Electronic Structure and Stability of Vacancy-Ordered Compounds of Transition Metal Carbides and Nitrides
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ELECTRONIC STRUCTURE AND STABILITY OF VACANCY-ORDERED COMPOUNDS OF TRANSITION METAL CARBIDES AND NITRIDES 34 2,3 1 4 J.P. LANDESMAN , P. TURCHI ' , F. DUCASTELLE AND G. TREGLIA I SESI, CEN, B.P. 6,92260 Fontenay-aux-Roses, France ; 2 Laboratoire de Dynamique du Rdseau et Ultrasons, Universitd Pierre et Marie Curie, Tour 22 4, Place Jussieu, 75005 Paris, France ; 3 ONERA, 29, Avenue de la Division Leclerc, 92320 Chitillon-sous-Bagneux, France ; 4 Laboratoire de Physique du Solide, B~t. 510, Universit4 Paris-Sud, 91405 Orsay, France
ABSTRACT We make a connection, via the calculation of the band energy, between the stability of MXI_, ordered phases (M being a transition metal, X being C or N, and a the vacancy concentration) and effective pair interactions on the metalloid sublattice of these NaCl type compounds. DESCRIPTION AND CLASSIFICATION OF THE
OBSERVED ORDERED STRUCTURES
Many transition metal carbides and nitrides exist in a wide range of stoichiometry (a). Their crystalline structure is of the NaCl type with vacancies on the carbon (nitrogen) sublattice only [I, 2]. Under some conditions (annealing temperature and duration) these vacancies may order and one obtains long range ordered phases (on the carbon or nitrogen sublattice) which are analogous to those appearing in substitutional alloys [3] : for example, the titanium carbide near the composition TiC0 .5. Indeed, after annealing in the temperature range 600-770'C for a few hours it presents an ordered structure (LII) equivalent to that found in CuPt alloys (we shall call it CuPt type of ordering in the following) [4]. We have carried out band energy calculations for a vacancy concentration of 50 % (M2 X compounds). The principle of this method is to calculate the Density of States (D 0 S) of the stable ordered phases (four in that case) occuring in the metallo~d-vacancy alloy that are predicted by an Ising model and second neighbour sublattice) limited to first (on the interstitial interactions (VIV 2 ) [5, 6]. Actually a review of all the structures observed in nonstoichiometric NaCl carbides and nitrides (for this composition and others) [1] strongly suggests that many of them can be accounted for within such an Ising model (Fig. 1 ; note that carbides and nitrides are well separated in this diagram). However further interactions would be necessary to explain the occurrence of the V8 C 7 structure, for example [7]. MODEL OF ELECTRONIC STRUCTURE The FCC metallic sublattice of the compounds that we are studying remains unchanged when the vacancy concentration varies, and its lattice parameter does not change very much [I]. Therefore the size effects are assumed to be negligible ; at present, in particular, the observed static displacements of the atoms are not taken into account. Finally we assume that the ordering energy is principally related to the band energy of these compounds. This approximation has been shown to yield very good results in the case of transition substitutional alloys [9]. To describe the electronic structure we use a tight-bindin
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