This paper outlines the roadmap towards the redefinition of the second, which was recently updated by the CCTF Task Force created by the CCTF in 2020. The main achievements of optical frequency standards (OFS) call for reflection on the redefinition of the second, but open new challenges related to the performance of the OFS, their contribution to time scales and UTC, the possibility of their comparison, and the knowledge of the Earth's gravitational potential to ensure a robust and accurate capacity to realize a new definition at the level of 10−18 uncertainty. The mandatory criteria to be achieved before redefinition have been defined and their current fulfilment level is estimated showing the fields that still needed improvement. The possibility to base the redefinition on a single or on a set of transitions has also been evaluated. The roadmap indicates the steps to be followed in the next years to be ready for a sound and successful redefinition.
The International Bureau of Weights and Measures (BIPM) was set up by the Metre Convention and has its headquarters near Paris, France. It is financed jointly by its Member States and operates under the exclusive supervision of the CIPM.
Its mandate is to provide the basis for a single, coherent system of measurements throughout the world, traceable to the International System of Units (SI). This task takes many forms, from direct dissemination of units (as in the case of mass and time) to coordination through international comparisons of national measurement standards (as in electricity and ionizing radiation).
The BIPM has an international staff of over 70 and its status vis-à-vis the French Government is similar to that of other intergovernmental organizations based in Paris.
ISSN: 1681-7575
The leading international journal in pure and applied metrology, published by IOP Publishing on behalf of Bureau International des Poids et Mesures (BIPM).
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N Dimarcq et al 2024 Metrologia 61 012001
Judah Levine et al 2023 Metrologia 60 014001
This paper explains the considerations that were important in 1972, when the current leap second procedure was adopted, to maintain a close connection between UTC, the international reference time scale, and UT1—a time scale based on the rotation of the Earth. Although some of these considerations are still relevant, the procedure for adding leap seconds creates difficulties in many modern applications that require a continuous and monotonic time scale. We present the advantages and disadvantages of the leap second procedure, and some of the problems foreseen if it is not reconsidered. We suggest the general outline of a way forward, which addresses the deficiencies in the current leap second system, and which will ensure that UTC remains an international standard that is useful and appropriate for all time and frequency applications. Further discussion and evaluation of the impact of any changes is required.
S Pommé 2015 Metrologia 52 S51
Half-life measurements of radionuclides are undeservedly perceived as 'easy' and the experimental uncertainties are commonly underestimated. Data evaluators, scanning the literature, are faced with bad documentation, lack of traceability, incomplete uncertainty budgets and discrepant results. Poor control of uncertainties has its implications for the end-user community, varying from limitations to the accuracy and reliability of nuclear-based analytical techniques to the fundamental question whether half-lives are invariable or not. This paper addresses some issues from the viewpoints of the user community and of the decay data provider. It addresses the propagation of the uncertainty of the half-life in activity measurements and discusses different types of half-life measurements, typical parameters influencing their uncertainty, a tool to propagate the uncertainties and suggestions for a more complete reporting style. Problems and solutions are illustrated with striking examples from literature.
Peter J Mohr and William D Phillips 2015 Metrologia 52 40
The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI, e.g. angular units like radians or steradians and counting units like radioactive decays or molecules. We show that an incoherence may arise when different units of this type are replaced by a single dimensionless unit, the unit 'one', and suggest how to properly include such units into the SI in order to remove the incoherence. In particular, we argue that the radian is the appropriate coherent unit for angles and that hertz is not a coherent unit in the SI. We also discuss how including angular and counting units affects the fundamental constants.
Michael Stock et al 2019 Metrologia 56 022001
On 16 November 2018 a revision of the International System of Units (the SI) was agreed by the General Conference on Weights and Measures. The definitions of the base units were presented in a new format that highlighted the link between each unit and a defined value of an associated constant. The physical concepts underlying the definitions of the kilogram, the ampere, the kelvin and the mole have been changed. The new definition of the kilogram is of particular importance because it eliminated the last definition referring to an artefact. In this way, the new definitions use the rules of nature to create the rules of measurement and tie measurements at the atomic and quantum scales to those at the macroscopic level. The new definitions do not prescribe particular realization methods and hence will allow the development of new and more accurate measurement techniques.
D B Newell et al 2018 Metrologia 55 L13
Sufficient progress towards redefining the International System of Units (SI) in terms of exact values of fundamental constants has been achieved. Exact values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant NA from the CODATA 2017 Special Adjustment of the Fundamental Constants are presented here. These values are recommended to the 26th General Conference on Weights and Measures to form the foundation of the revised SI.
Peter J Mohr et al 2022 Metrologia 59 053001
We show the implications of angles having their own dimension, which facilitates a consistent use of units as is done for lengths, masses, and other physical quantities. We do this by examining the properties of complete trigonometric and exponential functions that are generalizations of the corresponding functions that have dimensionless numbers for arguments. These generalizations provide functions of angles with the dimension of angle as arguments, but with no reference to units. This parallels most equations in physics which are valid for any units. This property also provides a consistent framework for including quantities involving angles in computer algebra programs without ambiguity that may otherwise occur. This is in contrast to the conventional practice in scientific applications involving trigonometric or exponential functions of angles where it is assumed that the argument is the numerical part of the angle when expressed in units of radians. That practice also assumes that the functions are the corresponding radian-based versions. These assumptions allow angles to be treated as if they had no dimension and no units, an approach that can lead to important difficulties such as incorrect factors of 2π, which can be avoided by assigning an independent dimension to angles.
S Pommé et al 2015 Metrologia 52 S3
Nuclear counting is affected by pulse pileup and system dead time, which induce rate-related count loss and alter the statistical properties of the counting process. Fundamental equations are presented to predict deviations from Poisson statistics due to non-random count loss in nuclear counters and spectrometers. Throughput and dispersion of counts are studied for systems with pileup, extending and non-extending dead time, before and also after compensation for count loss. Equations are provided for random fractions of the output events, applicable to spectrometry applications. Methods for loss compensation are discussed, including inversion of the throughput equation, live-time counting and loss-free counting. Secondary effects in live-time counting are addressed: residual interference from pileup in systems with imposed dead times and errors due to varying count rate when measuring short-lived radionuclides.
Bernd Güttler et al 2019 Metrologia 56 044002
Following the revision of the International System of Units (SI), that takes effect on 20 May 2019, the unit mole is defined by using a fixed number of elementary entities. This number is the fixed numerical value of the Avogadro constant, which is the defining constant of the unit mole. This definition was made possible because the determination of the Avogadro constant had reached a level of relative uncertainty that allowed its value to be fixed and, at the same time, safeguard continuity of measurement results before and after the definition. The motivation for the revision of the SI and the mole in particular will be explained and the experimental work that allowed it is summarized.
G Panfilo and F Arias 2019 Metrologia 56 042001
Coordinated Universal Time (UTC) has considerably changed in recent years. The evolution of UTC follows the scientific and industrial progress by developing appropriate models, more adapted calculation algorithms, more efficient and rapid dissemination processes and a well defined traceability chain. The enormous technical progress worldwide has resulted in an impressive number of atomic clocks now available for UTC calculation. The refined time and frequency transfer techniques are approaching the accuracy requested for the new definition of the SI second. The more regular operation of primary frequency standards (PFS) increases the accuracy of UTC and opens a possible new development for time scale algorithms. From the metrological point of view all the ingredients are available for major improvements to UTC. Dissemination of UTC is done by the monthly publication of results in BIPM Circular T. This document makes a quality evaluation of local representations of UTC, named UTC(k), in national institutes, and other organizations, by giving the evolution of their offsets relative to UTC and their respective uncertainties. The clock models adopted and the time transfer techniques have progressively improved over the years, assuring the long-term stability of UTC. Each computation of UTC processes data over one month with five-day sampling and publication. A rapid solution of UTC (UTCr) has existed since 2013, and consists of the processing of daily sampled data over four consecutive weeks, computed and published weekly. It gives quick access to UTC, and allows participating laboratories to better monitor the offsets of their realizations to the reference UTC. The traditional monthly publication, containing results of all the laboratories contributing data to the BIPM for the computation of UTC was complemented after the establishment of the Mutual Recognition Arrangement of the International Committee on Weights and Measures (CIPM MRA). This time comparison, which has been the responsibility of the BIPM since 1988, added as a complement the key comparison on time defined by the Consultative Committee for Time and Frequency (CCTF) in 2006 as CCTF-K001.UTC, where the results published are those of national metrology institutes (NMIs) signatories of the CIPM MRA, or designated institutes (DIs). The traceability issues are formalized in the framework of the CIPM MRA. The development of time metrology activities in the different metrology regions, supports the actions of the BIPM time department to improve the accuracy of [UTC–UTC(k)], where the coordination with the Regional Metrology Organizations (RMOs) has a key role. This paper presents an overview of UTC.
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Dr T Jing et al 2024 Metrologia 61 01003
This report summarizes the results and performances of APMP.EM-K12, APMP key comparison of AC-DC current transfer standards of 10 mA and 5 A at frequencies of 10 Hz, 55 Hz, 1 kHz, 10 kHz, 20 kHz, 50 kHz, and 100 kHz. Ten National Metrology Institutes participated in this key comparison, including NMC/A*STAR (Singapore, pilot Laboratory), NMIA (Australia), SCL (Hong Kong, China), NMIJ (Japan), KRISS (Rep of Korea), NIM (China), NMISA (South Africa), NIMT (Thailand), NMIM (Malaysia), and CMS/ITRI (Chinese Taipei). The key comparison is linked to the CCEM one, CCCEM-K12, with same measurement quantities through the performances of two laboratories, NMC and NMIA, in both key comparisons. The degrees of equivalence of individual participating laboratories with the reference values of CCEM-K12 were thus concluded in this report.
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 https://www.bipm.org/kcdb/.
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).
Michal Máriássy et al 2024 Metrologia 61 08009
The subsequent key comparison K73.2018.2 was performed to demonstrate the capability of the participating institutes to measure the amount content of H+ in hydrochloric acid as a follow-up of the previous key comparison CCQM-K73.2018. A HCl solution of a slightly different composition to that in CCQM-K73.2018 was used.
There were two institutes and SMU as the coordinating laboratory participating in this subsequent comparison. UkrCSM obtained results in good agreement with the reference value; INMETRO results exhibited a large bias due to a calculation error found only after disclosure of the results.
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 https://www.bipm.org/kcdb/.
The final report has been peer-reviewed and approved for publication by the CCQM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).
Sun Qiao et al 2024 Metrologia 61 09002
This is the final report for APMP supplementary comparison APMP.AUV.V-S2 in the area of 'vibration' (quantity of rotational speed). The aim of this comparison was to compare primary measurements of rotational speed in the range from 30 r/min to 99 996 r/min. Six Metrology Institutes from two RMOs, APMP and AFRIMETS, have participated in the comparison with the National Institute of Metrology, P.R. China as the pilot lab. NIM, NMC and NIS used a mechanical generator for calibration, with expanded uncertainties in the order from 10-3 to 10-5. NML, NIMT and KEBS used an optical simulator for calibration, with expanded uncertainties in the order from 10-4 to 10-5. All the participating laboratories provided their calibration results, which were all consistent within their declared expanded uncertainties for the measurement results. Each participant contributed to the SCRVs calculated for five rotational speed comparison values of two laser tachometers, NLYZ-02 and 03, except that NIS's measurement results of NLYZ-03 are invalid. Smaller measurement uncertainties than the order of 10-5 for the calibration of laser tachometers are difficult to achieve for either mechanical generators or optical simulators with the current technology of rotational speed standard devices and laser tachometers.
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 https://www.bipm.org/kcdb/.
The final report has been peer-reviewed and approved for publication by the CCAUV, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).
Evelyn de F Guimarães et al 2024 Metrologia 61 035004
Recertification is a common practice in National Metrology Institutes whenever advances are made in certified reference material (CRM) characterization procedures, which play a key role in metrological traceability. This article compares measurements of 16 priority polycyclic aromatic hydrocarbons (PAHs) in toluene by gas chromatography isotopic dilution mass spectrometry (IDMS) using either an calibration curve or the exact matching approach. The multi-point IDMS calibration curve was used on the original CRM certification and the exact matching approach was carried out on its recertification. The measurement uncertainties by exact matching approach (0.3%–1.0%) were approximately 5 times smaller than those obtained using the calibration curve (1.5%–4.4%) for all PAHs, reducing the uncertainty component due to characterization of PAH CRM. This new characterization study added reliability, increased accuracy and reduced the measurement uncertainty of the Inmetro CRM, with metrological traceability to the International System of Units. The exact-matching isotope dilution is an important technique to value assign organic compounds in CRMs, an action that consolidates the chemical metrology in the Brazilian Metrology Institute.
Ch Rothleitner and B Andreas 2024 Metrologia 61 035003
We investigate the bias due to the beam divergence of the collimator in a free-fall absolute gravimeter of type FG5X. First, we measure the beam parameters with a Shack-Hartmann sensor. Then, we use the parameters to simulate the relative gravitational acceleration error of an FG5X gravimeter, which employs an unbalanced Mach-Zehnder laser interferometer. This investigation we do with four different commercial collimators, providing different divergence angles. We compare the results to real gravity measurements using the same collimators. The larger the divergence angle, and the bigger the relative length error, the bigger is the bias in the gravity measurements. A good agreement between theory and experiment is found, resulting in a relative bias of ( μGal) for our standard collimator of type Thorlabs TC25APC, which is usually used for free-fall acceleration determinations. The outcome is also important for the realization of the SI unit kilogram via Kibble balance experiments that, on one side, employ laser interferometers for velocity measurements, and, on the other side, require accurate values of the gravitational acceleration. For example, if this divergence error is not corrected in the Kibble balance, then the mass determination would be biased by μg kg−1 (numbers are valid only for our gravimeter with our collimator and fiber).
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Samuel P Benz et al 2024 Metrologia 61 022001
Johnson noise thermometry (JNT) is a purely electronic method of thermodynamic thermometry. In primary JNT, the temperature is inferred from a comparison of the Johnson noise voltage of a resistor at the unknown temperature with a pseudo-random noise synthesized by a quantum-based voltage-noise source (QVNS). The advantages of the method are that it relies entirely on electronic measurements, and it can be used over a wide range of temperatures due to the ability of the QVNS to generate programmable, scalable, and accurate reference signals. The disadvantages are the requirement of cryogenic operation of the QVNS, the need to match the frequency responses of the leads of the sense resistor and the QVNS, and long measurement times. This review collates advice on current best practice for a primary JNT based on the switched correlator and QVNS. The method achieves an uncertainty of about 1 mK near 300 K and is suited to operation between 4 K and 1000 K.
N Dimarcq et al 2024 Metrologia 61 012001
This paper outlines the roadmap towards the redefinition of the second, which was recently updated by the CCTF Task Force created by the CCTF in 2020. The main achievements of optical frequency standards (OFS) call for reflection on the redefinition of the second, but open new challenges related to the performance of the OFS, their contribution to time scales and UTC, the possibility of their comparison, and the knowledge of the Earth's gravitational potential to ensure a robust and accurate capacity to realize a new definition at the level of 10−18 uncertainty. The mandatory criteria to be achieved before redefinition have been defined and their current fulfilment level is estimated showing the fields that still needed improvement. The possibility to base the redefinition on a single or on a set of transitions has also been evaluated. The roadmap indicates the steps to be followed in the next years to be ready for a sound and successful redefinition.
Juris Meija et al 2023 Metrologia 60 052001
Bayesian statistical methods are being used increasingly often in measurement science, similarly to how they now pervade all the sciences, from astrophysics to climatology, and from genetics to social sciences. Within metrology, the use of Bayesian methods is documented in peer-reviewed publications that describe the development of certified reference materials or the characterization of CIPM key comparison reference values and the associated degrees of equivalence. This contribution reviews Bayesian concepts and methods, and provides guidance for how they can be used in measurement science, illustrated with realistic examples of application. In the process, this review also provides compelling evidence to the effect that the Bayesian approach offers unparalleled means to exploit all the information available that is relevant to rigorous and reliable measurement. The Bayesian outlook streamlines the interpretation of uncertainty evaluations, aligning their meaning with how they are perceived intuitively: not as promises about performance in the long run, but as expressions of documented and justified degrees of belief about the truth of specific conclusions supported by empirical evidence. This review also demonstrates that the Bayesian approach is practicable using currently available modeling and computational techniques, and, most importantly, that measurement results obtained using Bayesian methods, and predictions based on Bayesian models, including the establishment of metrological traceability, are amenable to empirical validation, no less than when classical statistical methods are used for the same purposes. Our goal is not to suggest that everything in metrology should be done in a Bayesian way. Instead, we aim to highlight applications and kinds of metrological problems where Bayesian methods shine brighter than the classical alternatives, and deliver results that any classical approach would be hard-pressed to match.
Olav Werhahn et al 2023 Metrologia 60 042001
The CIPM Mutual Recognition Arrangement (CIPM MRA) provides a technical framework to the measurement community for comparability of measurement results and international recognition of metrological capabilities declared by the national metrology institutes throughout the globe. Since its founding in 1999, the participating institutes have now published more than 25 700 peer-reviewed calibration and measurement capabilities (CMCs) in the CIPM MRA database (Key Comparison Database (KCDB)). It is these capabilities and the technical evidence behind them that underpin the international acceptance of measurements around the world. The success and wide adoption of the CIPM MRA indicate the maturity of the arrangement, however, the accompanying increased workload for the participants motivated a review of the practices with the aim to increase the efficiency while maintaining the technical rigor. This review identified a number of key factors that formed the basis of the revision of the modus operandi, including the procedures and the database. The review resulted in recommendations for the CIPM Consultative Committees (CCs), regional metrology organizations (RMOs), participating institutes, as well as the BIPM. The revamped KCDB incorporated the whole lifecycle of CMCs, familiarizing with the new system being supported by the Capacity Building and Knowledge Transfer Programme of the BIPM. The result was an improvement in not only efficiency of the CIPM MRA, but also its effectiveness. For example, the time required for the Joint Committee of the RMOs and the BIPM (JCRB) review of CMCs has dropped by more than 50% to 59 d (median) in 2022, and the number of uncompleted key comparisons (KCs) have been reduced by a factor of three to a total of 38 in March 2023, representing now less than 3% of the total KCs. In this paper we look at the key factors through the various metrological areas addressing practices by each CCs.
S M Judge et al 2023 Metrologia 60 012001
The medical use of radionuclides depends on the accurate measurement of activity (Bq) for regulatory compliance, patient safety, and effective treatment or image quality. In turn, these measurements rely on the realization of primary standards of activity by national metrology institutes, with uncertainties that are fit for purpose. This article reviews the current status of primary standards of activity for radionuclides used in medical imaging and therapy applications. Results from international key comparisons carried out through the International Bureau of Weights and Measures transfer instruments (SIR and SIRTI) are used to verify that standards for a variety of radionuclides are consistent and conform with practitioners' expectations.
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Khosravi et al
In this paper, we described the design and construction of a new two-capillary viscometer with several novel technical solutions for viscosity and density measurements. Our design, which is based on the low-pressure principle, featured numerous improvements in hardware and procedure that allowed the greatly extended range of pressure. The new design adopted a (2×2) capillary configuration, utilizing different combinations of four capillaries to enable viscosity measurements with a wide range of flow rates, temperatures, and pressures. The design temperature range is 213 K – 473 K, and the pressure range is up to 100 MPa. The viscometer was specifically designed for measuring the viscosity of pure CO2 and CO2-rich mixtures, addressing the scarcity of data in conditions relevant to carbon capture, transport, and storage (CCS). Our facility is capable of viscosity measurements in different thermodynamic states; gaseous, liquid, supercritical, and critical regions. A commercial densimeter is integrated to measure density under the same temperatures and pressures. We aimed for a total uncertainty target of better than 0.03%. The performance of the viscometer was validated by measurements with pure CO2 at 298.15 K and zero density. We observed a deviation of less than 0.03% between the reference viscosity of CO2 of this work and accurately calculated data using ab initio quantum mechanics with a standard uncertainty of 0.2%. Our primary focus in this paper was to provide a detailed description of the design and construction of the apparatus, emphasizing improvements and introducing new solutions to other research groups in constructing similar instruments suitable for low- and high-pressure viscosity measurements with high accuracy.
Khosravi et al
High-pressure viscosity measurements are crucial for understanding CO2 transport and storage because CO2 is often transported as a supercritical fluid, at a high pressure and temperature above its critical point. In this study, we extended the operational range of our new two-capillary viscometer to handle pressures up to 20 MPa, focusing on the behaviour of CO2 at temperatures around 300 K. The analysis model is based on the low-pressure principle, which relied on virial descriptions of density and viscosity, proved inadequate under these conditions. Therefore, we introduced a modified hydrodynamic model as a function of density that is suitable for viscosity measurements at high pressure and liquid states. The modified model bypasses the need for a density virial correction. We conducted initial viscosity tests on pure CO2 at five isotherms: 280.01 K, 298.15 K, 300.01 K, 323.15 K, and 348.15 K to validate the performance of the new two capillary viscometer and the modified model at high pressures. The experimental viscosities agreed with the model predictions and comparable within the estimated uncertainty of the data. In addition, we thoroughly explained the calibrations and the analysis of uncertainty estimation. The uncertainty analysis showed a maximum extended combined uncertainty of 1.3% (k = 2) within all thermodynamic states– gas, liquid, and close to the critical region.

Gonzalez et al
We obtain gas viscosities with a pressure-based mass-flow controller used for semi-conductor manufacturing, a rate-of-change approach, and a physics-based calculation. The novelty of this method is that it is used in an industrial process whose main goal is not to measure viscosities. In this way, for pressures of the order of 10 kPa and 25$^{\circ}$C and 35$^{\circ}$C, we obtain for seven gases viscosities with mean absolute errors with respect to reference viscosities of less than 1 \%. Using this method, we report viscosities for two semiconductor-manufacturing gases not available in the open literature: hexafluoroisobutene (CAS \# 382-10-5) and 1,1,3,3,3-pentafluoropropene (690-27-7).
Lehman et al
[redundant material in this field can't be deleted(?)]

In this letter we examine the organization of the traditional base units and defining constants established in the 2019 redefinition of the International System of Units (SI). For the next redefinition of the SI, which will accompany the anticipated redefinition of the candela and second, we propose an organizational change to improve clarity while maintaining practicality. We propose three distinct categories of units: The first category contains only the four base-measurement units comprised of the second, meter, kilogram, and ampere. The second category contains physiologically-relevant derived units. The third category contains the remaining units derived from the base units.
Fu et al
In recent years, a growing demand for the capability of performing accurate measurements of the bidirectional transmittance distribution function (BTDF) has been observed in industry, research and development, and aerospace applications. However, there exists no calibration and measurement capabilities (CMC)-entry for BTDF in the database of the Bureau International des Poids et Mesures (BIPM) and to date no BTDF comparison has been conducted between different national metrology institutes (NMIs) or designated institutes (DIs). As a first step to a possible future key comparison and to test the existing capabilities of determining this measurand, two interlaboratory comparisons were performed. In comparison one, five samples of three different types of optical transmissive diffusers were measured by five NMIs and one DI. By specific sample choice, the focus for this study lay more on orientation-dependent scatter properties. In comparison two, where one NMI, one DI, one university, and three industrial partners investigated their measurement capabilities, the dependence on the orientation was not assessed, but two additional samples of the same material and different thickness were measured. Results of the two comparisons are presented, giving a good overview of existing experimental solutions, and showing specific sample-related problems to be solved for improved future BTDF measurements.
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Bahareh Khosravi et al 2024 Metrologia
In this paper, we described the design and construction of a new two-capillary viscometer with several novel technical solutions for viscosity and density measurements. Our design, which is based on the low-pressure principle, featured numerous improvements in hardware and procedure that allowed the greatly extended range of pressure. The new design adopted a (2×2) capillary configuration, utilizing different combinations of four capillaries to enable viscosity measurements with a wide range of flow rates, temperatures, and pressures. The design temperature range is 213 K – 473 K, and the pressure range is up to 100 MPa. The viscometer was specifically designed for measuring the viscosity of pure CO2 and CO2-rich mixtures, addressing the scarcity of data in conditions relevant to carbon capture, transport, and storage (CCS). Our facility is capable of viscosity measurements in different thermodynamic states; gaseous, liquid, supercritical, and critical regions. A commercial densimeter is integrated to measure density under the same temperatures and pressures. We aimed for a total uncertainty target of better than 0.03%. The performance of the viscometer was validated by measurements with pure CO2 at 298.15 K and zero density. We observed a deviation of less than 0.03% between the reference viscosity of CO2 of this work and accurately calculated data using ab initio quantum mechanics with a standard uncertainty of 0.2%. Our primary focus in this paper was to provide a detailed description of the design and construction of the apparatus, emphasizing improvements and introducing new solutions to other research groups in constructing similar instruments suitable for low- and high-pressure viscosity measurements with high accuracy.
Bahareh Khosravi et al 2024 Metrologia
High-pressure viscosity measurements are crucial for understanding CO2 transport and storage because CO2 is often transported as a supercritical fluid, at a high pressure and temperature above its critical point. In this study, we extended the operational range of our new two-capillary viscometer to handle pressures up to 20 MPa, focusing on the behaviour of CO2 at temperatures around 300 K. The analysis model is based on the low-pressure principle, which relied on virial descriptions of density and viscosity, proved inadequate under these conditions. Therefore, we introduced a modified hydrodynamic model as a function of density that is suitable for viscosity measurements at high pressure and liquid states. The modified model bypasses the need for a density virial correction. We conducted initial viscosity tests on pure CO2 at five isotherms: 280.01 K, 298.15 K, 300.01 K, 323.15 K, and 348.15 K to validate the performance of the new two capillary viscometer and the modified model at high pressures. The experimental viscosities agreed with the model predictions and comparable within the estimated uncertainty of the data. In addition, we thoroughly explained the calibrations and the analysis of uncertainty estimation. The uncertainty analysis showed a maximum extended combined uncertainty of 1.3% (k = 2) within all thermodynamic states– gas, liquid, and close to the critical region.

John H Lehman et al 2024 Metrologia
[redundant material in this field can't be deleted(?)]

In this letter we examine the organization of the traditional base units and defining constants established in the 2019 redefinition of the International System of Units (SI). For the next redefinition of the SI, which will accompany the anticipated redefinition of the candela and second, we propose an organizational change to improve clarity while maintaining practicality. We propose three distinct categories of units: The first category contains only the four base-measurement units comprised of the second, meter, kilogram, and ampere. The second category contains physiologically-relevant derived units. The third category contains the remaining units derived from the base units.
Jinglin Fu et al 2024 Metrologia
In recent years, a growing demand for the capability of performing accurate measurements of the bidirectional transmittance distribution function (BTDF) has been observed in industry, research and development, and aerospace applications. However, there exists no calibration and measurement capabilities (CMC)-entry for BTDF in the database of the Bureau International des Poids et Mesures (BIPM) and to date no BTDF comparison has been conducted between different national metrology institutes (NMIs) or designated institutes (DIs). As a first step to a possible future key comparison and to test the existing capabilities of determining this measurand, two interlaboratory comparisons were performed. In comparison one, five samples of three different types of optical transmissive diffusers were measured by five NMIs and one DI. By specific sample choice, the focus for this study lay more on orientation-dependent scatter properties. In comparison two, where one NMI, one DI, one university, and three industrial partners investigated their measurement capabilities, the dependence on the orientation was not assessed, but two additional samples of the same material and different thickness were measured. Results of the two comparisons are presented, giving a good overview of existing experimental solutions, and showing specific sample-related problems to be solved for improved future BTDF measurements.
Ch Rothleitner and B Andreas 2024 Metrologia 61 035003
We investigate the bias due to the beam divergence of the collimator in a free-fall absolute gravimeter of type FG5X. First, we measure the beam parameters with a Shack-Hartmann sensor. Then, we use the parameters to simulate the relative gravitational acceleration error of an FG5X gravimeter, which employs an unbalanced Mach-Zehnder laser interferometer. This investigation we do with four different commercial collimators, providing different divergence angles. We compare the results to real gravity measurements using the same collimators. The larger the divergence angle, and the bigger the relative length error, the bigger is the bias in the gravity measurements. A good agreement between theory and experiment is found, resulting in a relative bias of ( μGal) for our standard collimator of type Thorlabs TC25APC, which is usually used for free-fall acceleration determinations. The outcome is also important for the realization of the SI unit kilogram via Kibble balance experiments that, on one side, employ laser interferometers for velocity measurements, and, on the other side, require accurate values of the gravitational acceleration. For example, if this divergence error is not corrected in the Kibble balance, then the mass determination would be biased by μg kg−1 (numbers are valid only for our gravimeter with our collimator and fiber).
Helen S Margolis et al 2024 Metrologia
This paper gives a detailed account of the analysis underpinning the 2021 update to the list of standard reference frequency values recommended by the International Committee for Weights and Measures (CIPM). This update focused on a subset of atomic transitions that are secondary representations of the second (SRS) or considered as potential SRS. As in previous updates in 2015 and 2017, methods for analysing over-determined data sets were applied to make optimum use of the worldwide body of published clock comparison data. To ensure that these methods were robust, three independent calculations were performed using two different algorithms. The 2021 update differed from previous updates in taking detailed account of correlations among the input data, a step shown to be important in deriving unbiased frequency values and avoiding underestimation of their uncertainties. It also differed in the procedures used to assess input data and to assign uncertainties to the recommended frequency values, with previous practice being adapted to produce a fully consistent output data set consisting of frequency ratio values as well as absolute frequencies. These changes are significant in the context of an anticipated redefinition of the second in terms of an optical transition or transitions, since optical frequency ratio measurements will be critical for verifying the international consistency of optical clocks prior to the redefinition. In the meantime, the reduced uncertainties for optical SRS resulting from this analysis significantly increases the weight that secondary frequency standards based on these transitions can have in the steering of International Atomic Time (TAI).
Lutz Werner et al 2024 Metrologia 61 035002
The quantum yield in silicon has previously been assumed to be of significance only in the ultraviolet spectral range. Due to the low internal losses of induced-junction silicon photodiodes and their predictability it is possible for the first time to make more accurate estimation of the quantum yield. We report on measurement of quantum yield in induced-junction silicon photodiodes. The results show that the quantum yield can be larger than unity even at wavelengths around 450 nm. A model of the quantum yield has been fitted to the experimental data and can be implemented in the spectral responsivity models to maintain high accuracy predictability to around 160 ppm down to 360 nm.
Freya Malcher et al 2024 Metrologia 61 025011
The demand for traceable hydrophone calibrations at low frequencies in support of ocean monitoring applications requires primary standard methods that are able to realise the acoustic pascal. In this paper, a new method for primary calibration of hydrophones is described based on the use of a calculable pistonphone to cover frequencies from 0.5 Hz to 250 Hz. The design consists of a pre-stressed piezoelectric stack driving a piston to create a varying pressure in an air-filled enclosed cavity, the displacement (and so the volume velocity) of the piston being measured by a laser interferometer. The dimensions of the front cavity were designed to allow the calibration of reference hydrophones, but it may also be used to calibrate microphones. Examples of calibration results for several sensors are presented alongside an uncertainty budget for hydrophone calibration with expanded uncertainties ranging from 0.45 dB at 0.5 Hz to 0.30 dB at 20 Hz, and to 0.35 at 250 Hz (expressed for a coverage factor of k = 2). The metrological performance is demonstrated by comparisons with results for other calibration methods and an independent implementation of primary calibration methods at other institutes.
R Nolte and B Lutz 2024 Metrologia 61 025008
The primary reference instruments for neutron fluence measurements used at the Physikalisch-Technische Bundesanstalt are based on the primary standard for neutron measurements which is the differential neutron–proton scattering cross section. Such instruments require considerable effort for their operation and analysis. Therefore, routine measurements are carried out using a transfer instrument to facilitate the efficient provision of services to customers. A series of measurements was conducted to compare the transfer device to the primary reference instruments and ensure the traceability of neutron fluence measurements. This resulted in an improved characterisation of the instrument and new analysis procedures. For neutron energies between 144 keV and 14.8 MeV, the ratio of neutron fluence values measured with the primary reference instruments and the transfer instrument deviates from unity by less than the estimated standard measurement uncertainties of 2.6% to 3.2%. At neutron energies between 30 keV and 100 keV, however, the experimental fluence ratios deviate from unity by about 4% which exceeds the estimated uncertainties of 2.5% to 2.9%. At present, the reason for this inconsistency remains unresolved.
Yaowaret Pimsut et al 2024 Metrologia 61 025007
The four-terminal-pair impedance bridge using pulse-driven Josephson voltage standards at PTB has been fully automated. The same bridge configuration was employed to determine R:R and C:C ratios over the frequency range between 53 Hz to 50 kHz. Only minor changes are needed to cover this large frequency range: amplifiers to increase the sensitivity of the current detections for low frequencies and signal generators with higher resolution at high frequencies to reach 50 kHz. Furthermore, the bridge can be operated for quadrature R:(1/ωC) measurements. The combined standard uncertainties (k = 1) for the new bridge were evaluated for all operating frequencies. They reach 2 nF F−1 and 4 nΩ Ω−1 at 1233.15 Hz. At this frequency, the 10 nF:10 nF ratio matched the ratio of PTB's bridge employing inductive voltage dividers within 1 nF F−1 ± 3 nF F−1 (k = 1). Over 45 days, the 10 nF:10 nF ratio deviated less than −2 nF F−1 ± 3 nF F−1 (k = 1). The 12.9 kΩ:10 kΩ ratio at 53 Hz differed −2 nΩ Ω−1 ± 5 nΩ Ω−1 (k = 1) from the DC ratio measured by the PTB's cryogenic current comparator bridge. Using a 12.9 kΩ resistance standard and a graphene AC quantum Hall resistance, the 10 nF:10 nF ratios derived from quadrature measurements agreed with the PTB's inductive voltage divider bridge better than 9 nF F−1 ± 13 nF F−1 (k = 1).