Energy Transfer between Chromium Ions in Nonequivalent Sites in ${\mathrm{Li}}_2$${\mathrm{Ge}}_7$${\mathrm{O}}_{15}$

The temperature dependences of the relative intensities and lifetimes of the $R_1$ lines of chromium ions in nonequivalent sites in lithium germanate are reported. Above ∼100°K, the ratio of the fluorescent intensity of the ${R_1}^{\prime }$ line to that of the $R_1$ line is proportional to $\exp (-\frac{\Delta E}{\mathrm{kT}})$, where $\Delta E$ is the energy separation of the two lines. At lower temperatures, the intensity ratios deviate from this exponential temperature dependence. The fluorescent decay at the two lines is purely exponential with the same decay times above ∼100°K; but below this temperature, their decay times differ, and the $R_1$ line exhibits a double exponential decay for a sample with 0.038% ${\mathrm{Cr}}^{3+}$ and initial rises in the fluorescence for samples with 0.12 and 0.18% ${\mathrm{Cr}}^{3+}$. These results are interpreted in terms of energy transfer between chromium ions in nonequivalent sites, which is efficient enough at high temperatures to allow thermal equilibrium to be established between the two fluorescent systems, but which should permit pumping of the $R$ system by the $R^{\prime }$ system at low temperatures. Analysis of the rate equations of the populations of two interacting fluorescent systems yields qualitative results consistent with experimental observations of both the relative intensity and the lifetime measurements. The nature of the energy transfer mechanism is also considered in terms of both the overlap of the two lines and a phonon-assisted process.