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10 Handbook on the Physics and Chemistry of Rare Earths FIG. 5 Configurational coordinate Q Schematic illustration of configurational coordinate model. U1 state BE C D U2 U0 ΔU Q Ground Excited state A O Q0 ion with its nearest neighbors, usually regarded as the average distances between the active ion and the nearest neighbors. The horizontal dashed lines in ground state and excited state curves denote the vibrational states. For the total energy U, it is presumed that the bonding force between the active ion and the nearest neighbors can be expressed by Hooke’s law, so that the ener- gies of the ground state, Ug, and that of the excited state, Ue, are given by the following equations. U 1⁄4K Q2 gg2 ðQQ0Þ2 Ue 1⁄4 Ke 2 + U0 where Kg and Ke are the force constants of the chemical bond, Q0 represents the equilibrium distances of the ground state and the excited state, and U0 is the total energy at Q1⁄4Q0. When the activator absorbs some radiation light, an expansion of the lattice occurs in the vicinity of the activator ion and the activator is promoted to the excited state. The excitation and emission processes are illustrated by vertical arrows, showing that the nucleus of the activator stays at approximately the same position during these processes (so-called Franck–Condon principle). The energy difference between excita- tion and emission is the Stokes shift, equal to U1 (U0 U2). When the tem- perature of the phosphor exceeds some value, the vibrational energy makes the excited activator reach the E point of the excited state curve and then the activator relaxes to the ground state without radiation, which is called Total energy UPDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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