Improvements in ²³⁰Th dating, ²³⁰Th and ²³⁴U half-life values, and U–Th isotopic measurements by multi-collector inductively coupled plasma mass spectrometry

Highlights

• Technical details on the high precision (∑-level) measurements of U and Th isotopes.

• New ²³⁰Th and ²³⁴U half-life values from calcites likely in secular equilibrium.

• A test of ²³⁰Th dating accuracy via matching cave™ ¹⁸O record with solar insolation.

• Improvements in ²³⁰Th dating.

Abstract

We have developed techniques for measuring ²³⁴U and ²³⁰Th on Faraday cups with precisions of 1–3 epsilon units (1 ε-unit=1 part in 10⁴) using multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS). Using a Thermo-Scientific Neptune with desolvation nebulization, we obtained ionization/transmission efficiencies of 1–2% for both U and Th. We set up protocols to correct for tailing, prepared U and Th gravimetric standards, tested a Th mass fractionation correction procedure based on U isotopes, and identified natural calcite samples likely to be in U–Th isotopic secular equilibrium. The measured atomic ratios, ²³⁴U/²³⁸U=54.970 (±0.019)×10⁻⁶ and ²³⁰Th/²³⁸U=16.916 (±0.018)×10⁻⁶, for these calcite samples were identical within errors (quoted 2σ uncertainties calculated combining all sources of error). Half-life values calculated from these ratios are consistent with previous values, but have much smaller errors: 245,620±260 a for ²³⁴U and 75,584±110 a for ²³⁰Th (quoted 2σ uncertainties calculated using all sources of error). In calculating a ²³⁰Th age, some of the systematic errors included in estimating the full error in the half-lives effectively cancel. Removing these uncertainties (uncertainty in the ²³⁸U half-life value, uncertainty in our gravimetric uranium and thorium standards, and uncertainty in the absolute isotopic composition of the uranium standard), yields effective uncertainties for the purposes of ²³⁰Th dating of ±70 a for the ²³⁴U half-life value and ±30 a for the ²³⁰Th half-life value. Under ideal circumstances, with our methods, the 2σ uncertainty in age, including uncertainty in half-life values is ±10 a at 10 ka, ±100 a at 130 ka, ±300 a at 200 ka, ±1 ka at 300 ka, ±2 ka at 400 ka, ±6 ka at 500 ka, and ±12 ka at 600 ka. The isotopic composition of a sample with an age <800 ka can clearly be resolved from the isotopic composition of a sample in secular equilibrium, assuming closed system behavior. Using these techniques, we analyzed a Sanbao Cave (Hubei, China) stalagmite that formed between 510 and 640 ka ago. As the half-life values were determined independent of the Sanbao Cave ages, the observed co-variation between stalagmite δ¹⁸O and Northern Hemisphere summer insolation is consistent with accurate ages and half-life values.

Introduction

²³⁰Th dating, also referred to as U/Th dating or ²³⁸U–²³⁴U–²³⁰Th dating, plays an important role in characterizing a broad range of natural processes, including the timing and mechanisms of climate change, the calibration of the radiocarbon timescale, oceanographic processes, human evolution, tectonic and seismic processes, and magmatic processes (e.g., Bourdon et al., 2003 and chapters and references therein). This method involves calculating ages from radioactive decay and ingrowth relationships among ²³⁸U, ²³⁴U and ²³⁰Th. Before this work, ²³⁰Th dating was used to date materials as young as a few years and in excess of 600 ka (1000 a) (e.g., Edwards et al., 1987, Edwards, 1988, Ludwig et al., 1992, Richards et al., 1994, Henderson and Slowey, 2000, Stirling et al., 2001, Andersen et al., 2004, Andersen et al., 2008, Potter et al., 2005, Shen et al., 2008, Shen et al., 2012, Cheng et al., 2009a, Cheng et al., 2009b).

In the late 1980s, thermal ionization mass spectrometry (TIMS) techniques with per mil (‰) level precision largely replaced traditional decay counting methods for measuring U and Th isotopes, resulting in an improvement in precision of over an order of magnitude, and a decrease in sample size requirements of 1-2 orders of magnitude (Edwards et al., 1987). ²³⁰Th and ²³⁴U half-life values with per mil-level precision were determined by applying TIMS techniques to the measurement of ²³⁰Th/²³⁸U and ²³⁴U/²³⁸U in materials thought to be in secular equilibrium (Cheng et al., 2000). The half-life values were then calculated from the measured atomic ratios and the previously measured half-life for ²³⁸U (Jaffey et al., 1971).

During the past decade, further technical improvements have resulted from a shift from TIMS methods to techniques of multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) and ICP-sector field-MS (ICP-SF-MS) with precisions at the per mil or epsilon-unit (ε-unit) level (e.g., Luo et al., 1997, Stirling et al., 2000, Stirling et al., 2001, Stirling et al., 2006, Stirling et al., 2007, Shen et al., 2002, Shen et al., 2003, Robinson et al., 2002, Hellstrom, 2003, Andersen et al., 2004, Andersen et al., 2007, Andersen et al., 2008, Andersen et al., 2010, Potter et al., 2005, Eggins et al., 2005, Fietzke et al., 2005, Mortlock et al., 2005, Hoffmann et al., 2005, Hoffmann et al., 2007, Ball et al., 2008, Weyer et al., 2008, Stirling and Andersen, 2009, Mason and Henderson, 2010, Hiess et al., 2012), including applications of both electron multiplier and Faraday cup measurements.

The main substantive improvement that resulted from the use of mass spectrometric techniques has been an improvement in the proportion of ²³⁴U and ²³⁰Th atoms in the sample that one can detect. The increase led to higher counts, which in turn, reduced sample size as well as the error from counting statistics. Given the order of the half-lives of ²³⁰Th and ²³⁴U (10⁵ yr), one out of 10⁷ of each of these atoms decays during a 1-week counting time. Thus one in 10 million can be counted in a week using decay-counting methods. Using thermal ionization techniques, Edwards et al. (1987) demonstrated an ionization efficiency for Th of 0.1%, improving the number of counts for the same sample size by a factor of 10⁴. Esat (1995) reported a TIMS ionization efficiency for Th of ∼4%, but we are not aware of other reports of TIMS ionization efficiency (for Th) of this order. For MC-ICP-MS and ICP-SF-MS, previously reported ionization plus transmission efficiencies for U and Th for specific studies are in the 0.1–0.2% range (e.g. Luo et al., 1997, Shen et al., 2002). A review paper notes ICP-MS ionization plus transmission efficiencies of 0.5% in the text and a range of 0.01–1% in a table (Goldstein and Stirling, 2003), but without specific attribution to an instrument or method of nebulization. With our Thermo-Scientific Neptune (MC-ICP-MS), we attain 1–2% ionization plus transmission efficiency for both U and Th using desolvation introduction techniques, about an order of magnitude higher than the original TIMS ionization efficiency of Edwards et al. (1987) and previous ICP-MS studies that specifically mention ionization plus transmission efficiency. The measurements in this study were made at this efficiency. We take advantage of the 1–2% ionization/transmission efficiency in two different ways, depending on sample size. The breakeven point between Faraday cup measurement and electron multiplier measurement is about 5×10¹⁰ atoms (20 pg) for the lowest abundance isotope (²³⁰Th). At this level or higher, the ²³⁰Th⁺ beam current exceeds the 2σ noise of the amplifier by a factor of about 10⁴, making cup measurements, with uncertainties of a few ε-units or better possible. For ²³⁰Th loads of less than about 5×10¹⁰ atoms, we make measurements by peak-jumping on a discrete-dynode electron multiplier. For such measurements, uncertainties are close to theoretical counting statistics limits until 2σ counting errors reach values lower than about 1‰. To further reduce total errors, careful multiplier calibration is necessary (see Hayes and Schoeller, 1977, Cheng et al., 2000, Shen et al., 2002).

Using MC-ICP-MS techniques, other groups have demonstrated measurement errors better than 1‰ (Stirling et al., 2001) for ²³⁰Th and ²³⁴U, in some cases approaching ε-unit precision (e.g., Potter et al., 2005, Stirling and Andersen, 2009). Here, we demonstrate measurement of ²³⁰Th and ²³⁴U with precisions in the 1–3 ε-unit range. Fundamentally, the main difference between our measurements and previous ICP-MS studies that specifically report ionization plus transmission efficiency is the higher efficiency. Thus, as compared to these studies, our measurements are (a) for comparable sample size, about a factor of two more precise or (b) equally precise using a sample size several times smaller. In the past decade, several studies have reported precisions broadly comparable to those that we report for ²³⁴U (Andersen et al., 2004, Andersen et al., 2007, Andersen et al., 2010, Stirling and Andersen, 2009 in natural materials and for ²³⁰Th in standard solutions (Potter et al., 2005). None of these studies specifically report ionization plus transmission efficiency, but it is possible that they attained efficiencies similar to ours, as sample size in at least some of these studies is not grossly different from ours. In addition, we apply the same measurement techniques to materials inferred to be in secular equilibrium. By doing so, we determine a self-consistent set of half-life values (with ε-unit levels of precision) for use in the ²³⁰Th dating equation, thus improving the accuracy of ²³⁰Th ages to levels comparable to the precision of the isotopic measurements.

The main steps in our study include the following: (1) development of protocols for tailing corrections, (2) characterization of U and Th ionization/transmission efficiencies, (3) evaluation of the relationship between instrumental isotopic fractionation of U and Th, (4) standardization using high accuracy U isotopic standards, and (5) identification and measurement of calcites that we infer to be in secular equilibrium. Finally, we tested the accuracy of our methods by analyzing stalagmite samples from Sanbao Cave, Hubei, China. The Sanbao results were determined independent of our new half-life determinations. Dating accuracy (and therefore half-life accuracy) is supported by the agreement of the Sanbao oxygen isotope record with the calculated orbital-based insolation curve.