Chapter 9
U-series disequilibrium methods

In Section 2.4, we saw that the ²³⁵U-²⁰⁷Pb and ²³⁸U-²⁰⁶Pb decay series generally reach a state of secular equilibrium, in which the activity (expressed in decay events per unit time) of each intermediate daughter product is the same, so that:

as described by Equation 2.20. However, certain natural processes can disturb this equilibrium situation, such as chemical weathering, precipitation from a solution, (re-)crystallisation etc. The leads to two new types of chronometric systems:

1. An intermediate daughter isotope in the decay series is separated from its parent nuclide incorporated into a rock or sediment, and decays according to its own half life.
2. A parent nuclide has separated itself from its previous decay products and it takes some time for secular equilibrium to be re-established.

This idea is most frequently applied to the ²³⁸U-decay series, notably ²³⁰Th and ²³⁴U. The first type of disequilibrium dating forms the basis of the ²³⁴U-²³⁸U and ²³⁰Th methods (Sections 9.1 and 9.2). The second forms the basis of the ²³⁰Th-²³⁸U method (Section 9.3)

9.1 The ²³⁴U-²³⁸U method

The activity ratio of ²³⁸U to its third radioactive daughter ²³⁴U in the world’s oceans is A(²³⁴U)∕A(²³⁸U) ≡ γ_∘ ≈ 1.15. The slight enrichment of the ²³⁴U over ²³⁸U is attributed to α-recoil of its immediate parent ²³⁴Th and the fact that ²³⁴U is more ‘loosely bound’ inside the crystal lattice of the host mineral, because it is preferentially seated in sites which have undergone radiation damage. Once the oceanic U is incorporated into the crystal structure of marine carbonates, the radioactive equilibrium gradually restores itself with time. The total activity of ²³⁴U is made up of a component which is supported by secular equilibrium (and equals the activity of ²³⁸U) and an ‘excess’ component, which decays with time:

(9.1)

where A(²³⁴U)_∘^x is the initial amount of excess ²³⁴U and λ₂₃₄ = 2.8234 × 10^-6 yr^-1 (t_1∕2 = 245.5 kyr). Let A(²³⁴U)_∘ be the initial total ²³⁴U activity. Then:

(9.2)

Dividing by A(²³⁸U):

(9.3)

Which can be solved for t until about 1 Ma.

9.2 The ²³⁰Th method

U and Th are strongly incompatible elements. This causes chemical fractionation and disturbs the secular equilibrium of the ²³⁸U decay series in young volcanic rocks. It is commonly found that the activity ratio A(²³⁰Th)∕A(²³⁸U) > 1. As expected, the secular equilibrium between ²³⁴U and ²³⁸U is not disturbed by chemical fractionation, so that A(²³⁴U)∕A(²³⁸U) = 1. The total ²³⁰Th activity is given by:

(9.4)

where A(²³⁰Th)_∘^x is the initial amount of ‘excess’ ²³⁰Th at the time of crystallisation and A(²³⁸U) = A(²³⁴U) due to secular equilibrium of the U isotopes. Thus, the first term of Equation 9.4 increases with time from 0 to A(²³⁸U) while the second term decreases from A(²³⁰Th)_∘^x to 0. Dividing by A(²³²Th) yields a linear relationship between A(²³⁰Th)∕A(²³²Th) and A(²³⁸U)∕A(²³²Th):

(9.5)

This forms an isochron with slope (1 - e^{-λ₂₃₀t}), from which the age t can be calculated. This method is applicable to volcanic rocks and pelitic ocean sediments ranging from 3ka to 1Ma.

9.3 The ²³⁰Th-²³⁸U method

Uranium is significantly more soluble in water than Th. As a result, the intermediate daughter ²³⁰Th is largely absent from sea water. Thus, lacustrine and marine carbonate rocks contain some U but virtually no Th at the time of formation. The ²³⁰Th activity increases steadily with time as a result of ²³⁴U decay. The total ²³⁰Th activity consists of a growing component A(²³⁰Th)^s that is in secular equilibrium with ²³⁸U and a shrinking component A(²³⁰Th)^x of ‘excess’ ²³⁰Th produced by the surplus of ²³⁴U commonly found in ocean water (see section 9.1):

	A(230Th) = A(230Th)s + A(230Th)x	(9.6)
with:	A(230Th)s = A(238U)(1 - e-λ230t)	(9.7)
and:	A(230Th)x = A(234U) ∘x	(9.8)

In which the expression for A(²³⁰Th)^x follows from Equation 2.14 and A(²³⁴U)_∘^x denotes the initial amount of excess ²³⁴U activity (as in Section 9.1). Taking into account that A(²³⁴U)_∘^x = A(²³⁴U)_∘- A(²³⁸U), and dividing by A(²³⁸U), we obtain:

(9.9)

in which γ_∘≡ A(²³⁴U)∕A(²³⁸U) as defined in Section 9.1. The formation age of the carbonate can be calculated by substituting Equations 9.7 and 9.9 into 9.6 and solving for t.

(9.10)

If γ_∘ = 1 (i.e., the water is in secular equilibrium for U), then Equation 9.6 simplifies to:

(9.11)

If γ_∘≠0, Equation 9.11 yields ages that are systematically too old, unless t < 100ka and γ_∘≤ 1.15.