This paper gives the 2010 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. The 2010 adjustment takes into account the data considered in the 2006 adjustment as well as the data that became available from 1 January 2007, after the closing date of that adjustment, until 31 December 2010, the closing date of the new adjustment. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2010 set replaces the previously recommended 2006 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.

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CODATA Recommended Values of the Fundamental Physical Constants: 2006

One of the early projects established by CODATA was intended to provide a recommended set of the fundamental physical constants, which are so important to the analysis and interpretation of experimental data in many scientific disciplines. The first "Recommended Consistent Values of the Fundamental Physical Constants" appeared in 1973 and was subsequently adopted by most international and national bodies in their own recommendations. This process has contributed to improved compatibility of scientific and technical data in all fields of science. CODATA presents here a revised version of these recommendations which takes into account the significant advances in metrology that have occurred since the 1973 analysis. "The 1986 adjustment of the fundamental physical constants" represents a 5-year effort involving experts from the major metrological laboratories of the world. It is hoped that this recommended data set will receive the acceptance of the scientific community which was achieved by its predecessor.

The 1986 adjustment of the fundamental physical constants

National Sureau of Standards, Gaithersburg, Maryland 20899 One of the early projects established by CODATA was intended to provide a recommended set of the fundamental physical constants, which are so important to the analysis and interpretation of experimental data in many scientific disciplines, The first "Recommended Consistent Values of the Fundamental Physical Constants" appeared in 1973 and was subsequently adopted by most international and national bodies in their own recommendations. This process has contributed to improved compatibility of scientific and technical data in all fields of science. CODATA presents here a revised version of these recommendations which takes into account the significant advances in metrology that have occurred since the 1973 analysis. "The 1986 adjustment of the fundamental physical constants" represents a 5-year effort involving experts from the major metrological laboratories of the world. It is hoped that this recommended data set will receive the acceptance of the scientific community which was achieved by its predecessor.

The 1986 adjustment of the fundamental physical constants: a report of the codata task group on fundamental constants

The quantum Hall effect (QHE) provides an invariant reference for resistance linked to natural constants It is used worldwide to maintain and compare the unit of resistance The reproducibility reached today is almost two orders of magnitude better than the uncertainty of the determination of the ohm in the international system of units SI In this article, mainly the aspects of the QHE relevant for its metrological application are reviewed After a short introduction of the theoretical models describing the integer QHE, the properties of the devices used in metrology and the measurement techniques are described A detailed summary is given on the measurements carried out to demonstrate the universality of the quantized Hall resistance and to assess all the effects leading to deviations of the Hall resistance from the quantized value In addition, the present and future role of the QHE in the SI and the field of natural constants is discussed

https://iopscience.iop.org/article/10.1088/0034-4885/64/12/201/pdf

The quantum Hall effect as an electrical resistance standard

The measurement of the Planck constant, h, is entering a new phase. The CODATA 2010 recommended value is 6.626 069 57 × 10(-34) J s, but it has been a long road, and the trip is not over yet. Since its discovery as a fundamental physical constant to explain various effects in quantum theory, h has become especially important in defining standards for electrical measurements and soon, for mass determination. Measuring h in the International System of Units (SI) started as experimental attempts merely to prove its existence. Many decades passed while newer experiments measured physical effects that were the influence of h combined with other physical constants: elementary charge, e, and the Avogadro constant, N(A). As experimental techniques improved, the precision of the value of h expanded. When the Josephson and quantum Hall theories led to new electronic devices, and a hundred year old experiment, the absolute ampere, was altered into a watt balance, h not only became vital in definitions for the volt and ohm units, but suddenly it could be measured directly and even more accurately. Finally, as measurement uncertainties now approach a few parts in 10(8) from the watt balance experiments and Avogadro determinations, its importance has been linked to a proposed redefinition of a kilogram unit of mass. The path to higher accuracy in measuring the value of h was not always an example of continuous progress. Since new measurements periodically led to changes in its accepted value and the corresponding SI units, it is helpful to see why there were bumps in the road and where the different branch lines of research joined in the effort. Recalling the bumps along this road will hopefully avoid their repetition in the upcoming SI redefinition debates. This paper begins with a brief history of the methods to measure a combination of fundamental constants, thus indirectly obtaining the Planck constant. The historical path is followed in the section describing how the improved techniques and discoveries in quantum mechanics steadily reduced the uncertainty of h. The central part of this review describes the technical details of the watt balance technique, which is a combination of the mechanical and electronic measurements that now determine h as a direct result, i.e. not requiring measured values of additional fundamental constants. The first technical section describes the basics and some of the common details of many watt balance designs. Next is a review of the ongoing advances at the (currently) seven national metrology institutions where these experiments are pursued. A final summary of the recent h determinations of the last two decades shows how history keeps repeating itself; there is again a question of whether there is a shift in the newest results, albeit at uncertainties that are many orders of magnitude less than the original experiments. The conclusion is that there is room for further development to resolve these differences and find new ideas for a watt balance system with a more universal application. Since the next generation of watt balance experiments are expected to become kilogram realization standards, the historical record suggests that there is yet a need for proof that Planck constant results are finally reproducible at an acceptable uncertainty.

https://iopscience.iop.org/article/10.1088/0034-4885/76/1/016101/pdf

History and progress on accurate measurements of the Planck constant

Progress toward an understanding of the frequency dependence of capacitance and resistance standards at frequencies up to 10 MHz is presented. A qualitative comparison is also made for capacitance and dissipation factor measurements between the National Physical Laboratory (NPL) high-frequency four terminal-pair (4TP) bridge and a commercial impedance analyzer for the first time. A set of novel high-frequency calculable coaxial resistance standards, of nominal 100 /spl Omega/ and 1 k/spl Omega/ values, have been developed and their calculated frequency dependence up to 1 MHz is given.

Towards accurate measurement of the frequency dependence of capacitance and resistance standards up to 10 MHz

New measurements relating the quantized Hall resistance R H (= h/ie2), International System (SI) Ohm (Ω SI ), and the National Physical Laboratory maintained ohm (Ω NPL ) have now been completed at NPL in the U.K. with improvements and simplifications in the cryogenic current comparator measurements and 1000-Ω dc resistance measurements. From the measurements over the past four years the relationship between Ω NPL and Ω SI can be described by the equation Ω NPL − Ω SI = −1.049(0.020) − 0.0478(0.0074)[t − 1986.0] μΩ in which t is measured in years. For the previous two years the equivalent relationship between R H and Ω NPL is R H = 25 812.8(1 + 1.452(0.038) × 10 −6 + 0.0694(0.0772) · [t − 1986.0] × 10−6) Ω NPL in which the uncertainties (in parentheses) are one-standard-deviation (1σ) random uncertainties of the least squares fit to the data. Combining the most recent measurements of R H and Ω SI , using a more direct method of measurement R H = 25 812.8106(17) Ω SI in which the relative combined uncertainty is 0.067 × 10−6.

The relationship between the SI Ohm, the Ohm at NPL, and the quantized Hall resistance

Since 1990, the quantum Hall resistance measured with direct current (dc) has been established to represent and maintain the dc resistance unit and thereby has replaced the former derivation from calculated inductance and capacitance standards. Because of this success, it has been suggested to measure this quantum effect with alternating current (ac) and in this way to derive the units of resistance, capacitance and inductance consistently from the same quantum effect. In this paper, we recall the relations between these units, their role in the determination of the von Klitzing constant and the relations between the fundamental constants involved in the conventional and the quantum approach. Then, we review the first ac measurements of the quantum Hall resistance and show how the difficulties uncovered have been solved by relatively simple means. As a result, the measurement of the ac quantum Hall resistance has become as precise and reliable as its dc counterpart and much more accurate than any conventional impedance artefact.

https://iopscience.iop.org/article/10.1088/0957-0233/23/12/124009/pdf

The ac quantum Hall resistance as an electrical impedance standard and its role in the SI

Arbitrary impedance ratios can be determined with high accuracy by means of a programmable Josephson system. For a 1 : 1 resistance ratio at 10-kΩ level, we demonstrate that the novel system allows measurements over a wide frequency range from 25 Hz to 6 kHz. Uncertainties are in the range of a few parts in 108 and thus comparable to those of conventional impedance bridges. Two methods for four-terminal-pair impedance measurements have been investigated, i.e., the potential comparison circuit and the coaxial setup. Both methods are capable of measuring from dc to 6 kHz with uncertainties to a few parts in 108. The potential comparison circuit has an upper bound at 6 kHz due to the use of the sampling method. The four-terminal-pair coaxial setup has the potential to decrease the relative uncertainty down to 10-9 once systematic errors are analyzed and canceled.

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Programmable Josephson Arrays for Impedance Measurements

A new four terminal-pair bridge has been developed and used for traceable measurement of capacitance and resistance at frequencies up to 1 MHz. The apparent capacitance of a gas-filled 100-pF standard agrees with calculated values to better than 200 /spl mu/F/F at 1 MHz. This is an order of magnitude improvement on existing capabilities at NPL. The frequency dependence of the dissipation factor of capacitance standards is discussed, and the capacitance and dissipation factor of ceramic NPO-dielectric standards has also been measured. The frequency dependence measurements of the calculable coaxial 100-/spl Omega/ and 1-k/spl Omega/ resistance standards are also presented.

Bryan Kibble

Papers

Towards accurate measurement of the frequency dependence of capacitance and resistance standards up to 10 MHz

The relationship between the SI Ohm, the Ohm at NPL, and the quantized Hall resistance

The ac quantum Hall resistance as an electrical impedance standard and its role in the SI

Programmable Josephson Arrays for Impedance Measurements

A new four terminal-pair bridge for traceable impedance measurements at frequencies up to 1 MHz