Electronic spectra of 3d(n) transition ions in an octahedral ligand surrounding have been studied using the modified crystal field approach (MCFA), which includes a relativistic spin-orbital interaction. A new variable parameter, the effective nuclear charge Z(eff) of a metal ion that allows accounting implicitly the covalence degree of a metal-ligand bond, has been introduced. Energy diagrams similar to the Tanabe-Sugano ones have been calculated. To study the spin state evolution of the metal ion in an arbitrary distorted octahedral complex, a spin state diagram approach has been proposed. The intermediate-spin (IS) state problem for 3d(4), 3d(5), and 3d(6) metal ions has been considered and conditions for the IS state realization have been formulated. The regions of the mixed high-, intermediate-, and low-spin states have been found. The possibility of coexistence of the different spin states of 3d ions in the octahedral complexes has been considered using crystallography data for the YBaCo(2)O(5.5) layered cobaltite.

Spin state (SS) transitions in metal-containing pyramidal complexes that originate from crystallographic distortions are the research subject of this work. The transition elements are considered to be in the 3d6 configuration (Fe2+, Co3+), and they display three different SSs: low-spin (LS,S = 0), intermediate-spin (IS,S = 1) and high-spin (HS,S = 2) states. They have been studied in the frame of the crystal field approximation via the effective nuclear charge Zeff and under oxygen cage distortions. The features of the SS stability have been calculated with/without accounting for spin–orbit coupling. Some critical points at which an accidental degeneracy of the SSs exist have been revealed. Near the critical points, negligible distortions can crucially change the SS. It is demonstrated that the ground SS of the pyramidal MeO5 complex is very sensitive to the symmetry and magnitude of its distortions. SS diagrams in the parameter space ‘effective charge’–‘distortion magnitude’ have been established. It is revealed that the IS state exists as a ground state for all considered distortions with a corresponding choice of Zeff. Jahn–Teller distortions stabilize the IS state in a wide range of Zeff. The orbital-like reorientation of the electron density distribution was observed for the IS state at some threshold magnitude of Jahn–Teller distortions.

The diluted magnetic semiconductors Hg(1-x)Cr(x)Se (0.03≤x≤0.1) were prepared by the solid state recrystallization method. The structure microanalysis of the Hg(1-x)Cr(x)Se compounds, performed by using a scanning electron spectrometer, has shown that the HgCr(2)Se(4) spinel-like inclusions are present in the host matrix Hg(1-x)Cr(x)Se and their amount increases when the chromium content grows. ESR studies of Hg(1-x)Cr(x)Se samples were carried out in the temperature range 4.2-300 K. ESR spectra of the samples with different chromium contents demonstrate the same g-factors at room temperature and similar fine structure development with the temperature decrease. Numerical studies of g-factors, performed by the modified crystal field approach (MCFA), allowed us to reveal that Cr(2+)/Cr(3+) ions in the tetrahedral environment of the solid solution Hg(1-x)Cr(x)Se cannot lead to the ESR signal. The experimental g-factor is well reproduced by a numerical g-factor for Cr(3+) ions located in the octahedral environment, being specific for the HgCr(2)Se(4) spinel phase. The onset of the ESR fine structure is determined by the trigonal distortions of the (CrSe(6))(9-) octahedral cell. From our study it has been found that the spinel clusters are present in the Hg(1-x)Cr(x)Se solid solution even at low chromium content.

Equations for the derivatives of adiabatic and isothermal elastic constants with respect to the stress tensor for the initially stressed crystal of the arbitrary symmetry are deduced. The relation between the third order elastic constants determined under different thermodynamic boundary conditions are estimated in the general case. The proposed methods of obtaining the derivatives with respect to the stress tensor and the relations between different elastic constants may be applied to the elastic constants of higher order.