Order and disorder in transition metal carbides and nitrides: experimental and theoretical aspects

Abstract

Abstract

Ab InitioStudy of Phase Equilibria inTiCx

“…The existence of at least two vacancy-ordered structures, the cubic [5,6] and trigonal [6,7] forms of hemicarbide Ti 2 C, is now well established experimentally; see Ref. [8] for a review.…”

“…However, quite different ordering temperatures have been reported for Ti 2 C: As low as ϳ1000 K, Refs. [6][7][8][9][10], or as high as ϳ2000 K, Refs. [5,11].…”

Physical Properties of the NbC Carbide

“…The atoms in this structure have octahedral coordination, and the carbon atoms occupy half of the octahedral interstices of the metallic sub-lattice [3]. At temperatures around 1050°C, there is a order-disorder reaction resulting in a carbide with stoichiometry Nb 6 C 5 and trigonal structure (space group P3 1 ) [3,17,[27][28][29][30][31][32][33][34][35][36]. In this carbide, atomic planes with and without defects are stacked alternately [3].…”

“…Once the vacancy is created, the Nb atoms atoms would be displaced towards the interstice, causing the lattice parameter contraction with higher vacancy concentration (lower carbon content). However, experimental studies [28,32,58,59] show that the Nb atoms are displaced away from the vacancy, and if this were the only effect of the vacancy on the structure, the lattice parameter should increase for higher vacancy concentrations. Since this conclusion contradicts directly the results shown in Figure 3, the displacement of metallic and nonmetallic atoms beyond the first coordination shell of the vacancies has to be taken into account.…”

Tight-Binding Description of Tic_{x}

“…For a certain range of composition, the cubic phase seems to be thermodynamically stable solely at high temperatures. Several off-stoichiometric ordered structures of TiC x have been reported and investigated in the range of 0.48 < x < 0.96 [4][5][6]. In particular, the existence of at least two vacancy-ordered structures, the cubic and trigonal forms of hemicarbide Ti 2 C, is now well established experimentally [4,5].…”