title: Statistical approaches to the transient populations and to the macroscopic energy transfer rate for the upconversion phenomenon in monodoped amorphous solid.
abstract: In this article, statistical approaches to the first and the second excited state transient populations and to the temporal macroscopic energy transfer rate for the upconversion process in amorphous solid generic systems monodoped with trivalent lanthanide ions are reached. The plots of the expressions show general tendencies reported in the literature. The derivation and the analysis of the formalism allowed us to fulfill our main objective, that is, to make a theoretical study about the microscopic and statistical mechanisms present in the phenomenon and their relation with the classic kinetic analysis. The study shows that the inclusion of the minimum possible radius between two optical centers in a solid affects the initial slopes of the decay curves of the luminescence from the intermediate state. We also corroborate that the usual treatment of experimental data using direct equations for the dynamics of the populations in laser pulsed excitation experiments falls in the mistake of not considering the temporality of the macroscopic energy transfer rate. Finally, physical explanations are formulated about this temporal behavior and about the main factors that generate the characteristic simple exponential decay loss of the luminescence from the intermediate state.
authors.affiliation: Grupo de Química-Física Teórica, Instituto de Química, Universidad de Antioquia, A A. 1226, Medellín, Columbia. czhadad@matematicas.udea.edu.co
authors.forename: C Z
authors.initials: CZ
authors.lastname: Hadad