Metrologia

The unit of thermodynamic temperature, the kelvin, will be redefined in 2018 by fixing the value of the Boltzmann constant, k. The present CODATA recommended value of k is determined predominantly by acoustic gas-thermometry results. To provide a value of k based on different physical principles, purely electronic measurements of k were performed by using a Johnson noise thermometer to compare the thermal noise power of a 200  Ω sensing resistor immersed in a triple-point-of-water cell to the noise power of a quantum-accurate pseudo-random noise waveform of nominally equal noise power. Measurements integrated over a bandwidth of 575 kHz and a total integration time of about 33 d gave a measured value of k = 1.3806513(53)  ×  10 ⁻²³ J K ⁻¹, for which the relative standard uncertainty is 3.9   ×   10 ⁻⁶ and the relative offset from the CODATA 2010 value is +1.8   ×   10 ⁻⁶.

We have determined the acoustic and microwave frequencies of a misaligned spherical resonator maintained near the temperature of the triple point of water and filled with helium with carefully characterized molar mass g mol ⁻¹, with a relative standard uncertainty . From these data and traceable thermometry we estimate the speed of sound in our sample of helium at  K and zero pressure to be  m ² s ⁻² and correspondingly deduce the value  J mol ⁻¹ K ⁻¹ for the molar gas constant. We estimate the value  J K ⁻¹ for the Boltzmann constant using the currently accepted value of the Avogadro constant N _A. These estimates of R and k, with a relative standard uncertainty of 1.06  ×  10 ⁻⁶, are 1.47 parts in 10 ⁶ above the values recommended by CODATA in 2010.

The Boltzmann constant k has been determined from a measurement of the speed of sound in helium gas in a quasi-spherical resonator (volume 0.5 l) maintained at a temperature close to the triple point of water (273.16 K). The acoustic velocity c is deduced from measured acoustic resonance frequencies and the dimensions of the quasi-sphere, the latter being obtained via simultaneous microwave resonance. Values of c are extrapolated to the zero pressure limit of ideal gas behaviour. We find J⋅K ⁻¹, a result consistent with previous measurements in our group and elsewhere. The value for k, which has a relative standard uncertainty of 1.02 ppm, lies 0.02 ppm below that of the CODATA 2010 adjustment.

The principles, techniques and results from dielectric-constant gas thermometry (DCGT) are reviewed. Primary DCGT with helium has been used for measuring T– T ₉₀ below the triple point of water (TPW), where T is the thermodynamic temperature and T ₉₀ is the temperature on the international temperature scale of 1990 (ITS-90), and, in an inverse regime with T as input quantity, for determining the Boltzmann constant at the TPW. Furthermore, DCGT allows the determination of several important material properties including the polarizability of neon and argon as well as the virial coefficients of helium, neon, and argon. With interpolating DCGT (IDCGT), the ITS-90 has been approximated in the temperature range from 4 K to 25 K. An overview and uncertainty budget for each of these applications of DCGT is provided, accompanied by corroborating evidence from the literature or, for IDCGT, a CIPM key comparison.

In 2013, a team from NPL, Cranfield University and SUERC published an estimate of the Boltzmann constant based on precision measurements of the speed of sound in argon. A key component of our results was an estimate of the molar mass of the argon gas used in our measurements. To achieve this we made precision comparison measurements of the isotope ratios found in our experimental argon against the ratios of argon isotopes found in atmospheric air. We then used a previous measurement of the atmospheric argon isotope ratios to calibrate the relative sensitivity of the mass spectrometer to different argon isotopes. The previous measurement of the atmospheric argon isotope ratios was carried out at KRISS using a mass spectrometer calibrated using argon samples of known isotopic composition, which had been prepared gravimetrically.

We report here a new measurement made at KRISS in October 2014, which directly compared a sample of our experimental gas against the same gravimetrically-prepared argon samples. We consider that this direct comparison has to take precedence over our previous more indirect comparison. This measurement implies a molar mass which is 2.73(60) parts in 10 ⁶ lighter than our 2013 estimate, a shift which is seven times our 2013 estimate of the uncertainty in the molar mass.

In this paper we review the procedures used in our 2013 estimate of molar mass; describe the 2014 measurement; highlight some questions raised by the large change in our estimate of molar mass; and describe how we intend to address the inconsistencies between them. We also consider the effect of a new estimate of the low pressure thermal conductivity of argon at 273.16 K. Finally we report our new best estimate of the Boltzmann constant with revised uncertainty, taking account of the new estimates for the molar mass and the thermal conductivity of the argon.

For the quantitative surface characterization of a monocrystalline silicon sphere, PTB has constructed and put into operation an analytical instrument, which combines x-ray fluorescence and x-ray photoelectron spectroscopy techniques. The main objective of this novel instrument is the characterization of the oxide layer and unintentional contaminations, e.g. from hydrocarbons. It is equipped with a ball manipulator allowing measurements at each point on the surface of ball-shaped samples with a diameter of about 93.7 mm. Monocrystalline silicon spheres with this diameter allow a realization of the SI base unit of mass.

A criticism levelled at the Guide to the Expression of Uncertainty in Measurement (GUM) is that it is based on a mixture of frequentist and Bayesian thinking. In particular, the GUM’s Type A (statistical) uncertainty evaluations are frequentist, whereas the Type B evaluations, using state-of-knowledge distributions, are Bayesian. In contrast, making the GUM fully Bayesian implies, among other things, that a conventional objective Bayesian approach to Type A uncertainty evaluation for a number n of observations leads to the impractical consequence that n must be at least equal to 4, thus presenting a difficulty for many metrologists. This paper presents a Bayesian analysis of Type A uncertainty evaluation that applies for all , as in the frequentist analysis in the current GUM. The analysis is based on assuming that the observations are drawn from a normal distribution (as in the conventional objective Bayesian analysis), but uses an informative prior based on lower and upper bounds for the standard deviation of the sampling distribution for the quantity under consideration. The main outcome of the analysis is a closed-form mathematical expression for the factor by which the standard deviation of the mean observation should be multiplied to calculate the required standard uncertainty. Metrological examples are used to illustrate the approach, which is straightforward to apply using a formula or look-up table.

Metrology dedicated to electricity and magnetism has changed considerably in recent years. It encompasses almost all modern scientific, industrial, and societal challenges, e.g. the revision of the International System of Units, the profound transformation of industry, changes in energy use and generation, health, and environment, as well as nanotechnologies (including graphene and 2D materials) and quantum engineering. Over the same period, driven by the globalization of worldwide trade, the Mutual Recognition Arrangement (referred to as the CIPM MRA) was set up. As a result, the regional metrology organizations (RMOs) of national metrology institutes have grown in significance. EURAMET is the European RMO and has been very prominent in developing a strategic research agenda (SRA) and has established a comprehensive research programme. This paper reviews the highlights of EURAMET in electrical metrology within the European Metrology Research Programme and its main contributions to the CIPM MRA. In 2012 EURAMET undertook an extensive roadmapping exercise for proposed activities for the next decade which will also be discussed in this paper. This work has resulted in a new SRA of the second largest European funding programme: European Metrology Programme for Innovation and Research.

Electromagnetic (EM) probes are widely utilized in the measurement of EM fields for non-ionizing radiation, electromagnetic compatibility (EMC) testing and other applications in the frequency range 5 Hz–60 GHz. They must be calibrated by National Metrology Institutes (NMIs) or accredited calibration laboratories in accordance with international standards such as IEEE 1309. The existing NMIs or emerging NMIs should refer to the international comparison measurements in order to assure the quality of their measurement results. Therefore, the electric field comparison measurements organized by TUBITAK UME were performed between TUBITAK UME and SASO NMCC at the 100 Hz, 1 kHz, 10 MHz, 100 MHz, 1 GHz, 10 GHz and 18 GHz frequencies in order to obtain the correction factors of the electric field probes. The comparison measurements were carried out in accordance with the Technical Protocol prepared by TUBITAK UME. The measurements started in October 2017 and were completed in January 2017. There was good agreement found for the correction factors.

Main text

To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.

The final report has been peer-reviewed and approved for publication by the CCEM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

The evaluations of measurement uncertainty involving the application of statistical methods to measurement data (Type A evaluations as specified in the Guide to the Expression of Uncertainty in Measurement, GUM) comprise the following three main steps: (i) developing a statistical model that captures the pattern of dispersion or variability in the experimental data, and that relates the data either to the measurand directly or to some intermediate quantity ( input quantity) that the measurand depends on; (ii) selecting a procedure for data reduction that is consistent with this model and that is fit for the purpose that the results are intended to serve; (iii) producing estimates of the model parameters, or predictions based on the fitted model, and evaluations of uncertainty that qualify either those estimates or these predictions, and that are suitable for use in subsequent uncertainty propagation exercises.

We illustrate these steps in uncertainty evaluations related to the measurement of the mass fraction of vanadium in a bituminous coal reference material, including the assessment of the homogeneity of the material, and to the calibration and measurement of the amount-of-substance fraction of a hydrochlorofluorocarbon in air, and of the age of a meteorite.

Our goal is to expose the plurality of choices that can reasonably be made when taking each of the three steps outlined above, and to show that different choices typically lead to different estimates of the quantities of interest, and to different evaluations of the associated uncertainty. In all the examples, the several alternatives considered represent choices that comparably competent statisticians might make, but who differ in the assumptions that they are prepared to rely on, and in their selection of approach to statistical inference. They represent also alternative treatments that the same statistician might give to the same data when the results are intended for different purposes.

Metrology dedicated to electricity and magnetism has changed considerably in recent years. It encompasses almost all modern scientific, industrial, and societal challenges, e.g. the revision of the International System of Units, the profound transformation of industry, changes in energy use and generation, health, and environment, as well as nanotechnologies (including graphene and 2D materials) and quantum engineering. Over the same period, driven by the globalization of worldwide trade, the Mutual Recognition Arrangement (referred to as the CIPM MRA) was set up. As a result, the regional metrology organizations (RMOs) of national metrology institutes have grown in significance. EURAMET is the European RMO and has been very prominent in developing a strategic research agenda (SRA) and has established a comprehensive research programme. This paper reviews the highlights of EURAMET in electrical metrology within the European Metrology Research Programme and its main contributions to the CIPM MRA. In 2012 EURAMET undertook an extensive roadmapping exercise for proposed activities for the next decade which will also be discussed in this paper. This work has resulted in a new SRA of the second largest European funding programme: European Metrology Programme for Innovation and Research.

Discrete time control systems are widely used in time and frequency applications. Control systems can be designed to reduce phase and frequency offsets to a given reference either more or less aggressively depending on overall system needs. There are many methods available to aid in designing control systems, including techniques based on state space system models. Several state space control design methods will be shown. The control concepts covered in this paper are pole placement, minimum control effort, and linear quadratic Gaussian. The effects of steering limits on system performance will also be discussed.

Water in its three ambient phases plays the central thermodynamic role in the terrestrial climate system. Clouds control Earth’s radiation balance, atmospheric water vapour is the strongest ‘greenhouse’ gas, and non-equilibrium relative humidity at the air–sea interface drives evaporation and latent heat export from the ocean. On climatic time scales, melting ice caps and regional deviations of the hydrological cycle result in changes of seawater salinity, which in turn may modify the global circulation of the oceans and their ability to store heat and to buffer anthropogenically produced carbon dioxide. In this paper, together with three companion articles, we examine the climatologically relevant quantities ocean salinity, seawater pH and atmospheric relative humidity, noting fundamental deficiencies in the definitions of those key observables, and their lack of secure foundation on the International System of Units, the SI. The metrological histories of those three quantities are reviewed, problems with their current definitions and measurement practices are analysed, and options for future improvements are discussed in conjunction with the recent seawater standard TEOS-10. It is concluded that the International Bureau of Weights and Measures, BIPM, in cooperation with the International Association for the Properties of Water and Steam, IAPWS, along with other international organizations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions for these long standing metrological problems in climatology.

Salinity is a key variable in the modelling and observation of ocean circulation and ocean-atmosphere fluxes of heat and water. In this paper, we examine the climatological relevance of ocean salinity, noting fundamental deficiencies in the definition of this key observable, and its lack of a secure foundation in the International System of Units, the SI. The metrological history of salinity is reviewed, problems with its current definitions and measurement practices are analysed, and options for future improvements are discussed in conjunction with the recent seawater standard TEOS-10.

Water dissolves many substances with which it comes into contact, leading to a variety of aqueous solutions ranging from simple and dilute to complex and highly concentrated. Of the multiple chemical species present in these solutions, the hydrogen ion, H ⁺, stands out in importance due to its relevance to a variety of chemical reactions and equilibria that take place in aquatic systems. This importance, and the fact that its presence can be assessed by reliable and inexpensive procedures, are the reasons why pH is perhaps the most measured chemical parameter. In this paper, while examining climatologically relevant ocean pH, we note fundamental problems in the definition of this key observable, and its lack of secure foundation on the International System of Units, the SI. The metrological history of seawater pH is reviewed, difficulties arising from its current definition and measurement practices are analysed, and options for future improvements are discussed in conjunction with the recent TEOS-10 seawater standard. It is concluded that the International Bureau of Weights and Measures (BIPM), in cooperation with the International Association for the Properties of Water and Steam (IAPWS), along with other international organisations and institutions, can make significant contributions by developing and recommending state-of-the-art solutions for these long standing metrological problems.

This paper describes a Josephson-based full digital impedance bridge capable of comparing any two impedances, regardless of type (R-C, R-L, or L-C), over a large frequency range (from 1 kHz to 20 kHz). At the heart of the bridge are two Josephson arbitrary waveform synthesizer systems that offer unprecedented flexibility in high-precision impedance calibration, that is, it can compare impedances with arbitrary ratios and phase angles. Thus this single bridge can fully cover the entire complex plane. In the near future, this type of instrument will considerably simplify the realization and maintenance of the various impedance scales in many National Metrology Institutes around the world.

A knowledge of the effect of impurities at the level of parts per million on the freezing temperature of very pure metals is essential for realisation of ITS-90 fixed points. New information has become available for use with the thermodynamic modelling software MTDATA, permitting calculation of liquidus slopes, in the low concentration limit, of a wider range of binary alloy systems than was previously possible. In total, calculated values for 536 binary systems are given. In addition, new experimental determinations of phase diagrams, in the low impurity concentration limit, have recently appeared. All available data have been combined to provide a comprehensive set of liquidus slopes for impurities in ITS-90 metal fixed points. In total, liquidus slopes for 838 systems are tabulated for the fixed points Hg, Ga, In, Sn, Zn, Al, Ag, Au, and Cu. It is shown that the value of the liquidus slope as a function of impurity element atomic number can be approximated using a simple formula, and good qualitative agreement with the existing data is observed for the fixed points Al, Ag, Au and Cu, but curiously the formula is not applicable to the fixed points Hg, Ga, In, Sn, and Zn. Some discussion is made concerning the influence of oxygen on the liquidus slopes, and some calculations using MTDATA are discussed. The BIPM’s consultative committee for thermometry has long recognised that the sum of individual estimates method is the ideal approach for assessing uncertainties due to impurities, but the community has been largely powerless to use the model due to lack of data. Here, not only is data provided, but a simple model is given to enable known thermophysical data to be used directly to estimate impurity effects for a large fraction of the ITS-90 fixed points.

The watt balance relates force or mass to the Planck constant h, the metre and the second. It enables the forthcoming redefinition of the unit of mass within the SI by measuring the Planck constant in terms of mass, length and time with an uncertainty of better than 2 parts in 10 ⁸. To achieve this, existing watt balances require complex and time-consuming alignment adjustments limiting their use to a few national metrology laboratories. This paper describes a simplified construction and operating principle for a watt balance which eliminates the need for the majority of these adjustments and is readily scalable using either electromagnetic or electrostatic actuators. It is hoped that this will encourage the more widespread use of the technique for a wide range of measurements of force or mass. For example: thrust measurements for space applications which would require only measurements of electrical quantities and velocity/displacement.

We review the principles, techniques and results from primary acoustic gas thermometry (AGT). Since the establishment of ITS-90, the International Temperature Scale of 1990, spherical and quasi-spherical cavity resonators have been used to realize primary AGT in the temperature range 7 K to 552 K. Throughout the sub-range 90 K <  T < 384 K, at least two laboratories measured ( T −  T ₉₀). (Here T is the thermodynamic temperature and T ₉₀ is the temperature on ITS-90.) With a minor exception, the resulting values of ( T −  T ₉₀) are mutually consistent within 3 × 10 ⁻⁶  T. These consistent measurements were obtained using helium and argon as thermometric gases inside cavities that had radii ranging from 40 mm to 90 mm and that had walls made of copper or aluminium or stainless steel. The AGT values of ( T −  T ₉₀) fall on a smooth curve that is outside ± u( T ₉₀), the estimated uncertainty of T ₉₀. Thus, the AGT results imply that ITS-90 has errors that could be reduced in a future temperature scale. Recently developed techniques imply that low-uncertainty AGT can be realized at temperatures up to 1350 K or higher and also at temperatures in the liquid-helium range.

The kilogram is the last unit of the international system of units (SI) still based on a material artefact, the international prototype of the kilogram (IPK). The comparisons made in the last hundred years have clearly revealed a long-term relative drift between the IPK and the official copies kept under similar conditions at the Bureau International des Poids et Mesures. A promising route towards a new definition of the kilogram based on a fundamental constant is represented by the watt balance experiment which links the mass unit to the Planck constant h. For more than ten years, the Federal Institute of Metrology METAS has been actively working in the conception and development of a watt balance experiment. This paper describes the new design of the Mark II METAS watt balance. The metrological characteristics of the different components of the experiment are described and discussed.