Mendeleev Communications Electronic Version, Issue 5, 2001 1 Quantum-chemical simulation of the electronic structure and chemical bonding in the new ‘superstoichiometric’ titanium carbonitride Ti2CN4 Mikhail V. Ryzhkov* and Alexander L. Ivanovskii Institute of Solid State Chemistry, Urals Branch of the Russian Academy of Sciences, 620219 Ekaterinburg, Russian Federation. Fax: +7 3432 74 4495; e-mail: ryzhkov@ihim.uran.ru 10.1070/MC2001v011n05ABEH001488 The electronic properties and the nature of interatomic interactions in the new ‘superstoichiometric’ metal-like titanium carbonitride Ti2CN4 with the spinel structure have been predicted using the ab initio DFT-DV calculaions of large clusters. Two classes of compounds provide the basis for the quest of novel ceramic and composite materials.The first class includes compounds of d metals (M) with light sp elements. Among them are cubic (B1-type) carbides and nitrides [M(C,N)]1 which (i) have wide homogeneity regions [containing a variable number of vacancies in the non-metallic sublattice M(C,N)y 0.5<y<1.0] and (ii) form mutual solid solutions. The properties of solid solutions (for example, carbonitrides MCxNy, x + y £ 1.0) change non-monotonically with concentration.1,2 It is important that atoms in these systems have an octahedral environment and the relative content of atomic components does not exceed (C,N)/M £ 1.0.The exception being several ‘superstoichiometric’ nitrides (MNy > 1 obtained as films) where the ratio N/M > 1.0 is achieved due to the presence of vacancies in the M sublattice.3 The second class comprises refractory compounds of sp nonmetals [carbides, nitrides and oxides of B, Si and Al, multicomponent phases, for instance, silicon oxynitrides (Si2N2O), sialons (Alx + ySi6 – xOxN8 – x + y), etc.4] characterised by a tetrahedral atomic coordination.Recently, the synthesis (at P = 15 GPa and T » 2000 K) of the new polymorphous modification of silicon nitride with the cubic structure (c-Si3N4) was reported.5 According to estimates,5 its cohesive properties are similar to those of the hardest modification of SiO2 (stishovite).The new c-Si3N4 phase is of the spinel structural type and contains silicon atoms in octahedral [SioN6] and tetrahedral [SitN4] surroundings (Sio:Sit = 2:1). By substituting C or Ti for silicon in c-Si3N4, the simulation of novel compounds, namely, the cubic carbon nitride (Co 2CtN4)6 and the ‘superstoichiometric’ titanium nitride (Tio 2 TitN4)7 was made. These hypothetical phases include 2/3 (Co) or 1/3 (Tit) cations in an octahedral or tetrahedral environment, which are not typical (in the corresponding binary phases C3N4 and TiN), i.e., the proposed6,7 compounds are difficult to synthesise.According to our opinion, it is more realistic to obtain a new cubic phase with the spinel structure, viz., the ‘superstoichiometric’ titanium carbonitride of the formal composition Ti2CN4, which will be isoelectronic and isostructural with c-Si3N4 and will contain C and Ti cations in inherent to them (in binary nitrides) octahedral [TioN6] and tetrahedral [CtN4] coordinations. It may be suggested that, assembled of the main ‘structural fragments’ TiN and C3N4, the ‘superstoichiometric’ carbonitride Ti2CN4 may possess an unusual combination of their most attractive properties: the plasticity of a metal-like titanium nitride1,2 and the hardness of a high-covalence carbon nitride.8 We performed a quantum-chemical simulation of the electronic structure and interatomic bonds in Ti2CN4 and compared them with those of the known nitrides TiN and C3N4.The electronic structure was calculated in the density functional theory (DFT) approximation using the original code of the self-consistent discrete variational (DV)8 cluster method with local exchange-correlation potential.9 The basis set of numerical atomic orbitals (AO), which were the solutions of Hartree–Fock–Slater equations for isolated neutral atoms, included Ti 4p functions in addition to occupied AOs.The Diophantine integration grid with 4000 and 2000 sample points per each Ti and C(N) site, respectively, was used for the calculations of matrix elements. Ti2CN4 was simulated by the 185-atomic cluster Ti28C29N128 (point group symmetry Td).It is known10 that the positions of atoms in the spinel structure (space group Fd3m–O7 h) are determined by two parameters a and x. Assuming that the parameters of the coordination polyhedra [TioN6] and [CtN4] for Ti2CN4 are equal to those for TiN (RTi–N = 2.122 Å) and C3N4 (RC–N = 1.585 Å), we derived the values a = 8.098 Å and x = 0.363. To compare the electronic structure of Ti2CN4 and C3N4 obtained using a similar Figure 1 Total (top) and partial densities of states for the Ti28C29N128 cluster. 100 80 60 40 20 0 20 0 10 0 80 60 40 20 0 20 0 20 0 20 0 20 0 –20 –15 –10 –5 0 5 10 15 20 E/eV Ti 3d Ti 4s Ti 4p Ti28C29N128 C 2p C 2s N 2p N 2s Table 1 Overlap populations (OP, e) of the valence orbitals of neighbouring atoms in TiN, Ti2CN4 and C3N4 (×103, per pair of interacting centres) and effective atomic charges (Qef, e) in TiN, Ti2CN4 and C3N4 (the charges obtained according to the Mulliken scheme are given in brackets).OP TiN Ti2CN4 C3N4 N 2s N 2p N 2s N 2p N 2s N 2p Ti(Co) 3d 4s (2s) 4p (2p) 33 –25 87 121 77 68 37 –1 53 174 73 48 — –7 79 — 130 229 Ct 2s 2p —— —— 14 173 205 349 –15 127 202 348 Qef [Ti (Co)] 1.43 (0.82) 1.49 (0.88) 0.57 (0.29) Qef (Ct) — 0.55 (0.36) 0.54 (0.34) Qef (N) –1.59 (–0.83) –0.93 (–0.53) –0.42 (–0.23)Mendeleev Communications Electronic Version, Issue 5, 2001 2 approach, we also performed DFT-DV calculations of the cluster Co 28Ct 29N128 in the C3N4 structure with bond lengths of 1.585 and 1.676 A for Ct.N and Co.N, respectively.6 Boundary conditions in the ¡®extended cluster¡� scheme11,12 were used.The model densities of states (MDOS) of the cluster Ti28C29N128 are presented in Figure 1. The total band width of bonding states is about 10 eV. It is made up of the contributions from hybrid Ti 3d.N 2p (0.5 eV), N 2p.C 2p (5.7.5 eV) and N 2p.C 2s orbitals [7.5.10 eV below the Fermi level (EF)] that form Ti.N and C.N bonds in [TioN6] and [CtN4] polyhedra.Ti2CN4 has no forbidden gap (FG) and will exhibit metal-like properties. A comparison with DFT-DV results for the cluster Ti79N140 used to model TiN13 shows that the most essential differences in the electronic structures of TiN and Ti2CN4 concern the mutual arrangement of the Ti 3d and N 2p states. In the nitride, the upper edge of the N 2p band (total width of 5 eV) is 4 eV below EF located in the region of ¥�-like antibonding Ti 3d states.13 The cubic C3N4 has a FG of more than 3 eV according to our calculations (1.14 eV according to ref. 7); its spectrum (Figure 2) contains a continuous N 2s,p.C 2s,p band of the total width of 17 eV. The differences in the MDOS of Ct centres in C3N4 and Ti2CN4 are attributed to the considerable broadening of Ct 2s,2p bands, their shift to lower binding energies and a decrease of Ct 2s,2p.N 2s hybridization in the nitride.The differences in the MDOS of Ct and Co in C3N4 concern the different hybridization effects in [CtN4] and [CoN6] polyhedra. The orbital overlap populations (OP) of TiN, C3N4 and Ti2CN4 obtained by the same cluster DFT-DV method are listed in Table 1.It can be seen that on going from TiN to Ti2CN4 the OP of Ti 3d.N 2p AO, which provides the major contribution to the Ti.N bonding, increase appreciably, whereas the OP of Ti 4p.N 2s and Ti 4p.N 2p AO decrease slightly. In general, the Ti.N chemical bonding in the simulated carbonitride is not weaker than that in TiN. A comparison of the OP of Ct centres with the neighbours in Ti2CN4 and C3N4 shows that the Ct.N bonds in the carbonitride are stronger due to the Ct 2p.N 2s hybridization.The fact that the octahedral coordination is less advantageous for carbon is evident from a comparisonthe OP of Ct.N and Co.N in C3N4: all the contributions forming the Co.N bonding are on the average 1.5 times smaller than those for Ct.N. Let us compare effective atomic charges (Qef) in TiN, Ti2CN4 and C3N4 (Table 1), which were obtained by three-dimensional integration in the space between nuclei.11 The values of Qef at Ti in TiN and Ti2CN4 appear to be similar, whereas the charges at nitrogen atoms in the carbonitride are only ¡í 60% of the corresponding values for TiN.The fundamental difference between Ti2CN4 and the known B1 carbonitrides MCxNy (x + y ¡Ì 1.0) incorporating carbon in the anionic state2 is the cationic form of Ct, the effective charges of Ct in Ti2CN4 and C3N4 being very close.The charges at N in C3N4 are half as large as in Ti2CN4 and are lower than those in TiN by a factor of 4, i.e., Ti2CN4 is intermediate in the degree of ionicity among the binary nitrides under consideration. In conclusion, note that due to the similarity of the simulated ¡®superstoichiometric¡� titanium nitride Ti2CN4 and the familiar interstitial phase TiN, Ti2CN4 may be expected to have properties2 typical of those of titanium nitride, such as nonstoichiometry in the N sublattice (Ti2CN4 .y-type compositions) or the formation of multicomponent solid solutions by replacing Ti atoms by other d metals (for example, Ti2 .xZrxCN4 and Ti2 . xHfxCN4). The synthesis of more complicated phases, where Si or Ge partially substitute for carbon, is possible. This work was supported by the Russian Foundation for Basic Research (grant no. 01-03-32513). References 1 L. Toth, Transition Metal Carbides and Nitrides, Academic Press, New York, 1971. 2 V. A. Gubanov, A. L. Ivanovskii and V. P.Zhukov, Electronic Structure of Refractory Carbides and Nitrides, University Press, Cambridge, 1994. 3 M. Lerch, E. Fuglein and J. Wrba, Z. Anorg. Allg. Chem., 1996, 622, 367. 4 A. L. Ivanovskii and G. P. Shveikin, Kvantovaya khimiya v materialovedenii. Nemetallicheskie tugoplavkie soedineniya i nemetallicheskaya keramika (Quantum Chemistry in Material Science. Refractory Compounds of Non-Metals and Non-Metal Ceramic), Izd.UB RAS, Ekaterinburg, 2000 (in Russian). 5 A. Zerr, G. Miehe, G. Serghiou, M. Schwarz, E. Kroke, R. Riedel, H. Fuess, P. Kroll and R. Boehler, Nature, 1999, 400, 340. 6 S.-D. Mo, L. Ouyang, W. Y. Ching, I. Tanaka, Y. Koyama and R. Riedel, Phys. Rev. Lett., 1999, 83, 5046. 7 W. Y. Ching, S.-D. Mo, L. Ouyang, T. Tanaka and M. Yoshiya, Phys. Rev., 2000, B61, 10609. 8 M. R. Press and D. E. Ellis, Phys. Rev., 1987, B35, 4438. 9 O. Gunnarsson and B. I. Lundqvist, Phys. Rev., 1976, B13, 4274. 10 U. L. Bragg and G. Klaringbull, Crystalline Structure of Minerals, Mir, Moscow, 1967 (in Russian). 11 M. V. Ryzhkov, Zh. Strukt. Khim., 1998, 39, 1134 [J. Struct. Chem. (Engl. Transl.), 1998, 39, 933]. 12 M. V. Ryzhkov, T. A. Denisova, V. G. Zubkov and L. G. Maksimova, Zh. Strukt. Khim., 2000, 41, 1123 [J. Struct. Chem. (Engl. Transl.), 2000, 41, 927]. 13 M. V. Ryzhkov and A. L. Ivanovskii, Zh. Strukt. Khim., 1999, 40, 630 [J. Struct. Chem. (Engl. Transl.), 1999, 40, 515]. 100 80 60 40 20 0 20 0 10 0 40 20 0 20 0 60 40 20 0 20 0 .20 .15 .10 .5 0 5 10 15 E/eV C29C28N128 Ct 2p Ct 2s Co 2p Co 2s N 2p N 2s Figure 2 Total (top) and partial densities of states for the Co 28 Ct 29 N128 cluster. Received: 26th June 2001; Com. 01/18