Abstract
In this paper, we investigate the elastic properties, bond stiffness, hardness and Debye temperatures for hexagonal P63/mmc WX2 (X = B or N). It is observed that these two compounds are stable in mechanics. Both these two have three typical bonds, W-X bonds, X-X and W-W bonds. By investigating the bond stiffness of these three types of bonds, we found that the bulk modulus of WX2 is mainly determined by W-X and W-W bonds, while the shear modulus is mainly determined by X-X bonds. In addition, using a theoretical model, we evaluate the hardness of these two compounds. Results showed that the Vickers hardness of WN2 is much lower than that of WB2. What’s more, by calculating the Debye temperatures, we found the melting point of WN2 is much lower than WB2, and the overall chemical bonds in WB2 are stronger than that of WN2.
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Chung, H.-Y., Weinberger, M.B., Levine, J.B., Kavner, A., Yang, M., Tolbert, S.H., and Kaner, R.B., Synthesis of ultra-incompressible superhard rhenium diboride at ambient pressure, Science, 2007, vol. 316, no. 5823, pp. 436–439.
Chung, H.-Y., Weinberger, M.B., Yang, J.-M., Tolbert, S.H., and Kaner, R.B., Correlation between hardness and elastic moduli of the ultraincompressible transition metal diborides RuB2, OsB2, and ReB2, Appl. Phys. Lett., 2008, vol, 92, no. 26, pp. 261904.
Dubrovinskaia, N., Dubrovinsky, L., and Solozhenko, V.L., Comment on “synthesis of ultra-incompressible superhard rhenium diboride at ambient pressure”, Science, 2007, vol. 318, no. 5856, pp. 1550–1550.
Chung, H.-Y., Weinberger, M.B., Levine, J.B., Cumberland, R.W., Kavner, A., Yang, J.-M., Tolbert, S.H., and Kaner, R.B., Response to comment on “synthesis of ultra-incompressible superhard rhenium diboride at ambient pressure”, Science, 2007, vol. 318, no. 5856, pp. 1550–1550.
Chiodo, S., Gotsis, H.J., Russo, N., and Sicilia, E., OsB2 and RuB2, ultra-incompressible, hard materials: First-principles electronic structure calculations, Chem. Phys. Lett, 2006, vol. 425, no. 4–6, pp. 311–314.
Kiessling, R., The crystal structures of molybdenum and tungsten borides, Acta Chem. Scand., 1947, vol. 1, pp. 893–916.
Hao, X.F., Xu, Y., Wu, Z., Zhou, D., Liu, X., Cao, X., and Meng, J., Low-compressibility and hard materials ReB2 and WB2: Prediction from first-principles study, Phys. Rev. B, 2006, vol. 74, no. 22, art. 224112.
Yang, J., Sun, H., and Chen, C.F., Is osmium diboride an ultra-hard material?, J. Am. Chem. Soc., 2008, vol. 130, no. 23, pp. 7200–7201.
Li, Q., Zhou, D., Zheng, W.T., Ma, Y.M., and Chen, C.F., Global structural optimization of tungsten borides, Phys. Rev. Lett., 2013, vol. 110, no. 13, art. 136403.
Feng, S.Q., Guo, F., Li, J.Y., Wang, Y.Q., Zhang, L.M., and Cheng, X.L., Theoretical investigations of physical stability, electronic properties and hardness of transition-metal tungsten borides WBx (x = 2.5, 3), Chem. Phys. Lett., 2015, vol. 635, pp. 205–209.
Feng, S.Q., Yang, Y., Li, J.Y., Jiang, X.X., Li, H.N., and Cheng, X.L., Pressure effect on the hardness of diamond and W2B5:First-principle calculations, Modern Phys. Lett. B, 2017, vol. 31, no. 12, pp. 1750137.
Ordejón, P., Artacho, E., and Soler, J.M., Self-consistent order-N density-functional calculations for very large systems, Phys. Rev. B, 1996, vol. 53, no. 16, pp. R10441.
Strobel, R., Maciejewski, M., Pratsinis, S.E., and Baiker, A., Unprecedented formation of metastable monoclinic BaCO3 nanoparticles, Therm. Acta, 2006, vol. 445, no. 1, pp. 23–26.
Wu, Z.G. and Cohen, R.E., More accurate generalized gradient approximation for solids, Phys. Rev. B, 2006, vol. 73, no. 23, art. 2351161.
Perdew, J.P., Burke, K., and Ernzerhof, M., Generalized gradient approximation made simple, Phys. Rev. Lett., 1996, vol. 77, no. 18, pp. 3865.
Monkhorst, H.J. and Pack, J.D., Special points for Brillouin-zone integrations, Phys. Rev. B, 1976, vol. 13, no 12, pp. 5188–5192.
Wu, Z., Zhao, E., Xiang, H., Hao, X., Liu, X., and Meng, J., Crystal structures and elastic properties of superhard IrN2 and IrN3 from first principles, Phys. Rev. B, 2007, vol. 76, no. 5, art. 054115.
Hill, R., The elastic behaviour of a crystalline aggregate, Proc. Soc. London. A, 1952, vol. 65, pp. 349–349.
Chen, X.Q., Fu, C.L., Krcmar, M., and Painter, G.S., Electronic and structural origin of ultraincompressibility of 5d transition-metal diborides MB2 (M = W, Re, Os), Phys. Rev. Lett. 2008, vol. 100, no. 19, art. 196403.
He, X.D., Bai, Y.L., Zhu, C.C., Sun, Y., Li, M.W., and Barsoum, M.W., General trends in the structural, electronic and elastic properties of the M3AlC2 phases (M = transition metal): A first-principle study, Comput. Mater. Sci., 2010, vol. 49, no. 3, pp. 691–698.
He, X.D., Bai, Y.L., Zhu, C.C., and Barsoum, M. W., Polymorphism of newly discovered Ti4GaC3: A first-principles study, Acta Mater., 2011, vol. 59, no. 14, pp. 5523–5533.
Feng, S.Q., Li, X.D., Su, L., Li, H.N., Yang, H.Y., and Cheng, X.L., Ab initio study on structural, electronic properties, and hardness of re-doped W2B5, Solid. Stat. Commun., 2016, vol. 245, pp. 60–64.
Tian, Y.J., Xu, B., and Zhao, Z.S., Microscopic theory of hardness and design of novel superhard crystals, Int. J. Refract. Met. H., 2012, vol. 33, pp. 93–106.
Zhong, M.M., Kuang, X.Y., Wang, Z.H., Shao, P., Ding, L.P., and Huang, X.F., Phase stability, physical properties, and hardness of transition-metal diborides MB2 (M = Tc,W, Re, and Os): First-principles investigations, J. Phys. Chem. C, 2013, vol. 117, no. 20, pp. 10643–10652.
Gao, F.M., He, J.L., Wu, E.D., Liu, S.M., Yu, D.L., Li, D.C., Zhang, S.Y., and Tian, Y.J., Hardness of covalent crystals, Phys. Rev. Lett., 2003, vol. 91, no. 1, art. 015502.
Clarke, D.R., Materials selection guidelines for low thermal conductivity thermal barrier coatings, Surf. Coat Technol., 2003, vol. 163, pp. 67–74.
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Supported by the Key Research of Department Education of Henan Province (No. 17A140030), the cultivation project of young backbone teachers of Henan Province (2019GGJS137) and the Doctoral Fund of Zhengzhou University of Light Industry (2016XGGJS003).
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Li, J., Zhao, J., Tang, C. et al. Theoretical Investigation on the Elastic Properties, Bond Stiffness and Hardness of WX2 (X = B and N). J. Superhard Mater. 41, 434–440 (2019). https://doi.org/10.3103/S1063457619060078
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DOI: https://doi.org/10.3103/S1063457619060078