The time dependence of the luminescence decay following pulsed excitation is examined for a system in which excited paramagnetic ions decay by a combination of intrinsic relaxation processes, direct energy transfer to acceptor ions, and energy migration. Three limiting cases are considered: direct energy transfer in the absence of diffusion, rapid diffusion, and diffusion-limited relaxation. Investigations of the transient europium fluorescence from a chromiumdoped europium phosphate glass, where excited ${\mathrm{Eu}}^{3+}$ ions form the donor system and ${\mathrm{Cr}}^{3+}$ impurities act as energy acceptors, are reported which illustrate these limiting cases. By varying the temperature and ${\mathrm{Cr}}^{3+}$ concentration, transient fluorescence behavior characteristic of diffusion-limited relaxation is studied. The data are analyzed to determine the probability for direct ${\mathrm{Eu}}^{3+}$ → ${\mathrm{Cr}}^{3+}$ energy transfer, the critical transfer distance for energy exchange, and the diffusion constant $D$ for energy migration through the europium system. $D$ varies with temperature as levels having greater probabilities for resonant ${\mathrm{Eu}}^{3+}$-${\mathrm{Eu}}^{3+}$ energy transfer become thermally populated. In the diffusion-limited relaxation case the decay rate is predicted to be proportional to $D^{\frac{3}{4}}$; this $\frac{3}{4}$ power law is verified.

• Received 30 April 1971

DOI:https://doi.org/10.1103/PhysRevB.4.2932