Kinetic modeling of Fluorine vacancy/F center creation in LiF:Mg,Ti including vacancy-interstitial recombination: Evaluating the factors leading to the lack of supralinearity in the optical absorption F center concentration dose response

Kinetic model simulations of charge carrier transport following irradiation of LiF:Mg,Ti (TLD-100) including Fluorine vacancy/F center creation by the radiation and dose-dependent vacancy-interstitial recombination are presented which describe the experimentally measured linear/exponentially saturating optical absorption dose response of the electron trapping centers at 4.0 eV, 4.77 eV, 5.08 eV (F band) and 5.45 eV. Linear/exponentially saturating dose response is commonly observed for centers which are not created by the radiation. The creation of Fluorine vacancies by the radiation could therefore be expected to lead to a supralinear dose response of the F center before the onset of saturation. Nonetheless, the dose response is linear from 10 Gy to 500 Gy and can be fitted with a dose-filling constant β = 6.1 · 10^-5 Gy^-1 corresponding to a 5% and 25% decrease from linearity at 10³ Gy and 5 · 10³ Gy respectively. The model attempts to resolve a central question concerning the mechanisms leading to the linear/exponentially saturating dose response of the F band even though Fluorine vacancies are being continuously created during the irradiation. The electron-trapping characteristics of the created vacancies are assumed to differ somewhat from the vacancies originally present in un-irradiated samples due to differences in their immediate environment. Vacancy-interstitial recombination for separation distances less than a critical distance, d_c is demonstrated to be significant for D > 500 Gy (d_c = 36 Å) and is an important mechanism contributing to the F center saturation at high dose-levels. The kinetic model accurately simulates the experimentally observed F center dose response over the entire investigated dose range of 10-10⁵ Gy under the following conditions: (i) The concentration of vacancies initially present is unexpectedly high at ∼10²³ m^-3, possibly due to the highly doped, non-crystalline and hot-pressed nature of the LiF:Mg,Ti samples. (ii) The transition probability, A_n4o, for electron capture into the initially-present vacancies is ∼40 times greater than A_n4, the transition probability for the radiation-created vacancies. These two factors marginalize the effect of the created vacancies at low dose resulting in a linear dose response.