Metrologia

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.

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.

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.

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.

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.

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.

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 N_A 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.

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.

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.

This article presents an interlaboratory comparison (ILC) on Raman spectroscopy as a technique for relative quantification of the two most common polymorphs of titanium dioxide (TiO₂)—anatase and rutile—in binary mixtures. Some standard methods are currently employed internationally for the determination of TiO₂ content in samples (ISO 591-1, ASTM D3720-90), but require extensive sample preparation, do not distinguish between the two polymorphs or are accurate only for small fractions of either polymorph. Raman spectroscopy is a well-suited characterization technique for measuring and differentiating TiO₂ in a fast, non-invasive way, while requiring no particular reagent or sample preparation. Eleven international participants conducted the study under the framework of Versailles Project on Advanced Materials and Standards. The collected data was analyzed by means of partial least squares regression after spectral preprocessing. The resulting models all show discrepancies of lower than 2% from the nominal values in the quantitative analysis over the concentration range of 5%–95% mixture fractions, with many datasets showing substantial improvement margins on this figure. The results of this ILC provide validation of Raman spectroscopy as a reliable method for quantification of TiO₂ phases.

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.

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 $-2.77(24)\cdot10^{-9}$ ($-2.72(24)$ 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 $2.77(24)$ μg kg⁻¹ (numbers are valid only for our gravimeter with our collimator and fiber).

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.

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).

This paper reports on a numerical simulation of the optical characteristics of a dielectric mixture layer formed on a Si substrate using the finite-difference time-domain (FDTD) method. This study investigated the validity of using effective medium approximation (EMA) layers in thin mixture film problems with the optical constants of bulk materials. The complex reflection coefficients of Si substrates with randomly distributed thin mixture films fabricated from water/SiO₂ and water/carbonaceous materials were numerically evaluated at normal and oblique incidences of plane electromagnetic waves via the FDTD principle, and the possible effects of the mixture layers on the effective optical characteristics were investigated. We observed that Bruggeman's model based on EMA provides a good prediction of the behaviour of the plane wave reflected by the Si surface with randomly distributed mixture layers. The results also suggested that mixture layers have effects under oblique incidence, but they have no significant impact under normal incidence.

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.

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.

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.

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.

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.

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.

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 $-2.77(24)\cdot10^{-9}$ ($-2.72(24)$ 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 $2.77(24)$ μg kg⁻¹ (numbers are valid only for our gravimeter with our collimator and fiber).

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).

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.

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.

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.

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).

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.

The molar mass and isotopic composition of a new silicon single crystal material (Si28-31Pr11) highly enriched in ²⁸Si has been determined in the context of the x-ray crystal density method used for the realization and dissemination of the SI base units‒the mole and the kilogram. Isotope ratio measurements have been performed using a high-resolution multicollector-inductively coupled plasma mass spectrometer (MC-ICP-MS) with improved technical performance. By applying the Virtual-Element Isotope Dilution Mass Spectrometry method, different crystal areas enclosing the locations of two silicon spheres have been investigated with respect to the magnitude of tentative variations in the molar mass and isotopic composition of the respective samples as a function of their original location in the crystal ingot. In total, 18 subsamples from four different axial and several related radial positions have been characterized. An average molar mass M(Si28-31Pr11) = 27.976 941 464(41) g mol⁻¹ corresponding to a relative combined uncertainty u_c,rel(M(Si28-31Pr11)) = 1.4 × 10⁻⁹ was yielded. The average enrichment in ²⁸Si of the crystal is expressed by the mean amount-of-substance fraction x(²⁸Si) = 0.999 985 350(37). Two spheres were cut from the crystal ingot. The average molar masses of the spheres Si28kg_03_a and Si28kg_03_b are: M(Si28kg_03_a) = 27.976 941 467(43) g mol⁻¹ and M(Si28kg_03_b) = 27.976 941 461(44) g mol⁻¹, respectively. The results are discussed using uncertainty budgets according to the Guide to the expression of uncertainty in measurement. A homogeneous distribution of the molar mass throughout the crystal is suggested, qualifying it as a material for a primary standard–a silicon sphere–for the realization and dissemination of the mole and the kilogram. A comparison with enriched silicon crystals that are already available is given.

We consider the potential use of optical traps for precision measurements in atomic hydrogen (H). Using an implicit summation method, we calculate the atomic polarisability, the rates of elastic/inelastic scattering and the ionisation rate in the wavelength range (395–1000) nm. We extend previous work to predict three new magic wavelengths for the 1S–2S transition. At the magic wavelengths, the 1S–2S transition is unavoidably and significantly broadened due to trap-induced ionisation associated with the high intensity required to trap the 1S state. However, we also find that this effect is partially mitigated by the low mass of H, which increases the trap frequency, enabling Lamb–Dicke confinement in shallow lattices. We find that a H optical lattice clock, free from the motional systematics which dominate in beam experiments, could operate with an intrinsic linewidth of the order of 1 kHz. Trap-induced losses are shown not to limit measurements of other transitions.