Model for F-center production in alkali halides doped with divalent cation impurities that change their valence state by irradiation.

Abstract

A model for the radiation-induced F-center coloring in alkali halides doped with doubly valent metal impurity ions (${M}^{2+}$) that can change their valence state by irradiation is proposed in the present paper. The primary event is assumed to be the creation of F centers and interstitial halogen (H) pairs. The thermal- and radiation-induced processes associated with the dynamics of H defects and their trapping at defects leading to the stabilization of their counterpart F centers are taken into account during the three stages of the F-coloring curve. The fundamental traps for the interstitials are assumed to be the ${M}^{2+}$-cation vacancy dipoles. Therefore, a heterogeneous nucleation process around these complexes is one of the assumptions on which the model is based. It is proposed that stage I of the F-coloring curve is reached with the single process of the capturing of one H defect by a dipole producing an ${S}_{1}$ center. The trapping of one additional interstitial by ${S}_{1}$ generates a less stable center, ${S}_{2}$. The trapping of one or more interstitials by ${S}_{2}$ gives a stable aggregate center denoted by A, which is responsible for stage III. On the other hand, another way in which these dipoles may vary is through the capture of free electrons during the irradiation process to become either ${M}^{+}$ or ${M}^{0}$ states. It is assumed that these latter states have different capabilities for the trapping of interstitials than those of ${M}^{2+}$. The possibility of hole capture by these reduced states, which would allow them to return to the original ${M}^{2+}$ state, is also included in the model. These basic assumptions are used to postulate a set of ten differential equations which we have solved numerically using a Runge-Kutta iteration program. The numerical solutions of the equations are in good qualitative agreement with the more important features of the experimentally determined effects of room-temperature x-ray irradiation in europium- and lead-doped alkali halides. In some cases, semiquantitative agreement with experiment is obtained.