A Unified Calculation of the Optical and EPR Spectral Data for the Trigonal Cr³⁺Center in Cr³⁺-Doped α-RbAl(SO₄)₂·12H₂O Alum Crystal

Abstract

The optical band positions and the spin-Hamiltonian parameters (g factors g , g ⊥ , and zero-field splitting parameter D) of alum α-RbAl(SO4)2 · 12H2O:Cr 3+ are calculated by diagonalizing the 120 × 120 complete energy matrix based on the two-spin-orbit-coupling-parameter model. The model takes into account not only the contributions due to the spin-orbit-coupling parameter of central d n ion in the conventional crystal field theory, but also those due to ligands via covalence effect. The calculation indicates that the fourteen observed spectral data (eleven optical band positions and three spin-Hamiltonian parameters) can be reasonably and uniformly explained with four adjustable parameters (the Racah parameters B, C, intrinsic parameterĀ4(R) in the superposition model, and the trigonal distortion angle β). The calculations also suggest that contrary to the previous findings, the trigonal distortion of Cr 3+ (entering the Al 3+ site in the host crystal) center in α-RbAl(SO4)2 · 12H2O is induced mainly by the oxygen (or water) octahedron around the Cr 3+ ion rather than the more distant neighbors.