Once in a while, a really big discovery is made in science, a discovery that affects all mankind. Such was the discovery of radioactivity by Becquerel  in 1896, which effected a paradigm shift in our view of matter. An outcome of this finding was that the spontaneous decay of atoms from one chemical element to another gives rise to the possibility that atoms of the same chemical element might have different atomic weights (also called relative atomic masses). In 1911, Soddy demonstrated that mesothorium 1 (228Ra) was chemically identical to radium , and he concluded that there were chemical elements having different atomic weights. Soddy coined the name “isotope” for these atoms of a chemical element having different atomic weights. Three years later, J. J. Thomson discovered that neon had isotopes with mass numbers 20 and 22 . This discovery ushered in a new field in spectroscopy – the “spectroscopy of mass.”
The atomic weight of element E, Ar(E), in a material P is determined from the relation
where x(iE)P is the amount fraction of isotope iE in material P (also called the isotopic abundance or the mole fraction) and Ar(iE) is the relative atomic mass of isotope iE, where i is the mass number. The summation is over all stable isotopes of the element plus selected radioactive isotopes (having sufficiently long half-lives that characteristic terrestrial isotopic compositions can be determined, which enables a standard atomic weight to be determined) of the element. The atomic-mass values used to calculate the atomic-weight values given here derive from the 2012 Atomic Mass Evaluation .
In contrast to the atomic weight of an element in any given material, the standard atomic weight is a quantity that represents the atomic weight of an element in any normal material. By a normal material, the Commission on Isotopic Abundances and Atomic Weights means a material from a terrestrial source that satisfies the following criteria :
“The material is a reasonably possible source for this element or its compounds in commerce, for industry or science; the material is not itself studied for some extraordinary anomaly and its isotopic composition has not been modified significantly in a geologically brief period.”
Because of variations in isotopic abundances in various sources of some chemical elements, the standard atomic weight must be given with larger uncertainty for these elements than the measured atomic weight in any given sample of that element.
The identification of variations in abundances of stable isotopes and their effect on atomic weights was recognized at the September 1951 meeting of the Commission on Atomic Weights of the International Union of Pure and Applied Chemistry (IUPAC) and an atomic-weight “range” was assigned to an element – 32.066±0.003 to sulfur . By 1967, recognized variations in isotopic abundances caused the Commission to assign atomic-weight uncertainties to six elements (hydrogen, boron, carbon, oxygen, silicon, and sulfur) .
During the meeting of the Commission on Atomic Weights and Isotopic Abundances at the General Assembly of IUPAC in 1985 in Lyon, France, the Working Party on Natural Isotopic Fractionation (subsequently named the Subcommittee on Natural Isotopic Fractionation) was formed to investigate the effects of isotope-abundance variations of elements upon their standard atomic weights and atomic-weight uncertainties , . The aims of the Subcommittee were to (1) identify elements for which the uncertainties of the standard atomic weights are larger than measurement uncertainties in materials of natural terrestrial origin because of isotope-abundance variations caused by physical and chemical fractionation processes (excluding variations caused by radioactivity), and (2) provide information about the range of atomic-weight variations in specific substances and chemical compounds of each of these elements. The Subcommittee’s reports ,  compiled ranges of isotope-abundance variations and corresponding atomic weights in selected materials from peer-reviewed publications for twenty chemical elements (hydrogen, lithium, boron, carbon, nitrogen, oxygen, magnesium, silicon, sulfur, chlorine, calcium, chromium, iron, copper, zinc, molybdenum, palladium, tellurium, and thallium). Graphical plots were presented for 15 elements , . Atomic weights calculated from published variations in isotopic abundances for some elements can span relatively large intervals. For example, the atomic weight of hydrogen in normal materials (its standard atomic weight) spans the interval from 1.007 84 to 1.008 11 , , , whereas the uncertainty of the atomic weight calculated from the best measurement of the isotopic abundance of hydrogen is ±0.000 000 05 , , which is approximately 5000 times smaller than the difference between the lower and higher bounds. The Subcommittee’s reports formed the basis of the Commission’s decision in 2009 to express the standard atomic weight of ten elements (hydrogen, lithium, boron, carbon, nitrogen, oxygen, silicon, sulfur, chlorine, and thallium) as intervals to indicate that standard atomic weights are not always constants of nature , . In 2011, the Commission decided to express the standard atomic weights of two more elements (magnesium and bromine) as intervals .
The span of atomic-weight values in normal terrestrial materials is termed the interval. The interval [a, b] is the set of values x for which a≤x≤b, where b>a and where a and b are the lower and upper bounds, respectively . Neither the lower nor upper bounds have any uncertainty associated with them; each is a considered decision by the Commission based on professional evaluation and judgment. Writing the standard atomic weight of hydrogen as “[1.007 84, 1.008 11]” indicates that its atomic weight in any normal material will be greater than or equal to 1.007 84 and will be less than or equal to 1.008 11. Thus, the atomic-weight interval is said to encompass atomic-weight values of all normal materials. The range of an interval is the difference between b and a, that is b–a ; thus, the range of the atomic-weight interval of hydrogen is calculated as 1.008 11–1.007 84=0.000 27. The interval designation does not imply any statistical distribution of atomic-weight values between the lower and upper bounds (e.g. the mean of a and b is not necessarily the most likely value) ). Similarly, the interval does not convey a simple statistical representation of uncertainty.
The lower bound of an atomic-weight interval is determined from the lowest atomic weight determined by the Commission’s review and evaluation of peer-reviewed literature, and this evaluation takes into account the uncertainty of the measurement result as well as the variation in isotopic abundance of natural materials. Commonly, isotope-delta measurements , , ,  are the basis for the determination of the lower and upper atomic-weight bounds , . The isotope delta is obtained from isotope-number ratio R(iE, jE)P
where N(iE)P and N(jE)P are the numbers of each isotope, and iE denotes the higher (superscript i) and jE the lower (superscript j) atomic mass number of chemical element E in substance P. The isotope-delta value (symbol δ), also called the relative isotope-ratio difference, is a differential measurement obtained from isotope-number ratios of substance P and a reference material, Ref.
A more convenient short-hand notation for the isotope-delta value is typically found in scientific publications; δ(iE, jE)P,Ref is shortened to δiERef or to δiE. For example, δ(13C, 12C)P,VPDB is shortened to either δ13CVPDB or δ13C , , where VPDB is the Vienna Peedee belemnite–LSVEC scale for carbon isotope-delta measurements . Isotope-delta values are small numbers and therefore frequently presented in multiples of 10−3 or per mil (symbol ‰).
To match an isotope-delta scale of an element to an isotope-amount scale (both shown in Figs. 1–12), a substance is needed whose isotopic abundance is well known and whose isotope-delta value is also well known relative to the isotope-delta scale. Commonly this substance is an isotopic reference material that has served as the “best measurement” for determination of isotopic abundance . For example, consider hydrogen, shown in Fig. 1. The x(2H) scale is matched to the δ2HVSMOW scale through measurement of the isotopic reference material VSMOW (Vienna Standard Mean Ocean Water) (Fig. 1), which has been assigned the consensus δ2HVSMOW value of zero . The hydrogen isotope-number ratio of VSMOW, R(2H, 1H), has been measured by Hagemann et al.  and is 0.000 155 74(5). This measurement serves as the “best measurement” of a single terrestrial source . VSMOW is the zero point on the hydrogen isotope-delta scale and therefore δ2HVSMOW=0. Figure 1 and Table 1 shows δ2HVSMOW values for 19 materials or substances. The material having the lowest measured 2H abundance is a natural gas sample from Kansas, USA (Fig. 1) , which has a δ2HVSMOW value of –836‰. For this sample, the amount fraction of 2H, x(2H), is 0.000 0255, and Ar(H) is 1.007 8507. The material having the highest measured 2H abundance is benzaldehyde reagent produced by toluene catalytic oxidation (Fig. 1) , which has a δ2HVSMOW value of +802‰. For this sample, the amount fraction of 2H, x(2H), is 0.000 2806, and Ar(H) is 1.008 1074. If material P is the normal material having the lowest atomic weight of element E, then
where U[Ar(E)]P is the combined uncertainty that incorporates the uncertainty in the measurement of the delta value of material P and the uncertainty in relating the delta-value scale to the isotope-amount fraction and atomic-weight scales. The latter is the uncertainty in relating an isotope-delta scale to an atomic-weight scale. In an equivalent manner, the upper bound for the highest atomic weight is
For each of the twelve elements having interval values of standard atomic weight, the Commission published a figure that displayed lower and upper bounds of isotope-delta values, isotopic abundances, and atomic weights in selected substances and materials (Figs. 1–12 ). The lower and upper bounds of the isotope-delta values of the selected substances and materials are compiled in Tables 1–12. A supplemental file  lists the atomic weight and the isotopic abundances for each isotope of each of the twelve elements for each substance and material shown in Figs. 1–12 and Tables 1–12. Many uses of atomic-weight data, such as for trade and commerce, need a value that is not an interval. For these purposes, the Commission provides conventional atomic-weight values , and the associated isotope-delta and isotope-amount-fraction values are listed in the supplemental file . Additionally, the supplemental file lists the isotope-delta value and isotopic abundances of all stable isotopes corresponding to the lower and upper bounds of the standard atomic weights of the twelve elements discussed here. For the four elements with more than two stable isotopes, we assume mass-dependent isotopic fractionation when calculating isotopic abundances and atomic weights from isotope-delta values. For oxygen, R(17O, 16O)sample/R(17O, 16O)VSMOW=(R(18O, 16O)sample/R(18O, 16O)VSMOW)0.528, where the value 0.528 was determined by Meijer and Li . For magnesium, R(25Mg, 24Mg)sample/R(25Mg, 24Mg)DSM3=(R(26Mg, 24Mg)sample/R(26Mg, 24Mg)DSM3)0.5; for silicon, R(29Si, 28Si)sample/R(29Si, 28Si)NBS28=(R(29Si, 28Si)sample/R(29Si, 28Si)NBS28)0.5; for sulfur, R(33S, 32S)sample/R(33S, 32S)NBS28=(R(34S, 32S)sample/R(34S, 32S)NBS28)0.5 and R(34S, 32S)sample/R(34S, 32S)NBS28= (R(36S, 32S)sample/R(36S, 32S)NBS28)0.5.
Membership of the sponsoring body
Membership of the IUPAC Inorganic Chemistry Division Committee for the period 2014–2015 was as follows:
President: J. Reedijk (Netherlands); Secretary: M. Leskelä (Finland); Vice President: L. R. Öhrström (Sweden); Past President: R. D. Loss; Titular Members: T. Ding (China); M. Drábik (Slovakia); E. Y. Tshuva (Israel); D. Rabinovich (USA); T. Walczyk (Republic of Singapore); M. E. Wieser (Canada); Associate Members: J. Buchweishaija (Tanzania); J. Garcia-Martinez (Spain); P. Karen (Norway); A. Kilic (Turkey); K. Sakai (Japan); R.-N. Vannier (France); National Representatives: F. Abdul Aziz (Malaysia); L. Armelao (Italy); A. Badshah (Pakistan); V. Chandrasekhar (India); J. Galamba Correia (Portugal); S. Kalmykov (Russia); L. Meesuk (Thailand); S. Mathur (Germany); B. Prugovecki (Croatia); N. Trendafilova (Bulgaria).
Membership of the IUPAC Commission on Isotopic Abundances and Atomic Weights for the period 2014–2015 was as follows:
Chair: J. Meija (Canada); Secretary: T. Prohaska (Austria); Titular Members: W. A. Brand (Germany); M. Gröning (Austria); R. Schönberg (Germany); X.-K. Zhu (China); Associate Members: T. Hirata (Japan); J. Irrgeher (Austria); J. Vogl (Germany); National Representatives: P. De Bièvre (Belgium); T. B. Coplen (USA); Ex-officio member: J. Reedijk (Netherlands).
We thank Dr. Juris Meija (National Research Council Canada, Ottawa, Canada) and Prof. B. Brynn Hibbert (University of New South Wales, Sydney, Australia) for their valuable suggestions that improved this manuscript. The support of the U.S. Geological Survey National Research Program made this report possible. The following IUPAC projects contributed to this Technical Report: 2011-040-2-200, 2015-030-2-200, and 2011-027-1-200.
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Published Online: 2017-01-06
Published in Print: 2016-12-01
Citation Information: Pure and Applied Chemistry, Volume 88, Issue 12, Pages 1203–1224, ISSN (Online) 1365-3075, ISSN (Print) 0033-4545, DOI: https://doi.org/10.1515/pac-2016-0302.http://creativecommons.org/licenses/by-nc-nd/4.0/.