Table of contents

In view of the progress achieved in the field of the alternating current (ac) quantum Hall effect (QHE), the Working Group of the Comité Consultatif d'Électricité et Magnétisme (CCEM) on the ac QHE asked the authors of this article to write a compendium which integrates their experiences with ac measurements of the quantum Hall resistance. In addition to the important early work performed at the Bureau International des Poids et Mesures and the National Physical Laboratory, UK, further experience has been gained during a collaboration of the authors' institutes NRC, METAS and PTB, and excellent agreement between the results of different national metrology institutes has been achieved. This compendium summarizes the present state of the authors' knowledge and reviews the experiences, tests and precautions that the authors have employed to achieve accurate measurements of the ac QHE. This work shows how the ac QHE can be reliably used as a quantum standard of ac resistance having a relative uncertainty of a few parts in 10⁸.

A re-evaluation of the BIPM standards for air kerma in low- and medium-energy x-rays has been made. The changes to the air-kerma rate determination arise from three sources: (i) the results of Monte Carlo calculations of diaphragm correction factors for the standards, (ii) a measurement of the effect of scatter from the diaphragm support and (iii) a re-evaluation of the electron-loss corrections for the medium-energy standard. Scatter from the diaphragm support explains a long-standing trend observed in the results of international comparisons for medium-energy x-rays. The new standards were implemented on 1 September 2009.

Following the change to the BIPM standard for air kerma in ⁶⁰Co adopted in November 2007, a re-evaluation of the BIPM standard for air kerma in ¹³⁷Cs radiation has been made. The changes to the air-kerma rate determination arise from three sources: (i) the results of Monte Carlo calculations of correction factors for the standard; (ii) a re-evaluation of the correction factor for saturation; (iii) a new evaluation of the air volume of the standard using an experimental chamber of variable volume. The combined effect of these changes is an increase in the BIPM determination of the air-kerma rate by the factor 1.0030 and a reduction in the relative standard uncertainty of this determination to 1.9 parts in 10³. A full uncertainty budget is presented.

From 1 May 2009 the United Kingdom National Physical Laboratory (NPL) has changed its air kerma standards for Cs-137 and Co-60 γ-rays. Adoption of the new correction factors results in an increase in the NPL air kerma standard by ∼1% for both Cs-137 and Co-60 γ-rays. All NPL secondary standard calibrations issued after 1 May 2009 contain the revised correction factor.

This paper describes the metrological characterization of a new large area piston gauge (FRS5, Furness Rosenberg Standard) installed at the vacuum metrology laboratory of the Physikalisch-Technische Bundesanstalt (PTB). The operational procedure and the uncertainty budget for pressures between 30 Pa and 11 kPa are given. Comparisons between the FRS5 and a mercury manometer, a rotary piston gauge and a force-balanced piston gauge are described. We show that the reproducibility of the calibration values of capacitance diaphragm gauges is enhanced by a factor of 6 compared with a static expansion primary standard (SE2). Improvements of the SE2 performance by reducing the number of expansions and smaller uncertainties of expansion ratios are discussed.

A method for evaluating the uncertainty in linking a bilateral key comparison to another key comparison with several participants is presented theoretically and demonstrated with an actual comparison. Equations are derived for the uncertainties of the unilateral and mutual degrees of equivalence for the linked participant in the bilateral comparison. It is shown that the uncertainty components related to uncorrelated effects in the measurements of the linking participant play a critical role in determining the additional uncertainties due to the linking process. As a practical example, the results are applied to a bilateral comparison of the spectral irradiance scales of MIKES (Finland) and NIMT (Thailand) in the spectral range from 290 nm to 900 nm.

The Monte Carlo method is recommended to propagate distributions through the equation of the measurand in the first supplement to the GUM. The result of this method is an approximation of the probability density function (PDF) representing the output quantity of the measurement. This approximation can be used to calculate all necessary statistical parameters such as the expectation value or the standard uncertainty of the measurand. For computational reasons, it is advisable to use a block-by-block evaluation, the Monte Carlo block design, when implementing this method. The statistical parameters of the measurand are then calculated using the statistical parameters of equal sized blocks. This paper demonstrates that this procedure delivers reasonable estimators for the true statistical parameters of the PDF representing the measurand.

The paper presents an absolute Johnson noise thermometer (JNT), an instrument to measure the thermodynamic temperature of a sensing resistor, with traceability to voltage, resistance and frequency quantities. The temperature is measured in energy units, and can be converted to SI units (kelvin) with the accepted value of the Boltzmann constant k_B; or, conversely, it can be employed to perform measurements at the triple point of water and obtain a determination of k_B. The thermometer is composed of a correlation spectrum analyzer and a calibrator. The calibrator generates a pseudorandom noise (at a level suitable for traceability to an ac voltage standard) by digital synthesis, scaled in amplitude by a chain of electromagnetic voltage dividers and cyclically injected in series with the Johnson noise. First JNT measurements at room temperature are compatible with those of a standard platinum resistance thermometer within the estimated combined uncertainty of 60 µK K⁻¹ of both instruments. A path towards future improvements of JNT accuracy is also sketched.

For the new definition of the SI unit of mass based on a fundamental constant, a redetermination of Avogadro's constant is the goal of an international collaboration of numerous national laboratories and universities. Since a relative uncertainty of about 2 × 10⁻⁸ is aimed at, the macroscopic density, the isotopic composition and the volume of the unit cell of a silicon single crystal have to be measured with high precision. One step to improve the precision was the production of a silicon crystal of highly enriched ²⁸Si. This paper addresses the effect of thermal expansion of that material in order to account for a possible discrepancy between the coefficient of thermal expansion (CTE) of natural silicon and that of ²⁸Si. The results of two independent CTE measuring methods are presented and compared in this paper.

In the range between 0 °C and 961 °C, the International Temperature Scale of 1990 (ITS-90) depends to a great extent on the freezing points of the pure metals gallium, indium, tin, zinc, aluminium and silver. An up-to-date realization of these fixed points is based on cells containing metals of ultra-high purity (6N or better) and should include a correction for the influence of relevant impurities. Still, chemical analyses of the fixed-point material can show large amounts of oxygen, which had to be neglected so far, because of the lack of detailed knowledge about it, presuming it could be removed from the cell by applying a vacuum (less than 1 Pa) for a few hours.

In this paper we discuss an equilibrium of several forms of oxygen in a fixed-point cell, gaseous in the cell's atmosphere, dissolved in the fixed-point metal and as oxide in a separate (solid) phase. We will conclude that in many fixed points most of the oxygen is not dissolved in the metal, but bound in oxides of the fixed-point metal as well as oxides of some impurities. To demonstrate the impact that the precipitation of impurity oxides has on thermometry, two indium fixed-point cells were doped with magnesium and chromium, which leave the fixed-point temperature unchanged. Further evidence is drawn from earlier work. All these results support the presumed existence of (at least one) persistent separate oxide phase in the fixed points of indium, tin, zinc and aluminium, which renders them eutectic or peritectic points and is a more likely reason why the oxygen content of a cell does not influence the fixed-point temperature.

To complement these studies, thermodynamic calculations show how to treat the equilibrium in the cell quantitatively. Using available chemical data, a list is provided that indicates for each fixed-point metal (including the other metal fixed points of the ITS-90: mercury, gold, copper) the impurities that probably build oxides. Due to the agreement of the calculated values with the presented experimental results, we suggest excluding those impurities from the correction of a fixed-point temperature (e.g. the SIE method), unless there is strong evidence of their dissolution.

The half-life of ²³³U was determined by a specific activity method, in the frame of an international collaboration project of four metrology institutes. A purified, highly enriched ²³³U solution was prepared with certified concentration of uranium isotopes. The isotopic composition of the uranium material was determined by thermal ionization mass spectrometry. The ingrowth of daughter nuclides was calculated and confirmed by α-particle and γ-ray spectrometry measurements. Quantitative sources were prepared from aliquots of the ²³³U solution and their disintegration rate was determined by means of α-particle counting at a defined small solid angle, liquid-scintillation counting and 4π counting in a pressurized proportional counter and in a CsI(Tl) sandwich spectrometer. A half-life value of 1.5867 (14) × 10⁵ a was obtained, in which the relative standard uncertainty amounts to 0.09%. The result is lower than the currently recommended value of 1.592 (2) × 10⁵ a and a new best estimate of T_1/2(²³³U) = 1.5903 (13) × 10⁵ a was calculated from a partially weighted mean of a set of published data.

We present an investigation of iodine cell purity and influence of contaminations upon frequency shifts of iodine-stabilized frequency-doubled Nd : YAG lasers. The study combines measurements of laser-induced fluorescence and evaluation through the Stern–Volmer formula, with direct measurement of frequency shifts referenced by means of an optical comb to a radiofrequency clock etalon. These indirect and direct approaches are compared and provide feedback on the cell manufacturing procedure. Significant improvement of the apparatus for the measurement of induced fluorescence is reported, leading to better repeatability of the results. The ultimate precision that can be achieved in measurements of the absolute frequency of a stabilized laser is discussed in terms of the cell quality.

The trend towards an International System of Units (SI) based on fundamental constants has been confirmed and recent actions could result in the redefinition of the four units still necessary to cover all the quantities of interest for physics and chemistry. In this paper some issues whose solution is becoming critical with the approach of the General Conference on Weights and Measures (CGPM) of 2011 are discussed. The traditional kinds of definition and the new proposals are considered on the basis of their mathematical expressions and the advantageous features of the most advanced proposal are pointed out. The problem of choosing the set of fundamental constants to be adopted as reference quantities for the SI units is addressed and a general rule for verifying that the set is sufficient and non-redundant is pointed out in the form of a linear system giving also expressions of all the units as functions of the reference constants. A partial application to the most important units and different sets of constants offers some comparative criteria and shows the advantages of a set including both h and m_e. A general condition to be fulfilled by an experiment in order to realize an SI unit is given and a procedure suitable to optimize the availability of the best relization on a global basis is outlined. Finally, the dissemination process is analysed to show that the implied comparisons of standards at any level are not affected by the realization uncertainty, so that the process can be continued with the same standards, independently of any change in the basic reference quantities of the unit system.

A watt balance relates mechanical power to electrical power by comparing the gravitational force on a mass with the electromagnetic force on a current-carrying coil in a magnetic field. It is one of the favoured approaches to replacing the present artefact kilogram as it will allow the kilogram to be redefined in terms of the Planck constant. In this paper, we propose an oscillatory approach to the dynamic or moving mode of a watt balance experiment as an alternative to the traditional constant velocity approach. Features of an oscillatory dynamic mode include frequency selection and Fourier analysis to reduce noise due to vibration, the option of larger coil velocities (above 2 mm s⁻¹) and smaller coil movement amplitudes (of order ±1 mm) than the constant velocity approach, and direct measurement at the weighing position of the factor γ relating coil current to the gravitational force on the mass. An oscillatory dynamic mode can be used with some of the existing watt balance experiments with the potential to measure γ faster and more precisely than the constant velocity approach.

A Pd–C eutectic fixed point cell (1492 °C) was constructed to investigate its utility for thermocouple calibration. The primary aim of the study was to evaluate the long-term stability, immersion characteristics (influence of heat conduction along the thermocouple stem) and robustness of a Pd–C fixed point using a Pt/Pd thermocouple, especially constructed for this purpose. The performance of both devices at this relatively high temperature could therefore be tested. The melting and freezing plateaux at the Pd–C eutectic point were measured using the Pt/Pd thermocouple. The total exposure to the Pd–C melting temperature was about 850 h for the fixed point cell and 550 h for the thermocouple. The standard deviations of the melting and freezing points were 1.03 µV (0.041 °C) and 0.77 µV (0.031 °C) respectively. The emfs of the thermocouple at the melting point were observed to drift by about 0.1 °C. The immersion measurements show that for the current cell design, the measuring junction should be at most 30 mm from the bottom of the thermowell to be properly immersed. The long-term performance and robustness of the fixed point indicate a promising future for its use as a fixed point for calibration of noble metal thermocouples.

Various techniques are used to measure the mean particle size (PS) and the particle size distribution (PSD) and relevant uncertainties of the measured mean PS and PSD can be obtained by using statistical treatments. Among those techniques, microscopic analysis methods provide the possibility to observe individual particles, allowing detailed information about the PS. However, there is no existing method to estimate the uncertainty of the PSD from a finite number of data obtained by microscopic measurement. We found that it is possible to adopt the method of deducing the standard deviation of the sample standard deviation to estimate the PSD uncertainty from the result of a microscopic analysis when the sample data follow a normal or log-normal distribution. The recommended minimum number of data for the application of developed statistical methods was deduced by simulation with population data sets of pseudorandom numbers. It was found that the PS of gold nanoparticles (NPs) synthesized by the conventional reduction method in aqueous solution followed a log-normal distribution, indicating that this method is applicable to estimate the PSD uncertainty of synthetic Au NPs from the measured PS data obtained by microscopic methods.

A set-up for the calibration of a heterodyne laser-vibrometer is described. By a distinctive optical set-up it is possible to use the laser of the device under test as the single source for the calibration device. In this way many difficulties of the optical adjustment usually encountered in set-ups for laser-vibrometer calibration are avoided and exceptionally low measurement uncertainties are achieved.

This article describes the set-up for the case of a commercially available device which is additionally modified to provide the means for primary traceability. The measurement results are discussed for the analogue output usually used in industrial applications as well as for the output of the photodetector signal, which is used if the device is part of a primary calibration system. Special attention is given to the provisions necessary to achieve low measurement uncertainties.

Surface tension effects in capillary viscometry play an important role in the accuracy of the measurements of kinematic viscosity. An experimental evaluation of these effects has been carried out using capillary viscometers having the same shape and size of the upper and lower bulbs, the same timing bulb, the same capillary radius, but different capillary lengths. The measurement method applied for evaluating the correction factor and its associated uncertainty is described. As an example, results of the kinematic viscosity of the liquid n-nonane, obtained with two Ubbelohde viscometers, which have been calibrated with bi-distilled water, are presented.

National measurement institutes (NMIs) participate in international key comparisons organized by the Bureau International des Poids et Mesures (BIPM), the Regional Metrology Organizations (RMOs) or the Consultative Committees of the Comité International des Poids et Mesures (CIPM) in order to provide evidence of equivalent reference standards and measurement capabilities. The US National Institute of Standards and Technology (NIST) and the National Measurement Institute of Australia (NMIA) have recently examined power loading and several other influences on the value of precision transportable 1 Ω resistors that can increase the uncertainty of key comparisons. We have studied the effects of temperature, barometric pressure, humidity, power loading and heat dissipation in oil on transportable wire-wound 1 Ω resistance standards that are based on different alloys and construction principles. This work focuses on standards manufactured from 1970 through 2000 by the NMIA made of Evanohm alloy and on Thomas-type resistors designed in the 1930s and made of Manganin alloy. We show that the relative standard uncertainty related to transport can be less than 0.01 μΩ Ω⁻¹ when using certain resistors of these two types that are characterized and selected for stability. We describe the characterization process, and relate the environmental influences to the physical design, as well as to the mechanical properties and condition of the standards.

The variance of temperature measurements made with the NIST Johnson noise thermometer has been reduced by the use of improved cross-correlation electronics and a unique method for measuring and reducing non-linearities. The spectral response of the voltage noise and the reproducibility of the measured temperature were improved by the use of a lower-noise preamplifier with better common-mode rejection and by removal of a systematic aliasing error through additional filtering. Even with these improvements, however, measurements with precision multi-tone comb and two-tone waveforms, which were synthesized with the quantum voltage noise source, showed that distortion generated by non-linearities in the electronics still limited the measurement standard deviation to (3–5) µK/K greater than that expected for uncorrelated white noise. The new electronics and the measurement techniques used to characterize the non-linearities are described. Synthesized waveforms that have higher tone density are shown to reduce the distortion generated by the remaining non-linearities so that the variance of the measurement is no longer limited and continues to decrease with measurement time as expected.

Critical tests of the accuracy of ab initio theoretical values of the helium virial coefficients have been made based on experiments with a new dielectric-constant gas thermometry (DCGT) setup established at PTB. As the main starting point, most accurate experimental results for the thermodynamic temperature and the dielectric polarizability of ³He and ⁴He have been deduced recently. This paper now concentrates on the results for the two- and three-particle interaction described by the second and third density virial coefficients of helium. A comparison between experimental DCGT results and new highly accurate theoretical ab initio results shows an impressive agreement. The experimental uncertainties have been estimated via Monte-Carlo simulations and are comparable to the uncertainty of the latest theory.

In this paper it is shown that the size-of-source effect (SSE) of a radiation thermometer measured for a range of source diameters D_i, can be fitted by means of empirical analytical approximations F(D), selected on the basis of quite general arguments. This is necessary to analytically process SSE data and to rigorously quantify the uncertainties associated with the correction for the SSE. To test the proposed fitting scheme 35 size-of-source curves, measured by five institutes for different radiation thermometers, have been analysed. In a companion paper the uncertainty in the correction for the SSE will be elaborated in detail for two examples.

In the first part of this paper a procedure is described for calculating the standard uncertainty u[F(D)] in the approximation F(D) to the size-of-source effect σ(D_i), measured for a range of source diameters D_i, for two examples out of a total of 35 considered in an accompanying paper. The overall uncertainty includes the uncertainty s_fit of the approximation F(D) to the experimental data and other components such as the repeatability of the measurements, the effect of interreflections and the in-focus/out-of-focus shift. In the main part of the paper this procedure is tailored to the calculation of the uncertainty u_SSE[S(D_ref)]/S(D_ref) in the correction for the size-of-source effect as a function of the reference diameter D_ref, a relationship characteristic for a given thermometer–source combination. The source considered here is a eutectic fixed-point radiator, Re–C, radiating at the eutectic temperature of 2747 K. The correction is carried out by transformation of the directly obtained results, in terms of the signals S measured under the local prevailing measurement conditions, to univocal results associated with a specified reference condition. The utility of the formalism is demonstrated by some practical applications given in an appendix to the paper.

The dependence of the eigenvalues of the TM1n and TE1n electromagnetic triplet modes on the shape of a triaxial ellipsoid cavity resonator is investigated. For an ellipsoid with semi-axes proportional to 1 : (1 + ₁) : (1 + ₂) the fractional perturbations of the triplet components are found to second order in ₁ and ₂. The formulae are derived from the results of Kokkorakis and Roumeliotis (1997 J. Electromagn. Waves Appl.11 279–92) for prolate and oblate spheroids. Finite-element calculations were carried out to confirm the accuracy of the formulae and to determine the next correction terms.

Test leaks with a gas flow to atmospheric pressure are often called sniffer test leaks. They are used to calibrate leak detectors for sniffing applications. Sniffer test leaks need calibration against a standard. A primary standard for the calibration of sniffer test leaks with relatively low measurement uncertainties is described. It is assured that the measurement result is traceable to the relevant SI units and that there is a well-known and complete measurement uncertainty budget. The measurement range of the system is from 4 × 10⁻¹¹ mol s⁻¹ (corresponding to 10⁻⁴ Pa l s⁻¹ at 23 °C) to 4 × 10⁻⁹ mol s⁻¹ (10⁻² Pa l s⁻¹ at 23 °C), which is the most often needed range in industry of around 1 g loss per year of the cooling agent R134a. The temperature where the calibration can be carried out may vary from 18 °C to 30 °C. The flow rate of any test gas not condensing in this temperature range can be measured.

We show how to solve two problems of optimal linear estimation from a set of noisy measurements of clock phase. The phase is modelled as a process with stationary dth increments, e.g. a sum of processes with power-law spectra. The additive measurement noise can be any mean-zero process with a known autocovariance function. The estimation targets are the phase at a given time and the coefficient of the overall trend, e.g. the frequency drift. A feasibility condition called 'invariance' is imposed according to the target and the degree of non-stationarity of the phase model. The solution of a set of linear equations gives the regression coefficients and the mean squared error of the best linear invariant estimate. Proofs of these results are available from the online version of this journal.

This paper describes the result of work performed at the Laboratoire National de Métrologie et d'Essais (LNE) aiming at characterizing the metrological performance of analogue-to-digital converters of a commercial digital voltmeter in the 20 Hz to 400 Hz frequency range. In order to reach uncertainties at the 10⁻⁶ level, ac–dc thermal transfer techniques have been used to determine the most suitable sampling parameters for these digitizers with respect to the measured signal frequency. Under such conditions, the agreement between the sampling technique and thermal ac–dc transfer is of the order of 2 µV V⁻¹.

Recent developments have cast doubt on the value for the electron stopping power for graphite used in dosimetry. Information has come from a number of areas: a new measurement of the mean excitation energy, I, for graphite; experiments indicating that the crystallite density for graphite, rather than its bulk density, should be used to evaluate the stopping power; experiments in medium-energy x-rays comparing free-air and cavity ionization chambers and Monte Carlo calculations of the behaviour of graphite-walled cavity chambers in ⁶⁰Co gamma-rays and medium-energy x-rays. The stopping powers for graphite currently recommended were evaluated using an I-value of 78 eV. The use of the more recent value I = 86.9 eV reduces the graphite stopping power for ⁶⁰Co by around 1.5%, which in a simple analysis increases the W-value for air by a similar amount. However, such an increase is in conflict with the evidence that the W-value is close to the value 33.97 eV currently recommended. This paper presents the various components and constraints, analyses the uncertainties and shows that the use of a graphite I-value of 82.5 eV, a W-value of 33.97 eV and the crystallite density of graphite reasonably explain the experimental observations. The standard uncertainty of this I-value determination is 1.5 eV.

Two methods for comparing the pressures of different media generated by gas and hydraulic pressure balances are examined in order to improve the consistency between gas and hydraulic pressure standards. One method uses a gas–liquid separator and the other uses a liquid-lubricated pressure balance. The pressure range examined is 0.5 MPa to 7 MPa. For both methods, a precise pressure transducer is used as a comparator to determine the equilibrium state between the two pressure balances. In this paper, the measurement results and the uncertainties obtained for the respective methods are presented. It is shown that the results obtained by using both methods agree within the combined standard uncertainty over the entire pressure range. Thus, both methods examined in this study are found to be useful for comparing gas and hydraulic pressure balances accurately.

An opto-electronic device for the stabilization of laser beam intensity in a narrow frequency band based on a numeric corrector driving the radio-frequency signal of an acousto-optic modulator is applied to improve the signal-to-noise ratio of the detected signal in saturation spectroscopy of iodine in a cell at 501.7 nm, both in the FM spectroscopy technique and in the transfer modulation technique. In the latter case, a 30 dB rejection of the amplitude noise of the probe beam is achieved and, when the laser frequency is locked to the saturation signal, the enhancement of the sensitivity of the frequency jitter detection is demonstrated in a frequency band extending up to 1 kHz. For the long term stabilization the laser is locked to a narrow line detected in a low pressure cell. A relative Allan deviation of about 10⁻¹³ is found for 1 s integration time and a deviation of 10⁻¹⁴ is reached for 500 s. Linewidths smaller than 40 kHz (FWHM) are also demonstrated at low saturating power for hyperfine components of the transition R(26)62-0 at 501.7 nm.