Variation of lead isotopic composition and atomic weight in terrestrial materials (IUPAC Technical Report)

1 Introduction

Lead has four stable isotopes (²⁰⁴Pb, ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb), each of which is entirely – as with ²⁰⁴Pb – or partially – as with ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb – composed of primordial components from stellar neutron capture [1], [2]. The heavier three stable isotopes, ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb, have radiogenic components, which are used to date rocks and minerals or trace and identify lead sources in the environment. Overviews of measurements and applications of the isotopes of lead include [3], [4], [5].

The three heaviest isotopes are the stable end-products of the radioactive decay of uranium (²³⁸U to ²⁰⁶Pb; ²³⁵U to ²⁰⁷Pb) and thorium (²³²Th to ²⁰⁸Pb), resulting in substantially variable atomic-weight values of lead in naturally occurring materials. The “atomic weight,” which is the ratio of the average mass per atom of an element to 1/12 of the mass of an atom of nuclide ¹²C, is also known as “relative atomic mass” [6]. Alternatively, “relative atomic mass (atomic weight), A_r” is “The ratio of the average mass of the atom to the unified atomic mass unit” [7]. Although atomic weight is a dimensionless quantity and, thus, is not a weight, a consensus on the meaning of atomic weight was achieved during the 1975 and 1977 IUPAC General Assemblies as documented on page 1540 of De Bièvre and Peiser [8]. ²⁰⁸Pb, the heaviest known stable isotope, comprises about half of the lead in the Solar System and most terrestrial materials [[2] and references therein]. ²⁰⁸Pb is produced in part by the decay of radioactive ²³²Th, which has a total half-life of approximately 1.40 × 10¹⁰ years, via the thorium decay series [9]. ²⁰⁷Pb and ²⁰⁶Pb are also produced, in part, by radiogenic decay of ²³⁵U and ²³⁸U via the actinium and uranium decay series, respectively, with half-lives of 7.07 × 10⁸ years and 4.468 × 10⁹ years [10]. Certain minerals, such as zircon and monazite, readily incorporate uranium and/or thorium in their structure when forming, but do not incorporate primary lead. As a result, all lead in such minerals is radiogenic, with no ²⁰⁴Pb present, and specimens can have anomalously high amount fractions of ²⁰⁶Pb and ²⁰⁸Pb [e.g., x(²⁰⁶Pb) > 0.6 or x(²⁰⁸Pb) > 0.6]. Comparing abundances of parent uranium or thorium to daughter lead from the three above mentioned decay series is fundamental in geochronology [11].

The standard atomic weight of lead, A_r(Pb), is 207.2 ± 0.1, and it was assigned by the Commission on Atomic Weights and Isotopic Abundances in 1969 [12], based on the work of Brown [13] and Catanzaro et al. [14], showing natural variations in the atomic weight of lead ranging from 207.184 to 207.293. The Commission assigned the annotation “r” to lead to indicate that the range in isotopic composition of lead in normal materials precludes a more precise standard atomic weight being assigned. The Commission assigned annotation “g” to indicate that geological materials are known in which lead has an isotopic composition outside its standard atomic weight [12]. The variability in the atomic weight of lead is due to a combination of primordial and radiogenic components in natural lead-bearing materials [[15] and references therein]. At the 2017 meeting of the Commission on Isotopic Abundances and Atomic Weights, it was reiterated that the standard atomic weight with its uncertainty is a consensus (decisional) value [16], [19], [23], and the footnote

• For 71 elements, A_r(E) values and their decisional uncertainties are given for normal materials and include evaluations of measurement uncertainty and variability. The atomic weight of a normal material should lie between the lower and upper bounds of the standard atomic weight with great certitude. If a more accurate A_r(E) value for a specified material is required, it should be determined.

At the 2009 meeting of the Commission on Isotopic Abundances and Atomic Weights in Vienna, Austria, the Commission for the first time in its history assigned standard atomic-weight intervals to 10 elements (hydrogen, lithium, boron, carbon, nitrogen, oxygen, silicon, sulfur, chlorine, and thallium) [16]. These intervals were based on an International Union of Pure and Applied Chemistry (IUPAC) project review of peer-reviewed, published literature for isotopic-abundance data that included these 10 elements [17], [18]. In 2011, standard atomic-weight intervals were assigned to two more elements (magnesium and bromine) [19]. Subsequently, isotopic abundances and atomic-weight values of selected substances for these 12 elements were published [20], [21], [22], [23], [24]. At the 2017 Commission meeting in Groningen, Netherlands, argon was assigned a standard atomic weight that was expressed as an interval [25], [26]. Currently, there are seven elements (helium, nickel, copper, zinc, selenium, strontium, and lead) that have been assigned footnote “r” in the table of standard atomic weights and which would benefit from an IUPAC project review of the peer-reviewed, published literature for isotopic-abundance data.

This article presents results of an IUPAC project [27] for evaluation of peer-reviewed, published literature for isotopic-abundance data of lead. This study is the second to address the variation in isotopic composition and atomic weight of an element with radiogenic/nucleogenic components. The first study to do so addressed the variation of atomic weight of argon [28].

2 Literature search of lead isotopic abundances and atomic weights of selected materials

A comprehensive literature search of lead isotopic abundances evaluated several hundred peer-reviewed publications containing more than 8000 samples (see Supplementary Materials). Isotopic abundance values were compiled from peer-reviewed publications following the methods used in IUPAC project evaluations of the previous 13 elements assigned standard atomic-weight interval values [17], [18], [19], [25], [28]. Literature values have not been evaluated for mutual compatibility and have not been normalized to a common set of isotope ratios for the common lead National Institute of Standards and Technology (NIST) standard reference material (SRM) 981 [14], [29], rather values have been collected from peer-reviewed publications and used without recalculation. Uncertainties due to calibration differences among laboratories have not been taken into account. As in previous evaluations, only samples of normal materials [30] were evaluated and extraterrestrial samples were excluded [15]. To calculate A_r(Pb) values, the 2012 Atomic Mass Evaluation report (AME2012), the most recent version available at the time of preparation of this report, was used [31]. Since the preparation of this report, the 2016 Atomic Mass Evaluation report (AME2016) was published. As shown below, it is immaterial which Atomic Mass Evaluation values are used because of the relative high uncertainties of lead isotopic composition measurements compared to the uncertainties of atomic masses.

Lead-bearing substances were categorized into 25 categories as shown in Fig. 1, which presents variation in A_r(Pb) with amount fraction of ²⁰⁴Pb, x(²⁰⁴Pb) of selected lead-bearing material. These categories were selected because they represent effectively the geological (mineralogical), environmental, and biological materials analyzed regularly for lead isotopic composition. Because the isotopic-abundance variations of ²⁰⁴Pb, ²⁰⁶Pb, ²⁰⁷Pb, and ²⁰⁸Pb are not mass dependent, individual figures for each of these four isotopes are needed (Figs. 1–4). The A_r(Pb) and x(²⁰⁴Pb) values in Fig. 1 are scaled so that they coincide exactly only at the lower and upper bounds of A_r(Pb) and x(²⁰⁴Pb), which explains why the A_r(Pb) and x(²⁰⁴Pb) values of the common lead SRM 981 [14], [29] (solid circles labeled “SRM 981”) and the reference material NRC HIPB-1 [32] are not superimposed. The axes on Figs. 2–4 are scaled in like manner, so that atomic-weight values and isotopic-abundance values only coincide at minimum and maximum values.

Fig. 1:

Variation in atomic weight (solid black lines) of lead, A_r(Pb), with amount fraction (solid orange lines) of ²⁰⁴Pb, x(²⁰⁴Pb), of selected lead-bearing materials (data from Tables 1 and 2 and supplementary data file). Because lead has four isotopes whose variations are not mass dependent, the A_r(Pb) and x(²⁰⁴Pb) values of the 25 materials shown in this figure coincide exactly only at the lower bound of A_r(Pb), which explains why the A_r(Pb) and x(²⁰⁴Pb) values of the common lead standard reference material 981 (solid circles labelled “SRM 981”) and NRC HIPB-1 [32] are not superimposed.

Fig. 2:

Variation in atomic weight (solid black lines) of lead, A_r(Pb), with amount fraction (solid green lines) of ²⁰⁶Pb, x(²⁰⁶Pb), of selected lead-bearing materials (data from Tables 1 and 2 and supplementary data file). Because lead has four isotopes whose variations are not mass dependent, the A_r(Pb) and x(²⁰⁶Pb) values of the 25 materials shown in this figure coincide exactly only at the lower and upper bounds of A_r(Pb), which explains why the A_r(Pb) and x(²⁰⁶Pb) values of the common lead standard reference material 981 (solid circles labelled “SRM 981”) and NRC HIPB-1 [32] are not superimposed.

Fig. 3:

Variation in atomic weight (solid black lines) of lead, A_r(Pb), with amount fraction (solid blue lines) of ²⁰⁷Pb, x(²⁰⁷Pb), of selected lead-bearing materials (data from Tables 1 and 2 and supplementary data file). Because lead has four isotopes whose variations are not mass dependent, the A_r(Pb) and x(²⁰⁷Pb) values of the 25 materials shown in this figure coincide exactly only at the lower bound of A_r(Pb), which explains why the A_r(Pb) and x(²⁰⁷Pb) values of the common lead standard reference material 981 (solid circles labelled “SRM 981”) and NRC HIPB-1 [32] are not superimposed.

Fig. 4:

Variation in atomic weight (solid black lines) of lead, A_r(Pb), with amount fraction (solid pink lines) of ²⁰⁸Pb, x(²⁰⁸Pb), of selected lead-bearing materials (data from Tables 1 and 2 and supplementary data file). Because lead has four isotopes whose variations are not mass dependent, the A_r(Pb) and x(²⁰⁸Pb) values of the 25 materials shown in this figure coincide exactly only at the lower and upper bounds of A_r(Pb), which explains why the A_r(Pb) and x(²⁰⁸Pb) values of the common lead standard reference material 981 (solid circles labelled “SRM 981”) and NRC HIPB-1 [32] are not superimposed.

3 Discussion

The peer-reviewed publications that provide the data shown in Figs 1–4 date from 1958 to 2015, although the majority were published in the 1990s and 2000s. The lowest and highest values of x(²⁰⁴Pb), x(²⁰⁶Pb), x(²⁰⁷Pb), x(²⁰⁸Pb), and A_r(Pb) for each of the 25 selected materials shown in Figs. 1–4 are presented in Tables 1 and 2, respectively, and these data are available as a Supplementary data file.

All publications identifying an isotopic reference material used as the reference for lead isotopic-abundance or isotope-ratio measurements used the elemental common lead NIST SRM 981 [14], [29]. Other lead isotopic reference materials [33] include NIST SRM 610 lead in glass [34] and NRC HIPB-1 common lead [32]. Analytical uncertainty has improved substantially over the five-decade interval during which publications were generated; nevertheless, uncertainties of atomic-weight values are variable among publications. Uncertainties were listed in many publications, but not provided in many others. Although uncertainties of atomic-weight values may be of the order of 0.0005, others are higher. Therefore, we have rounded the atomic-weight values in Tables 1 and 2 and in the Supplemental data file to a thousandth. On average, the atomic weight in these data sources is thought to be accurate to within ±0.003. Over recent decades, the accuracy of lead-isotope measurements produced by thermal ionization mass spectrometers and multi-collector inductively coupled plasma mass spectrometers has improved. Although discussions of state-of-the-art measurement practices is beyond the scope of this article, interested readers are directed to Taylor et al. [35], who discuss correction of instrumental mass fractionation, including thallium spiking, sample-standard bracketing, and double/triple spiking.

As an example of the calculation of lead atomic weight from measurements of lead isotope ratios in a natural material (elephant tusks and bones), consider the measurements of Vogel et al. [36]. Vogel et al. state, “Mass fractionation corrections for the lead ratios are based on replicates of NBS SRM 981.” They do not state what isotope-number ratios or isotope-amount fractions they assumed for SRM 981, but we assumed that they normalized their results using the values on the NIST SRM 981 Certificate of Analysis [29], which are:

Although Vogel et al. [36] do state that they used NBS SRM 981, regularly publications report measured values with no mention of the isotopic reference material used to calibrate their mass spectrometer.

Vogel et al. [36] published the following isotope-number ratios for their sample C4100 (elephant bone):

We need to calculate x(²⁰⁴Pb), x(²⁰⁶Pb), x(²⁰⁷Pb), and x(²⁰⁸Pb). We have three equations and four unknowns, and for the fourth equation, we can use:

Solving simultaneously and rounding to four digits after the decimal separator, which is all that is warranted considering uncertainties of measurements in publications found in this study, we find:

The atomic weight of sample C4100 elephant bone determined using the value in the 2012 Atomic Mass Evaluation [31] is:

Using the 2016 Atomic Mass Evaluation [32], we find:

Thus, both the 2012 and 2016 atomic masses yield the same atomic weight. This atomic weight of 207.219 is listed in Table 2 and is the highest lead atomic weight value for the subcategory “Animals.”

Occasionally lead isotope-delta values are reported in the literature, but none of the authors cited in this article reported results as lead isotope-delta values. Had data been reported as lead isotope-delta values, we would have converted them into isotope-number ratios as described on page 426 of Brand et al. [33]. Then, these isotope-number ratios would have been used to calculate lead atomic weight values as exemplified above.

The lowest reported atomic weight of lead is 206.1462 ± 0.0028 (k = 2) for a growth of the phosphate mineral monazite around a garnet relic from an Archean high-grade metamorphic terrain in north-western Scotland, which contains mostly ²⁰⁶Pb and almost no ²⁰⁴Pb [37]. The highest reported atomic weight of lead is 207.9351 ± 0.0005 (k = 2) for monazite from a micro-inclusion in a garnet relic, also from a high-grade metamorphic terrain in north-western Scotland, which contains almost pure radiogenic ²⁰⁸Pb [37]. The atomic-weight interval derived from these data is [206.14, 207.94]. It is the consensus of the authors, who in total have nearly a century of data evaluation expertise with the Commission on Isotopic Abundances and Atomic Weights (and its predecessors), that 207.2 be adopted for the single atomic-weight value of lead for education, commerce, and industry. This value of 207.2 corresponds well with the previously published standard atomic-weight value for lead of 207.2 ± 0.1 [16], [19], [23], and it is noted that 207.2 ± 0.1 encompasses most lead atomic-weight variation in normal materials (Figs. 1–4). In 2009, the Commission recognized that some users of atomic-weight data of elements having atomic weights expressed as an interval only need single values, such as for education, trade, and commerce. For these users the Commission provided conventional atomic-weight values [16], [19], [23], [26]. The resulting cell for lead for the IUPAC Periodic Table of Elements and Isotopes [26] is shown in Fig. 5 with the conventional atomic-weight value of 207.2 shown in white.

Fig. 5:

Proposed element cell for lead for the IUPAC Periodic Table of the Elements and Isotopes [26]. The pink background designates an element having two or more isotopes that are used to determine the standard atomic weights. The isotopic abundances and atomic weights vary in normal materials, and these variations exceed measurement uncertainty and are well known. The standard atomic-weight value is given as a lower and upper bounds within square brackets [ ]. The single atomic-weight value for education, commerce, and industry of 207.2, corresponding to previously published conventional atomic-weight values [16], [19], [23], is shown in white.

4 Conclusion

The atomic weight of lead in normal materials is variable because it is an element with radiogenic/nucleogenic components. A comprehensive literature search of lead isotopic abundances evaluated more than 200 peer-reviewed publications that included analyses for lead in more than 8000 samples. The lowest reported atomic weight of lead is 206.1462 ± 0.0028 (k = 2) for a growth of the phosphate mineral monazite around a garnet relic from an Archean high-grade metamorphic terrain in north-western Scotland, which contains mostly ²⁰⁶Pb and almost no ²⁰⁴Pb. The highest reported atomic weight of lead is 207.9351 ± 0.0005 (k = 2) for monazite from a micro-inclusion in a garnet relic, also from a high-grade metamorphic terrain in north-western Scotland, which contains almost pure radiogenic ²⁰⁸Pb. The atomic-weight interval derived from these data is [206.14, 207.94]. It is proposed that a value of 207.2 be adopted for the single atomic-weight value for education, commerce, and industry, corresponding to previously published conventional atomic-weight values [16], [19], [23].

5 Membership of sponsoring body

Membership of the IUPAC Inorganic Chemistry Division Committee for the period 2016–2017 was as follows:

President: J. Reedijk (The Netherlands); Secretary: M. Leskelä (Finland); Vice President: L. R. Öhrström (Sweden); Past President: R. D. Loss (Australia); Titular Members: L. Armelao (Italy); T. Ding (China); P. Karen (Norway); D. Rabinovich (USA); T. Walczyk (Republic of Singapore); M. E. Wieser (Canada); Associate Members: Y. Abdul Aziz (Malaysia); J. Colón (Puerto Rico); M. Drábik (Slovakia); L. Meesuk (Thailand); K. Sakai (Japan); N. Trendafilova (Bulgaria); National Representatives: J. Darkwa (South Africa); M. Diop (Senegal); J. G. Correia (Portugal); M. Hasegawa (Japan); S. N. Kalmykov (Russia); A. Kiliç (Turkey); P. Knauth (France); G. J. Leigh (United Kingdom); S. Mathur (Germany); K. B. Yoon (South Korea).

Membership of the IUPAC Commission on Isotopic Abundances and Atomic Weights for the period 2016–2017 was as follows:

Chair: J. Meija (Canada); Secretary: T. Prohaska (Austria); Titular Members: M. Gröning (Austria); J. Irrgeher (Germany); J. Vogl (Germany); X.-K. Zhu (China); Associate Members: L. Chesson (USA); H. A. J. Meijer (Netherlands); A. Possolo (USA); Ex-officio member: J. Reedijk (The Netherlands).