
Open University UraniumSeries Laboratory  
Earth and Environmental Sciences, The Open University, Milton Keynes, UK  
Mass
spectrometry 

The
development of chemical and mass spectrometric techniques for the measurement
of U, Th, Pa and Ra isotopes has provided an exciting new
approach to the understanding of many geological processes active over
the last 300,000 years. Analysis of ^{230}Th/^{232}Th
in authigenic minerals is relatively straightforward with the routine
use of ion counting and has been successfully performed since Edwards
et al., (1987) and Chen et al., (1990). Analysis of silicates has been
routine since the development of devices to improve the abundance sensitivity
of the mass spectrometers (van Calsteren & Schwieters, 1995). Techniques
use samples that may contain as little as a few ng of Th, and fg of Ra
(Cohen et al., 1992; McDermott et al., 1993; van Calsteren & Schwieters,
1995), and this has had a major impact in providing precise time scales.
Examples include studies of climate change (Edwards et al., 1987; Baker
et al., 1999; Stirling et al., 1995); McDermott et al., 1999) and of human
evolution (McDermott et al., 1993; Grün & McDermott, 1994). These
techniques also have considerable potential in hydrothermal and groundwater
systems (Osmond & Cowart, 1992), and they have had a major impact
on models for melt generation and magma differentiation processes on the
timescales of 1000s to 300,000 years (McKenzie, 1985; Lundstrom et al.,
1998; Cohen & O'Nions, 1993; Chabaux et al., 1999, 1994; Bourdon et
al., Nature; Huang et al., 1997; Elliott et al., 1997; Hawkesworth et
al., 1997; Heath et al., 1998). 

Methodology 

The law of radioactivity states that the number of atoms disintegrating per unit time is proportional to the number of radioactive atoms N. Thus dN/dt=λN where λis the proportionality or decay constant. On integration this becomes: N_{0}=Ne^{tλ}, where N_{0} is the number of radioactive parent isotopes at the time of the formation of the sample, N is the number present today and e is the base of the natural logarithm. The number of radiogenic isotopes N_{r} today plus the number of radioactive isotopes still present is equal to N_{0} and the equation above may be rewritten as: 

N_{r}=N(e^{t λ}1). 
Equation 1 

Halflife is defined as the time that is takes for N to become equal to N_{r} and is given by the equation: halflife=ln2/λ where ln2 is the natural logarithm of 2. Most radiogenic clocks that are of geological significance have a halflife of the order or millions or billions of years. 

The main advantage
of the Useries methods is that after about 5 halflifes of ^{230}Th,
the nuclide with the longest halflife, the system is in ‘secular
equilibrium’. This means that all nuclides in the chain decay at the
same rate and their ratios are the same as the ratios of their decay constants.
This can be expressed in terms of ‘activity’, the product of
the abundance and the decay constant of a nuclide, i.e.: A^{230}Th
=λ^{230}Th
x C^{230}Th, and in secular equilibrium all activities are equal
to 1. Useries data can be conveniently displayed on an ‘activity
diagram’ for instance (^{230}Th/^{232}Th) vs
(^{238}U/^{232}Th) and the brackets are used to distinguish
this diagram from an isotope ratio diagram. There is, of course, no difference
in principle, only in scaling, and this diagram is similar to an isochron
diagram where a straight line may have age significance. The isochron equation is 

Equation 2 

of a line on a (^{230}Th/^{232}Th) vs (^{238}U/^{232}Th) diagram representing an age T
Ages for authigenic minerals can be calculated for single samples on the assumption that all ^{230}Th has been produced by in situ decay of ^{234}U. Equation 2 was derived by Kaufman and Broecker (1965) 


Equation 3 

assuming
that all ^{230}Th is derived from is situ radioactive decay and
that neither Th nor U has been lost from the system. The equations cannot
be solved for T but by inserting a time estimate the equation can be solved
to any required degree of accuracy. The assumption that all ^{230}Th
is authigenic is rarely justified and it is common to assume that when
significant ^{232}Th is present in the system, a correction
has to be made based on an assumed ^{230}Th/^{232}Th ratio.
This assumed ^{230}Th/^{232}Th is usually taken to be
the ratio in silicate and is frequently referred to as the ‘detrital
correction’. Many other methods for detrital correction have been
investigated, including some chemical leaching techniques, but results
have been difficult to reproduce. 



Baker et al., 1999, Earth and Planetary Science
Letters 165, 157–162. 

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© Peter van Calsteren  Last
updated:
23 December, 2011 11:31
