Mendeleev Communications Electronic Version, Issue 4, 1998 (pp. 129–168) Quantum-chemical analysis of the chemical stability and cohesive properties of hexagonal TiB2, VB2, ZrB2 and NbB2 Alexander L. Ivanovsky,* Nadezhda I. Medvedeva and Julia E. Medvedeva Institute of Solid State Chemistry, Ural Branch of the Russian Academy of Sciences, 620219 Ekaterinburg, Russian Federation. Fax: +3 432 74 4495; e-mail: ivanovskii@ihim.uran.ru The cohesive properties and chemical stability of diborides MB2 have been analysed using the results of full-potential LMTO calculations.A comparison of interatomic M–M, M–B and B–B interactions in MB2 phases (M = Ti, V, Zr, Nb) shows that the changes in the cohesive properties are mainly controlled by the strength of the covalent M–B bonds. Among the known transition metal (TM) borides the hexagonal diborides of IVa and Va group metals (MB2) possess the highest melting temperatures, hardness and chemical stability.1,2 The stability and thermomechanical properties of MB2 depend on the kind of metal and get noticeably worse with the growth in TM atomic number (z) in the period and with reduction of z in the group of the Periodic Table.1,2 In the phenomenological models of the electronic structure of MB2 phases their properties are attributed to one of several possible types of interatomic interactions (see reviews 3 and 4).For example, it is supposed5 that B–B interactions are responsible for the structural peculiarities of diborides. The calculations of energy band structure were carried out by the authors of refs. 6 and 7 for some MB2 phases. Based on the total and local densities of states (TDOS, LDOS), the cohesive properties of MB2 (with the growth of z in the period) were explained by the changes in occupation of antibonding states with valence electron concentration (vec) in the cell. This approach6,7 is widely employed to interpret the thermodynamic properties of diborides such as melting temperature, entropy characteristic energies, etc.8 The model fails, however, to explain the differences in the properties of isostructural and isoelectronic MB2 (for example, TiB2 and ZrB2 or VB2 and NbB2).1,2 In the present paper the first-principle analysis of the chemical stability of MB2 (M = Ti, V, Zr, Nb) is performed and the contributions of different types of interatomic interactions to the cohesive energy of these phases are considered.The electronic energy band structure of MB2 was calculated using the self-consistent full-potential linear muffin-tin orbitals method (FP-LMTO).9 The structural data for diborides were taken from ref. 2. TDOS and LDOS of ZrB2, NbB2 are given in Figure 1. It was found that, in conformity with previous computations (reviews 3 and 4), the characteristic feature of the electronic structure of MB2 is the local TDOS minimum (pseudogap) between the bands of bonding (Md–Bp)- and antibonding Md*, Bp-states.For ZrB2 (vec = 3.33 e atom–1), the Fermi level (EF) is located at this TDOS minimum. This corresponds to the condition of maximum chemical stability of the crystal: bonding states are completely occupied and antibonding states are vacant.Going to NbB2 (vec = 3.67 e atom–1) the bands of the antibonding states become partially occupied and DOS on the Fermi level [N(EF)] increases: N(EF) = 4.35 and 15.56 Ry–1 for ZrB2 and NbB2, respectively. According to the traditional band concept of stability of chemical compounds,10,11 this determines a decrease in cohesive energy and chemical stability of NbB2 as compared with ZrB2.Analogous conclusions can be drawn from the TDOS for TiB2 and VB2. From numerous experimental data1,2 it follows that in accordance with cohesive properties these diborides make up the series ZrB2 > NbB2 > TiB2 > VB2. In the framework of the FP-LMTO9 method the cohesive energy of the system is N(E)/Ry–1 E/Ry EF 40 0 20 0 10 0 –0.5 0.0 0.5 1.0 1.5 2.0 0.0 1.0 N(E)/Ry–1 EF E/Ry 40 0 20 0 10 0 ZrB2 Zr(s,p,d) B(s,p) NbB2 Nb(s,p,d) B(s,p) Figure 1 Total and local densities of states of ZrB2 and NbB2.aE(M–M) and E(B–B) correspond to the Edif values from a calculation of hypothetical M 2 and B2 compounds. bDE is the energy difference for 3dand 4d-metal borides. Table 1 Cohesive energies (Edif/Ry cell–1) of Ti, V, Zr, Nb diborides and energies of different types of bonds according to FP-LMTO calculations.Phase –Edif(MB2) –E(M–M)a –E(B–B)a –[E(M–M) + E(B–B)] –E(M–B) TiB2 1.58 0.36 0.86 1.22 0.36 VB2 1.53 0.40 0.88 1.28 0.25 DEb 0.05 –0.04 –0.02 –0.06 0.11 ZrB2 1.78 0.44 0.82 1.26 0.52 NbB2 1.78 0.56 0.85 1.41 0.37 DE 0.00 –0.12 –0.03 –0.15 0.15Mendeleev Communications Electronic Version, Issue 4, 1998 (pp. 129-168) calculated as Edif = Etot – SEat, where Etot is the total energy of the crystal and Eat is the energy of free atoms constituting its lattice. Edif was found to decrease in the order ZrB2 ~ ~ NbB2 > TiB2 > VB2 (see Table 1), i.e. in conformity with the experimentally established regularity. The value of Edif is an integral characteristic of chemical bonding and describes the overall energy effect of atomic interaction rearrangement in the lattice.Therefore, our next aim was to determine the role of separate interatomic interactions in the formation of the cohesive properties of MB2. The main types of chemical bonding in diborides are M–M, B–B interactions in metal and boron plane nets (Figure 2) and the covalent ‘interlayer’ M–B bond.These types of interatomic bonds in different planes of the ZrB2 unit cell are visually illustrated in Figure 3. To evaluate the energy contributions of separate bonds [E(M–M), E(B–B) and E(M–B)] to Edif, the electronic structure of isolated diboride sublattices — hypothetical defect structures M 2 and B2 — (M = Ti, V, Zr, Nb; = = vacancies in the corresponding sublattice) was calculated with retention of their geometry in real phases.The energies of M–M and B–B bonds were then determined as The energy of the covalent M–B interaction was defined as the difference between the cohesion energy of the real phase and the sum of the cohesive energies of its non-interacting sublattices It follows from Table 1 that the main contribution to the chemical bonding for diborides is due to strong B–B bonds. The bonding between B atoms dominates both M–M and M–B interactions.E(B–B) in hypothetical B2 compounds depends only on the interatomic distances B–B in the structure of MB2 and closely follows any changes occurring in them.2 The values of E(M–M) for M 2 correlate with the known cohesive energies for pure 3d, 4d-metals (Nb > Zr > V > Ti).11,12 The sum of Edif for two non-interacting sublattices (M 2+ B2) gives a change in chemical stability: NbB2 > VB2 > ZrB2 > TiB2.Thus, the interlayer M–B interaction has a determining effect on the integral Edif value for these phases (see Table 1). The first-principle analysis of chemical stability and cohesive properties of diborides performed here makes it possible to draw the following conclusions.The thermomechanical properties of MB2 result from the strength of the M–M, M–B and B–B bonds. In spite of the leading role of B–B interatomic interactions they are not responsible for the variety of diboride properties, as proposed in some phenomenological models. Depending on the nature of the metallic sublattice the changes in separate types of bonding take place in different ways.The cohesive energy of these diborides changes mainly owing to interlayer covalent M–B interactions and E(M–B) increases with the growth of metal atomic number z in the group and decreases as z grows in the period. Hence, it is possible to assert that the relative change in chemical stability and cohesive properties of the diborides considered is controlled by the covalent boron-metal interaction.References 1 H. J. Goldschmidt, Interstitial Alloys, Butterworths, London, 1967, vol. 1. 2 T. I. Serebryakova, V. A. Neronov and P. D. Peshev, Vysokotemperaturnye Boridy (High-Temperature Borides), Metallurgia, Moscow, 1991 (in Russian). 3 G. P. Shveikin and A. L. Ivanovskii, Usp.Khim., 1994, 63, 751 (Russ. Chem. Rev., 1994, 63, 711). 4 A. L. Ivanovskii and G. P. Shveikin, Kvantovaya khimiya v materialovedenii. Bor, ego splavy i soedineniya (Quantum Chemistry in Materials Science. Boron, its Alloys and Compounds), Izd. ‘Ekaterinburg’, Ekaterinburg, 1997 (in Russian). 5 E. Dempsy, Phil. Mag., 1963, 8, 285. 6 J. K. Burdett, E. Canadell and G. J.Miller, J. Am. Chem. Soc., 1986, 108, 6561. 7 X.-B. Wang, D.-C. Tian and L.-L. Wang, J. Phys.: Condens. Matter, 1994, 6, 10185. 1 2 3 x y z M B Figure 2 Fragment of the crystal structure of diborides MB2. Designated are the planes of metallic atoms (1), boron atoms (3) and ‘interlayer’ plane (2). E(M–M) = Edif(M 2) = Etot(M 2) – Eat(M), E(B–B) = Edif( B2) = Etot( B2) – 2Eat(B). E(M–B) = Edif(MB2) – [Edif(M 2) + Edif( B2)].B 1.00 0.80 0.60 0.40 0.20 0.00 1.20 1.40 1.60 B B Zr Zr Zr 0.00 0.20 0.40 1.00 0.80 0.60 0.40 0.20 0.00 0.20 0.40 0.60 0.80 1.00 Figure 3 Contour maps of total charge density of ZrB2 in different planes of the unit cell [(1)–(3), Figure 2] showing the main types of interatomic interactions in the crystal: Zr–Zr (1), Zr–B (2) and B–B (3). FP-LMTO calculations. 3 2 1 BMendeleev Communications Electronic Version, Issue 4, 1998 (pp. 129–168) 8 A. F. Guillermet and G. Grimvall, J. Less Common Metals, 1991, 169, 257. 9 M. Methfessel and M. Scheffler, Physica, 1991, B172, 175. 10 A. R. Williams, C. D. Gelatt, J. W. D. Connolly and V. Moruzzi, in Alloy Phase Diagrams, eds. L. H. Bennett, T. B. Massalski and B. Giessen, North-Holland, New York, 1983, p. 17. 11 J. Xu and A. J. Freeman, Phys. Rev., 1989, B40, 11927. 12 R. E.Watson, G.W. Fernando, M.Weinert, Y.Wang and J.W. Davenport, Phys. Rev., 1991, B43, 1455. 13 P. H. T. Philipsen and E. J. Baerends, Phys. Rev., 1996, B54, 5326. Received: Moscow, 5th May 1998 Cambridge, 25th June 1998; Com. 8/03646B