Multiphonon non-radiative relaxation rates and Judd–Ofelt parameters of lanthanide ions in various solid hosts

Abstract
The pre-exponential factor β of the near exponential energy-gap law, which has previously been treated as a phenomenological parameter and recently as an electronic factor, is shown to be directly related, through the squared maximum phonon energy, to the sum of products of the intensity parameters τλ by the squared matrix elements ‖Uλ‖2 of the Judd–Ofelt tensor. Calculated β for several lanthanide ions Ln3+ in six crystalline and six glass hosts are in very good agreement with the experimental values. A modified Franck–Condon factor F expression is derived for slightly displaced undistorted parabolae using van Dijk's and Schuurmans' ν=[(ΔE/ħωM)– 1] argument (where ΔE/ħωM is the original phonon number). Among fifty-eight calculated non-radiative probabilities knr(=βF), fifteen differed from the experimental knr by more than one order of magnitude, but by less than a factor of 50, thus promising a theoretical evaluation of any unknown knr of an Ln3+ transition for which the Huang–Rhys parameter S is known or can be determined spectroscopically. It can also be shown that the vanishing of the proposed β expression when ΔE/ħωM= 1 is relaxed if vibrations lower than the most energetic one are also effective. The possibility of some relation between S(measuring, in effect, the lattice relaxation energy) and the material parameter Ω2(assumed to reflect degree of covalency) is explored. It is found that the average of S, for several transitions of Er3+ in nine solid hosts, has an inverse exponential dependence on Ω2.

This publication has 0 references indexed in Scilit: