Introduction b-SiAlON ceramics are solid solutions (SS) of the variable composition Si 6Àx Al x O x N 8Àx (0 < x 4:27) formed by substitution of (Si, N) by (Al, O) atomic pairs in the b-Si 3 N 4 structure [1]. b-SiAlONs possess an interesting combination of thermal and mechanical properties and therefore they are currently of great scientific, technological and commercial importance (see for example, [2]).The first studies of the electronic properties of SiAlONs were made by Tanaka et al. [3,4] within the cluster model. Ching et al. [5] reported LDA-OLCAO band structure calculations of b-Si 6Àx Al x O x N 8Àx , x ¼ 0; 1; 2; 3; 4. It was found that as x increases, the dielectric gap (DE g ) is reduced due to the appearance of new impurity-like states near the lower edge of the conduction band (CB), the overall bond strength decreasing slightly. Ching with co-workers [5] pointed out that atomic ordering in b-SiAlONs may affect the electronic properties of these materials, but did not perform any studies in this area.Pioneering investigations of the atomic ordering effects in b-SiAlONs in the framework of the semi-empirical tight-binding band structure approach were presented in our papers [6,7]. 28-and 126-atomic supercells were used to model the local ordering of (Al, O) atoms in the b-Si 3 N 4 matrix and possible ways of their long-range ordering. The most stable structures having a shape of extended 1D-''impurity channels" were predicted and explained as a result of chemical bond reconstruction. Based on these calculations, the concentration dependences of some physical and chemical properties of b-SiAlONs were interpreted.In this paper we consider the band structure and the cohesion energy of b-Si 3 N 4 and also of b-SiAlONs in the disordered (d) and ordered (o) states.
Models and Method of CalculationTo simulate ordering effects in b-SiAlONs, we chose nonrelaxed 56-atomic supercells (2 Â 2 Â 1) including also 48 ''empty" spheres if the method needs, Fig. 1. Three compounds have been examined: (i) pure b-Si 3 N 4 (by Si 24 N 32 supercell) and b-Si 6Àx Al x O x N 8Àx , x ¼ 1:5 (by Si 18 Al 6 O 6 N 26 supercells) in both disordered (ii) and ordered (iii) states. For d-SiAlON, we assumed that Al-O pairs do not ''interact" (distant), while in the o-state the interaction between Al-O pairs gives rise to impurity channels according to the model proposed in [6]. The structural parameters of b-Si 3 N 4 and b-Si 6Àx Al x O x N 8Àx (x ¼ 1:5) corresponded to those reported in [1]. The band structure of these systems was calculated by the self-consistent full-potential linear muffin-tin orbital method (FP-LMTO) [8] using the Barth-Hedin formula for the exchange-correlation potential.
Results andDiscussion b-Si 3 N 4 : The band structure and the total density of states (TDOS) of b-Si 3 N 4 are shown in Fig. 2a. The valence band (VB) has a full width of 18.3 eV and is split into two parts by a gap of 4.3 eV. The lower subband of the VB is made up mainly of N2s states and has a width of 4.0 eV. The upper subband (of mixed N2...