Cross-relaxation process between +3 rare-earth ions inLiYF4crystals

The cross-relaxation probability (${\sec }^{\mathrm{-}1}$) involving the ${}_{}{}^5{}_{}{}^{}$ ${\mathit{S}}_2$ and ${}_{}{}^5{}_{}{}^{}$ ${\mathit{I}}_8$ levels of holmium ions in ${\mathrm{LiYF}}_4$ was investigated and its concentration dependence determined. By using a random distribution function of ions in the crystal, it was possible to determine the concentration dependence of the nonradiative probability for the ion-ion energy transfer by dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole electric interactions. The applied model shows that the ion-ion cross-relaxation transfer between ${\mathrm{Ho}}^{3+}$ ions in ${\mathrm{LiYF}}_4$ crystals, cannot account for the experimental results. At a high concentration level of activators (≳1%), the excited ion must interact with two neighbors of same specie competing with the single ion cross-relaxation transfer. © 1996 The American Physical Society.