Attenuation of beta radiation in granular matrices: implications for trapped-charge dating

Mineral grains within sediment or rock absorb a radiation dose from the decay of radionuclides in the host matrix. For the beta dose component, the estimated dose rate must be adjusted for the attenuation of beta particles within the mineral grains. Standard calculations, originally designed for thermoluminescence dating of pottery, assume that the grain is embedded in a homogenous medium. However, most current applications of trapped-charge dating concern sand- or silt-sized dosimeters embedded in granular sediment. In such cases, the radionuclide sources are not homogeneous but are localised in discrete grains or held on grain surfaces. We show here that the mean dose rate to dosimeter grains in a granular matrix is dependent on the grain-size distributions of the source grains and of the bulk sediment, in addition to the grain size of the dosimeters. We further argue that U and Th sources are likely to be held primarily on grain surfaces, which causes the dose rate to dosimeter grains to be significantly higher than for sources distributed uniformly throughout grains. For a typical well-sorted medium sand, the beta dose rates derived from surface U and Th sources are higher by ∼ 20 % and ∼ 30 %, respectively, compared to a homogenous distribution of sources. We account for these effects using an expanded model of beta attenuation - including the effect of moisture - and validate the model against Monte Carlo radiation transport simulations within a geometry of packed spheres.