A simple theoretical model for the radiative lifetime of a fluorescent ion in a particle of a powder is described. The model predicts that the lifetime depends on the size of the particle, the density of the powder, and the refractive index of the surrounding medium. For a dilute system of very small particles the lifetime should be inversely proportional to the index of the surroundings. In Nd-doped yttrium aluminum garnet (YAG) and ${\mathrm{Y}}_2$${\mathrm{O}}_3$ powders, prepared by different methods, the ${\mathrm{Nd}}^{3+}$: ${}_{}{}^4{}_{}{}^{}F_{\frac{3}{2}}^{}{}_{}{}^{}$ decay rate was measured and compared to the particle size, the powder density, and the refractive index of the surroundings. In agreement with the theory the decay is slower the smaller the particles, the less dense the powder, and the lower the refractive index. For index-matched conditions the decay rate is close to what is observed in the bulk single crystal.

• Received 6 April 1981

DOI:https://doi.org/10.1103/PhysRevB.25.1467