A formalism was developed which described the time evolution of bimolecular processes in fractal spaces. The so-called stretched second-order solutions were particularly applicable to radiation-induced electron-hole pairs and/or vacancy-interstitial pairs in insulating glasses. The solutions were functions of (kt)β, where β was between zero and unity and k was a rate coefficient. The new second-order formalism was used to fit experimental data. Two material systems were investigated: optical fibers with Ge-doped silica cores, and fibers with low-OH/low-chloride pure-silica cores. Successful fitting of the growth curves for Ge-doped silica-core fibers at 4 widely separated dose rates was achieved by using solutions for color-center concentrations, N[(kt)β], which approached steady-state values with time. The parametrization of these fits revealed useful empirical rules concerning the dose-rate dependences of β, k, and Nsat in the fractal regime (0 < β < 1). Similar rules also applied to color centers in the pure-silica core fibers.

Fractal Kinetics of Radiation-Induced Point-Defect Formation and Decay in Amorphous Insulators - Application to Color Centers in Silica-Based Optical Fibers. D.L.Griscom: Physical Review B, 2001, 64[17], 174201 (14pp)