Table of contents

In a previous paper (2011 Metrologia48 L7–11) we have calculated a reference prior for a calibration model where a state-of-knowledge distribution of the coefficients of the calibration function is provided. Observed values of the response for a fixed value of the stimulus are also available. They are assumed to conform to a Gaussian probability distribution of unknown standard deviation. The calculation of the reference prior is revised here using a different sequence of subsets of the parameter space. This choice is preferable to the earlier one with respect to the properties of the ensuing posterior. In contrast to the former result the revised reference prior leads to the same posterior distribution as the application of Supplement 1 to the 'Guide to the Expression of Uncertainty in Measurement'.

The Boltzmann constant has been determined by performing isotherm measurements around the triple point of neon with dielectric-constant gas thermometry (DCGT). The necessary thermodynamic reference has been established with an uncertainty of about two tenths of a millikelvin, via realizing the International Temperature Scale of 1990, ITS-90, and exploiting the recently published results for the deviation between thermodynamic temperature and the ITS-90. In combination with a detailed treatment of uncertainty estimates and correlations, a value for the Boltzmann constant of k_LT = 1.380 657 × 10⁻²³ J K⁻¹ with a standard uncertainty of 15.9 parts per million (ppm) has been determined. This value deviates from the CODATA value, published in 2008, by only 4.7 ppm and is in very good agreement with the value obtained by DCGT at the triple point of water k_TPW = 1.380 654 × 10⁻²³ J K⁻¹ with an uncertainty of 9.2 ppm. The weighted mean of k_LT and k_TPW leads to the DCGT estimate for the Boltzmann constant of k = 1.380 655 × 10⁻²³ J K⁻¹ with an uncertainty of 7.9 ppm.

The next revision to the International System of Units will emphasize the relationship between the base units (kilogram, metre, second, ampere, kelvin, candela and mole) and fundamental constants of nature (the speed of light, c, the Planck constant, h, the elementary charge, e, the Boltzmann constant, k_B, the Avogadro constant, N_A, etc). The redefinition cannot proceed without consistency between two complementary metrological approaches to measuring h: a 'physics' approach, using watt balances and the equivalence principle between electrical and mechanical force, and a 'chemistry' approach that can be viewed as determining the mass of a single atom of silicon. We report the first high precision physics and chemistry results that agree within 12 parts per billion: h (watt balance) = 6.626 070 63(43) × 10⁻³⁴ J s and h(silicon) = 6.626 070 55(21) × 10⁻³⁴ J s. When combined with values determined by other metrology laboratories, this work helps to constrain our knowledge of h to 20 parts per billion, moving us closer to a redefinition of the metric system used around the world.

The modelling of electrical connections of single, or several, multiterminal quantum Hall effect (QHE) devices is relevant for electrical metrology: it is known, in fact, that certain particular connections allow (i) the realization of multiples or fractions of the quantized resistance, or (ii) the rejection of stray impedances, so that the configuration maintains the status of quantum standard. Ricketts–Kemeny and Delahaye equivalent circuits are known to be accurate models of the QHE: however, the numerical or analytical solution of electrical networks including these equivalent circuits can be difficult. In this paper, we introduce a method of analysis based on the representation of a QHE device by means of the indefinite admittance matrix: external connections are then represented with another matrix, easily written by inspection. Some examples, including the solution of double- and triple-series connections, are shown.

The Electron Counting Capacitance Standard currently pursued at PTB aims to close the Quantum Metrological Triangle with a final precision of a few parts in 10⁷. This paper reports the considerable progress recently achieved with a new generation of single-electron tunnelling devices. A five-junction R-pump was operated with a relative charge transfer error of five electrons in 10⁷, and was used to successfully perform single-electron charging of a cryogenic capacitor. The preliminary result for the single-electron charge quantum has an uncertainty of less than two parts in 10⁶ and is consistent with the value of the elementary charge.

Counting is at the base of many high-level measurements, such as, for example, frequency measurements. In some instances the measurand itself is a number of events, such as spontaneous decays in activity measurements, or objects, such as colonies of bacteria in microbiology. Countings also play a fundamental role in everyday life. In any case, a counting is a measurement. A measurement result, according to its present definition, as given in the 'International Vocabulary of Metrology—Basic and general concepts and associated terms (VIM)', must include a specification concerning the estimated uncertainty. As concerns measurements by counting, this specification is not easy to encompass in the well-known framework of the 'Guide to the Expression of Uncertainty in Measurement', known as GUM, in which there is no guidance on the topic. Furthermore, the issue of uncertainty in countings has received little or no attention in the literature, so that it is commonly accepted that this category of measurements constitutes an exception in which the concept of uncertainty is not applicable, or, alternatively, that results of measurements by counting have essentially no uncertainty. In this paper we propose a general model for measurements by counting which allows an uncertainty evaluation compliant with the general framework of the GUM.

We consider an estimation problem described in the Guide to the Expression of Uncertainty in Measurement (GUM). The problem is concerned with estimating a measurand that is a non-linear function of input quantities. The GUM describes two methods for estimating the measurand—method 1 is based on the same non-linear function of input-quantity estimates and method 2 is based on the mean of that function of individual measurements. We use several examples to compare the two methods based on their mean-squared errors and to demonstrate that a uniformly preferred method may not be available except for the simplest cases. We also consider an approach based on the Monte Carlo method in Supplement 1 of the GUM for the problem and compare it with the two methods.

During the monitoring of the long term stability of two accelerometers intended for use in the CIPM key comparison CCAUV.V-K2, significant deviations of the magnitude results of the single-ended transducer were discovered. These deviations depend on whether the calibration was performed on an armature made of beryllium or of ceramic. After first investigations which led to an interpretation as a relative motion effect published in Täubner et al (2010 Metrologia47 58–64), now, more detailed measurements combined with modelling and system identification have led to a better understanding of what is happening. The measurements, model considerations and corresponding results are presented and discussed in order to further the understanding of this important issue of primary accelerometer calibration. This contribution can be considered a sequel to the former publication (Täubner et al 2010 Metrologia47 58–64) on the topic.

Investigating accurately the acoustic behaviour of small fluid-filled cavities and ducts and their association is a problem of persistent importance, because nowadays both experimental investigations and theoretical modelling must provide results of increasingly higher precision. The motivation here is provided mainly by the acoustic measurement tools used for both the calibration of microphones and the artificial ear (IEC 60318-1). Both improved analytical models of small acoustic components (small tubes and slits), which account for the effects of the viscous and thermal boundary layers accurately in the frequency range of interest (20 Hz to 20 kHz), and experimental characterization of their input impedances (with a relative uncertainty of the order of magnitude of 10⁻²) have been proposed recently (Rodrigues et al 2008 J. Sound Vib.315 890–910). Existing analytical procedures for coupled components suffer from strong approximations at the interfaces between narrow tubes and slits or other elements as well as the open space. A dedicated numerical model can be used in order to investigate accurately the acoustic field at these interfaces. The numerical model presented in the paper relies on a suitable linear exact formulation, based upon two coupled equations involving particle velocity and temperature variation (Joly 2010 Acta Acust. United Acust.96 102–14) and utilizes an adaptive anisotropic meshing technique to model correctly the strong variations which occur around the geometrical discontinuities and inside the boundary layers. Application to a 2D axisymmetrical device (annular slit ending in an aperture in an infinite screen) is considered to present the ability of the method. Acoustic pressure, temperature variation and particle velocity distributions inside and around the end of the slit are depicted, and the input acoustic admittance of the slit obtained numerically is compared with both experimental and analytical results available.

High precision levelling is an indispensable method used to monitor benchmark and terrain stability at the Bureau International des Poids et Mesures (BIPM). Associated with the International Comparison of Absolute Gravimeters (ICAG), levelling measurements were carried out repeatedly over the past decades. A local gravity field strongly depends on vertical terrain deformation. 1 cm displacement implies about 2 µGal change in the vertical gravity acceleration. The precision of absolute and relative gravimetry nowadays is about 1 µGal.

At the beginning of the century, a strategy was outlined that the ICAG should be upgraded to a metrological Key Comparison of the CIPM MRA (Mutual Recognition Arrangement) recognized officially by the designated governmental organizations. As a result of this decision, BIPM site B was constructed and completed in Spring 2001. The site B pillar is 4 m × 6 m × 1.5 m in dimension and more than 80 ton in weight. Such a large, newly built concrete body produces local deformation due to its sinking or tilting. This in turn influences the local gravity field. Rigorous levelling measurements have been performed by the Bureau de Recherches Géologiques et Minières (BRGM), France, since 2001 and repeated together with the 4-year ICAGs of 2001, 2005 and 2009. ICAG-2009 was characterized by becoming the first Comité International des Poids et Mesures (CIPM) Key Comparison which supported meanwhile the BIPM watt balance (WB) project. The WB pillar was built in Spring 2009. The Institut Géographique National (IGN), France, has hence been invited to participate in the levelling. The latter also measured the link between the BIPM local network and external stations of the French national height reference system IGN69.

In this paper, we report the final results of the levelling programmes of 2001, 2005 and 2009 and compare the results. We investigate stability of the BIPM gravity-levelling stations. We conclude that the existing and the newly built stations can be considered as stable for the purposes of the ICAGs and the WB, although further repeat measurement may be required for the WB site.

For the first time, detailed and complete levelling data and results are publishedOnly the final result of the 2005 levelling mission was published in [4] where, instead of NGF, the height reference system used was IGN69. This is incorrect and is corrected in this paper.. After 30 years of organizing and holding eight ICAGs, the BIPM will hand over the KC ICAG-2013 to another CIPM MRA designated institute. This paper serves as a technical and historical report of precision levelling, a sub-task of the ICAGs.

In this paper we present a new prediction algorithm for the generation of International Atomic Time (TAI). The new prediction algorithm takes into account the frequency drift which affects most of the participating atomic clocks. In particular, we focus on the effect of the application of the new model on the prediction term for the frequency drift affecting the free atomic time scale (EAL). We also present its effect on TAI performance and on atomic clock weights.

At present, the applicable spatial techniques used in UTC (Coordinated Universal Time) computation are GPS, TWSTFT (Two-Way Satellite Time and Frequency Transfers) and GLONASS. To enable accuracy and robustness for the generation of UTC, a multi-technique strategy for UTC time transfer is indispensable. Over the last two decades efforts have been made to use GLONASS for accurate time transfer. The first GLONASS time link that presents in UTC was introduced in November 2009, BIPM Circular T 263.

For present and future accurate time transfers, GLONASS is comparable to GPS with the same types of observations. In this paper, we first recall principles of the GNSS Common-View and All in View time transfers; we present the technical issues for the use of GLONASS in UTC, i.e. short- and long-term stabilities, frequency biases, calibration and its practical implementation. Finally, we outline the prospects for the use of GLONASS in accurate time transfer.

Amount of substance is one of the base quantities that form the International System of units. The quantity measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons and other particles. In order to count atoms with a relative uncertainty of better than 2 × 10⁻⁸, here we formulate the amount of substance measurement homogeneity principle. A consequence of this principle is that the accuracy of a measurement of amount of substance is limited by the homogeneity of the sample. We propose a criterion of sample preparation for the accurate determination of molar mass which is to ensure complete chemical conversions, no fractionation, homogeneity at the molecular level and less contamination. Based on this philosophy, a more accurate molar mass of natural single crystal silicon was achieved. We found that there was an isotope fractionation in the preparation process of the NaOH solution method. It led to an Avogadro constant value 1.0 × 10⁻⁶ lower. The corrected value is higher than previous data, and compatible with recent values of the Planck constant.

Measurements of forces less than a micronewton are critical when examining the mechanical behaviour of materials and devices at characteristic length scales below a micrometre. As a result, specification standards for nanomechanical tests and test equipment are being proposed by international standards organizations, and an infrastructure for traceable small force calibration is developing. In this context, results are reported from the first interlaboratory comparison of micronewton-level force metrology. The basis of the comparison was the calibration of a set of five piezoresistive cantilever force sensors similar to those used for atomic force microscopes but employed here as transfer artefacts. The artefacts were circulated among four national metrology institutes with each using their own force balance to calibrate the stiffness (force change per unit displacement) and sensitivity (signal output change per unit force) of the artefacts. By considering the weighted mean of the stiffness and sensitivity values reported for a given artefact, reference values were obtained. The largest contributing uncertainty components were due to the transfer artefacts themselves, rather than from the measurements of the physical quantities of force, voltage and displacement. The results imply that it should be possible to determine cantilever stiffness using force balance techniques with an accuracy of better than 1% if necessary, but that improvements in the ability to orient the transfer artefacts, to characterize the non-linearity of their output, and to compensate for the stiffness of the associated fixtures and load frames are required if the resolution of future comparisons is to improve.

We evaluate the frequency error from distributed cavity phase in the caesium fountain clock PTB-CSF2 at the Physikalisch-Technische Bundesanstalt with a combination of frequency measurements and ab initio calculations. The associated uncertainty is 1.3 × 10⁻¹⁶, with a frequency bias of 0.4 × 10⁻¹⁶. The agreement between the measurements and calculations explains the previously observed frequency shifts at elevated microwave amplitude. We also evaluate the frequency bias and uncertainty due to the microwave lensing of the atomic wave packets. We report a total PTB-CSF2 systematic uncertainty of 4.1 × 10⁻¹⁶.

Five iron–carbon (Fe–C) eutectic fixed-point cells have been constructed between NPL and LNE-Cnam to investigate the robustness and to measure the agreement of their melting temperatures. Each cell was constructed with a different selection of materials sourced by NPL and LNE-Cnam. The measured emfs at the Fe–C fixed-point temperature (∼1153 °C), compared between cells, agree within around 1.98 µV (∼90 mK), where the most important contribution to the uncertainty of each measurement is the inhomogeneity associated with the measuring Pt/Pd thermocouple. This demonstrates that these cells are suitable for use as secondary fixed-point cells in contact thermometry but the robustness of the presented cells is not found to be sufficient for maintaining their integrity during repeated cycling procedures.

The 8th International Comparison of Absolute Gravimeters (ICAG-2009) and the associated Relative Gravity Campaign (RGC2009) took place at the Bureau International des Poids et Mesures (BIPM) between July and October 2009. Altogether 24 institutes with 22 absolute gravimeters and 9 relative gravimeters participated in the ICAG/RGC campaign. Accurate absolute and relative gravity measurements as well as precision levelling measurements were performed on the micro-gravity 3D-grid at the BIPM.

The 2009 comparison was the first to be organized as a Comité International des Poids et Mesures (CIPM) metrological Key Comparison under the CIPM MRA (Mutual Recognition Arrangement), which means that the result will be officially recognized by the governmental organizations responsible. As a consequence, the relative gravimeters employed were carefully selected and the measurement schedules were rigorously enforced compared with earlier campaigns. Thus the quality of the RGC2009 and the determination of the BIPM local gravity network were improved.

After 30 years and eight successive ICAGs, the BIPM has decided to transfer its role to the national metrological institutes, although the CIPM will continue to organize the key comparison as ICAGs. The background to the RGC2009, and the organization, data processing and final results of the gravity and vertical gravity gradients, are presented in this paper. This report is more detailed than previous final reports of the RGCs.

Measurements made with watt balances are paving the way to a new definition of the kilogram based upon a fixed value of the Planck constant. The Bureau International des Poids et Measures (BIPM) are developing a simultaneous moving and weighing variant of the watt balance technique, which requires a superconducting coil to reach its ultimate uncertainty. The BIPM technique has the advantage that it eliminates the requirement for extreme stability in the magnetic field employed by conventional watt balances, but requires cryogenic operation of parts of the balance to achieve a low uncertainty.

This paper proposes a simple method, by which the BIPM technique can be made to operate at room temperature with no loss of accuracy. The superconducting coil is replaced by a bifilar coil and the measurement procedure is modified to eliminate any inequality between the two conductors in the bifilar coil. The new technique is not subject to the many secondary sources of uncertainty arising from cryogenic operation.

After the elimination of significant mechanical problems, the NPL Mark II moving-coil watt balance made an initial series of measurements in the period from October 2006 to March 2007. Incremental improvements were made to the apparatus in the period from June 2007 to November 2008 and measurements of the Planck constant h were made up to June 2009, with the aim of providing further information to the ongoing efforts to redefine the SI kilogram in terms of a fixed value of the Planck constant. The apparatus was sold to NRC-INMS in early 2009 and was dismantled and shipped to Canada in the period between June and August 2009.

In June 2009, just prior to the shipment, a possible source of significant type-B uncertainty in the mass/force exchange was discovered. There was insufficient time to fully investigate and correct the effect so a component has been added to the uncertainty budget to account for its estimated magnitude. The standard uncertainty of the apparatus, without allowance for the mass/force exchange problem, is estimated to be 36 nW W⁻¹, which represents an improvement of almost a factor of two from the previously reported uncertainty of 66 nW W⁻¹, but, allowing for the problem, the uncertainty increases to 200 nW W⁻¹. Further work, once the apparatus is rebuilt in Canada, should eliminate the source of the added uncertainty. The value of h calculated from the measurements made from 2006 to 2009 is 6.626 071 23(133) × 10⁻³⁴ J s, which represents a change of 43 nW W⁻¹ from the value reported in 2007. The corresponding value of the Avogadro constant, N_A, is 6.022 139 78(120) × 10²³ mol⁻¹.

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