LMTO-GF calculations

The electronic states of the phases in Ti-(A1, Ge)-(C, N) systems were studied by Ivanovsky et al (1987b, 1988b), using quantum-chemical calculations. The authors considered the initial stage of formation of these compounds and carried out LMTO-GF calculations of isolated Al impurities replacing Ti or C (N) atoms in the cubic TiC or TiN lattice. As can be seen from Fig. 5.15 for the TiC + Al system, Al is located at a site in the metal sublattice, Als states are hybridised mainly with the p-d-like subband of the matrix, while the Alp states are concentrated near the upper edge of the TiC valence band. On the Al - C substitution, s and p states of the impurity are shifted to the lower part of the occupied TiC band, and form nonbonding atom-like peaks at the DOS minima. A... 

An analysis of electronic factors affecting the structural stability of the alloys of a-MoC with d-metals has been made by Ivanovsky et al (1989), using LMTO-GF calculations of the MoC-M systems (M = ma-vna subgroup 3d- and 4d-metals). 

Table 7.1 Total one-electron energy changes of TiC and TiN (Ry) when doped by Mo and Ni impurities (LMTO-GF calculation).

The LDOSs of a single B impurity in TiC, TiN, VN and MoC have been calculated by Ivanovsky (1988) and Anisimov et al (1986a) using the LMTO-GF method. These calculations show that the B2p-type LDOS overlaps completely with the main valence-bonding band of the carbide, while B2s states are localised between C2s and p-d-TiC subbands. 

Therefore, in order to study the electron structure of Be-containing solid solutions a large number of calculations have been performed by Ivanovsky and coworkers (Ivanovsky and Anisimov, 1988 Ivanovsky et al, 1988c) for the TiC-Be and NbC-Be systems using the self-consistent LMTO-GF method. Different possible positions of impurity centres in the bulk crystals have been considered. LDOSs of isolated Be impurities located at the sites of C (1) or metal (2) sublattices and the DOS of the initial carbides are shown in Fig. 5.13. 

The most studied of these so far is the electronic structure of isolated impurities of 3d- and 4d-metals in cubic carbides and nitrides of Sc, Ti, V, Zr, Nb (see Ivanovsky (1988) and Ivanovsky et al (1987a,b, 1988a,b, 1989)). They have been calculated by the LMTO-GF method. 

Using the spin-polarised LMTO-GF method, Ivanovsky (1988) carried out systematic electronic structure calculations for the 3d- and 4d-metal impurities in Sc, Ti, V and Zr carbides and Sc and Ti nitrides. The choice... 

A first attempt to study the electron states of C phases for TiC and TiN-based composites with a Ni-Mo binder was made by Ivanovsky (1988). It has been found from the structure investigations of Fedorenko, that the material of the grain boundary entering the hard alloy composite is the cubic solid solution of Mo (or M02C) in TiC or TiN with small additions of nickel. For this reason, TiC and TiN with Mo atoms in some metal sites of the lattice were considered as the C phase model. Since Zhilyaev et al (1981) pointed out the possible implantation of metallic components in the C and N vacancies, calculations have also been performed for TiC-Mo and TiN-Mo systems, where Mo was placed in the nonmetal sublattice site. The role of each of the binder components in the formation of the C phase electronic states was elucidated when comparing calculated results for the described systems and the TiN-Ni alloy, where some substitution of atoms in Ti and N sublattices for Ni atoms is possible. The calculations were carried out by the LMTO-GF method. 

Several calculations were devoted to the study of the influence of a single, isolated vacancy on the electronic structure of an otherwise perfect crystal. It is assumed that the results obtained by investigating a single vacancy are also characteristic for crystals with somewhat higher vacancy concentrations. Ivanovsky et al. (131) considered an isolated vacancy as an impurity and proposed a self-consistent solution for this problem. These authors started from the LMTO procedure and the KKR-GF equations and developed an LMTO-GF method, which they applied to the calculation of the electronic structure of TiC, TiN, TiO, VC, VN, and VO containing... 

All calculations have been performed taking fixed positions for the atoms in the structures, so that no relaxations are considered. The Siesta method, however, allows relaxations and molecular dynamics by calculating the forces on the atoms and the stress tensor from the Hellman-Feynman theorem with Pulay corrections The computational cost would be much higher than in the frozen geometry calculations, but the calculations for complex magnetic systems are cheaper than with other ab initio methods (KKR, FLAPW, LMTO). Apart from the use of pseudopotentials and a minimal basis set, the supercell construction does not require the inclusion of empty spheres as it is the case for the LMTO-ASA method. Besides, going from 2D to 3D supported clusters of similar size does not increase the computational cost like in the KKR-GF method where Green-Functions have to be computed. 

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