Characterization of ferric ions diffusion in Fricke gel dosimeters by using inverse problem techniques

JOSE VEDELAGO; ANDRES QUIROGA; MAURO VALENTE

RADIATION EFFECTS AND DEFECTS IN SOLIDS

TAYLOR & FRANCIS LTD

Lugar: Londres; Año: 2014 vol. 169 p. 845 - 854

1042-0150

Diffusion of ferric ions in ferrous sulfate (Fricke) gels represents one of the main drawbacks of some radi-ation detectors, such as Fricke gel dosimeters. In practice, this disadvantage can be overcome by promptdosimeter analysis, and constraining strongly the time between irradiation and analysis, implementing spe-cial dedicated protocols aimed at minimizing signal blurring due to diffusion effects. This work presentsa novel analytic modeling and numerical calculation approach of diffusion coefficients in Fricke gelradiation sensitive materials. Samples are optically analyzed by means of visible light transmission mea-surements by capturing images with a charge-coupled device camera provided with a monochromaticfilter corresponding to the XO-infused Fricke solution absorbance peak. Dose distributions in Fricke gelsare suitably delivered by assessing specific initial conditions further studied by periodical sample imageacquisitions. Diffusion coefficient calculations were performed using a set of computational algorithmsbased on inverse problem formulation. Although 1D approaches to the diffusion equation might provideestimations of the diffusion coefficient, it should be calculated in the 2D framework due to the intrinsicbi-dimensional characteristics of Fricke gel layers here considered as radiation dosimeters. Thus a suitable2D diffusion model capable of determining diffusion coefficients was developed by fitting the obtainedalgorithm numerical solutions with the corresponding experimental data. Comparisons were performedby introducing an appropriate functional in order to analyze both experimental and numerical values.Solutions to the second-order diffusion equation are calculated in the framework of a dedicated methodthat incorporates finite element method. Moreover, optimized solutions can be attained by gradient-typeminimization algorithms. Knowledge about diffusion coefficient for a Fricke gel radiation detector ishelpful in accounting for effects regarding elapsed time between dosimeter irradiation and further anal-ysis. Hence, corrections might be included in standard dependence of optical density differences andactual, non-diffused, absorbed dose distributions. The obtained values for ferric ion diffusion coefficientare around 0.65 mm2 h−1 , being in good agreement with previous works corresponding to similar Frickegel dosimeter compositions. Therefore, more accurate 2D and 3D dose mapping might be attained, thusconstituting valuable improvements in Fricke gel dosimetry, and parallely a high precision method ofdiffusion modeling and calculation has been developed.