Open University UraniumSeries 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 Useries 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 solidstate
diffusion coefficients are so low that time is insufficient and the system
remains ‘closed’. Dissolutionprecipitation processes are orders
of magnitude faster than solidstate diffusion of trace elements. Selective
or partial dissolution are the relevant ‘open system’ processes
for Useries systematics at environmental conditions. 

Dissolution 

The
main process that drives traceelement loss is focussed dissolution of the
mineral phase. Water permeates along grain boundaries and microcracks (sometimes
these cracks are formed by recrystallisation of aragonite to calcite) and
removes, or replaces atoms from the grain and subgrain 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 Useries context there is the added complication usually referred to as
αrecoil’.
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, 10110
nm for ^{238}U to ^{234}Th and it leaves a tube in the crystal
of that length. Furtherdecay
of ^{234}Th to ^{234}U has little effect because the kinetic
energy of αdecay
is much smaller than γdecay.
If uranium is not homogeneously distributed throughout the sample then the
effect of ^{234}U displacement is that Urich domains will evolve
to (^{234}U/^{238}U)<1 and the opposite for Upoor 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 αrecoil
effect only affects daughter isotopes such as ^{234}Th and its daughter
^{234}U and not the ^{238}U because ^{238}U is not
radiogenic. Permeability is selectively enhanced for the ^{234}U
daughter isotope and the leaching process results in nonmass dependant
isotope fractionation where the solid phase is depleted in (^{234}U/^{238}U)
and the liquid phase is enriched. The extent of nonmass dependant isotope
fractionation depends on the extent of the total surface layer with αrecoil
enhanced permeability and is therefore dependent on the grainsize distribution
of the material in contact with water. One important consequence of (^{234}U/^{238}U) fractionation by the recoil process is that this ratio in water can be very different from the secular equilibrium value. (^{234}U/^{238}U) 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 ^{234}U mobility as a consequence
of αrecoil
using the equations derived by Henderson et al., (1999). The secular equilibrium
value of (^{234}U/^{238}U) in pore water depends largely
on the grain size of the matrix and the matrix to porevolume 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 (^{234}U/^{238}U) to the equilibrium value calculated with Equation 8 is given by: 

Equation 5  
As
a simple example we assume a situation of seawaterderived pore water that
is stagnant in a matrix of grains and that the grainsize 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 (^{234}U/^{238}U) in the pore water depends on two processes, radioactive decay, from (^{234}U/^{238}U)=1.145 in seawater to the equilibrium value (^{234}U/^{238}U)=1, and the preferential addition of ^{234}U from the αrecoil zone, and can be calculated with Equation 8. The rate of increase of (^{234}U/^{238}U) depends on the total area of the enhanced permeability grain surface layer that is in contact with the porewater, and therefore on the grainsize, and the effect is quite marked. The equilibrium (^{234}U/^{238}U) 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 (^{234}U/^{238}U) approaches a value of 1 after five halflifes 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 grainsize variation on the equilibrium value of (^{234}U/^{238}U),
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 recoiltrack length and homogeneous
grain size. 

Figure 2. The
effect of grainsize variation on the time required to attain (^{234}U/^{238}U)
equilibrium calculated with Equation 4, same assumptions as above. 

Even
from these simplistic calculations some interesting inferences could be
made about differences in (^{234}U/^{238}U) 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, (^{234}U/^{238}U) in the pore water will deviate significantly from the seawater value after seawater percolation ceases, within the lifespan of many sessile organisms. Based on data for NE Atlantic deepsea sediments Thomson et al, (in review 2005) argue that bioturbation causes mixing of the top 12 cm of sediment and, based on ^{14}C arguments that the average age of the homogenised layer is of the order of 2000 y for an average sedimentation rate of 47 cm per thousand year. The averaged (^{234}U/^{238}U) of pore water depends on the grain size distribution of the mixed sediment but for grainsizes <40 μm, the (^{234}U/^{238}U) will be >3. Authigenic carbonate precipitate in the mixed layer is unlikely to have a seawater (^{234}U/^{238}U) value. Continental shelf sediments tend to accumulate intermittently allowing more time for (^{234}U/^{238}U) evolution, and it should be expected that neither authigenic precipitates nor subsurface feeders, have seawater (^{234}U/^{238}U) 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 (^{234}U/^{238}U) values. Buried molluscs and gastropods that live in or on the sediment surface and feed by processing detritus, are unlikely to maintain seawater (^{234}U/^{238}U) ratios. For carbonate that has been precipitated within ocean water it is reasonable to expect that the (^{234}U/^{238}U) value is within analytical uncertainty of the seawater value but the (^{234}U/^{238}U) ratio within sediment can change rapidly, depending on grain size distribution and pore water flow. By implication, the (^{234}U/^{238}U) ratio in detritus feeders could very well be above seawater values. 

Recoil modelling 

Two
important observations regarding αrecoil
have been made by Henderson et al, (2001) and Villemant and Feuillet (2003).
These authors have highlighted the fact that both ^{238}U and ^{234}U
decay to thorium isotopes, ^{234}Th with a halflife of 24 days
and ^{230}Th with a halflife of 75 ky, respectively. They have
also pointed out that αrecoil
damage accumulates with time and is directly related to the radioactive
decay of the parent nuclides. The αrecoil
damage to the mineral lattice from both αdecay
processes depends on the energy of the αrecoil
reactions which is determined for a given mineral by the nuclear reaction
characteristics, and is very similar for both nuclides. The similarity of
both ^{238}U and ^{234}U recoil processes allows them to
be coupled and Useries data can be modelled assuming that αrecoil
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 ^{230}Th,
the detrital correction 

The
Villemant and Feuillet, (2003) model can explain the scatter in Useries
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 ^{230}Th
but crucially assumes that the initial (^{234}U/^{238}U)
is known. (^{234}U/^{238}U) 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 porewater uranium
during early diagenesis can result in evolving (^{234}U/^{238}U).
Moreover, there are many other situations where (^{234}U/^{238}U)
is not known such as in marginal or hydrothermally affected sea areas. In
cases where equilibrium (^{234}U/^{238}U) from porewater
analysis is not available, (^{234}U/^{238}U) is actually
a free parameter. Figure 8 is a (^{234}U/^{238}U) vs
(^{234}U/^{238}U) diagram with five, nearly straight isochron
curves and four evolution curves for different degrees of opensystem behaviour
with the closedsystem curve indicated by f=1. Datapoints (black squares)
are for four carbonate samples from Lake Tswaing (Thorpe, et al., 2005).
Lake Tswaing is an intracontinental aquiferfed hypersaline closed lake
in a depression formed by a meteorite impact and the four datapoints define
an age of 165 ka, after correction for a small allogenic contribution. In
Figure 3 the datapoints plot near a 165 ka isochron for (^{234}U/^{238}U)=2.85
and then indicate ‘f’ values of 0.80.9 and negligible allogenic
230Th, inferred from a low (^{230}Th/^{234}U) initial value
at zero age. The distribution of datapoints along isotope ratio evolution
curves indicates that a small amount of ^{234}U loss, inferred from
an open system factor ‘f’ of within 15% of the closed system
value of unity still given valid Useries ages, as was also observed by
Villemant and Feuillet, (2003) for Quaternary marine terraces. The inferred
(^{234}U/^{238}U)=2.85 is within expectations for carbonate
that has precipitated from phreatic water that slowlypercolated through
an aquifer. 

Figure 3. (^{234}U/^{238}U)
vs (^{230}Th/^{234}U) diagram. Solid, nearly straight
curves are sochrons. Evolution curves for different degrees of opensystem
behaviour as indicated by the ‘f’ values, are broken lines with
the closedsystem solid curve indicated by f=1. Curves and isochrones are
calculated with the equations in Villemant and Feuillet (2003). The initial
value for (^{230}Th/^{234}U), indicating the allogenic contribution,
is very low; the initial value for (^{234}U/^{238}U) may
indicate the ambient ratio during precipitation but is essentially unconstrained. 

In
a situation where the equilibrium (^{234}U/^{238}U) can
be constrained either by assuming equilibrium with a seawater value or by
data from porewater analysis, an age can be calculated. Conversely, (^{234}U/^{238}U)
can be inferred with the Villemant and Feuillet (2003) model if the age
can be independently constrained. The (^{234}U/^{238}U) vs (^{230}Th/^{234}U) diagram can also be used to indicate an open system situation if datapoints plot 0.8>f>0 where f=0 indicates systematic ^{234}U and ^{238}U loss. Figure 9 is a (^{234}U/^{238}U) vs (^{230}Th/^{234}U) diagram similar to Figure 8 but the datapoints are from a section of finelylaminated lake sediments of Laguna Piuray, Peru (M. Burns and B. Aston, pers.com. 2005). The carbonate sediments are probably PostGlacial and became exposed when a moraine dam eroded. It can be concluded from the scattering of the datapoints over the diagram that exposure to rain and groundwater percolation resulted in extensive disruption to the Useries system. Datapoints 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, 1012 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
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December 23, 2011 11:36
