N.M. Avram

Optical properties of 3d-ions in crystals : spectroscopy and crystal field analysis

Recent developments in laser crystals doped with 3d-ions.- Spectral properties of cobalt complexes within the ZnSe crystals as new absorbers for the non-linear optical devices.- Exchange charge model of crystal field for 3d ions.- Superposition Model and its Applications.- First-principles calculations of absorption spectra of 3d ions in laser crystals.- Vibronic transitions in spectra of 3d ions in crystals.- Jahn-Teller effect for the 3d3 (3d7) ions in the octahedral (tetrahedral) impurity centers.- Dynamical Jahn-Teller effect in crystals doped with 3d ions.- Spin-Hamiltonian parameters and lattice distortions around 3dn impurities.

Crystal field analysis of the ground and excited state absorption of a Cr4+ ion in LiAlO2 and LiGaO2 crystals

The exchange charge model of crystal field theory has been used to analyze the ground and excited state absorption of tetrahedrally coordinated Cr4+ ion in lithium aluminum oxide LiAlO2 (γ-phase) and lithium dioxogallate LiGaO2. The parameters of the crystal field acting on the Cr4+ ion are calculated from the crystal structure data, taking into account the crystal lattice ions located at distances up to 12.744 Å in LiGaO2 and 13. 180 Å in LiAlO2. The obtained energy level schemes were compared with experimental ground and excited state absorption spectra and literature data on the application of other crystal field models (the angular overlap model and Racah theory) to the considered crystals; a good agreement with experimental data is demonstrated.

Exchange charge model of crystal field for 3d ions

In the second chapter of the book the authors present the results of theoretical studies ofthe energy levels schemes of all 3dn (n=1, 9) ionsin various crystals at the substitutionalsites. Systematic calculations are described in all details; they include the overlap integrals between the impurityions’ and ligands’ wave functions; the crystal field parameters calculations, and diagonalization of the crystal field Hamiltonians for each considered case. The calculated results arediscussed and compared with experimental data and with similar results from literature. The chapter also contains a comprehensive literature review on the properties of 3d-ions doped crystals.

Numerical Calculations of the Overlap Integrals Between the Wave Functions of 3d Ions and Ligands

The overlap integral determine the covalent effects in a considered complex and significantly influences the crystal field effects experienced by impurity ions, and, finally, plays an important role in formation of the impurity center optical properties. In this paper we have calculated the two center overlap integrals between the wave functions of two ions, which can be typically an impurity ion in a crystal and one of its nearest neighbors. Some examples of applications are given.

Jahn–Teller Effect for the 3d Ions (Orbital Triplets in a Cubic Crystal Field)

Jahn–Teller effect and related phenomena attract considerable attention of researchers during last several decades. In the present chapter aimed at the students and postgraduates first of all, as well as at the beginners in this field, we review thoroughly the main mechanisms underlying the Ham effect (which means quenching of the spin–orbit interaction due to the interaction of the electronic energy levels with the crystal lattice vibrations). To make the chapter complete from the educational and pedagogical points of view, all necessary mathematical equations needed for calculations are derived and explained. It is shown how the effective second-order spin-Hamiltonian can be used for a description of the Ham effect and estimation of the Jahn–Teller stabilization energy. In addition, an alternative method of determining the Jahn–Teller stabilization energy based on the harmonic approximation and geometrical consideration of the adiabatic surfaces of the potential energy of the ground and excited electronic states is described. The chapter is followed by an attachment with the derivation of the Ham reduction factor.

Semi-empirical and ab initio DFT modeling of the spin-Hamiltonian parameters for Fe6+: K2MO4 (M = S, Cr, Se)

In this paper we calculated the spin-Hamiltonian parameters (g factors , and zero field splitting parameter D) for Fe6+ ions doped in K2MO4 (M = S, Cr, Se) crystals, taking into account the actual site symmetry of the Fe6+ impurity ion. The suggested method is based on the successful application of two different approaches: the crystal field theory (CFT) and density functional based (DFT). Within the CFT model we used the cluster approach and the perturbation theory method, based on the crystal field parameters, which were calculated in the superposition model. Within the DFT approach the calculations were done at the self-consistent field (SCF) by solving the coupled perturbed SCF equations. Comparison with experimental data shows that the obtained results are quite satisfactory, which proves applicability of the suggested calculating technique.

First principles and crystal field calculations of the spectral, structural and electric properties of (Na, Li)VSi 2 O 6 clinopyroxenes crystals

In the present paper we report on the results of theoretical modeling of the structural, spectral and electronic properties of (Na, Li)VSi2O6 clinopyroxenes crystals. At first, the semi-empirical model of crystal field theory, namely, the exchange charge model was employed for modeling the crystal field parameters (CFP), taking into account the effects of the covalent bond formation between the V 3+ and O 2– ions. The calculated CFP values were used for diagonalization of the crystal field Hamiltonian matrix in a complete basis set spanned by all 25 wave functions of the LS terms of the 3d 2 electron configuration. The second approach, the ab initio density functional theory (DFT)-based calculations, was employed for the structural optimization, analysis of the band structure, density of the states and the pressure effects of the considered compounds. All obtained results are discussed and compared with available experimental data.

Ab initio calculations of the structural, electronic and elastic properties of K3CrF6

This paper presents the results from our ab initio calculations of the optimized crystal structure, band structure, density of states (DOS) and elastic properties of K3CrF6. The electronic configurations were 2s 2 2p 5 for fluorine, 3s 2 3p 6 3d 5 4s 1 for chromium and 4s 2 3p 6 4s 1 for potassium. Ab initio calculations of DOSs allowed us to evaluate the contribution of each ion to the calculated bands. In addition, the spin-polarized calculations allowed us to find the difference between the densities of the spin-up and spin-down states of the sixfold coordinated Cr 3+ ion.

The parameters of the free ions Mn5+ and Fe6+

The analysis of the behavior of iron-group ions in crystals, using a free-ion Hamiltonian that involves terms with only three parameters (B, C and ξ), seems to be erroneous since it is incapable of correctly predicting the levels of even a free ion. Such calculations may lead to erroneous conclusions concerning the crystal-field effects and the electron–phonon interaction. In this paper, we present the results of the most exact calculation of the parameters for free ions and the energy levels of Mn5+ and Fe6+ with 3d2 configuration. In the single-configuration approximation, the effective Hamiltonian of the free ions takes into account not only the electrostatic and the spin–orbit interactions, but also the relativistic ones (spin–spin, orbit–orbit and spin–other–orbit) and the linear correlation effect. For both free ions we have calculated the semi-empirical parameters included in the interaction Hamiltonian and the energy level scheme. The values of these parameters are obtained by fitting experimental data with the minimum value of rms errors. The final results are discussed.

Spin-Hamiltonian Parameters For CrLi3+ Doped In LiNbO3

Abstract By using crystal field theory, the spin-Hamiltonian parameters [zero-field splitting D, the giromagnetic factors g (g|| and g⊥) and the first excited state splitting δ(2E)] for the CrLi3+ doped in LiNbO3 have been calculated from the higher-order perturbation formulas. The method used is based on the two-spin-orbit coupling parameter model, in a cluster approach. The g parameters were also calculated as a second derivative of the energy, method implemented into ORCA computer program. The results were discussed and good agreement with experimental data was demonstrated.