FERDE. WILLIAMS
780
VOl. 57
THEORY OF THE LUMINESCENCE OF IMPURITY-ACTIVATED IONIC CRYSTALS BY FERDE. WILLIAMS General Electric Research Laboratory, Schenectady, N . Y . Reccined March i 2, 1965
The absolute theory of the absorption and emission of impurity-activated ionic crystals is reviewed. The detailed atomic rearrangements following the optical transitions and the e uilibrium distributions among accessible atomic configurations of the activator system are determined quantitatively. T f e spectra can be determined either from the Franck-Condon principle or by direct evaluation of the matrix elements for the transitions from the vibrational levels of the initial state to the vibrational levels of the final state. Important refinements in the theory of activator systems are reported and are shown to improve the agreement of the theory with experiment. The angular dependence of the wave functions of excited states of thallous and manganous activator ions is shown to affect the properties of their activator systems in alkali halide phosphors. The first order perturbation of the energies of activator ions by the crystal field is evaluated and found to be appreciably different for the ground and excited states of the thallous ion in alkali halides.
I. Introduction An absolute theory of solid state luminescence has been formulated and applied to impurity-activated ionic crystals.' From fundamental considerations and the properties of the constituent ions, the theoretical absorption and emission spectra of thalliumactivated potassium chloride have been evaluated and found to be in satisfactory agreement with experiment. In addition, the dependence on temperature of these spectra2t3 and the activation energy for radiationless de-excitation4 have been computed. Trapping originating from metastable states of the activator has been shown t o be quantitatively interpretable by the model.6 Finally, the mercury-activated harmotome phosphor was predicted from the theory.6 11. The Activator System The atomic configuration of the activator system for KC1:Tl is shown in Fig. 1. The binding for the ground state is ionic as demonstrated by Mayer' in evaluating the lattice energies of pure alkaltand thallous halides. Seitzs concluded that excited states of T1+, rather than electron transfer processes, are responsible for the luminescence of thallium-activated alkali halide phosphors. Energy and transition probability considerations suggest
that the 2460 i. absorption and the 3050 A. emission bands arise from the 'So 3P10 transitions. The radial charge densities of the outershell electrons of free 'SOand 3P10T1+have been evaluated by the Hartree self-consistent field method. For both states the outershell electrons are quite localized. Therefore, the ionic model is applicable to the excited as well as the ground state of the activator system. The polarizabilities and ionic radii, and the compressibilities of 'So and 3P10Tl+interacting with C1- can be computed from the radial charge densities. The changes in lattice energy arising from substituting 'So or aP1oT1+for K + in IC1 and from distorting the atomic configuration of perfect KC1 are determined. Madelung, exchange repulsion, van der Waals, ion-induced dipole and coulomb overlap energies are included. The tight binding character of SO and aP,oT1+ in KCl was confirmed by Johnson and Williams6 in calculating the change in lattice energies AE and AE' arising from substituting T1+ and Tl++, respectively, for I
