Chemical Bonding and Lattice Relaxation in Substoichiometric Titanium Carbide and Nitride

Abstract

The rearrangement of interatomic interactions and redistribution ofelectron densities in titanium carbide and nitride resulting from the existence of the nonmetal vacancy are studied by the CND0/2 method. The local lattice relaxation is taken into account and the differences and common features in the behaviour of the nonmetal vacancy in titanium carbide and nitride are discussed.Die Umordnung der interatomaren Wechselwirkungen und die Umverteilung der Elektronendichte im Titankarbid und -nitrid, die aus der Existenz der nichtmetallischen Leerstelle folgen, werden mit der Hilfe der CNDO/2-Methode untersucht. Die lokale Gitterrelaxation wird beriicksichtigt und die Unterschiede und gemeinsamen Eigenschaften der nichtmetallischen Leerstelle im Titankarbid und -nitrid werden diskutiert.

Tight-Binding Description of Tic_{x}

“…In contrast to previous results [25,44,46], we find for TiC an inhomogeneous tetragonal outward relaxation of the Ti and C atoms around the C-vacancy. Such a situation has been confirmed in TiN, VN [20,46] and NbC [3]. As seen in figure 4, the creation of the non-metal vacancies leads to the appearance of the d-vacancy states at the Fermi level.…”

“…We also established that, in TiC x , for x > 0.94, the remote vacancy configuration is preferable as compared to the configurations with the opposite or adjacent non-metal vacancies in good agreement with the findings of structural investigations of substoichiometric transition metal compounds [1,2,4,9]. In contrast to previous results [25,44,46], we find for TiC an inhomogeneous tetragonal outward relaxation of the Ti and C atoms around the C-vacancy. Such a situation has been confirmed in TiN, VN [20,46] and NbC [3].…”

“…The results predicted an outward shift of the metal atoms near the vacancy of 0.107Å for the single vacancy in the Ti 6 C 18 cluster [46], 0.049Å for TiC 0.88 and 0.08Å for TiC 0.5 [25], 0.100Å for TiC x , x = 1.0−0.5 [44] and 0.038Å for TiC 0.5 [26]. It was found that, for the ordered phases, the atomic shift increases with increasing a vacancy concentration, which is consistent with the experimental results [4].…”

“…Various theoretical attempts have been made to explain the above mentioned experimental findings of both stoichiometric [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] and off-stoichiometric [35][36][37][38][39][40][41][42][43][44][45][46] titanium carbides. We classify the recent theoretical works devoted to the study of TiC x in table 1.…”

“…The rearrangement of the atomic configuration in TiC x caused by the presence of the non-metal vacancies was theoretically studied by using different procedures [25,26,44,46] (table 1). The results predicted an outward shift of the metal atoms near the vacancy of 0.107Å for the single vacancy in the Ti 6 C 18 cluster [46], 0.049Å for TiC 0.88 and 0.08Å for TiC 0.5 [25], 0.100Å for TiC x , x = 1.0−0.5 [44] and 0.038Å for TiC 0.5 [26].…”