12.4 Daughter deficiency methods

12.4.1 ²³⁰Th: theory

The tendency described above for adsorption of thorium onto clay minerals leads to low Th levels in groundwaters, in contrast to their moderate U levels. Thus, when biogenic or authigenic calcite is formed, it tends to contain appreciable U concentrations (a few ppm) but negligible Th. This leads to a situation where ²³⁰Th is strongly deficient relative to its parent, ²³⁴U. The subsequent regeneration of ²³⁰Th can then be used as a dating tool.

The first application of this ‘²³⁰Th deficiency’ technique was made as early as 1926 by Khlapin, who used short-lived ²²⁶Ra as a measure of ²³⁰Th activity. Khlapin (1926) assumed that the ²³⁴U parent taken up by calcite was itself in secular equilibrium with ²³⁸U, and that Th uptake was negligible. Under these conditions, we can treat ²³⁰Th production from ²³⁴U as if it were derived directly from ²³⁸U. To calculate the net ²³⁰Th accumulation, we must then subtract the fraction which has decayed to ²²⁶Ra. Substituting into the relevant Bateman equation [1.13], the abundance (not activity) of ²³⁰Th after time t is given as follows:

8₂₃₈

n²³⁰Th = ))))))) @ n²³⁸U_I (e^{!8238 t} ! e^{!8230 t}) [12.21]

8₂₃₀ ! 8₂₃₈

where I signifies the initial ratio. But these abundances are easily converted into activities by dividing by the relevant decay constants:

²³⁰Th 8₂₃₈ ²³⁸U_I

)))) = ))))))) @ )))) (e^{!8238 t} ! e^{!8230 t}) [12.22]

8₂₃₀ 8₂₃₀ ! 8₂₃₈ 8₂₃₈

Now on cancelling 8₂₃₈ and multiplying both sides by 8₂₃₀ we obtain:

8₂₃₀

²³⁰Th = ))))))) @ ²³⁸U_I (e^{!8238 t} ! e^{!8230 t}) [12.23]

8₂₃₀ ! 8₂₃₈

However, because of the very long half-life of ²³⁸U relative to the other species, its activity is effectively constant over time. Therefore initial ²³⁸U activity can be approximated by ²³⁸U, e^{!8238 t} is approximately 1 and 8₂₃₀!8₂₃₈ is approximately 8₂₃₀, which then cancels to yield:

²³⁰Th = ²³⁸U (1 ! e^{!8230 t}) [12.24]

Finally, dividing through by ²³⁸U activity yields the decay equation which can be used for dating:

²³⁰Th

)))) = 1 ! e^{!8230 t} [12.25]

²³⁸U

However, it was noted above that ²³⁴U and ²³⁸U activities in natural waters are very rarely in secular equilibrium. This introduces a complication into the decay equation, since there is an extra contribution to ²³⁰Th activity by excess ²³⁴U, until the latter has decayed away. ²³⁰Th production by excess ²³⁴U (X) is given by an equation analogous to [12.23]:

8₂₃₀

²³⁰Th_X = ))))))) @ ²³⁴U_I^X (e^{!8234 t} ! e^{!8230 t}) [12.26]

8₂₃₀ ! 8₂₃₄

But excess ²³⁴U activities can only conveniently be measured as a ratio against ²³⁸U. Therefore we divide both sides of equation [12.26] by ²³⁸U activity. This is effectively constant over time, due to its long half-life, so that present and initial ²³⁸U activities are interchangeable:

(²³⁰Th)^X 8₂₃₀ (²³⁴U)^X

())))) = ))))))) @ ()))) (e^{!8234 t} ! e^{!8230 t}) [12.27]

(²³⁸U ) 8₂₃₀ ! 8₂₃₄ (²³⁸U)_I

But the excess activity ratio is equal to the total activity ratio minus one (corresponding to secular equilibrium). So:

(²³⁰Th)^X 8₂₃₀ | (²³⁴U) |

())))) = )))))) @ | ()))) ! 1 | @ (e^{!8234 t} ! e^{!8230 t}) [12.28]

(²³⁸U ) 8₂₃₀ ! 8₂₃₄ | (²³⁸U)_I |

We can substitute equation [12.6] into this equation in order to convert initial ²³⁴U/²³⁸U activities to the present day measured activities (P):

(²³⁰Th)^X 8₂₃₀ | (²³⁴U) | (e^{!8234 t} ! e^{!8230 t})

())))) = )))))) @ | ()))) ! 1 | @ ))))))))))) [12.29]

(²³⁸U ) 8₂₃₀ ! 8₂₃₄ | (²³⁸U)_P | e^{!8234 t}

But the final term simplifies to yield:

(²³⁰Th)^X 8₂₃₀ | (²³⁴U) |

())))) = )))))) @ | ()))) ! 1 | @ (1 ! e^{!(8230 ! 8234) t}) [12.30]

(²³⁸U ) 8₂₃₀ ! 8₂₃₄ | (²³⁸U)_P |

Finally, on adding the ²³⁰Th production from equilibrium and excess ²³⁴U, (equations [12.25] and [12.30]), we obtain:

²³⁰Th [12.31]

)))) = 1 ! e^{!8230 t}

²³⁸U

8₂₃₀ | ²³⁴U |

+ )))))) @ | ))) ! 1 | @ (1 ! e^{!(8230 ! 8234) t})

8₂₃₀ ! 8₂₃₄ | ²³⁸U |

This equation could be used directly to solve ages, but it has become normal procedure to rearrange it by multiplying through by ²³⁸U/²³⁴U. This yields:

[12.32]

²³⁰Th 1 ! e^{!8230 t}

)))) = )))))))

²³⁴U ²³⁴U/²³⁸U

8₂₃₀ | 1 |

+ )))))) @ | 1 ! )))))) | @ (1 ! e^{!(8230 ! 8234) t})

8₂₃₀ ! 8₂₃₄ | ²³⁴U/²³⁸U |

This equation was plotted as an isochron diagram (Fig. 12.20) by Kaufman and Broecker (1965). Effectively, the calibration line for ²³⁴U/²³⁸U activity = 1 (secular equilibrium) yields the age in terms of ²³⁰Th build-up, while the near-vertical isochron lines apply the correction for non-equilibrium U isotope compositions. As can be seen on the diagram, this correction is unnecessary for samples less than ca. 30 kyr old. The maximum dating range of the ²³⁰Th method is ca. 300 kyr by " counting, but this may be extended to over 400 kyr by mass spectrometry.

Fig. 12.20. Th)U isochron diagram for systems containing no ²³²Th. Labelled, steeply-dipping lines are isochrons; lateral lines are growth lines. Error bar shows typical uncertainty for " spectrometry. After Kaufman and Broecker (1965).

12.4.2 ²³⁰Th: applications

The ²³⁰Th)²³⁴U method is applicable to the dating of any closed-system carbonate which is free from contamination by initial detrital thorium. It can provide far better precision for coral dating than the ²³⁴U)²³⁸U method alone. This is illustrated in Fig. 12.21 by a compilation of high-precision " spectrometry data for un-recrystallised corals (Veeh and Burnett, 1982). It can be seen that typical measurement errors in ²³⁴U/²³⁸U ratio lead to age uncertainties of over 100%, whereas errors in ²³⁰Th/²³⁴U lead to age errors of only 10%.

Fig. 12.21. Plot of ²³⁴U/²³⁸U versus ²³⁰Th/²³⁴U activity ratio for un-recrystallised coral data with 2F errors better than 5% . Heavy near-horizontal curve shows the decay path starting from present-day seawater. Vertical lines are isochrons. After Veeh and Burnett (1982).

The precision of ²³⁰Th coral dating has been further enhanced by the mass spectrometric method, as demonstrated by the analysis of live reef-forming corals from the Vanuatu arc, east of Australia (Edwards et al., 1988). In these specimens, ²³⁰Th ages were compared with historical ages based on yearly growth bands. The latter are about 1 cm wide, and can be accurately counted in specimens at least 200 years old. ²³⁰Th ages were determined with errors as low as " 3 yr (2F), and were in excellent agreement with the historical age of the corals (Fig. 12.22). ²³⁰Th dating of corals between 9000 and 40 000 yr old has been used very effectively to calibrate the radiocarbon time-scale (section 14.1.5).

Fig. 12.22. Comparison of mass spectrometric ²³⁰Th ages of living corals with historical ages based on annual growth bands. After Edwards et al. (1988).

One of the most important applications of ²³⁰Th dating is in the study of Pleistocene (Quaternary age) climatic variations associated with glacial cycles. These cycles caused periodic variations in the global ice mass at the expense of seawater, and therefore left two types of record. The first is the direct variation of sea-level through time, while the second is an indirect record of sea-level variations, due to the fractionation of oxygen isotopes as large amounts of seawater were converted into ice. These oxygen isotope variations can be seen in marine and terrestrial carbonate deposits, as well as in ice records. The ²³⁰Th (daughter deficiency) method can be used to date both of these climatic records: direct sea-level variations, and oxygen isotope variations recorded in terrestrial carbonates. These dates can then be used to test the third main record of Quaternary climatic variation, the so-called SPECMAP record of marine oxygen isotope variations.

The SPECMAP model (Imbrie et al., 1984) attributes Pleistocene glacial cycles, recorded as the oxygen isotope variations in marine forams, to variations in the intensity of solar radiation. This is based on the theory of Milankovitch (1941), who suggested that changes in Pleistocene climate were largely due to changes of ‘insolation’ in the northern hemisphere, caused by variations in the Earth’s orbit. Because the Earth’s orbital variations can be precisely calculated and projected back in time, it is possible to model insolation variations back though several million years. Then, if the Milankovitch theory is correct, these orbital variations can be used to ‘tune’ the climatic record of oxygen isotope variations in order to date glacial cycles precisely (termed ‘Milankovitch forcing’).

Reef-building corals provide a useful record of past sea-level variations, because sea-level highs during interglacial periods become marked by coral terraces which are stranded when sea-level falls again. In general there is a good correlation between sea-level highs and northern hemisphere insolation, providing support for the Milankovitch theory. However, " counting dates revealed inconsistencies at the beginning of the last interglacial (marked by high sea-level stage 5e in the stable isotope record). Ages for this sea-level stand spread over a very large range, from 120 to 140 kyr, causing it to be divided into two sub-parts. However, this uncertainty was partly due to the large size of the error bars on " counting ages, which were almost of equal magnitude to the duration of glacial cycles.

This problem is illustrated in Fig. 12.23 by comparing " spectrometry dates with the calculated insolation curve at the time of the last interglacial (stage 5e). A 129 kyr coral terrace date is correctly centred on the insolation high, corresponding to an interglacial. However, two other " counting dates on coral terraces, from the Huon Peninsula of Papua New Guinea (Bloom et al., 1974), were situated between two insolation highs, on the intervening insolation low. Mass spectrometic dates on the same samples were in all three cases within 2F error of the " counting determinations, but are now centred unequivocally on the insolation high at 127 kyr (Edwards et al., 1987).

Fig. 12.23. Plot of solar insolation against time, to compare the duration of glacial cycles with analytical uncertainties for mass spectrometric and " counting U-series ages. Dates shown are for coral terraces from the last interglacial (oxygen isotope stage 5e). After Edwards et al. (1987).

Another approach for constraining Pleistocene sea-level variations is ²³⁰Th dating of speleothems (stalactites, stalagmites etc.) from submarine caves. These formations grow during periods of low sea-level stand, when they are exposed sub-aerially to percolating calcareous solutions. When sea-level rises and they become drowned, growth stops, and an erosional hiatus occurrs. The densely crystalline form of speleothem deposits is conducive to good closed-system behaviour, so this material is ideal for U-series dating. Therefore, drowned speleothem and coral terraces form a complementary couple for Pleistocene sea-level studies. The first mass spectrometric dating study on such material was made by Li et al. (1989) on a sample from 12 m depth in a Bahamas ‘blue hole’. A detailed sequence of U-series age determinations on the 12 cm-thick flowstone showed that carbonate deposition had occurred over a period of 280 kyr (Fig. 12.24). Within this period, there were four internal hiatuses corresponding to sea-level stands above !12 m (relative to present-day sea-level). These data supported the orbitally tuned SPECMAP record in suggesting that the last interglacial began after 140 kyr ago.

Fig. 12.24. Pleistocene sea-level curve for the Bahamas (dashed lines), based on U-series ages on drowned speleothems. ( ! ) = mass spectrometric data. ( Q, € ) = speleothem and coral terrace ages by " spectrometry. After Li et al. (1989).

Winograd (1990) challenged this evidence on the grounds of apparent conflict with the older "-counting ages from coral terraces (Bloom et al., 1974). However, Lundberg et al. (1990) showed that, if careful attention is paid to the quoted analytical error limits of the " counting and mass spectrometric data, then there is no conflict between the speleothem and coral ages. In other words, the " counting ages on coral terraces are consistent with sea-level rise after 140 kyr when their large error bars are taken into account. In this connection, it is important to remember that the 1F error limits traditionally quoted for " spectrometry correspond to only 68% confidence that the ‘true’ age is within the quoted limits. Therefore, all such error limits should be doubled to generate (more realistic) 2F error limits (95% confidence), which is the accepted practice in other fields of isotopic dating.

Speleothems can also be used as inventories of past atmospheric oxygen isotope variations, which are also linked to glacial cycles. These records are well suited to dating by the ²³⁰Th (daughter deficiency) method. Hence, climatic variations can be dated by measuring *¹⁸O signatures and U-series ages on the same cave deposits. For example, Winograd et al. (1992) made a combined U-series and stable-isotope study on the calcite lining of a water-filled cavern in Nevada (USA) called Devils Hole. The results of this study suggested similar glacial cycles to the SPECMAP oceanic record, but, like the data of Bloom et al. (1974), the warming trend associated with the last interglacial (at around 140 kyr) appeared to precede the increase in solar insolation which should have driven this warming (Fig. 12.25). This led Winograd et al. to question the SPECMAP model.

Fig. 12.25. Comparison of various lines of evidence for the onset of the last interglacial, based on Devils Hole, Northern Hemisphere insolation, and the SPECMAP oxygen isotope record. After Zhao et al. (2001).

In response to these difficulties, numerous explanations have been proposed. One possibility was that the Devils Hole age measurements were biased by a breakdown in the dating assumptions. For example, Edwards and Gallup (1993) suggested that the incorporation of unusually large amounts of initial ²³⁰Th from the water reservoir in the Devils Hole fracture system could bias the ages in an unforseen manner. However, this possibility was excluded by additional dating work (Edwards et al., 1997), which demonstrated concordance between ²³⁰Th and ²³¹Pa ages for two Devils Hole calcites.

Another suggestion (Imbrie et al., 1993), was that the mis-match between the Devils Hole and SPECMAP chronologies was caused by a more complex relationship between *¹⁸O and paleoclimate in continental groundwater tan in seawater. This suggestion prompted new dating measurements on the Huon Peninsula coral terraces which first began this debate. The new data (Esat et al. 1999) suggested that the main peak of high stand VII occurred 130 kyr ago, but that an earlier but probably smaller sea-level rise occurred beginning around 140 kyr ago. Because this earlier sea-level rise was lower, it was not recorded in the Bahamas blue hole stalagmite at –12 m depth (Fig. 12.24), and the two records are therefore not in contradiction. The Devils Hole signal apparently records the earlier event, but this was followed by a glacial re-advance similar to the Younger Dryas event of the last deglaciation (13 kyr ago). Subsequently, deglaciation resumed, with the beginning of the last interglacial (sensu stricto) around 130 kyr ago.

This work was confirmed by more detailed sampling of coral terraces from Barbados (Gallup et al., 2002). The occurrence of sea-level rise in two stages with a retreat in between suggests that this warming event was quite complex, possibly with more than one orbital forcing mechanism. This may therefore explain the difficulty in accurately modelling the causes of glacial advance and retreat, as discussed by Karner and Muller (2000).

12.4.3 ²³⁰Th: dirty calcite

Because fossil bones may be encased by subsequent tufa deposits, U-series analysis of such material has been very useful for dating Pleistocene human and animal remains (e.g. Schwarcz and Blackwell, 1991). However, the most interesting tufas are often impure, for the very reason that if they contain bones they will probably contain other detrital material. This introduces initial ²³⁰Th, which if not corrected for, may cause serious errors in calculated ages.

In cases where detrital contamination is minor, the same laboratory technique may be used as for clean material: the sample is leached with dilute nitric acid in an attempt to dissolve the carbonate fraction without disturbing the detrital component. This may diminish the contamination to a level where it is swamped by other errors. However, the detrital component is not usually inert in nitric acid, but often contains a certain fraction of loosely bound uranium and thorium which is removed by the leaching process. The extent of this leakage may be monitored by measuring the activity of ²³²Th. If this reaches a level of more than a few per cent of ²³⁰Th activity then it may be necessary to correct the carbonate data for leaching of radionuclides from the contaminating detrital phase (Ku and Liang, 1984).

U-series data for dirty calcites are best visualised on an isochron diagram. The most common form involves ratioing both ²³⁰Th and ²³⁴U against ²³²Th (Fig. 12.26). If all U and Th isotopes are leached from the residue with equal efficiency then a cord joining the leachate and residue points can be interpreted as an isochron line. The slope will then yield the ²³⁰Th/²³⁴U ratio of the carbonate component, which can be used to calculate the sample age in the same way as for clean material (Fig. 12.20).

Fig. 12.26. U)Th isochron diagrams showing results from leaching artificial mixtures of calcite and mud with 5 ) 7 M nitric acid. ( ! , L ) = leachates; ( Q , R ) = residues from leaching; numbers indicate % of mud in the sample. Diagram (b) is a blow-up of the lower left corner of (a). After Przybylowicz et al. (1991).

Przybylowicz et al. (1991) performed leaching experiments on artificial mixtures of pure calcite speleothems and mud in order to test the reliability of the leaching method in dating dirty calcites (e.g. Fig. 12.26). The results show that residues are displaced slightly (occasionally substantially) above the array of leachate compositions. This is probably due to slight preferential leaching of uranium relative to thorium from the detrital phase during the leaching process, and may yield apparent ages somewhat below the true value. Schwarcz and Latham (1989) argued that this problem could be diminished by regressing leachate analyses alone. In this case it is no longer necessary to assume a lack of differential isotopic fractionation during the leaching process. Isotopic fractionation is permitted, provided that the amount of such fractionation is the same in all samples. This has the effect of shifting the isochron line sideways in Fig. 12.26b but not changing its slope.

A similar type of correlation diagram can also be used to correct the ²³⁴U/²³⁸U ratio for detrital contamination. Figure 12.27 shows these data for the experiment described above. However, this is less important, since the ²³⁰Th age is only weakly dependent on the ²³⁴U/²³⁸U ratio in samples less than 300 kyr old.

Fig. 12.27. Correlation plot to correct for detrital perturbation of uranium isotope ratios in impure carbonates. ( ! ) = leachates; ( Q ) = residues. After Przybylowicz et al. (1991).

An application of the ‘leach)leach’ technique to dating natural mixtures is shown in Fig. 12.28 for contaminated travertines which enclose the ‘Mousterian cultural layer’ at Tata, Hungary (Schwarcz and Skoflek, 1982). Regression of four leachates leads to an age of 101 " 4 kyr for carbonate enclosing the cultural layer, which is bracketed between the ages of 78 " 5 and 118 " 37 kyr in overlying and underlying clean travertine layers.

Fig. 12.28. ²³⁰Th/²³²Th versus ²³⁴U/²³²Th isochron diagram for leachates of contaminated travertine from Tata, Hungary. Ellipses portray correlated error limits. Modified after Schwarcz and Latham (1989).

In order to achieve a high-precision result from the leach)leach technique it is desirable to leach three or more samples with variable detrital contents from the horizon to be dated. However, under these circumstances it is possible that different samples might undergo variable degrees of isotopic fractionation during leaching. This problem can be avoided by total digestion of a suite of variably contaminated samples from the same deposit. If they all contain the same detrital component (i.e. have the same initial ²³⁰Th/²³²Th ratio) and have remained as closed systems, then they will define a perfect isochron line.

Bischoff and Fitzpatrick (1991) tested the relative performance of the total dissolution, leach)leach and leachate)residue methods on a series of artificial mixtures of natural detritus and carbonate. (They also tested the effect of leaching with various acid strengths). Typical results showed that the total dissolution method was superior to the other two techniques for artificial mixtures (Fig. 12.29). The total dissolution method is also more versatile, in that it can be applied to the dating of any type of Pleistocene material with a homogeneous initial ratio and showing closed-system behaviour (Luo and Ku, 1991). However, it may be difficult to obtain a large enough range of detrital)carbonate variations to define a good regression line. Furthermore, in the pursuit of such a range of mixtures, samples with variable initial ratios may be analysed. Therefore, the total-dissolution, leach)leach and leach)residue methods may all be viable alternatives for dating dirty calcite in different circumstances.

Fig. 12.29. U)Th isochron diagram showing tests of different dating approaches on artificial mixtures of carbonate and detritus. ( € ) = whole-rock (total dissolution); ( " ) = leachate; ( + ) = residue. After Bischoff and Fitzpatrick (1991).

One problem with the data presentation in Fig. 12.26 and 12.27 is that the two variables become very highly correlated as the ²³²Th fraction diminishes in size. The large error bars should therefore be represented by elongated error ellipses (e.g. Fig. 12.28) rather then rectangular error boxes. Similarly, a regression program utilising correlated errors should be used to calculate isochron slopes.

An alternative isochron presentation, utilised by Kaufman (1971) but not shown here, involves plotting ²³⁰Th/²³⁴U against ²³²Th/²³⁴U. On this ‘Th–U’ isochron diagram, the age of the sample is represented by the intercept on the y axis, and increasing detrital contamination is indicated by displacement away from the y axis. Similar plots have been used more widely in U-series studies of silicate systems (section 13.1.2.). Th/U isochrons offer some advantages over the more popular U/Th isochron presentation because Th/U isochrons minimise the problem of error correlation between the variables. To show how Th/U isochrons yield the composition of the detrital-free component in a dirty calcite system, Ludwig and Titterington (1994) plotted synthetic data in three dimensions. They also presented a maximum likelihood method for calculation of the best-fit isochron, an approach already applied to some other isotopic systems (section 2.6.2).

12.4.4 ²³¹Pa

The build-up of ²³¹Pa in carbonates can be used as a dating tool in a way analogous to ²³⁰Th. The immediate parent of ²³¹Pa (²³¹Th) is assumed to be always in equilibrium with its parent (²³⁵U) due to its short half-life of 26 hours. Hence, the age relationship is analogous to the simple form of equation [12.25] for the build-up of ²³⁰Th:

²³¹Pa

))))) = 1 ! e^{!8231 t} [12.33]

²³⁵U

Because ²³⁵U is so much less abundant than ²³⁸U, measured " counting rates for ²³¹Pa and its daughters are twenty times lower than for ²³⁰Th. Since counting statistics are the major source of uncertainty in U-series dating, the ²³⁰Th method has been much preferred to ²³¹Pa as a practical dating tool. However, the ²³¹Pa technique is potentially valuable as a concordance test for ²³⁰Th dates, and the two systems can be used together to date partially open systems (section 12.5.1).

Mass spectrometry potentially offers the same advantages for ²³¹Pa analysis as for ²³⁰Th, involving an order of magnitude improvement in precision. However, a problem encountered in this work is the lack of any long-lived nuclides for use as spike isotopes. Apart from ²³¹Pa, with a half-life of 32.76 kyr, the second most long-lived isotope of protactinium is ²³³Pa, with a half-life of 27.4 days. This must be prepared anew every few months and must be repeatedly calibrated so that its concentration is known on the exact day of its analysis!

Two methods of preparing ²³³Pa are in use. The first, described by Pickett et al. (1994), involves periodically ‘milking’ ²³³Pa from a solution of ²³⁷Np. This is done by ion exchange chemical separation, but it must be done under a stringent radiological protection regime because the parent isotope is very highly active. An alternative method, described by Bourdon et al. (1999) is much less hazardous. This involves periodic neutron activation of ²³²Th in a reactor, to produce ²³³Th. This short-lived species (half-life 22 mins) then decays into ²³³Pa. Because the parent (²³²Th) has low activity, the ion-exchange purification can be done under normal laboratory conditions, after allowing short-lived by-products of the activation process to die away.

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