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The biennial review of atomic-weight determinations and other cognate data has resulted in changes for the standard atomic weights of five elements. The atomic weight of bromine has changed from 79.904(1) to the interval [79.901, 79.907], germanium from 72.63(1) to 72.630(8), indium from 114.818(3) to 114.818(1), magnesium from 24.3050(6) to the interval [24.304, 24.307], and mercury from 200.59(2) to 200.592(3). For bromine and magnesium, assignment of intervals for the new standard atomic weights reflects the common occurrence of variations in the atomic weights of those elements in normal terrestrial materials. © 2013 IUPAC.

The biennial review of atomic-weight determinations and other cognate data has resulted in changes for the standard atomic weights of 19 elements. The standard atomic weights of four elements have been revised based on recent determinations of isotopic abundances in natural terrestrial materials: cadmium to 112.414(4) from 112.411(8), molybdenum to 95.95(1) from 95.96(2), selenium to 78.971(8) from 78.96(3), and thorium to 232.0377(4) from 232.038 06(2). The Commission on Isotopic Abundances and Atomic Weights (ciaaw.org) also revised the standard atomic weights of fifteen elements based on the 2012 Atomic Mass Evaluation: aluminium (aluminum) to 26.981 5385(7) from 26.981 5386(8), arsenic to 74.921 595(6) from 74.921 60(2), beryllium to 9.012 1831(5) from 9.012 182(3), caesium (cesium) to 132.905 451 96(6) from 132.905 4519(2), cobalt to 58.933 194(4) from 58.933 195(5), fluorine to 18.998 403 163(6) from 18.998 4032(5), gold to 196.966 569(5) from 196.966 569(4), holmium to 164.930 33(2) from 164.930 32(2), manganese to 54.938 044(3) from 54.938 045(5), niobium to 92.906 37(2) from 92.906 38(2), phosphorus to 30.973 761 998(5) from 30.973 762(2), praseodymium to 140.907 66(2) from 140.907 65(2), scandium to 44.955 908(5) from 44.955 912(6), thulium to 168.934 22(2) from 168.934 21(2), and yttrium to 88.905 84(2) from 88.905 85(2). The Commission also recommends the standard value for the natural terrestrial uranium isotope ratio, N(²³⁸U)/N(²³⁵U)=137.8(1).

The Commission on Isotopic Abundances and Atomic Weights (ciaaw.org) of the International Union of Pure and Applied Chemistry (iupac.org) has revised the Table of Isotopic Compositions of the Elements (TICE). The update involved a critical evaluation of the recent published literature. The new TICE 2013 includes evaluated data from the “best measurement” of the isotopic abundances in a single sample, along with a set of representative isotopic abundances and uncertainties that accommodate known variations in normal terrestrial materials.

In 2009, the Commission on Isotopic Abundances and Atomic Weights (CIAAW) of the International Union of Pure and Applied Chemistry (IUPAC) introduced the interval notation to express the standard atomic weights of elements whose isotopic composition varies significantly in nature. However, it has become apparent that additional guidance would be helpful on how representative values should be derived from these intervals, and on how the associated uncertainty should be characterized and propagated to cognate quantities, such as relative molecular masses. The assignment of suitable probability distributions to the atomic weight intervals is consistent with the CIAAW’s goal of emphasizing the variability of the atomic weight values in nature. These distributions, however, are not intended to reflect the natural variability of the abundances of the different isotopes in the earth’s crust or in any other environment. Rather, they convey states of knowledge about the elemental composition of “normal” materials generally, or about specific classes of such materials. In the absence of detailed knowledge about the isotopic composition of a material, or when such details may safely be ignored, the probability distribution assigned to the standard atomic weight intervals may be taken as rectangular (or, uniform). This modeling choice is a reasonable and convenient default choice when a representative value of the atomic weight, and associated uncertainty, are needed in calculations involving atomic and relative molecular masses. When information about the provenance of the material, or other information about the isotopic composition needs to be taken into account, then this distribution may be non-uniform. We present several examples of how the probability distribution of an atomic weight or relative molecular mass may be characterized, and also how it may be used to evaluate the associated uncertainty.

The isotopic composition and atomic weight of argon (Ar) are variable in terrestrial materials. Those variations are a source of uncertainty in the assignment of standard properties for Ar, but they provide useful information in many areas of science. Variations in the stable isotopic composition and atomic weight of Ar are caused by several different processes, including (1) isotope production from other elements by radioactive decay (radiogenic isotopes) or other nuclear transformations (e.g., nucleogenic isotopes), and (2) isotopic fractionation by physical-chemical processes such as diffusion or phase equilibria. Physical-chemical processes cause correlated mass-dependent variations in the Ar isotope-amount ratios ( Ar/ Ar, Ar/ Ar), whereas nuclear transformation processes cause non-mass-dependent variations. While atmospheric Ar can serve as an abundant and homogeneous isotopic reference, deviations from the atmospheric isotopic ratios in other Ar occurrences limit the precision with which a standard atomic weight can be given for Ar. Published data indicate variation of Ar atomic weights in normal terrestrial materials between about 39.7931 and 39.9624. The upper bound of this interval is given by the atomic mass of Ar, as some samples contain almost pure radiogenic Ar. The lower bound is derived from analyses of pitchblende (uranium mineral) containing large amounts of nucleogenic Ar and Ar. Within this interval, measurements of different isotope ratios ( Ar/ Ar or Ar/ Ar) at various levels of precision are widely used for studies in geochronology, water–rock interaction, atmospheric evolution, and other fields.

The Large-Scale Structure of Inductive Inference investigates the relations of inductive support on the large scale, among the totality of facts comprising a science or science in general. These relations form a massively entangled, non-hierarchical structure which is discovered by making hypotheses provisionally that are later supported by facts drawn from the entirety of the science. What results is a benignly circular, self-supporting inductive structure in which universal rules are not employed, the classical Humean problem cannot be formulated and analogous regress arguments fail. The earlier volume, The Material Theory of Induction, proposed that individual inductive inferences are warranted not by universal rules but by facts particular to each context. This book now investigates how the totality of these inductive inferences interact in a mature science. Each fact that warrants an individual inductive inference is in turn supported inductively by other facts. Numerous case studies in the history of science support, and illustrate further, those claims. This is a novel, thoroughly researched, and sustained remedy to the enduring failures of formal approaches to inductive inference. With The Large-Scale Structure of Inductive Inference, author John D. Norton presents a novel, thoroughly researched, and sustained remedy to the enduring failures of formal approaches of inductive inference.

The Commission on Isotopic Abundances and Atomic Weights uses annotations given in footnotes that are an integral part of the Tables of Standard Atomic Weights to alert users to the possibilities of quite extraordinary occurrences, as well as sources with abnormal atomic-weight values outside an otherwise acceptable range. The basic need for footnotes to the Standard Atomic Weights Table and equivalent annotations to the Table of Isotopic Compositions of the Elements arises from the necessity to provide users with information that is relevant to one or more elements, but that cannot be provided using numerical data in columns. Any desire to increase additional information conveyed by annotations to these Tables is tempered by the need to preserve a compact format and a style that can alert users, who would not be inclined to consult either the last full element-by-element review or the full text of a current Standard Atomic Weights of the Elements report. Since 1989, the footnotes of the Tables of Standard Atomic Weights and the annotations in column 5 of the Table of Isotopic Compositions of the Elements have been harmonized by use of three lowercase footnotes, “g”, “m”, and “r”, that signify geologically exceptionally specimens (“g”), modified isotopic compositions in material subjected to undisclosed or inadvertent isotopic fractionation (“m”), and the range in isotopic composition of normal terrestrial material prevents more precise atomic-weight value being given (“r”). As some elements are assigned intervals for their standard atomic-weight values (applies to 12 elements since 2009), footnotes “g” and “r” are no longer needed for these elements.

Waclaw Sierpinski described fractal geometries such as Sierpinski triangle, gasket and carpet. In this paper, Sierpinski triangle is used to find any equation between the atomic number and the atomic weight of elements in the periodic table. First by using Matlab program, an algorithm is written to create a right angle triangle between the atomic numbers and atomic weights. Then this original triangle is divide to 8 smaller triangles on the hypotenuse of the original triangle to get more accurate results and reduce errors. Finally, equations of correlation between the atomic numbers and the atomic weights of elements are obtained to calculate the atomic weights of the elements in eighth period.

The spin Hall conductivity (SHC) and anomalous Hall conductivity (AHC) in about 120 full Heusler compounds are calculated using the density functional theory in a high-throughput way. The electronic structures are mapped to the Wannier basis and the linear response theory is used to get the conductivity. Our results show that the mechanism under the SHC or AHC cannot be simply related to the valence electron numbers or atomic weights. It is related to the very details of the electronic structures, which can only be obtained by calculations. A high-throughput calculation is efficient to screen out the desired materials. According to our present results, Rh 2 MnAl and Cu 2 CoSn, as well as Co 2 MnAl and Co 2 MnGa are candidates in spintronic materials regarding their high SHC and AHC values, which can benefit the spin-torque-driven nanodevices.

The periodic system, which intertwines order and similarity among chemical elements, arose from knowledge about substances constituting the chemical space. Little is known, however, about how the expansion of the space contributed to the emergence of the system—formulated in the 1860s. Here, we show by analyzing the space between 1800 and 1869 that after an unstable period culminating around 1826, chemical space led the system to converge to a backbone structure clearly recognizable in the 1840s. Hence, the system was already encoded in the space for about two and half decades before its formulation. Chemical events in 1826 and in the 1840s were driven by the discovery of new forms of combination standing the test of time. Emphasis of the space upon organic chemicals after 1830 prompted the recognition of relationships among elements participating in the organic turn and obscured some of the relationships among transition metals. To account for the role of nineteenth century atomic weights upon the system, we introduced an algorithm to adjust the space according to different sets of weights, which allowed for estimating the resulting periodic systems of chemists using one or the other weights. By analyzing these systems, from Dalton up to Mendeleev, Gmelin’s atomic weights of 1843 produce systems remarkably similar to that of 1869, a similarity that was reinforced by the atomic weights on the years to come. Although our approach is computational rather than historical, we hope it can complement other tools of the history of chemistry.