An Absolute Theory of Solid-State Luminescence

The absorption and emission spectra of the thallium-activated potassium chloride phosphor at various temperatures has been computed theoretically. An ionic model is used. The radial charge densities of free Tl+ in the ground 1S0 state and in the excited 3P10 state are evaluated using the Sommerfeld modification of the Fermi-Thomas method for the core and the Hartree self-consistent field method for the two outershell electrons. From these wave functions and from the known ionic radius, polarizability, and repulsion energy constant ρ for the ground state, these parameters are evaluated for the Tl+ in the excited state interacting with Cl−. The variation of repulsion energy with interatomic distance a is shown to be equal to the variation of S2/a with a, where S is an overlap integral. The Tl+ in the 1S0 and the 3P10 states are substituted in dilute concentrations for the K+ in KCl, and the change in total energy of the system is calculated as a function of the change in the Tl+ nearest Cl− distance Δa with the condition that the remainder of the lattice rearranges to minimize the total energy. Madelung, exchange repulsion, van der waals, ion-dipole and coulomb overlap interactions are included. The absorption spectrum is computed by recognizing that the various atomic configurations of the system in the ground state have probabilities in accord with a Boltzmann function. The emission spectrum is similarly determined by summing over configurations of the system in the excited state. The computed spectra at various temperatures are found to be in good agreement with experiment. In addition, new insight is obtained on the detailed mechanism of solid-state luminescence.