First-Principles Study Of Origin Of Hardness In Superhard WB₄

Superhard materials (Hv≥40GPa)are widely used in modern technical industrial applications. Along with science and technology development, intense efforts have been focused on superhard materials in recent years. Traditionally, it is commonly accepted that superhard materials (diamond, cubic-BN, and BC₂N etc.) are those strongly covalent bonded compounds formed by light elements (LEs), namely, B, C, N, and O. Recently, another family of materials consisting of heavy transition metal (TM) and LE are proposed to be potential superhard. Several TM-LE compounds have been synthesized (ReB2, OsB2, PtN2, etc.), however, they are not superhard. Very recently, Gu et al. synthesized superhard tungsten tetraboride (WB₄) and the measured average hardness is very high exceeding 46.2 GPa. WB₄ is the LE rich material and has the highest LE: TM ratio of 4:1 reported so far to have such a high hardness. Thus the understanding of the hardness origin in WB₄ is greatly motivated to help for exploring and designing other superhard materials. To design new TM-LE superhard materials, we must understand what makes WB₄ special.Due to the advantages of moderate computational load, wide application, higher accuracy, and direct comparison with experimental results, the first-principle method based on density functional theory has become one of the most important approaches in the field of computational materials. Applying this method, our simulated lattice parameters, bulk modulus, and hardness of WB₄ are in excellent agreement with the experimental data. Through systematical research on the crystal structure, electronic and mechanical properties of WB₄, we have obtained the innovative results as follows:First, based on comprehensive analysis of difference charge density contour plots, the density of states DOS curves and Mulliken population data, we conclude that a three-dimensional B network with a peculiar B2 dimer along the z-axis and a xy planar honeycomb B sub lattice is mainly responsible for the high hardness of WB₄, to resist either plastic or elastic shape deformation. We analyzed WB₄'s unique special bonding structure through the following aspects:(1) One observes an intriguing bonding situation in the DOS of WB₄ that W and B forms extremely weak covalent bonds as suggested by the mismatching W-d and B-p curve shapes. This is different from the other reported transition metal compound ReB2, OsB2 or PtN2 etc.(2) The difference charge density distribution reflects charge transfer and bonding nature. Such a distribution is obtained by subtracting the density obtained from the overlap of the undistorted atomic densities separated by a distance R, from the molecule/crystal charge distribution evaluated at the same value of R. Wherever this density difference is positive (negative) in value it means that the electron density in the molecule/crystal is greater (less) than that obtained from the overlap of the original atomic densities. The strong covalent B1-B1 bonding within the honeycomb lattice, the highly ionic nature of W atoms, and the extremely strong covalent bonding for the interstitial B2 dimer are evidenced from the difference charge density plots. Much weaker W-B and B1-B2 covalent bonding are also revealed. Here, the weak W-B bonding also supported by the DOS calculation is unique, and in contrast to those in ReB2, OsB2, and PtN2, where strong covalent boding between TM and LE forms.(3) To qualitatively understand the bonding nature of WB₄, we applied Mulliken population analysis. A high overlap corresponds to a high degree of covalency in the bond, and value close to zero indicates little interaction between two atoms. The results confirm our above analysis on the bonding behavior of WB₄. Comparing with the Mulliken overlap population of C-C bond in diamond and in graphite, it is found that the two B1-B1 bonds within the honeycomb plane are comparable to that of diamond in bond strength, while B2-B2 bond strength exceeds that of C-C bond in diamond, and even in graphite. The strong B-B bonding behavior in WB₄ is understandable. (I), each B atom has three valence electrons that are used to form three coplanarσ-bonds (sp2-hybridization) in the honeycomb lattice. This resembles diamond where four C-Cσ-bonds (sp3-hybridization) stabilize. Moreover, the atomic average Mulliken charges are 1.49, 1.47, -0.47, and -0.06 for W1, W2, B1, and B2, respectively. This indicates a significant charge transfer from W (both W1 and W2) atoms to B1 atoms, which help for strengthening the B1-B1 bonds. (II), for the B2-B2 bond in the B2 dimer, all the three valence electrons contribute to one single triplelike exceptionally strong bond. The existence of a B2 dimer along z-axis is crucial in the high hardness. This dimer together with xy planar honeycomb B lattice forms a 3D B network to effectively resist the elastic and plastic deformation, in contrast to that in two-dimensional graphite where there is negligible resistance (Van der Waals force) between layers.Second, the origin of hardness in WB₄ implies that for heavy TM-LE compounds, strong covalent bonding between LEs as well as the high lectron density mainly contributed by TM is necessary for the high hardness. It was suggested that strong and directional covalent bonding and high valence electron density are the necessary conditions for superhard materials to resist both elastic and plastic deformation. We note that TM-LE compounds satisfy the criteria of high electron density due to large electron contributions from TMs. Incorporating B into TM does not significantly change the high electron densities. However, the"strong and directional covalent bonding"should be met by bonding between LEs. The polar covalent bondings between TM and LE inevitably express ionic nature, which have negative impact on hardness. This is why many other TM compounds (e.g. OsB2 and PtN2) with high electron densities are not superhard even though strong hybridization between TM and LE forms.Third, the finite electron DOS at the Fermi level indicates a metallic feature in WB₄. It was previously argued that metallic compounds possess relatively low hardness and most superhard materials are either insulator or semiconductors. However, the current WB₄'s metallic character suggests that metallic materials are not necessarily of low hardness.Forth, we predicted that five other transition metal B compounds TMB4 (TM= Re, Mo, Ta, Os, and Tc) within the WB₄ structure are potential superhard (Hv≥40GPa). They all satisfies the Born stability criteria, i.e., they are mechanically stable, except for ReB4. Based on elastic constants Cij, we obtained the Voigt shear modulus Gv ranging from 52.2 GPa to 181.6 GPa for the studied materials, which are not very large. This suggests that there is no clear connection between hardness and shear modulus.Besides, we studied all the hardness calculation methods published so far, and summarized their advantages and shortcomings. We are looking forward further development of first-principles calculation on hardness based on components and electronic structure, to finally solve the problem of hardness calculation.