References
- L. Topor and O.J. Kleppa, Standard enthalpies of formation of RhTi, RhZr, and RhHf. J. Less-Common Met. 135 (1987), pp. 67–75. doi: 10.1016/0022-5088(87)90339-0
- Q. Guo and O.J. Kleppa, Standard enthalpies of formation of some alloys formed between group IV elements and group VIII elements, determined by high-temperature direct synthesis calorimetry II. Alloys of (Ti, Zr, Hf) with (Co, Ni). J. Alloy. Compd. 269 (1998), pp. 181–186. doi: 10.1016/S0925-8388(98)00246-1
- S.W. Cho, C.S. Han, C.N. Park, and E. Akiba, Hydrogen storage characteristics of Ti–Zr–Cr–V alloys. J. Alloy. Compd. 289 (1999), pp. 244–250. doi: 10.1016/S0925-8388(99)00162-0
- R. Jerlerud-Perez and B. Sundman, Thermodynamic assessment of the Mo–Zr binary phase diagram. CALPHAD 27 (2003), pp. 253–262. doi: 10.1016/j.calphad.2003.09.003
- K. Mahdouk and J. Gachon, Calorimetric study of the Hf–Os and Os–Ti systems. J. Alloy. Compd. 278 (1998), pp. 185–189. doi: 10.1016/S0925-8388(98)00219-9
- W. Xing, X.-Q. Chen, D. Li, Y. Li, C.L. Fu, S.V. Meschel, and X. Ding, First-principles studies of structural stabilities and enthalpies of formation of refractory intermetallics: TM and TM3 (T = Ti, Zr, Hf; M = Ru, Rh, Pd, Os, Ir, Pt). Intermetallics 28 (2012), pp. 16–24. doi: 10.1016/j.intermet.2012.03.033
- E.A. Brandes and G.B. Brook, Smithells Metals Reference Book, Butterworth-Heinemann, London, 1992.
- D.G. Pettifor, Bonding and Structure of Molecules and Solids, Oxford University Press, Oxford, 1995.
- J.K. Burdett, S. Lee, and T.J. McLarnan, Coloring problem. J. Am. Chem. Soc. 107 (1985), pp. 3083–3089. doi: 10.1021/ja00297a012
- T.G. Mazhuga, T.Y. Velikanova, A.V. Gapon, P.S. Martsenyuk, and E.L. Semenova, The Ti–TiNi–TiOs system. J. Alloy. Compd. 363 (2004), pp. 194–198. doi: 10.1016/S0925-8388(03)00450-X
- T.B. Massalski, H. Okamoto, P. R. Subramanian, and L. Kacprzak, Binary Alloy Phase Diagrams, ASM International: Materials Park, Russell, OH1990.
- J.M. Zhang and G.Y. Guo, Electronic structure and phase stability of three series of B2 Ti-transition-metal compounds. J. Phys.: Condens. Matter. 7 (1995), pp. 6001–6017.
- N. Arikan and Ü Bayhan, Ab initio calculation of structural, electronic and phonon properties of ZrRu and ZrZn in B2 phase. Physica B. 406 (2011), pp. 3234–3237. doi: 10.1016/j.physb.2011.05.031
- R.A. Waterstrat and R. Kuentzler, Structural instability in the B2-type ordered alloys Zr(Ru, Rh) and Zr(Ru, Pd). J. Alloy. Compd. 359 (2003), pp. 133–138. doi: 10.1016/S0925-8388(03)00187-7
- L. Topor and O.J. Kleppa, Thermochemistry of the intermetallic compounds RuTi, RuZr, and RuHf. Metall. Mater. Trans. A. 19 (1988), pp. 1061–1066. doi: 10.1007/BF02628390
- Q.J. Liu, N.C. Zhang, F.S. Liu, and Z.T. Liu, Structural, mechanical and electronic properties of OsTM and TMOs2 (TM = Ti, Zr and Hf): First-principles calculations. J. Alloy. Compd. 589 (2014), pp. 278–282. doi: 10.1016/j.jallcom.2013.11.215
- N. Novaković, N. Ivanović, V. Koteski, I. Radisavljević, J. Belošević-Čavor, and B. Cekić, Structural stability of some CsCl structure HfTM (TM = Co, Rh, Ru, Fe) compounds. Intermetallics 14 (2006), pp. 1403–1410. doi: 10.1016/j.intermet.2006.01.050
- W. Kohn and L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 (1965), pp. 1133–1138. doi: 10.1103/PhysRev.140.A1133
- M.D. Segall, P.J.D. Lindan, M.J. Probert, C.J. Pickard, S.J. Clark, and M.C. Payne, First-principles simulation: Ideas, illustrations and the CASTEP code. J. Phys. Condens. Matter. 14 (2002), pp. 2717–2744. doi: 10.1088/0953-8984/14/11/301
- J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77 (1996), pp. 3865–3868. doi: 10.1103/PhysRevLett.77.3865
- N. Arikan, O. Örnek, Z. Charifi, H. Baaziz, Ş Uğur, and G. Uğur, A first-principle study of Os-based compounds: Electronic structure and vibrational properties. J. Phys. Chem. Solids. 96–97 (2016), pp. 121–127. doi: 10.1016/j.jpcs.2016.05.009
- R. Ray, B.C. Giessen, and N.J. Grant, The constitution of metastable titanium-rich Ti-Fe alloys: An order-disorder transition. Metall. Mater. Trans. B. 3 (1972), pp. 627–629. doi: 10.1007/BF02642743
- E. Raub and E. Roeschel, The alloys of ruthenium with titanium and zirconium. Z. Metallkd. 54 (1963), pp. 455.
- A.E. Dwight, CsCl-type equiatomic phases in binary alloys of transition elements. Trans. Metall. Soc. Aime. 215 (1959), pp. 283–286.
- V.N. Eremenko, T.D. Shtepa, and V.G. Sirotenko, Intermediate phases in alloys of Ti with Ir, Rh and Os indicate possibility of polymorphism. Poroshk. Metall. 6 (1966), pp. 68–72.
- P. Villars and L.D. Calvert, Pearson’s Handbook of Crystallographic Data for Intermetallic Phases. 2nd ed., ASM International, Materials Park, Russell, OH, 1991.
- J. Yang, M. Shahid, C. Wan, J. Feng, and W. Pan, Anisotropy in elasticity, sound velocities and minimum thermal conductivity of zirconia from first-principles calculations. J. Eur. Ceram. Soc. 37 (2017), pp. 689–695. doi: 10.1016/j.jeurceramsoc.2016.08.034
- H. Shou and Y. Duan, Anisotropic elasticity and thermal conductivities of (α, β, γ)-LiAlSi2O6 from the first-principles calculation. J. Alloy. Compd. 756 (2018), pp. 40–49. doi: 10.1016/j.jallcom.2018.05.040
- M. de Jong, W. Chen, T. Angsten, A. Jain, R. Notestine, A. Gamst, M. Sluiter, C.K. Ande, S. van der Zwaag, J.J. Plata, C. Toher, S. Curtarolo, G. Ceder, K.A. Persson, and M. Asta, Charting the complete elastic properties of inorganic crystalline compounds. Sci. Data. 2 (2015), pp. 150009. doi: 10.1038/sdata.2015.9
- M. Born and K. Huang, Dynamical Theory of Crystal Lattices, Oxford University Press, Oxford, 1998.
- W. Voigt, Handbook of Crystal Physics, Taubner, Leipzig, 1928.
- A. Reuss, Calculation of the flow limits of mixed crystals on the basis of the plasticity of monocrystals. Z. Angew. Math. Mech. 9 (1929), pp. 49–58. doi: 10.1002/zamm.19290090104
- R. Hill, The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. A. 65 (1952), pp. 349–354. doi: 10.1088/0370-1298/65/5/307
- W. Bao, D. Liu, P. Li, and Y. Duan, Structural properties, elastic anisotropies and thermal conductivities of tetragonal LnB2C2 (Ln = rare earth) compounds from first-principles calculations. Ceram. Int. 45 (2019), pp. 1857–1867. doi: 10.1016/j.ceramint.2018.10.077
- S.F. Pugh, XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals. Philos. Mag. 45 (1954), pp. 823–843. doi: 10.1080/14786440808520496
- L. Ma, Y. Duan, and R. Li, Phase stability, anisotropic elastic properties and electronic structures of C15-type laves phases ZrM2 (M = Cr, Mo and W) from first-principles calculations. Philos. Mag. 97 (2017), pp. 2406–2424. doi: 10.1080/14786435.2017.1334135
- B. Huang, Y.H. Duan, Y. Sun, M.J. Peng, and S. Chen, Electronic structures, mechanical and thermodynamic properties of cubic alkaline-earth hexaborides from first principles calculations. J. Alloy. Compd. 635 (2015), pp. 213–224. doi: 10.1016/j.jallcom.2015.02.128
- S.I. Ranganathan and M. Ostoja-Starzewski, Universal elastic anisotropy index. Phys. Rev. Lett. 101 (2008), pp. 055504. doi: 10.1103/PhysRevLett.101.055504
- C. Zener, Elasticity, Anelasticity of Metals, University of Chicago, Chicago, 1948.
- D.H. Chung and W.R. Buessem, The elastic anisotropy of crystals. J. Appl. Phys. 38 (1967), pp. 2010–2012. doi: 10.1063/1.1709819
- L. Ma, Y. Duan, and R. Li, Structural, elastic and electronic properties of C14-type Al2M (M = Mg, Ca, Sr and Ba) laves phases. Physica B. 507 (2017), pp. 147–155. doi: 10.1016/j.physb.2016.12.004
- R.F.S. Hearmon and A.A. Maradudin, An introduction to applied anisotropic elasticity. Phys. Today. 14 (1961), pp. 48. doi: 10.1063/1.3057153
- J.F. Nye, Physical Properties of Crystals, Oxford University Press, Oxford, 1985.
- Y. Kong, Y. Duan, L. Ma, and R. Li, Phase stability, elastic anisotropy and electronic structure of cubic MAl2 (M = Mg, Ca, Sr and Ba) Laves phases from first-principles calculations. Mater. Res. Express 3 (2016), pp. 106505. doi: 10.1088/2053-1591/3/10/106505
- M.A. Hopcroft, W.D. Nix, and T.W. Kenny, What is the young’s modulus of silicon? J. Microelectromechanical Syst. 19 (2010), pp. 229–238. doi: 10.1109/JMEMS.2009.2039697
- D. Music, A. Houben, R. Dronskowski, and J.M. Schneider, Ab initio study of ductility in M2AlC (M = Ti, V, Cr). Phys. Rev. B. 75 (2007), pp. 174102. doi: 10.1103/PhysRevB.75.174102
- S. Chen, Y. Sun, Y.H. Duan, B. Huang, and M.J. Peng, Phase stability, structural and elastic properties of C15-type laves transition-metal compounds MCo2 from first-principles calculations. J. Alloy. Compd. 630 (2015), pp. 202–208. doi: 10.1016/j.jallcom.2015.01.038
- W. Bao, D. Liu, and Y. Duan, A first-principles prediction of anisotropic elasticity and thermal properties of potential superhard WB3. Ceram. Int. 44 (2018), pp. 14053–14062. doi: 10.1016/j.ceramint.2018.05.002