Diffusion Effects in the Inhomogeneously Broadened Case: High-Temperature Saturation of the F-Center Electron Spin Resonance
An experimental and theoretical study is made of the effects of a random spectral diffusion process on the saturation behavior of a normally inhomogeneously broadened resonance. The random type of spectral diffusion process results, for example, if a spin diffuses on a set of sites having a distribution of local fields giving the inhomogeneous width but such that local fields at adjacent sites are uncorrelated. The calculation shows a transition in saturation properties to those characteristic of a homogeneously broadened resonance as the quantity β=ωD(ω1+ωD)ω1ω2* approaches unity, where ω1, ωD, and ω2* represent, respectively, the spin-lattice relaxation rate, the spectral diffusion rate, and the inhomogeneous width. A study of the transition behavior can yield values of ω1 and ωD in the transition range. The analysis is shown to apply in the transition range 470 to 550°C for the KCl F center. Analysis of the transition saturation data yields a value of ω1 which agrees with the expression of Feldman, Warren, and Castle, which for absolute temperatures T large compared with 210°K becomes ω1=3.5×10-1T2 sec-1. The spectral diffusion rate in zone-refined samples is given by ωD=12ν0 exp (-EmkT), where ν0=3.7×1015×10+/-1.2 sec-1, and Em=1.6+/-0.2 eV. The spectral diffusion is interpreted as resulting from diffusion of the F center in  steps of length 2a, where a is the interionic distance, with attempt frequency ν0 and motion energy Em. This process does not account for the diffusion coefficient of the F center, which results from diffusion of ionized electrons to anion vacancies, and which is limited in the case of dense coloration by charge compensating vacancy diffusion.