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The spin Hamiltonian parameters (the g factors, the hyperfine structure constants, and the superhyperfine parameters) and the local structures for various Rh(2+) centers OI, OII, and RTAX in NaCl are theoretically investigated from the perturbation formulas of these parameters for a 4d(7) ion in tetragonally and orthorhombically elongated octahedra. The related molecular orbital coefficients and the ligand unpaired spin densities are determined quantitatively from the cluster approach in a uniform way. The centers OI, OII (orthorhombic) or RTAX (tetragonal) are attributed to the substitutional Rh(2+) on Na(+) site, associated with two, one or none next nearest neighbour cation vacancies V(Na) along [100] (or [010]) axis, respectively. The ligand octahedra in the orthorhombic centers OI and OII are found to suffer the relative elongations Delta Z approximate to 0.071 and 0.068 angstrom along the [001] axis due to the Jahn-Teller effect, and the intervening ligand(s) in the V(Na) and the Rh(2+) may undergo the inward dis-placements Delta X approximate to 0.001 and 0.011 angstrom towards Rh(2+), respectively. As for the tetragonal center RTAX, the uncompensated [RhCl(6)](4-) cluster is found to experience the relative elongation Delta Z approximate to 0.067 angstrom along the [001] axis of the Jahn-Teller nature. The calculated spin Hamiltonian parameters based on the above local structures show good agreement with the observed values for all the centers.

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