Open University Uranium-Series Laboratory  
Earth and Environmental Sciences, The Open University, Milton Keynes, UK  

The diffusion-adsorption model

 

   

Millard & Hedges (1996) developed a U uptake model based on a physico-chemical description of U–bone-mineral interaction. Put simply, it describes U in the groundwater as uranyl complexes entering the bone pore-space by a process of diffusion, where it adsorbs on to the large surface presented by the bone mineral, hydroxyapatite. At the core of their model is the parameter D/R which is a function of the diffusion coefficient and the partition coefficient of U for bone. It is related to the structure of the bone and the hydrology of the burial environment.

The model not only predicts the rate of U uptake, but also the spatial distribution of U within a bone. Figure 1 shows the development of U profiles over time according to the model assuming constant conditions. U is taken up rapidly at the edges of the bone to form a U-shaped profile that gradually flattens with time until equilibrium is reached between U in the groundwater and U in the bone.

 
 

 

 
 
 

Figure 1

Simulated U profiles in bone. The parameter t’ which defines the shape of the profile is related to time and the parameter D/R

 
 

Pike et al.,(2002) deveoped the the diffusion-adsorption model to incorporate U-series disequilibrium to dating of bone. The model predicts the development of U and Th isotope ratios across a bone section, shown in Figure 2 as closed system U-series dates. The figure shows the modelled results for a 10ky bone and different values of the parameter D/R. The edges of the bone, that reach equilibrium relatively quickly, give closed system dates close to 10ky, but the centre of the bone may give a gross underestimation of the age.

 
   

 

 
 
 

Figure 2

Simulated closed system date profiles in a 10ky bone. The parameter D/R is related to the structure of both the bone and the soil.

 
   

Millard, A.R. and Hedges, R.M., 1996, Geochim. Cosmochim. Acta, 60, 2139-2152.
Pike et al., 2002, Geochimica et Cosmochimica Acta 66, 4273-4286.

 
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© Peter van Calsteren
Last updated: December 23, 2011 11:37
 
December 23, 2011 11:37