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Group Electronegativity for Prediction of Materials Hardness Keyan Li,† Peng Yang,† Lingxiao Niu,† and Dongfeng Xue*,†,‡ †

School of Chemical Engineering, Dalian University of Technology, Dalian 116024, People's Republic of China State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People's Republic of China

‡

ABSTRACT: We have developed a method to predict the hardness of materials containing ultrastrong anionic polyhedra, dense atomic clusters, and layers stacked through van der Waals bonds on the basis of group electronegativity. By considering these polyhedra, clusters, and layers as groups that behave as rigid unities like superatoms bonding to other atoms or groups, the hardness values of materials such as oxysalts, Tcarbon, and graphite were quantitatively calculated, and the results are consistent with the available experiments. We found that the hardness of materials containing these artificial groups is determined by the bonds between the groups and other atoms or groups, rather than by the weakest bonds. This work sheds light on the nature of materials hardness and the design of novel inorganic crystal materials.

1. INTRODUCTION Hardness, which is defined as the resistance of a solid to both elastic and plastic deformations, is one of the hottest topics in materials science driven by the important applications of superhard materials in modern science and technology. However, hardness is a complex physical property governed by both intrinsic factors (e.g., composition and crystallographic structure) and extrinsic factors (e.g., defect, morphology, and crystallite size). The hardness of a material is highly dependent on its morphology that has different exposed crystallographic planes.1 Moreover, decreasing the crystallite size down to the “strongest size” of about 10−20 nm can lead to an increase of hardness values by a factor of about two for many materials.2 Experimentally, different processing parameters such as sintering temperature, pressure, and time lead to different crystallite sizes and morphologies for a material.3 Therefore, the measured hardness value for a given material may be quite scattered, indicating that we still face many inherent difficulties to achieve widely acceptable and precise hardness data. Consequently, considerable efforts have been devoted to reveal the nature of hardness, and some theoretical models have been proposed to predict the hardness of materials from the viewpoint of chemical bonds.4−6 Usually, the hardness of materials is considered as an average of contributions of all constituent chemical bonds according to these models. However, this “average” idea is not applicable to the materials in which the bond strengths are quite different such as the pyrite-structured PtN2 and graphite, and the bond distribution is extremely anisotropic such as T-carbon. To solve these problems, it was proposed that the hardness of materials can be reflected by the weakest bonds.6 For example, because the hardness of the N−N bond is much higher than that of a diamond indenter and thus might not be broken in the hardness testing, the hardness of the pyrite© 2012 American Chemical Society

structured PtN2 was estimated as the hardness of weak Pt−N bonds. On the basis of the bond valence model and graph theory, an extended electronegativity (EN)-based method was developed to describe the hardness of layered, molecular, and low-symmetry crystal structures, and the hardness of graphite was proposed to be determined by both the strong sp2 bonds within layers and the weak van der Waals bonds (VDWBs) between layers.7 More recently, a novel carbon allotrope called T-carbon was proposed (by substituting each atom in diamond with a carbon tetrahedron) and predicted to be a kind of superhard materials with a Vickers hardness of 61.1 GPa,8 which is unbelievable when considering its low bulk modulus (169 GPa) and shear modulus (70 GPa). A superatom approach was then suggested to calculate the hardness of Tcarbon.9 By considering the C4 tetrahedron in T-carbon as an artificial superatom due to its high strength and rigidity, Tcarbon was predicted to be not superhard with a hardness less than 10 GPa, which is consistent with its much lower density. Very recently, we dealt with graphite and hexagonal BN (h-BN) by regarding each C1(C2)3 or NB3 triangle as a unity and obtained satisfactory results.10,11 The above studies indicate that some special structural units in the crystallographic frames may behave as groups bonding to other atoms or groups to contribute to the hardness, which inspires us to develop a general method to predict the hardness of materials containing these special structural units from the viewpoint of groups. All materials considered in this work can be classified into three categories: (I) containing ultrastrong anionic polyhedra, such as borates, carbonates, phosphates, and sulfates; (II) containing dense atomic clusters, such as T-carbon and rare Received: April 4, 2012 Revised: May 19, 2012 Published: June 4, 2012 6911

dx.doi.org/10.1021/jp3032258 | J. Phys. Chem. A 2012, 116, 6911−6916

The Journal of Physical Chemistry A

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where χG(A) is the EN of group G or atom A, d is the bond length between G and G(A), and f w is the weakening factor, which is expressed as f w = |χG − χG(A)|/z2(χG + χG(A)) [z is the charge transfer number between G and G(A), equaling the formal group charge in a given compound. For example, the values of z for CO3 in carbonates and B6 in LaB6 are 2 and 3, respectively]. Herein, the group EN, χG, is defined in terms of our covalent EN model13

earth hexaborides; and (III) consisting of layers stacked through VDWBs, such as graphite and MoS2. In our previous work, EN, which characterizes “the power of an atom in a molecule to attract electrons to itself”, was used to describe the bonding behaviors of chemical bonds and then to calculate and predict the hardness of crystal materials.5,10 In this work, we consider these special structural units, that is, polyhedra, clusters, and layers, as groups, and the concept of EN is extended from atoms to groups, which represents “the power of a group (G) to attract electrons to itself from another bonded atom or group”, to describe the bonding behaviors of group− atom or group−group bonds, which determines the hardness of materials. We then quantitatively calculated the hardness of materials containing these special structural units using our ENbased hardness model by substituting the atom EN with group EN. This work provides much implication for deeply understanding the hardness of materials.

χG = 0.481NG/R G

(3)

where NG is the number of bonding electrons of the group and RG is the radius of the group, which is influenced by the bonding environments of the group. Bonds in crystals are classified into different subsystems according to different constituents. Combined with bond density ρ, the hardness of a subsystem Hi can be expressed as Hi = aδt(b i)ρic

2. METHODS From the viewpoint of chemical bonds, bonds in crystals suffer from both stretching and bending deformations during the indentation hardness testing.12 Therefore, two strengths, that is, stretching strength and bending strength, were proposed to characterize the resistances of a bond in crystals against these two deformations.10 For the materials containing ultrastrong anionic polyhedra, dense atomic clusters and layers stacked through VDWBs, these special structural units can be regarded as groups bonded with other atoms or groups to play roles in the hardness of materials. Therefore, the hardness of these materials is determined by the bonds between groups and other atoms or groups. Taking LaPO4 as an example (as shown in Figure 1), the hardness of LaPO4 results from the bonds

(4)

where a, b, and c are constants, equaling 1.5 (1.3), 1 (1), and 0.5 (0.5) for Vickers (Knoop) hardness, respectively. δt(i) and ρi are the total strength of bonds and the bond density of the i-th subsystem, δt = δ bδs

⎛1 π2 ⎞ δs⎟ ⎜ δb + 16 ⎠ ⎝4

ρi = ni /Vi

(5) (6)

where ni is the bond number of the i-th subsystem, Vi is the volume of the i-th subsystem, and 1/4 and π2/16 are the square of the average projections of a bond in all directions and into all planes, respectively.10 Then, the hardness of a material with j subsystems can be expressed as a geometric average of hardness of all subsystems ⎡ j ⎤1/ n H = ⎢∏ Hini ⎥ ⎢⎣ i = 1 ⎥⎦

(7)

where n is the bond number in a unit cell.

3. RESULTS AND DISCUSSION 3.1. EN of Groups in Different Materials. In this work, we deal with the materials containing three kinds of structural units, that is, the anionic polyhedra, the dense atomic clusters, and the layers stacked by VDWBs. Considering that the anionic polyhedra AOy (A = B, C, P, S) in oxysalts MxAOy are ultrastrong, which cannot be broken in the hardness testing, the dense atomic clusters have much higher bond density as compared with other constituent bonds, and the covalent bonds within the layers are much stronger than the VDWBs between the layers; these polyhedra, clusters, and layers are considered as groups to bond with other atoms or groups to contribute to the hardness. To describe the bonding characteristics of group−atom or group−group bonds and then calculate the hardness of materials based on our EN-based hardness model, the EN of groups is the most important parameter and should be determined first. Figure 2 illustrates the calculation method of EN for AO4 group. For a polyhedral anionic group AOy, the core of the group locates at A, the bonding radius (RG) equals the sum of A−O average distance and the radius of O atom, the bonding electron number (NG) is the difference between the sum of valence electrons of A and O atoms, and the electrons localized in A−O bonds. For an atomic cluster

Figure 1. Bonding interactions in LaPO4 by considering each PO4 tetrahedron as a group.

between La atoms and anionic group PO4, that is, La−G(PO4) bonds, if we consider each PO4 tetrahedron as a group G(PO4). The stretching strength δs and bending strength δb of bonds can be expressed as χG χG(A) δs = 26.9 0.5 (1) d χG χG(A) −9.7f δ b = 33.5 e w (2) d2 6912



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participating in the covalent bonding for the effective atoms of subgroup,10 and the RG of subgroup can be obtained by the same way as AOy group mentioned above. On the basis of eq 3, the EN values of groups in different materials were calculated, and the results and related parameters were tabulated in Table 1. From the table, we can see that the group EN decreases from the AOy polyhedra to the Ax clusters to the subgroups of layered materials. It was proposed that the EN value of a given group is influenced by its bonding environment,14 which can be reflected by the EN values of a small range for a given group (for example, the EN of BO3 group varies from 3.316 to 3.681) due to its variable bonding radius with the category and distribution of cations. For the AOy polyhedra, the group EN values decrease in the order of SO4 > PO4 > BO4 > CO3 > BO3, which indicates that the group EN value depends on the number of valence electrons of central atom A and the number of O atoms, that is, the more valence electrons of A and the larger y lead to a higher group EN. The EN values of AOy lie in the range of 3.316− 5.246, which approximate to that of O (4.375),13 and will induce a large ionicity between M and AOy groups in oxysalts. For the Ax clusters, the EN values of C4 (2.276) and B6 (1.605−1.886) clusters are close to those of C (2.500) and B (1.641) atoms, respectively, while the N2 dimer has a lower EN (2.720−2.939) as compared with the N atom (3.437).13 Besides, the very low EN of subgroups (0.428−0.854) in layered materials contributes to the weak VDWBs between the layers. 3.2. Oxysalts Containing Ultrastrong Anionic Polyhedra. The oxysalts such as borates and phosphates have been widely applied as functional crystals for optoelectronic devices, and they usually have low hardness. For the oxysalts, the bonding interaction between M and G(AOy) is highly ionic due to the large EN difference between M and G(AOy). To calculate the hardness of oxysalts, the bond length between M and G(AOy) is necessary. If M connects just one O atom of G(AOy), the length of M−G(AOy) bond is considered as the M−A distance, while if M connects two or three O atoms of G(AOy), the bond between M and G(AOy) can be regarded as a “double” or “triple” bond, and the length of the MG(AOy) or MG(AOy) bond should be shorter than the distance between

Figure 2. Scheme of AO4 anionic group. NA and NO are the valence electron number of central atom A and O atoms, respectively, “2” labeled in the bonds is the localized electron number on each A−O bond, NG is the bonding electron number of group, RG is the bonding radius of group, and χG is the EN of group.

group Ax such as C4 tetrahedron, B6 octahedron, and N2 dimer, the core locates at the center of the cluster, the RG equals the sum of A−center distance and the radius of A, and the NG is the difference between the sum of valence electrons of A atoms and the electrons localized in A−A bonds. For T-carbon, hypothesizing that each triangle in the C4 tetrahedral group is a three-center/two-electron (3c/2e) bond, we obtain the bonding electron number of C4 group being 8. Similarly, for MB6 hexaborides, supposing that each bond between neighboring B6 groups is a normal 2c/2e covalent bond and each BBB triangle in the B6 group has x electrons, we obtain 10/8, 11/8, and 10.5/8 electrons for each BBB triangle in the B6 group by satisfying the eight electrons of B atoms and, hence, 8, 7, and 7.5 bonding electrons for B6 group to bond with neighboring groups and M atoms in SiB6, CaB6, and rare earth hexaborides, respectively. For the layers stacked through VDWBs, the groups are represented by the local subgroups, for example, C1(C2)3 is the subgroup in graphite. The NG of subgroup is the remaining valence electron number after

Table 1. Structure, Bonding Electron Number (NG), Radius (RG), EN (χG), and Bonding Interaction of Groups in Materials

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M and A. Taking LaPO4 as an example (Figure 1), one La atom connects two O atoms of the PO4 tetrahedral group in LaPO4, and the bond length dLaG(PO4) of the “double” bond La G(PO4) can be calculated by 1/dLaG(PO4) = 1/(dLa1−O1 + dO1−P) + 1/(dLa1−O2 + dO2−P). Using eqs 1−7, the hardness values of some oxysalts including borates, carbonates, phosphates, and sulfates were calculated, and the results are listed in Table 2. From the table,

is higher than that of trivalent metal borates, which may be caused by the fact that the quinquevalent metals contribute more valence electrons to bond with groups and hence higher strength of M−G(AOy) bonds and higher hardness of materials. 3.3. Materials Containing Dense Atomic Clusters. Materials containing dense atomic clusters may have ionic M−G(Ax) interactions (e.g., MNx), covalent G(Ax)−G(Ax) interactions (e.g., T-carbon), or both of the two interactions (e.g., MB6). As shown in Figure 3, the bond between La and

Table 2. Calculated (Hcal in GPa) and Experimental (Hexp in GPa) Hardness Values of Oxysalts Containing Ultrastrong Anionic Polyhedra crystala

Hcalc

Hexp

AlBO3 NbBO4 TaBO4 LaBO3 NdGa3(BO3)4 REFe3(BO3)4f MgCO3 CaCO3 SrCO3 BaCO3 MnCO3 FeCO3 ZnCO3 CdCO3 PbCO3 MgCa(CO3)2 AlPO4 GaPO4 ScPO4 YPO4 LaPO4 CePO4 PrPO4 NdPO4 EuPO4 CaSO4 SrSO4 BaSO4 CuSO4 PbSO4

8.4 12.2 12.1 5.4 5.8 6.0 1.8 0.8 0.7 0.6 1.5 1.9 1.6 1.1 0.7 1.1 5.2 5.0 6.9 5.3 4.5 4.9 4.9 5.0 4.5 1.4 1.3 1.2 1.3 0.9

11.1b 11.2−13.7c 11.2−13.7c 6.89−9.97d 3.9−5.4e 7.2−11.4e 2.1g 0.9g 1.4g 1.4g 1.8g 2.6g 2.6g 1.4−2.1c 1.2g 1.4g 8.9h 5.4h 4.1i 2.1−4.1c 4.48−5.2,j 5k 5.4l 5k 5k 5k 1.4g 1.2g 1.2g 1.4g 0.51−0.88c

Figure 3. Bonding interactions between B6 group and La atom in LaB6. The black dot is the center (Ct) of the B6 group.

G(B6) is considered as a “triple” bond LaG(B6) in LaB6, and its bond length, dLaG(B6), is calculated by 1/dLaG(B6) = 1/ (dLa1−B1 + dB1−Ct) + 1/(dLa1−B2 + dB2−Ct) + 1/(dLa1−B3 + dB3−Ct), where Bi and Ct mean different B atoms and the center of the B6 group. Table 3 shows the calculated and experimental hardness values of T-carbon, hexaborides, and transition metal nitrides. We can see that our calculated values of hardness are in accordance with the available experimental or other calculated values. Recently, by considering each C tetrahedron as an artificial superatom due to the high bond strength and density within it, Chen et al. predicted the hardness of Tcarbon to be 8.2, 7.7, and 5.6 GPa according to Gao's, Simunek's, and their own models,9 which is in good agreement with its low shear strength of 7.3 GPa along the (100)⟨001⟩ slip system (the upper bound of its mechanical strength) and in contrast with the previous work, which attributed to T-carbon a high hardness of 61.1 GPa.8 Our calculation shows a hardness of 7.1 GPa for T-carbon, which indicates that T-carbon is not superhard, and this result is consistent with Chen's work. The atomic density of T-carbon is about 0.075 atom per Å3, and that of diamond is about 0.176 atom per Å3, while the lengths of C− C bonds within C4 tetrahedra and between neighboring C4 tetrahedra in T-carbon are 1.502 and 1.417 Å, respectively, both of which are shorter than those of diamond (1.544 Å). This fact suggests that there are big holes formed by C4 tetrahedra in Tcarbon, which makes it much softer than diamond. Moreover, considering that the EN of C4 tetrahedron (2.276) is very close to that of C atom in diamond (2.500),13 the long distance between C4 tetrahedra is the main cause leading to the much lower hardness of T-carbon as compared with diamond. For MB6 hexaborides, SiB6 is the hardest one with a Knoop hardness of 32.8 GPa, and CaB6 behaves as the softest one with a Knoop hardness of 5.9 GPa, which hints that some candidates

a

The crystal structural data are from Inorganic Crystal Structure Database,15 and similarly hereinafter unless otherwise noted. b Converted from Mohs value16 by Hv = 0.0325(Hm)3 (ref 17). c Converted from Mohs values.18 dRef 19. eRef 20. fRE = La, Nd, Gd, and Tb. gConverted from Mohs values.21 hConverted from Mohs values.22 iConverted from Mohs value.23 jRef 24. kRef 25. lRef 26.

we can see that our calculated hardness values are consistent with the experimental ones, indicating that our group-based method is reasonable to predict the hardness of oxysalts. The borates and phosphates are harder than the carbonates and sulfates, and all of these oxysalts have a low hardness, although the bonds within the anionic groups are highly covalent. This is because the anionic polyhedra behave as unities during the indentation hardness testing, and the highly ionic bonding interaction of M−G(AOy) bonds caused by the high EN of anionic polyhedra leads to the low hardness of oxysalts. Herein, the borates exhibit different hardness values for cations with different valences. The hardness of quinquevalent metal borates 6914



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C1(C2)3, NB3, and MX6, respectively. Figure 4 shows the subgroup and the bonding interactions between groups in

Table 3. Calculated (Hcal in GPa) and Experimental (Hexp in GPa) Hardness Values of Materials Containing Dense Atomic Clusters crystal

Hcalca

Hexpa

T-carbonb SiB6 LaB6 CeB6 PrB6 NdB6 SmB6 EuB6 CaB6 WN2h PtN2j OsN2j IrN2n IrN3p

7.1 32.8d 14.4d 15.9d 15.7d 15.2d 15.3d 13.1d 5.9 16.1 17.7 19.2 19.5 16.6

5.6,c 7.7,c 8.2c 24.7−28.1e 19.8f 19.35f 18.8f 19.35f 17.8f 18.15f 4−8g 26.2i 22.8k 25.6,l 19.1m 23.9o 18.8o

a

All values, unless otherwise noted, are Vickers scales and similarly hereinafter. bRef 8. cCalculated values.9 dKnoop scale. eKnoop hardness value.27 fKnoop hardness values.28 gRef 29. hSpace group is P6̅m2, ref 30. iCalculated by Chen's model31 using bulk (B) and shear (G) modulus data from ref 30. jWith marcasite structure, ref 32. k Calculated by Chen's model using B and G data from ref 33. l Calculated by Chen's model using B and G data from ref 34. m Calculated value.34 nWith FeAs2 structure, ref 35. oCalculated by Chen's model using B and G data from ref 36. pSpace group is Im3̅, ref 36.

Figure 4. Bonding interactions between the groups and the bodycentered triangular prism MoS6 subgroup in MoS2.

MoS2. According to eqs 1 and 2, the low EN of subgroup and the long distance between the subgroups of neighboring layers lead to the low strength of bonding between groups and, thus, very low hardness of layered materials. Experimentally, these layered materials exhibit ultrasoft because the big interspaces between the neighboring layers will be readily caved in or ruptured during the indentation hardness testing. Previous hardness models4−6 usually give good results for simple highsymmetry structures; however, the results are much less satisfactory for the low-symmetry and anisotropic structures, especially for the layered structures.7 The hardness values of some layered materials were predicted in terms of eqs 1−7, and the results were presented in Table 4. According to the table,

of superhard materials may exist in nonmetal hexaborides. Our calculated Knoop hardness values of rare earth hexaborides are in the range of 13.1−15.9 GPa, which are slightly lower than the microhardness values of 17.8−19.8 GPa measured by Futamoto et al. under a load of 200 gf (about 2 N).28 Besides, Takashima et al. obtained Vickers hardness of 4−8 GPa for CaB6 under a load of 98 N,29 which implies that our calculated hardness values for hexaborides approach their load independent hardness. Transition metal nitrides are predicted to be not superhard with hardness in the range of 16.1−19.6 GPa because the N2 dimer behaves as a rigid unity, and then, the valence electrons of N atoms do not fully contribute to the bonding with M. Consequently, we can infer that MN2 with fluorite structure will be harder than those with pyrite and marcasite structures since the valence electrons of N atoms in the former structure completely bond with M. From the EN viewpoint, the larger EN of N atom as compared with N2 dimer leads to the stronger bonding between N and other atoms; therefore, the N atom is superior to N2 dimer to obtain materials with high hardness. 3.4. Layered Materials Stacked through VDWBs. Some inorganic materials such as graphite and MoS2 exhibit excellent lubrication capabilities due to the layered lattice structure and weak interlayer bonding force, indicating that they are ultrasoft. In their crystal structures, the atoms connect to each other within the layers by covalent bonds, while the layers themselves are relatively far apart and stacked through the weak VDWBs. However, the weak VDWBs cannot be neglected due to its necessity to maintain the three-dimensionality of crystals, which will contribute more to the hardness. Therefore, the hardness of this kind of materials can be reflected by the VDWBs between the subgroups of neighboring layers, the bond length of which equals the distance between subgroups of neighboring layers. For graphite, h-BN, and MX2, the subgroups of the layers are

Table 4. Calculated (Hcal in GPa) and Experimental (Hexp in GPa) Hardness Values of Layered Materials crystal

Hcalc

Hexpt

graphite h-BN MoS2 WS2 MoSe2

0.28 0.29 0.33 0.33 0.24

0.14,a 0.12b 0.082−0.094c 0.1,d 0.03−0.11e 0.51e 0.46−0.58f

a

Ref 37. bKnoop hardness value.21 cRef 38. dConverted from Mohs value.21 eConverted from Mohs values.18 fRef 18.

we can see that the calculated hardness values approach to the experimental ones, which testifies the validity of our method in dealing with the materials with special layered structures.

4. CONCLUSIONS In this work, by considering the ultrastrong anionic polyhedra, dense atomic clusters, and layers stacked by VDWBs as groups due to the very high strength or density of chemical bonds within them, a general method based on the concept of group EN has been proposed to predict the hardness of materials containing these special structural units. Our results show a reasonable accordance with the available experiments and other calculations. It can be concluded that these “superhard” groups behave as unities to bond with other atoms or groups, that is, 6915



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(29) Takashima, N.; Mori, K.; Kawano, J. I.; Miyazawa, Y.; Miyamoto, Y.; Nishi, Y.; Tanaka, S.; Matsushita, J. I. J. Adv. Sci. 1998, 10, 179. (30) Li, X. F.; Liu, Z. L.; Ding, C. L.; Fu, H. Z.; Ji, G. F. Mater. Chem. Phys. 2011, 130, 14. (31) Chen, X. Q.; Niu, H.; Li, D.; Li, Y. Intermetallics 2011, 19, 1275. (32) Chen, W.; Tse, J. S.; Jiang, J. Z. Solid State Commun. 2010, 150, 181. (33) Yu, R.; Zhan, Q.; Zhang, X. F. Appl. Phys. Lett. 2006, 88, 051913. (34) Wang, Z. H.; Kuang, X. Y.; Zhong, M. M.; Lu, P.; Mao, A. J.; Huang, X. F. Europhys. Lett. 2011, 95, 66005. (35) Yu, R.; Zhan, Q.; De Jonghe, L. C. Angew. Chem., Int. Ed. 2007, 46, 1136. (36) Wu, Z. J.; Zhao, E. J.; Xiang, H. P.; Hao, X. F.; Liu, X. J.; Meng, J. Phys. Rev. B 2007, 76, 054115. (37) Patterson, J. R.; Catledge, S. A.; Vohra, Y. K.; Akella, J.; Weir, S. T. Phys. Rev. Lett. 2000, 85, 5364. (38) Pierson, H. O. Handbook of Refractory Carbides and Nitrides; Noyes Publications: Westwood, NJ, 1996.

ionic M−G interactions and covalent or van der Waals G−G interactions, which determines the hardness of these materials. This work answers why the hardness of some materials is very low, although they contain very strong covalent bonds, and provides new insight into the nature of hardness.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We express grateful acknowledgement for the financial support from the National Natural Science Foundation of China (Grant Nos. 50872016, 20973033, and 51125009).

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REFERENCES

(1) Levine, J. B.; Betts, J. B.; Garrett, J. D.; Guo, S. Q.; Eng, J. T.; Migliori, A.; Kaner, R. B. Acta Mater. 2010, 58, 1530. (2) Veprek, S.; Argon, A. S.; Zhang, R. F. Philos. Mag. 2010, 90, 4101. (3) Bux, S. K.; Rodriguez, M.; Yeung, M. T.; Yang, C.; Makhluf, A.; Blair, R. G.; Fleurial, J. P.; Kaner, R. B. Chem. Mater. 2010, 22, 2534. (4) Simunek, A.; Vackar, J. Phys. Rev. Lett. 2006, 96, 085501. (5) Li, K.; Wang, X.; Zhang, F.; Xue, D. Phys. Rev. Lett. 2008, 100, 235504. (6) Gao, F.; Gao, L. J. Superhard Mater. 2010, 32, 148. (7) Lyakhov, A. O.; Oganov, A. R. Phys. Rev. B 2011, 84, 092103. (8) Sheng, X. L.; Yan, Q. B.; Ye, F.; Zheng, Q. R.; Su, G. Phys. Rev. Lett. 2011, 106, 155703. (9) Chen, X. Q.; Niu, H.; Franchini, C.; Li, D.; Li, Y. Phys. Rev. B 2011, 84, 121405. (10) Li, K.; Yang, P.; Xue, D. Acta Mater. 2012, 60, 35. (11) Yang, P.; Li, K.; Xue, D. Funct. Mater. Lett. 2012, 5, 1250003. (12) Gilman, J. J.; Cumberland, R. W.; Kaner, R. B. Int. J. Refract. Met. Hard Mater. 2006, 24, 1. (13) Li, K.; Wang, X.; Xue, D. J. Phys. Chem. A 2008, 112, 7894. (14) Leyssens, T.; Geerlings, P.; Peeters, D. J. Phys. Chem. A 2006, 110, 8872. (15) Karlsruhe, FIZ. Inorganic Crystal Structure Database; Leibniz Institute for Information Infrastructure: Karlsruhe, 2008. (16) Lee, H. K.; Zerbetto, S.; Colombo, P.; Pantano, C. G. Ceram. Int. 2010, 36, 1589. (17) Sirdeshmukh, D. B.; Sirdeshmukh, L.; Subhadra, K. G.; Rao, K. K.; Laxman, S. B. Bull. Mater. Sci. 2001, 24, 469. (18) Anthony, J. W.; Bideaux, R. A.; Bladh, K. W.; Nichols, M. C. Handbook of Mineralogy; Mineralogical Society of America: Chantilly, VA, 2010. (19) Jain, A.; Razdan, A. K.; Kotru, P. N.; Wanklyn, B. M. J. Mater. Sci. 1994, 29, 3847. (20) Leonyuk, N. I.; Leonyuk, L. I. Prog. Cryst. Growth Charact. Mater. 1995, 31, 179. (21) Lide, D. R. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 2007. (22) Xu, G.; Li, J.; Wang, J.; Zhao, H.; Liu, H. Cryst. Growth Des. 2008, 8, 3577. (23) Bernhard, F.; Walter, F.; Ettinger, K.; Taucher, J.; Mereiter, K. Am. Mineral. 1998, 83, 625. (24) Wang, R.; Pan, W.; Chen, J.; Fang, M.; Cao, Z.; Luo, Y. Mater. Chem. Phys. 2003, 79, 30. (25) Perriere, L.; Bregiroux, D.; Naitali, B.; Audubert, F.; Champion, E.; Smith, D. S.; Bernache-Assollant, D. J. Eur. Ceram. Soc. 2007, 27, 3207. (26) Zhou, Z.; Pan, W.; Xie, Z. J. Eur. Ceram. Soc. 2003, 23, 1649. (27) Rizzo, H. F.; Bidwell, L. R. J. Am. Ceram. Soc. 1960, 43, 550. (28) Futamoto, M.; Aita, T.; Kawabe, U. Mater. Res. Bull. 1979, 14, 1329. 6916
