Applied Geochemistry 26 (2011) S20–S23
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Applied Geochemistry
journal homepage: www.elsevier.com/locate/apgeochem
Determination of chemical weathering rates from U series nuclides in soils
and weathering profiles: Principles, applications and limitations
François Chabaux a,⇑, Lin Ma b,1, Peter Stille a, Eric Pelt a, Mathieu Granet a, Damien Lemarchand a,
Raphael di Chiara Roupert a, Susan L. Brantley b
a
b
Université de Strasbourg and CNRS, Laboratoire d’Hydrologie et de Géochimie de Strasbourg, EOST, 1 rue Blessig, 67084 Strasbourg Cedex, France
Earth and Environmental Systems Institute, Pennsylvania State University, University Park, PA 16802, USA
a r t i c l e
i n f o
Article history:
Available online 22 March 2011
a b s t r a c t
The development of U-series nuclides for investigating weathering processes has been significantly stimulated by the analytical improvement made over the last decades in measuring the 238U series with intermediate half-lives (i.e., 234U–230Th–226Ra). It is proposed in this paper to present principles and methods
that are now being developed to determine weathering rates from the study of U-series nuclides in soils
and weathering profiles. Mathematical approaches, developed to calculate such rates, are based on some
implicit assumptions that are also presented and must be kept in mind if one wants to correctly interpret
the obtained ages.
Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction
By the 1960s it was recognized that U-series nuclides have great
potential for study of weathering processes and rates (Rosholt
et al., 1966; Hansen and Stout, 1968). This is because the nuclides
are fractionated during water–rock interaction and have radioactive decay half-lives of the same order of magnitude as the time
constants of many weathering processes (e.g. Ivanovich and Harmon, 1992; Chabaux et al., 2003a, 2008). Recent developments in
this field of research are clearly related to the analytical improvements made during the past decades in measuring 238U series nuclides with intermediate half-lives (i.e., 234U–230Th–226Ra) (e.g., in
Bourdon et al., 2003). In contrast to cosmogenic nuclides, or the
U–Th/He chronometer, which provide information on denudation
rates, U-series nuclides in soils relate directly to production rates
of regolith (soils, weathering profiles). Applying both types of chronometers to the same weathering system should allow significant
progress in understanding the coupling between weathering and
erosion processes (Ma et al., 2010). In this paper principles and
methods that are now being developed to determine weathering
rates from the study of U-series nuclides in soils and weathering
profiles are presented, and some of their limitations discussed.
⇑ Corresponding author. Tel.: +33 3 6885 0406.
E-mail address: [email protected] (F. Chabaux).
Present address: Department of Geological Sciences, University of Texas at El
Paso, El Paso, TX 79968, USA.
1
0883-2927/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.apgeochem.2011.03.019
2. Fractionation among U-series nuclides in soils and
weathering profiles
Determining weathering front propagation rates in regolith
with U-series nuclides is based on the assumption that fractionation among nuclides from the same radioactive decay series is
controlled by weathering processes. The earliest studies showed
that U-series disequilibrium across a weathering profile cannot often be described by a simple scheme in which fractionation occurs
at the base of the profile and the U–Th system subsequently returns to secular equilibrium in the overlying horizons (e.g., Rosholt
et al., 1966; Boulad et al., 1977; Rosholt, 1982; Mathieu et al.,
1995; Dequincey et al., 1999). One example of a system with such
simple behavior is a basaltic clast from an alluvial terrace in Costa
Rica (Pelt et al., 2008). In that system, U–Th were fractionated at
the transition between the fresh basalt and the weathering rind
(marked by an U enrichment) and no further fractionation occurred within the rind itself. All other studies show that U–Th
fractionations extend into weathering profiles above the base of
the regolith (Dequincey et al., 2002; Dosseto et al., 2008; Blaes
et al., 2009; Ma et al., 2010).
Interpreting (and hence modeling) U–Th disequilibria in weathering profiles, therefore, requires a complete understanding of the
fractionation of U–Th and the relevant daughter isotopes. Such
information can be retrieved by the comparison of U-series data
with mineralogical and/or other geochemical data (major and trace
element concentrations, Sr isotope ratios, etc.) (Dequincey et al.,
2002; Chabaux et al., 2003a; Pelt et al., 2008; Ma et al., 2010; Blaes
et al., 2009). These studies show that, in contrast to earlier assumptions, U–Th fractionation in weathering profiles cannot only be
F. Chabaux et al. / Applied Geochemistry 26 (2011) S20–S23
described in terms of U leaching/loss processes but also by U gain.
Such scenarios involving gain and loss of U easily explain, for instance, the occurrence of (234U/238U) activity ratios > 1 with
(230Th/238U) ratios < 1 within the same regolith sample, which is
otherwise hard to reconcile with simple U leaching (Chabaux
et al., 2008). Several of these studies have also shown that Th, often
supposed to be immobile during weathering, can be mobilized
(e.g., Ma et al., 2010; Chabaux et al., 2008). Analogous to U, Th
mobilization can occur by Th complexation with inorganic (phosphates, fluorides, Fe-Al oxy-hydroxides) and organic (humic, fulvic
acids) ligands and more generally by Th adsorption on colloidal soil
phases including clays. The modeling of U-Th fractionation in soil
and weathering profiles can, therefore, no longer be solely explained by U gain and loss processes, but must also involves Th
mobility.
The enrichment of U and probably of Th in soils might have
multiple origins. In the African (Kaya) lateritic toposequence, U–
Th disequilibrium in the saprolite can be related to the downward
migration of U originating from the breakdown of the uppermost
iron cap; in this case the U enrichments in specific soil levels result
from local redistributions of U within the regolith profile (Dequincey et al., 2002, 2006; Chabaux et al., 2003b). This is also illustrated
in the U–Th study of the Shale Hill Critical Zone observatory in
Pennsylvania (Ma et al., 2010). Uranium-enrichments recorded in
those profiles/toposequences thus do not require any external
(e.g., atmospheric) contribution. This is consistent with studies
suggesting that the impact of atmospheric U input onto the U river
budget is generally negligible (Riotte and Chabaux, 1999; Chabaux
et al., 2005). Nevertheless, the generalization of such a conclusion
is probably not justified. Pett-Ridge et al. (2007) have shown that
dry deposition contributes significantly to the U budget of Hawaiian soils. Similarly, isotope ratios in two basaltic soil profiles developed on Mount Cameroun point to an African eolian dust
contribution of about 10% in the U and Th budget (Pelt, 2007). Future studies, including the analysis of atmospheric deposits along
with soil toposequences, are needed to constrain the contribution
of atmospheric deposits to the U and Th budgets of soils and
weathering profiles.
3. Modeling U-series nuclides mobility within weathering
profiles
Interpretation of the U-series radioactive disequilibria within
soils and weathering profiles requires understanding migration
mechanisms of U-series nuclides during loss or gain of the radionuclides. The mathematical formalism of this dual process is obviously not unique. However, given the nature of the soil formation
processes and the radioactive decay of the nuclides, these data can
often be interpreted in terms of continuous processes (e.g., Dequincey et al., 2002). Moreover, given the limited knowledge of the precise mechanisms controlling the mobility of these nuclides within
weathering profiles, it seems premature to model these processes
by overly complex mechanistic laws. Therefore, simple mathematic models are used where the loss processes are represented
by first-order and the gain processes by zero-order kinetic rate
laws. The general equations controlling these dual processes are given below for the parental nuclide p and an intermediary nuclide i
of a radioactive decay series:
p
dN
¼ F p kp Np kp Np
dt
i
dN
¼ F i ki Ni ki Ni þ ki1 Ni1
dt
ð1Þ
ð2Þ
where Ni and NP represents the number of nuclides i and p respectively, ki (kp) is the decay constant of nuclide i (or p), ki and kp are
S21
the first-order rate constants describing the loss of nuclides i and
p, and Fi (Fp) is the input flux of nuclide i (p) gained by the regolith
sample (i 1 is the parent nuclide of nuclide i).
Such equations have been applied in all recent studies to calculate regolith formation rates from 238U–234U–230Th disequilibria
(Dosseto et al., 2008; Pelt et al., 2008; Ma et al., 2010; Blaes
et al., 2009), and also, in some studies, to estimate the transfer time
of sediments in an alluvial plain (Granet et al., 2007, 2010). They
can be generalized for any other nuclide of the 238U-series, especially for 226Ra (Blaes et al., 2009), or the short half-life nuclides
from the 232Th series.
4. Solutions to the mathematical equations
Usually the determination of a production rate from U-series
disequilibrium in soils and weathering profiles relies on simplistic
reasoning: it is assumed that weathering advances into underlying
protolith in one direction, and samples collected along this direction are «dated» by U–Th disequilibrium chronometry (the age of
the sample corresponds to the time when the sample became part
of the weathering zone). Age variations along the weathering
direction can then be used to determine the mean production rate
of the regolith (i.e., the weathering advance rate). In most of the
studies, it has been implicitly supposed that the principal weathering direction is vertical, and hence the production rate of a profile
is determined by using age variations of soil samples from the base
to the top of the profile. Usually, for such calculations the weathering advance rate is assumed to be constant in time along the
weathering direction, which in turn implies the weathering to be
isovolumetric (see also discussion in Ma et al. (2010)).
Generally speaking, the weathering parameters in the above
equations (leaching and input parameters) are not known, and
the measurement of radioactive disequilibrium of a single soil
sample is not sufficient for the determination of its age. For instance, in the case of the 238U–234U–230Th chronometry, the three
associated equations contain six unknown parameters (leaching
and gain parameters) and one variable (time). The analysis of
238
U–234U–230Th disequilibrium in one sample yields only two
independent data [(234U/238U) and (230Th/234U) activity ratios],
which are not enough to determine the age of the sample.
A first approach to solve the equations and to obtain ages of the
soil samples and hence the production rate of the regolith is to consider the model parameters to be constant in the whole or in parts
of the weathering profile (e.g. the Shale Hill study; Ma et al., 2010).
In this case, the determination of the weathering rate necessitates
the determination of the 238U–234U–230Th disequilibria in only four
samples collected at different depths from a weathering profile.
The sample number necessary for modeling decreases if other constraints can be introduced in the model: e.g., Th immobility during
weathering, as reported for instance in the case of a lateritic profile
in central Amazonia (Manaus, Brazil) (Pelt, 2007), reduces the
parameter number to 4 (mobility coefficients) and allows the
determination of weathering rates from 238U–234U–230Th analysis
of only three samples. For the weathering rind of the basaltic clast
from the Costa Rica Terrace (Pelt et al., 2008), the analysis of only
two rind sub-samples would be sufficient in theory to determine
the rind formation rate since the U and Th isotopes were thought
to be immobile. In all of those cases, zones within the weathering
profiles were identified where the nuclide mobility parameters
were constant: in other words, more than the required minimum
number of samples were analyzed and the isotopic variations were
consistent with the trends predicted by the model.
If there is no zone with constant mobility parameters, the above
equation system is under-constrained. The age calculation of a soil
sample is in this case only possible using an ‘‘inverse method’’,
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F. Chabaux et al. / Applied Geochemistry 26 (2011) S20–S23
which necessitates a priori assumptions of model parameters. Solving the model equations involves an iterative procedure until convergence, at which point the solution yields a set of parameter
values that satisfy the equations. Today, inverse methods often involve Monte Carlo randomized algorithms, which, with sensitivity
analysis, help pinpoint the parameters that are the most influential
in the model (Fajraoui et al., 2011). To the authors’ knowledge, inverse approaches have been rarely involved for the determination
of weathering rates in soils. In a first attempt, it was applied in the
U–Th study of the African Kaya lateritic profile (Chabaux et al.,
2003b). This approach yielded time information about U redistribution after the breakdown of the iron cap in this weathering profile and revealed information relating U migration to climatic
changes during the Quaternary.
5. Limits in the models
The weathering rates obtained from the U-series nuclides
clearly depend on the model parameters; this is common in modeling and does not diminish the interest of the method. It only
means that before using the model, its applicability to the studied
case has to be verified/validated.
For instance, the kinetic laws used in the model equations for
describing the radionuclide leaching (kN terms in Eqs. (1) and
(2), with k leaching kinetic constant of the nuclide N from the sample) implies that all the nuclides of the analyzed sample are mobile. When a fraction (aim) of a nuclide N is not mobilizable, the
kinetic law to be utilized should be: k⁄N with k⁄ = k0 (1 aim).
Similarly, if the nuclide N is carried by different mineral phases,
each characterized by a specific leaching coefficient (the classical
case of differential weathering), then the mean leaching coefficient
used in Eqs. (1) and (2) should be written as follows: k⁄ = R[kiai],
with ki the leaching coefficient of the nuclide N out of the mineral
i and ai the fraction of the nuclide N of the whole sample contained
in the mineral i. In this case, except in some specific conditions, the
mean k⁄ leaching coefficient of the nuclide N in the whole sample
cannot be considered as constant over time. The consequence for
such a weathering system is that the results derived from model
equations, which assume the leaching coefficients to be constant
over a part of the profile, have to be used with caution, i.e. not applied without validation.
Another point that has to be considered is the way to describe
the ejection of a radioactive series nuclide from the solid grain
due to alpha recoil. During an alpha radioactive decay, the nuclide
recoil can be sufficient to induce an ejection of the daughter nuclide into solution (Kigoshi, 1971; Fleischer, 1988 and ref. therein),
which occurs in addition to direct leaching of the nuclide from the
rock. The content of an intermediary nuclide i of a radioactive decay series in a dissolving solid thus depends both on leaching and
recoil alpha ejection whose intensity is proportional to the amount
of the parent nuclide i 1. The content of any intermediary nuclide
of a radioactive series in a dissolving solid is, therefore, described
by the equation:
dNi
¼ ki Ni ki Ni þ ki1 ð1 fa ÞNi1
dt
ð3Þ
with fa being the a-recoil loss fraction. This value is a function of the
grain radius and the surface area, and ki is the leaching coefficient of
the nuclide Ni (the leaching process again approximated by first-order kinetic laws). From a mathematical point of view, this equation
is not equivalent to the equation given in (2). This would only be the
case if the ejection by alpha recoil were negligible compared to
mobilization by leaching, or if the parent – daughter system remained close to secular equilibrium (i.e., kiNi ki1Ni1).
In conclusion, it is important to stress here that within the
discussed limitations the mathematical approach developed to
calculate weathering rates is based on some implicit model
assumptions. These must be kept in mind and validated if one
wants to correctly interpret the obtained ages. Further studies on
physical–chemical parameters controlling absorption, desorption,
complexation, etc. are needed in order to better constrain the processes and hence the models, controlling the mobility of radionuclides in the environment.
Acknowledgments
REALISE (Réseau Alsace de Laboratoires en Ingénierie et Sciences pour l’Environnement) and the Region of Alsace, France are
thanked for their financial support to the Strasbourg group. SLB
and LM acknowledge support from Department of Energy (DOE)
grant DE-FG02-05ER15675.
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