An Overview of Isotope Geochemistry in Environmental Studies

Abstract

Isotopes of many elements have been used in terrestrial, atmospheric, and aqueous environmental studies, providing powerful tracers and rate monitors. Short-lived nuclides that can be used to measure time are continuously produced from nuclear reactions involving cosmic rays, both within the atmosphere and exposed surfaces, and from decay of long-lived isotopes. Nuclear activities have produced various isotopes that can be used as atmospheric and ocean circulation tracers. Production of radiogenic nuclides from decay of long-lived nuclides generates widespread distinctive isotopic compositions in rocks and soils that can be used to identify the sources of ores and trace water circulation patterns. Variations in isotope ratios are also generated as isotopes are fractionated between chemical species, and the extent of fractionation can be used to identify the specific chemical processes involved. A number of different techniques are used to separate and measure isotopes of interest depending upon the half-life of the isotopes, the ratios of the stable isotopes of the element, and the overall abundance of the isotopes available for analysis. Future progress in the field will follow developments in analytical instrumentation and in the creative exploitation of isotopic tools to new applications.

Appendices

Appendix 1: Decay Energies of Decay Series Isotopes

Table 2.7 Commonly measured isotopes of the ²³⁸U decay series data taken from Firestone and Shirley (1999)

Table 2.8 Commonly measured isotopes of the ²³⁵U decay series data taken from Firestone and Shirley (1999)

Table 2.9 Commonly measured isotopes of the ²³²Th decay series data taken from Firestone and Shirley (1999)

Appendix 2: Decay Series Systematics

Within a decay series, the evolution of the abundance of a daughter radioactive isotope is dependent upon its decay rate as well as production from its radioactive parent. Since the abundance of the parent is in turn dependent upon that of its parent, and so on up the decay chain, the systematics can become complicated, although for most applications simplifying circumstances can be found. The evolution of the abundances of isotopes within a decay series is described by the Bateman equations (see Bourdon et al. 2003 for derivations). For a decay series starting from the long-lived parent N₁ and ending with a stable isotope S,

$$ {{\hbox{N}}_1} \to {{\hbox{N}}_2} \to {{\hbox{N}}_3} \to {{\hbox{N}}_4} \to....{\hbox{S}}{.} $$

(2.13)

The long-lived parent evolves according to the basic decay equation:

$$ \left( {{{\hbox{N}}_1}} \right) = {\left( {{{\hbox{N}}_1}} \right)_0}{{\hbox{e}}^{ - {{\rm{\lambda }}_1}{\rm{t}}}}. $$

(2.14)

(N₁) is the activity, so that

$$ \left( {{{\hbox{N}}_1}} \right) = \frac{{{\text{d}}{{\text{N}}_1}}}{\hbox{dt}} = {{{\lambda }}_1}{{\hbox{N}}_1}. $$

(2.15)

The next two nuclides in the decay series evolves according to the equations

$$(N_2) =\frac {\lambda _2}{{\lambda _2} - {\lambda _1}} (N_1)_0 (e^{ -\lambda_1t} - {e^{ -\lambda_2t}}) + (N_2)_0{e^{ -\lambda_2t}}$$

(2.16)

$$ \begin{array}{c} N_3 = \frac{{\left( {N_1 } \right)_0 \lambda _2 \lambda _3 }}{{\lambda _2 - \lambda _1 }}\left( {\frac{{e^{ - \lambda _1 t} }} {{\left( {\lambda _2 - \lambda _1 } \right)\left( {\lambda _3 - \lambda _1 } \right)}} + \frac{{e^{ - \lambda _2 t} }} {{\left( {\lambda _1 - \lambda _2 } \right)\left( {\lambda _3 - \lambda _2} \right)}} + \frac{{e^{ - \lambda _3 t} }} {{\left( {\lambda _1 -\lambda _3 } \right)\left( {\lambda _2 - \lambda _3 } \right)}}}\right). + \frac{{\left( {N_2 } \right)_0 \lambda _3 }}{{\left( {\lambda _3 - \lambda _2 } \right)}}\left( {e^{ - \lambda _2 t} - e^{ - \lambda _3 t} } \right) \hfill \\ + \left( {N_3 } \right)_0 e^{ - \lambda _3 t}. \hfill \\\end{array} $$

(2.17)

The equations become increasingly complex, but are rarely necessary for environmental applications. Further, these equations can be greatly simplified under most circumstances.

• For all environmental timescales, the abundance of the long-lived parent (N₁) of the chain is constant, and ${{\hbox{e}}^{ - {{\rm{\lambda }}_1}{\rm{t}}}} \approx 1$. Further, ${{{\lambda }}_2} - {{{\lambda }}_1} \approx {{{\lambda }}_2}$ and ${{{\lambda }}_3} - {{{\lambda }}_1} \approx {{{\lambda }}_3}$.

• When a system has been closed for a long time, i.e. when ${{\hbox{e}}^{ - {{\rm{\lambda }}_2}{\rm{t}}}} \approx {{\hbox{e}}^{ - {{\rm{\lambda }}_3}{\rm{t}}}} \approx 0$, the above equations reduce to $\left( {{{\hbox{N}}_1}{{{\lambda }}_1}} \right) = \left( {{{\hbox{N}}_2}{{{\lambda }}_2}} \right) = \left( {{{\hbox{N}}_3}{{{\lambda }}_3}} \right)$, so that all the nuclides have the same activity as their parents, i.e. are in secular equilibrium, and the entire chain has the same activity as that of the long-lived parent. This is the state within very long-lived materials, such as unweathered rocks, and is the state all systems evolve towards when nuclides are redistributed.

• The activity of the daughter evolves towards secular equilibrium with its parent according to its half-life (and not that of the half life of its parent). This could be grow-in, where the daughter starts with a lower activity, or decay when the daughter starts with a higher activity; in either case it is the difference in the activities that declines at a rate determined by the half-life of the daughter. Therefore, the half-life of the daughter dictates the time-scale for which it is useful.

The linking of all the isotopes in the chain can lead to considerable complexity, since the parent concentration of each nuclide is changing, and so potentially the concentrations of the entire chain must be considered. However, for most applications, this can be greatly simplified by the following considerations:

• When a nuclide is isolated from its parent, then it becomes the head of the decay chain and simply decays away according to the decay equation (2.1); that is, it becomes the top of the chain. An example is ²¹⁰Pb, which is generated in the atmosphere from ²²²Rn and then transferred to sediments in fallout, where its activity simply diminishes according to (2.14) with a 22.3a half-life.

• Where the time scale of interest is short compared to the half-life of an isotope, the abundance of that isotope can be considered to be constant. In this case, this nuclide can be considered the head of the decay chain, and the influence of all nuclides higher in the decay series, can be ignored. For example, over periods of several 1,000 years, ²³⁰Th (t_1/2 = 75ka) remains essentially constant, while ²²⁶Ra (t_1/2 = 1.6ka) will grow into secular equilibrium according to (2.16).

• Where the time scale of interest is long compared to the half-life of an isotope, the activity of that isotope can be considered to be equal to that of the parent. For example, in a closed mineral, the ²²²Rn activity will be equal to that of parent ²²⁶Ra after several weeks, and so while the activity of ²¹⁰Pb will grow-in towards that of its parent ²²²Rn, this can be represented by measurements of ²²⁶Ra. Therefore, shorter-lived intermediate isotopes can be ignored.

• The most common circumstance when (2.17) is required is dating materials that have incorporated U from waters. Since the (²³⁴U/²³⁸U) ratio of waters is often above that of secular equilibrium, obtaining an age from the grow-in of ²³⁰Th requires considering the chain ${}^{238}{\hbox{U}} \to {}^{234}{\hbox{U}} \to {}^{230}{\hbox{Th}} \to$.