# Fig xA Dependence of the PL

Energy transfer is generally associated with multipolar interactions, radiation reabsorption, or exchange interaction. Among them, multipolar interactions are usually prevalent which have several types, such as dipole–dipole (d–d), dipole–quadrupole (d–q), and quadrupole–quadrupole (q–q) interactions. Exchange interaction is generally limited to interactions between RE ions in the nearest or next nearest neighbor. If migration is rapid compared to direct transfer, quenching tends to be proportional to quenching-ions concentration [46]. For a better understanding of SB269970 HCl transfer in the host, the relationship of emission intensity and activator concentration is discussed. As the report of Van Uitert and Ozawa, the type of energy transfer can be determined from the change in the emission intensity from the emitting level [47]. The emission intensity (I) per activator ion follows the equation:equation(3)Ix=K[1+β(x)Q/3]−1where x is the activator concentration, I/x is the emission intensity (I) per activator concentration (x), and K and β are constants for the same excitation condition for a given host crystal. According to Eq. (3), θ=3 for the energy transfer among the nearest-neighbor ions, while θ=6, 8, 10 for d–d, d–q, q–q interactions, respectively. Further, Eq. (3) can simply be rearranged as follows:equation(4)ln(Ix)=k′−θ3lnx(k′=lnk−lnβ)From the slope of Eq. (4), θ can be obtained. Then we use this equation to fit the experimental results of the relationship between integrated emission intensity and Sm3+ concentration. The curve of ln I/x vs. ln x in Y2Mo4O15:Sm3+ phosphor is shown in Fig. 9. From the curves, it can be found that the slope is −1.03, so θ is approximately equal to 3, which means that the quenching is directly proportional to the ion concentration. The result indicates that the concentration quenching for the Sm3+-site emission centers is caused by exchange interaction in the Y2Mo4O15:Sm3+ phosphor.