Perspective on descriptors of mechanical behaviour of cubic transition-metal carbides and nitrides

References

• W.S. Williams, Cubic carbides. Science 152 (1966), pp. 34–42.
   PubMed Web of Science ®Google Scholar
• G.E. Hollox, Microstructure and mechanical behavior of carbides. Mater. Sci. Eng. 3 (1968), pp. 121–137.
   Google Scholar
• L.E. Toth, Transition Metal Carbides and Nitrides, Academic Press, New York, 1971.
   Google Scholar
• K. Balasubramanian, S.V. Khare, and D. Gall, Valence electron concentration as an indicator for mechanical properties in rocksalt structure nitrides, carbides and carbonitrides. Acta Mater. 152 (2018), pp. 175–185.
   Web of Science ®Google Scholar
• P.H. Mayrhofer, C. Mitterer, L. Hultman, and H. Clemens, Microstructural design of hard coatings. Prog. Mater. Sci. 51 (2006), pp. 1032–1114.
   Web of Science ®Google Scholar
• H. Holleck, Material selection for hard coatings. J. Vac. Sci. Technol. A Vac. Surf. Films 4 (1986), pp. 2661–2669.
   Web of Science ®Google Scholar
• W.G. Fahrenholtz, G.E. Hilmas, I.G. Talmy, and J.A. Zaykoski, Refractory diborides of zirconium and hafnium. J. Am. Ceram. Soc. 90 (2007), pp. 1347–1364.
   Web of Science ®Google Scholar
• F. Monteverde, A. Bellosi, and L. Scatteia, Processing and properties of ultra-high temperature ceramics for space applications. Mater. Sci. Eng. A 485 (2008), pp. 415–421.
   Web of Science ®Google Scholar
• S. Ramanathan, and S. Oyama, New catalysts for hydroprocessing: Transition metal carbides and nitrides. J. Phys. Chem. 99 (1995), pp. 16365–16372.
   Web of Science ®Google Scholar
• J.G. Chen, Carbide and nitride overlayers on early transition metal surfaces: Preparation, characterization, and reactivities. Chem. Rev. 96 (1996), pp. 1477–1498.
   PubMed Web of Science ®Google Scholar
• W. Cai, G. Li, K. Zhang, G. Xiao, C. Wang, K. Ye, Z. Chen, Y. Zhu, and Y. Qian, Conductive nanocrystalline niobium carbide as high-efficiency polysulfides tamer for lithium-sulfur batteries. Adv. Funct. Mater. 28 (2018), pp. 1704865.
   Web of Science ®Google Scholar
• F.H. Baumann, D.L. Chopp, T.D. de la Rubia, G.H. Gilmer, J.E. Greene, H. Huang, S. Kodambaka, P. O'Sullivan, and I. Petrov, Multiscale modeling of thin-film deposition: Applications to Si device processing. MRS Bull. 26 (2001), pp. 182–189.
   Web of Science ®Google Scholar
• H. Kindlund, D.G. Sangiovanni, J. Lu, J. Jensen, V. Chirita, I. Petrov, J.E. Greene, and L. Hultman, Effect of WN content on toughness enhancement in V1-xWxN/MgO(001) thin films. J. Vac. Sci. Technol. A 32 (2014), pp. 030603.
   Web of Science ®Google Scholar
• H. Kindlund, D.G. Sangiovanni, L. Martinez-de-Olcoz, J. Lu, J. Jensen, J. Birch, I. Petrov, J.E. Greene, V. Chirita, and L. Hultman, Toughness enhancement in hard ceramic thin films by alloy design. APL Mater. 1 (2013), pp. 042104.
   Web of Science ®Google Scholar
• W.F. Gale, and T.C. Totemeier, Smithells Metals Reference Book, Elsevier Science, Oxford, 2003.
   Google Scholar
• S. Guo, C. Ng, J. Lu, and C.T. Liu, Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys. J. Appl. Phys. 109 (2011), pp. 103505.
   Web of Science ®Google Scholar
• F.Y. Tian, L.K. Varga, N.X. Chen, J. Shen, and L. Vitos, Empirical design of single phase high-entropy alloys with high hardness. Intermetallics 58 (2015), pp. 1–6.
   Web of Science ®Google Scholar
• J.C. Grossman, A. Mizel, M. Côté, M.L. Cohen, and S.G. Louie, Transition metals and their carbides and nitrides: Trends in electronic and structural properties. Phys. Rev. B 60 (1999), pp. 6343–6347.
   Web of Science ®Google Scholar
• S.H. Jhi, J. Ihm, S.G. Louie, and M.L. Cohen, Electronic mechanism of hardness enhancement in transition-metal carbonitrides. Nature 399 (1999), pp. 132–134.
   Web of Science ®Google Scholar
• S. Divilov, H. Eckert, D. Hicks, C. Oses, C. Toher, R. Friedrich, M. Esters, M.J. Mehl, A.C. Zettel, Y. Lederer, E. Zurek, J.-P. Maria, D.W. Brenner, X. Campilongo, S. Filipović, W.G. Fahrenholtz, C.J. Ryan, C.M. DeSalle, R.J. Crealese, D.E. Wolfe, A. Calzolari, and S. Curtarolo, Disordered enthalpy–entropy descriptor for high-entropy ceramics discovery. Nature 625 (2024), pp. 66–73.
   PubMed Web of Science ®Google Scholar
• M. Lim, and D.W. Brenner, Predicting properties of high entropy carbides from their respective binaries. Comput. Mater. Sci. 226 (2023), pp. 112255.
   Web of Science ®Google Scholar
• C. Toher, C. Oses, M. Esters, D. Hicks, G.N. Kotsonis, C.M. Rost, D.W. Brenner, J.-P. Maria, and S. Curtarolo, High-entropy ceramics: Propelling applications through disorder. MRS Bull. 47 (2022), pp. 194–202.
   Web of Science ®Google Scholar
• M.D. Hossain, T. Borman, C. Oses, M. Esters, C. Toher, L. Feng, A. Kumar, W.G. Fahrenholtz, S. Curtarolo, D. Brenner, J.M. LeBeau, and J.-P. Maria, Entropy landscaping of high-entropy carbides. Adv. Mater. 33 (2021), pp. 2102904.
   Web of Science ®Google Scholar
• M. Esters, C. Oses, D. Hicks, M.J. Mehl, M. Jahnátek, M.D. Hossain, J.-P. Maria, D.W. Brenner, C. Toher, and S. Curtarolo, Settling the matter of the role of vibrations in the stability of high-entropy carbides. Nat. Commun. 12 (2021), pp. 5747.
   PubMed Web of Science ®Google Scholar
• M.D. Hossain, T. Borman, A. Kumar, X. Chen, A. Khosravani, S.R. Kalidindi, E.A. Paisley, M. Esters, C. Oses, C. Toher, S. Curtarolo, J.M. LeBeau, D. Brenner, and J.P. Maria, Carbon stoichiometry and mechanical properties of high entropy carbides. Acta Mater. 215 (2021), pp. 117051.
   Web of Science ®Google Scholar
• T.J. Harrington, J. Gild, P. Sarker, C. Toher, C.M. Rost, O.F. Dippo, C. McElfresh, K. Kaufmann, E. Marin, L. Borowski, P.E. Hopkins, J. Luo, S. Curtarolo, D.W. Brenner, and K.S. Vecchio, Phase stability and mechanical properties of novel high entropy transition metal carbides. Acta Mater. 166 (2019), pp. 271–280.
   Web of Science ®Google Scholar
• P. Sarker, T. Harrington, C. Toher, C. Oses, M. Samiee, J.-P. Maria, D.W. Brenner, K.S. Vecchio, and S. Curtarolo, High-entropy high-hardness metal carbides discovered by entropy descriptors. Nat. Commun. 9 (2018), pp. 4980.
   PubMed Web of Science ®Google Scholar
• D.G. Sangiovanni, K. Kaufmann, and K. Vecchio, Valence electron concentration as key parameter to control the fracture resistance of refractory high-entropy carbides. Sci. Adv. 9 (2023), pp. eadi2960.
   PubMed Web of Science ®Google Scholar
• D.G. Sangiovanni, W. Mellor, T. Harrington, K. Kaufmann, and K. Vecchio, Enhancing plasticity in high-entropy refractory ceramics via tailoring valence electron concentration. Mater. Des. 209 (2021), pp. 109932.
   Web of Science ®Google Scholar
• D.G. Sangiovanni, F. Tasnádi, T. Harrington, M. Odén, K.S. Vecchio, and I.A. Abrikosov, Temperature-dependent elastic properties of binary and multicomponent high-entropy refractory carbides. Mater. Des. 204 (2021), pp. 109634.
   Web of Science ®Google Scholar
• L. Chen, J. Paulitsch, Y. Du, and P.H. Mayrhofer, Thermal stability and oxidation resistance of Ti-Al-N coatings. Surf. Coat. Technol. 206 (2012), pp. 2954–2960.
   PubMed Web of Science ®Google Scholar
• R. Rachbauer, D. Holec, M. Lattemann, L. Hultman, and P.H. Mayrhofer, Electronic origin of structure and mechanical properties in Y and Nb alloyed Ti-Al-N thin films. Int. J. Mater. Res. 102 (2011), pp. 735–742.
   Web of Science ®Google Scholar
• L. Chen, D. Holec, Y. Du, and P.H. Mayrhofer, Influence of Zr on structure, mechanical and thermal properties of Ti-Al-N. Thin Solid Films 519 (2011), pp. 5503–5510.
   PubMedGoogle Scholar
• H. Willmann, P.H. Mayrhofer, P.O.A. Persson, A.E. Reiter, L. Hultman, and C. Mitterer, Thermal stability of Al-Cr-N hard coatings. Scr. Mater. 54 (2006), pp. 1847–1851.
   Web of Science ®Google Scholar
• P.H. Mayrhofer, A. Horling, L. Karlsson, J. Sjolen, T. Larsson, C. Mitterer, and L. Hultman, Self-organized nanostructures in the Ti-Al-N system. Appl. Phys. Lett. 83 (2003), pp. 2049–2051.
   Web of Science ®Google Scholar
• C. Mitterer, J. Komenda-Stallmaier, P. Losbichler, P. Schmölz, W.S.M. Werner, and H. Störi, Sputter deposition of decorative boride coatings. Vacuum 46 (1995), pp. 1281–1294.
   Web of Science ®Google Scholar
• J. Patscheider, Nanocomposite hard coatings for wear protection. MRS Bull. 28 (2003), pp. 180–183.
   Web of Science ®Google Scholar
• K.P. Budna, J. Neidhardt, P.H. Mayrhofer, and C. Mitterer, Synthesis-structure-property relations for Cr-B-N coatings sputter deposited reactively from a Cr-B target with 20 at% B. Vacuum 82 (2008), pp. 771–776.
   Web of Science ®Google Scholar
• M. Rühle, and A.G. Evans, High toughness ceramics and ceramic composites. Prog. Mater. Sci. 33 (1989), pp. 85–167.
   Web of Science ®Google Scholar
• W.J. Clegg, K. Kendall, N.M.N. Alford, T. Button, and J. Birchall, A simple way to make tough ceramics. Nature 347 (1990), pp. 455–457.
   Web of Science ®Google Scholar
• I.L. Shabalin, Y. Wang, A.V. Krynkin, O.V. Umnova, V.M. Vishnyakov, L.I. Shabalin, and V.K. Churkin, Physicomechanical properties of ultrahigh temperature heteromodulus ceramics based on group 4 transition metal carbides. Adv. Appl. Ceram. 109 (2010), pp. 405–415.
   Web of Science ®Google Scholar
• F.D. Minatto, P. Milak, A. De Noni, Jr., D. Hotza, and O.R.K. Montedo, Multilayered ceramic composites – a review. Adv. Appl. Ceram. 114 (2014), pp. 127–138.
   Web of Science ®Google Scholar
• S. Zhang, H.L. Wang, S.E. Ong, D. Sun, and X.L. Bui, Hard yet tough nanocomposite coatings–present status and future trends. Plasma Processes Polym. 4 (2007), pp. 219–228.
   Web of Science ®Google Scholar
• J. Karch, R. Birringer, and H. Gleiter, Ceramics ductile at low temperature. Nature 330 (1987), pp. 556–558.
   Web of Science ®Google Scholar
• Z.G. Wu, X.J. Chen, V.V. Struzhkin, and R.E. Cohen, Trends in elasticity and electronic structure of transition-metal nitrides and carbides from first principles. Phys. Rev. B 71 (2005), pp. 214103.
   Web of Science ®Google Scholar
• D.V. Suetin, I.R. Shein, and A.L. Ivanovskii, Elastic and electronic properties of hexagonal and cubic polymorphs of tungsten monocarbide WC and mononitride WN from first-principles calculations. Phys. Status Solidi B 245 (2008), pp. 1590–1597.
   Google Scholar
• D.G. Sangiovanni, V. Chirita, and L. Hultman, Electronic mechanism for toughness enhancement in TixM1−xN (M = Mo and W). Phys. Rev. B 81 (2010), pp. 104107.
   Web of Science ®Google Scholar
• D. Holec, R. Franz, P.H. Mayrhofer, and C. Mitterer, Structure and stability of phases within the NbN-AlN system. J. Phys. D Appl. Phys. 43 (2010), pp. 145403.
   Web of Science ®Google Scholar
• Z. Sun, R. Ahuja, and J.E. Lowther, Mechanical properties of vanadium carbide and a ternary vanadium tungsten carbide. Solid State Commun. 150 (2010), pp. 697–700.
   Web of Science ®Google Scholar
• D. Holec, R. Rachbauer, L. Chen, L. Wang, D. Luef, and P.H. Mayrhofer, Phase stability and alloy-related trends in Ti-Al-N, Zr-Al-N and Hf-Al-N systems from first principles. Surf. Coat. Technol. 206 (2011), pp. 1698–1704.
   PubMed Web of Science ®Google Scholar
• H. Li, L.T. Zhang, Q.F. Zeng, K. Guan, K.Y. Li, H.T. Ren, S.H. Liu, and L.F. Cheng, Structural, elastic and electronic properties of transition metal carbides TMC (TM = Ti, Zr, Hf and Ta) from first-principles calculations. Solid State Commun. 151 (2011), pp. 602–606.
   Web of Science ®Google Scholar
• Z. Gao, and S. Kang, First-principles investigation of the elastic, electronic, and thermodynamic properties of a nitrogen-doped (Ti0.75W0.25)C solid solution. Solid State Commun. 156 (2013), pp. 25–30.
   Web of Science ®Google Scholar
• X.W. Sun, X.Y. Zhang, Y. Zhu, S.H. Zhang, J.Q. Qin, M.Z. Ma, and R.P. Liu, First-principles study of ZrCxN1-x alloys with electron concentration modulation. J. Mater. Sci. 48 (2013), pp. 7743–7748.
   Web of Science ®Google Scholar
• L. Wu, Y. Wang, Z. Yan, J. Zhang, F. Xiao, and B. Liao, The phase stability and mechanical properties of Nb–C system: Using first-principles calculations and nano-indentation. J. Alloys Compd. 561 (2013), pp. 220–227.
   Web of Science ®Google Scholar
• L. Wu, T. Yao, Y. Wang, J. Zhang, F. Xiao, and B. Liao, Understanding the mechanical properties of vanadium carbides: Nano-indentation measurement and first-principles calculations. J. Alloys Compd. 548 (2013), pp. 60–64.
   Web of Science ®Google Scholar
• X.-X. Yu, G.B. Thompson, and C.R. Weinberger, Influence of carbon vacancy formation on the elastic constants and hardening mechanisms in transition metal carbides. J. Eur. Ceram. Soc. 35 (2015), pp. 95–103.
   Web of Science ®Google Scholar
• H. Kindlund, D.G. Sangiovanni, J. Lu, J. Jensen, V. Chirita, J. Birch, I. Petrov, J.E. Greene, and L. Hultman, Vacancy-induced toughening in hard single-crystal V0.5Mo0.5Nx/MgO(001) thin films. Acta Mater. 77 (2014), pp. 394–400.
   Web of Science ®Google Scholar
• H. Kindlund, D.G. Sangiovanni, I. Petrov, J.E. Greene, and L. Hultman, A review of the intrinsic ductility and toughness of hard transition-metal nitride alloy thin films. Thin Solid Films 688 (2019), pp. 137479.
   Web of Science ®Google Scholar
• D.G. Sangiovanni, L. Hultman, and V. Chirita, Supertoughening in B1 transition metal nitride alloys by increased valence electron concentration. Acta Mater. 59 (2011), pp. 2121–2134.
   Web of Science ®Google Scholar
• S.-H. Jhi, S.G. Louie, M.L. Cohen, and J. Ihm, Vacancy hardening and softening in transition metal carbides and nitrides. Phys. Rev. Lett. 86 (2001), pp. 3348–3351.
   PubMed Web of Science ®Google Scholar
• S.H. Jhi, S.G. Louie, M.L. Cohen, and J. Morris, Jr., Mechanical instability and ideal shear strength of transition metal carbides and nitrides. Phys. Rev. Lett. 87 (2001), pp. 75503.
   Web of Science ®Google Scholar
• K. Chen, L.R. Zhao, J. Rodgers, and J.S. Tse, Alloying effects on elastic properties of TiN-based nitrides. J. Phys. D Appl. Phys. 36 (2003), pp. 2725–2729.
   Web of Science ®Google Scholar
• H. Kindlund, J. Lu, J. Jensen, I. Petrov, J.E. Greene, and L. Hultman, Epitaxial V0.6W0.4N/MgO(001): Evidence for ordering on the cation sublattice. J. Vac. Sci. Technol. A 31 (2013), pp. 040602.
   Web of Science ®Google Scholar
• G. Greczynski, H. Kindlund, I. Petrov, J. Greene, and L. Hultman, Sputter-cleaned epitaxial VxMo(1-x)Ny/MgO(001) thin films analyzed by X-ray photoelectron spectroscopy: 2. single-crystal V0.47Mo0.53N0.92. Surf. Sci. Spectra 20 (2013), pp. 74–79.
   Google Scholar
• H. Kindlund, G. Greczynski, E. Broitman, L. Martínez-de-Olcoz, J. Lu, J. Jensen, I. Petrov, J.E. Greene, J. Birch, and L. Hultman, V0.5Mo0.5Nx/MgO(001): Composition, nanostructure, and mechanical properties as a function of film growth temperature. Acta Mater. 126 (2017), pp. 194–201.
   Web of Science ®Google Scholar
• R. Zhang, X. Gu, K. Zhang, X. Gao, C. Liu, and C. Chen, Core electron count as a versatile and accurate new descriptor for sorting mechanical properties of diverse transition metal compounds. Adv. Mater. 35 (2023), pp. 2304729.
   Web of Science ®Google Scholar
• Q. Yang, W. Lengauer, T. Koch, M. Scheerer, and I. Smid, Hardness and elastic properties of Ti(CxN1−x), Zr(CxN1−x) and Hf(CxN1−x). J. Alloys Compd. 309 (2000), pp. L5–L9.
   Web of Science ®Google Scholar
• D.B. Miracle, and O.N. Senkov, A critical review of high entropy alloys and related concepts. Acta Mater. 122 (2017), pp. 448–511.
   Web of Science ®Google Scholar
• J. Zhang, B. Xu, Y. Xiong, S. Ma, Z. Wang, Z. Wu, and S. Zhao, Design high-entropy carbide ceramics from machine learning. NPJ Comput. Mater. 8 (2022), pp. 5.
   Web of Science ®Google Scholar
• S. Zhai, H. Xie, P. Cui, D. Guan, J. Wang, S. Zhao, B. Chen, Y. Song, Z. Shao, and M. Ni, A combined ionic Lewis acid descriptor and machine-learning approach to prediction of efficient oxygen reduction electrodes for ceramic fuel cells. Nat. Energy 7 (2022), pp. 866–875.
   Web of Science ®Google Scholar
• J. Zhang, X. Xiang, B. Xu, S. Huang, Y. Xiong, S. Ma, H. Fu, Y. Ma, H. Chen, Z. Wu, and S. Zhao, Rational design of high-entropy ceramics based on machine learning – a critical review. Curr. Opin. Solid State Mater. Sci. 27 (2023), pp. 101057.
   Web of Science ®Google Scholar
• A. Šimůnek, How to estimate hardness of crystals on a pocket calculator. Phys. Rev. B 75 (2007), pp. 172108.
   Web of Science ®Google Scholar
• S. Pugh, XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Lond. Edinb. Dublin Philos. Mag. J. Sci. 45 (1954), pp. 823–843.
   Web of Science ®Google Scholar
• A. Savin, O. Jepsen, J. Flad, O.K. Andersen, H. Preuss, and H.G. Vonschnering, Electron localization in solid-state structures of the elements – the diamond structure. Angew. Chem. Int. Ed. 31 (1992), pp. 187–188.
   Web of Science ®Google Scholar
• U. Haussermann, S. Wengert, P. Hofmann, A. Savin, O. Jepsen, and R. Nesper, Localization of electrons in intermetallic phases containing aluminum. Angew. Chem. Int. Ed. Engl. 33 (1994), pp. 2069–2073.
   Web of Science ®Google Scholar
• A.D. Becke, and K.E. Edgecombe, A simple measure of electron localization in atomic and molecular-systems. J. Chem. Phys. 92 (1990), pp. 5397–5403.
   Web of Science ®Google Scholar
• U. Haussermann, S. Wengert, and R. Nesper, Unequivocal partitioning of crystal-structures, exemplified by intermetallic phases containing aluminum. Angew. Chem. Int. Ed. Engl. 33 (1994), pp. 2073–2076.
   Web of Science ®Google Scholar
• W. Tang, E. Sanville, and G. Henkelman, A grid-based Bader analysis algorithm without lattice bias. J. Phys. Condes. Matter 21 (2009), pp. 084204.
   PubMed Web of Science ®Google Scholar
• M. Mizuno, I. Tanaka, and H. Adachi, Chemical bonding in titanium-metalloid compounds. Phys. Rev. B 59 (1999), pp. 15033–15047.
   Web of Science ®Google Scholar