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

Closed system behaviour  
Uranium loss  
In common with other isotope systems, and relevant to all U-series systems discussed so far, understanding open system behaviour, i.e., the uptake or loss of parent or daughter isotopes from the system, is essential for correct interpretation of the data. At environmental temperatures solid-state diffusion coefficients are so low that time is insufficient and the system remains ‘closed’. Dissolution-precipitation processes are orders of magnitude faster than solid-state diffusion of trace elements. Selective or partial dissolution are the relevant ‘open system’ processes for U-series systematics at environmental conditions.
Dissolution
 
The main process that drives trace-element loss is focussed dissolution of the mineral phase. Water permeates along grain boundaries and micro-cracks (sometimes these cracks are formed by re-crystallisation of aragonite to calcite) and removes, or replaces atoms from the grain and sub-grain surface layers. Dissolution may be selective and trace elements such as uranium can be removed faster than the major elements of the mineral.
Recoil
 
In a U-series context there is the added complication usually referred to as α-recoil’. The term derives from physics where it describes the displacement of a radiogenic daughter isotope in the crystal lattice, when the radioactive parent nuclide has experienced a decay reaction. The displacement is not trivial, 10-110 nm for 238U to 234Th and it leaves a tube in the crystal of that length. Further-decay of 234Th to 234U has little effect because the kinetic energy of α-decay is much smaller than γ-decay. If uranium is not homogeneously distributed throughout the sample then the effect of 234U displacement is that U-rich domains will evolve to (234U/238U)<1 and the opposite for U-poor domains. A recoil track that intersects the grain surface provides an easy path for the decayed atom to move through. In effect, recoil creates a thin layer with enhanced permeability. However, the α-recoil effect only affects daughter isotopes such as 234Th and its daughter 234U and not the 238U because 238U is not radiogenic. Permeability is selectively enhanced for the 234U daughter isotope and the leaching process results in non-mass dependant isotope fractionation where the solid phase is depleted in (234U/238U) and the liquid phase is enriched. The extent of non-mass dependant isotope fractionation depends on the extent of the total surface layer with α-recoil enhanced permeability and is therefore dependent on the grain-size distribution of the material in contact with water.
One important consequence of (234U/238U) fractionation by the recoil process is that this ratio in water can be very different from the secular equilibrium value. (234U/238U) can be very high, values as high as 6 have been reported (Reynolds et al., 2003).
Simple modelling
 
It is instructive to model some of the consequences of 234U mobility as a consequence of α-recoil using the equations derived by Henderson et al., (1999). The secular equilibrium value of (234U/238U) in pore water depends largely on the grain size of the matrix and the matrix to pore-volume ratio and is given by:
 
Equation 4
Where r is the grain size radius, α is the α–recoil distance, ρ is the density and φ is the porosity and other symbols as before.
The approach of (234U/238U) to the equilibrium value calculated with Equation 8 is given by
:
 
Equation 5
As a simple example we assume a situation of seawater-derived pore water that is stagnant in a matrix of grains and that the grain-size is homogeneous rather than a distribution. Also assuming U=3 μg.g-1 in the grains and U=3 ng.g-1 in seawater and an average recoil length of 55 nm.
The (234U/238U) in the pore water depends on two processes, radioactive decay, from (234U/238U)=1.145 in seawater to the equilibrium value (234U/238U)=1, and the preferential addition of 234U from the α-recoil zone, and can be calculated with Equation 8. The rate of increase of (234U/238U) depends on the total area of the enhanced permeability grain surface layer that is in contact with the pore-water, and therefore on the grain-size, and the effect is quite marked. The equilibrium (234U/238U) in static pore water is >100 at 0.6 μm and almost 40 at 2 m. But at larger than 0.6 mm, decay dominates and (234U/238U) approaches a value of 1 after five half-lifes of 234U. The rate at which the equilibrium value is approached can be calculated with Equation 9 and equilibrium is achieved fairly rapidly with small grain sizes, 30 years for 0.6 μm and 100 years for 2 μm. Figures 1 and 2illustrate some results of these model calculations.
 
Figure 1. The effect of grain-size variation on the equilibrium value of (234U/238U), calculated with Equation 5, assuming 3 μg.g-1 uranium concentration in the grains, 3 ng.g-1 uranium concentration in the stagnant pore water, 55 nm average recoil-track length and homogeneous grain size.
 
Figure 2. The effect of grain-size variation on the time required to attain (234U/238U) equilibrium calculated with Equation 4, same assumptions as above.
 
   
Even from these simplistic calculations some interesting inferences could be made about differences in (234U/238U) between seawater and authigenic carbonate, accepting that the assumptions are reasonably realistic.
At a seafloor sediment precipitation rate of 1 cm per 1000 year with the average grain size in the normal range for pelagic clay, (234U/238U) in the pore water will deviate significantly from the seawater value after seawater percolation ceases, within the life-span of many sessile organisms. Based on data for NE Atlantic deep-sea sediments Thomson et al, (in review 2005) argue that bioturbation causes mixing of the top 12 cm of sediment and, based on 14C arguments that the average age of the homogenised layer is of the order of 2000 y for an average sedimentation rate of 4-7 cm per thousand year. The averaged (234U/238U) of pore water depends on the grain size distribution of the mixed sediment but for grain-sizes <40 μm, the (234U/238U) will be >3. Authigenic carbonate precipitate in the mixed layer is unlikely to have a seawater (234U/238U) value. Continental shelf sediments tend to accumulate intermittently allowing more time for (234U/238U) evolution, and it should be expected that neither authigenic precipitates nor sub-surface feeders, have seawater (234U/238U) values in this situation.
It is still a reasonable assumption that plankton and coral which feed by filtering seawater and extract the ions required for building a calcite skeleton from seawater, should have seawater (234U/238U) values. Buried molluscs and gastropods that live in or on the sediment surface and feed by processing detritus, are unlikely to maintain seawater (234U/238U) ratios.
For carbonate that has been precipitated within ocean water it is reasonable to expect that the (234U/238U) value is within analytical uncertainty of the seawater value but the (234U/238U) ratio within sediment can change rapidly, depending on grain size distribution and pore water flow. By implication, the (234U/238U) ratio in detritus feeders could very well be above seawater values.
 
Recoil modelling
 
Two important observations regarding α-recoil have been made by Henderson et al, (2001) and Villemant and Feuillet (2003). These authors have highlighted the fact that both 238U and 234U decay to thorium isotopes, 234Th with a half-life of 24 days and 230Th with a half-life of 75 ky, respectively. They have also pointed out that α-recoil damage accumulates with time and is directly related to the radioactive decay of the parent nuclides. The α-recoil damage to the mineral lattice from both α-decay processes depends on the energy of the α-recoil reactions which is determined for a given mineral by the nuclear reaction characteristics, and is very similar for both nuclides. The similarity of both 238U and 234U recoil processes allows them to be coupled and U-series data can be modelled assuming that α-recoil is the only other process that affects isotope ratios, as well as radioactive decay. The equations that describe the combined processes of radioactive decay and recoil are essentially an expansion of the Kaufman and Broecker (1965) equation with an ‘f’ factor for each of the recoil reactions and maintaining a fixed relation between the two ‘f’ factors. The ‘f’ factor represents the fraction of daughter isotope lost or gained and can be seen as the ‘open system’ factor.
 
Initial 230Th, the detrital correction
 
The Villemant and Feuillet, (2003) model can explain the scatter in U-series data for various Quaternary marine terraces and uses a simplified inversion procedure for the calculation of the ages of these terraces. The Villemant and Feuillet (2003) model also allows for the input of inherited 230Th but crucially assumes that the initial (234U/238U) is known. (234U/238U) is 1.145 for precipitation of uranium in equilibrium with seawater in the open ocean. However, as indicated in the simple model calculations above, interaction with pore-water uranium during early diagenesis can result in evolving (234U/238U). Moreover, there are many other situations where (234U/238U) is not known such as in marginal or hydrothermally affected sea areas. In cases where equilibrium (234U/238U) from pore-water analysis is not available, (234U/238U) is actually a free parameter. Figure 8 is a (234U/238U) vs (234U/238U) diagram with five, nearly straight isochron curves and four evolution curves for different degrees of open-system behaviour with the closed-system curve indicated by f=1. Data-points (black squares) are for four carbonate samples from Lake Tswaing (Thorpe, et al., 2005). Lake Tswaing is an intra-continental aquifer-fed hyper-saline closed lake in a depression formed by a meteorite impact and the four data-points define an age of 165 ka, after correction for a small allogenic contribution. In Figure 3 the data-points plot near a 165 ka isochron for (234U/238U)=2.85 and then indicate ‘f’ values of 0.8-0.9 and negligible allogenic 230Th, inferred from a low (230Th/234U) initial value at zero age. The distribution of data-points along isotope ratio evolution curves indicates that a small amount of 234U loss, inferred from an open system factor ‘f’ of within 15% of the closed system value of unity still given valid U-series ages, as was also observed by Villemant and Feuillet, (2003) for Quaternary marine terraces. The inferred (234U/238U)=2.85 is within expectations for carbonate that has precipitated from phreatic water that slowly-percolated through an aquifer.
 
Figure 3. (234U/238U) vs (230Th/234U) diagram. Solid, nearly straight curves are sochrons. Evolution curves for different degrees of open-system behaviour as indicated by the ‘f’ values, are broken lines with the closed-system solid curve indicated by f=1. Curves and isochrones are calculated with the equations in Villemant and Feuillet (2003). The initial value for (230Th/234U), indicating the allogenic contribution, is very low; the initial value for (234U/238U) may indicate the ambient ratio during precipitation but is essentially unconstrained.
 
   
In a situation where the equilibrium (234U/238U) can be constrained either by assuming equilibrium with a seawater value or by data from pore-water analysis, an age can be calculated. Conversely, (234U/238U) can be inferred with the Villemant and Feuillet (2003) model if the age can be independently constrained.
The (234U/238U) vs (230Th/234U) diagram can also be used to indicate an open system situation if data-points plot 0.8>f>0 where f=0 indicates systematic 234U and 238U loss. Figure 9 is a (234U/238U) vs (230Th/234U) diagram similar to Figure 8 but the data-points are from a section of finely-laminated lake sediments of Laguna Piuray, Peru (M. Burns and B. Aston, pers.com. 2005). The carbonate sediments are probably Post-Glacial and became exposed when a moraine dam eroded. It can be concluded from the scattering of the data-points over the diagram that exposure to rain and groundwater percolation resulted in extensive disruption to the U-series system. Data-points close to the f=0 evolution curve indicate almost total loss of all uranium isotopes. In this case the Villemant and Feuillet (2003) model can be used to argue that it is unlikely that age information may be recovered from these data.
 

Henderson et al., 1999. Earth and Planetary Science Letters 169(1–2), 99–111.
Henderson et al., 2001. Geochimica et Cosmochimica Acta 65 (16), 2757–2770.
Kaufman and Broecker, 1965. Journal of Geophysical Research 70, 4039–4054.
Reynolds et al., 2003. Geochimica et Cosmochimica Acta 67(11), 1955–1972.
Thomson et al, 2006, Earth and Planetary Science Letters.
Thorpe et al., 2005. Abstract, PAGES Second Open Science Meeting, 10-12 August 2005, Beijing, China.
Villemant and Feuillet, 2003. Earth and Planetary Science Letters 210(1–2), 105–118.
 
   
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© Peter van Calsteren
Last updated: December 23, 2011 11:36