short and strong C–C covalent bonding network. It is seen that the energy of the failure structure (M3 and N3) is nearly the same as that of the initial structure (M1 and N1) for bc8-C and diamond. Meanwhile, the volume of bc8-C has only a slight expansion with a ratio of about 5% and the volume of diamond is almost unchanged, due to the restriction effect by pressure. At high pressure (200GPa), this transformation to the low-density phase is suppressed for diamond since the expansion of the volume would increase the enthalpy (H = E + pV) of the structure more significantly than at lower pressure. Here, bc8-C before (N2) and after (N3) structural fracture has a lower energy difference (309.7 meV/atom) compared to atmospheric condition between B2 and B3 structure, only about 21.9% of the situation of diamond, but the kinetic barrier of 13



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N1→N2 structure (371.6 meV/atom) is significantly higher than B1→B2 (118.9 meV/atom) and thus generate a significant enhancement of ideal shear strength in bc8-C. It is noticed that all the C-C bonds that nearly perpendicular to the cleavage planes (d1 and d2 in bc8-C, and d3 in diamond) in two materials are responsible for the structural failure break simultaneously under shear strains. Interestingly, the C-C bonds (d2) retract to the much shorter length, while another C-C bonds (d1) are linearly stretched in the process of cubic-to-graphitic transformation for bc8-C, but they abruptly break under the shear strain at critical point. At high pressure (e.g., 200 GPa), the C-C bonds (d2) in bc8-C are not fractured due to the inhibition of pressure compared to atmospheric conditions, while, the C-C bonds (d3) that nearly perpendicular to the cleavage planes in diamond have been broken, similar with the situation at ambient conditions, and then new bonds (d4) generate, as shown in Figure 7, which explains that the ideal shear strength of bc8-C exceeds that of diamond under the action of pressure.

4. CONCLUSIONS Here, taking diamond and bc8-C with strong covalent bonds as prototypes, we show by first-principles strain-stress calculations on the comparison of the mechanical properties between the high pressure and low pressure phases, and expect to give implications for searching for new superhard materials. Our theoretical results show that bc8-C exhibits excellent elastic properties at ambient pressure, but the ideal shear strength is well below than that of diamond. In subsequent calculations, the shear strength calculations indicate that bc8-C possess the superior shear strength at high pressure. We examined the atomistic bonding structural variations and the associated energetic, volume to elucidate the microscopic mechanism for the obtained stress-strain relation of bc8-C and diamond. The constraint by pressure effect suppresses the usual ambient shear deformation modes and promotes new mechanisms that leads to unexpected large strength enhancement of bc8-C, making it stronger than diamond. 14


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AUTHOR INFORMATION Corresponding Authors *E-mail for Quan Li.: [email protected]. *E-mail for Yanhui Liu.: [email protected].

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China under Grants Nos. 11622432, 11474125, 11704262, and 11534003, the National Key Research and Development Program of China under Grant No. 2016YFB0201200, the 2012 Changjiang Scholars Program of China, Educational Scientific Research Project of Liaoning Province under Grant Nos. L2014172 and Program for JLU Science and Technology Innovative Research Team. Part of the calculation was performed in the high-performance computing center of Jilin University and at Tianhe2-JK in the Beijing Computational Science Research Center.

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