Atsushi Waseda

We performed lattice comparison measurements between ²⁸ Si-enriched crystals using a self-referenced lattice comparator (SRLC). The relative lattice spacing difference between two crystals sectioned from the same ingot were measured, showing agreement with values calculated from impurity and vacancy corrections, as well as with those obtained by other measurement techniques. Further comparison involving crystals from different ingots enabled an independent determination of the {220} lattice-plane spacing of a ²⁸ Si enriched crystal as 192.014 712 91(55) nm, confirming previously reported values. When applied to the realization of the kilogram via the x-ray crystal density method, the uncertainty contribution from the SRLC measurement corresponds to 8.4 μg uncertainty in the mass of a 1 kg silicon sphere, supporting its role in the accurate realization of the kilogram.

Main text: This report presents the results of the key comparison CCM.D-K1.2023 of solid density measurements by hydrostatic weighing, which was carried out through May 2022 to June 2024. As transfer standard act a 1 kg sphere made of natural silicon, which is compared directly or indirectly to primary density standards calibrated by mass and dimensional measurements. Ten laboratories participated in this key comparison of five regional metrology organizations (RMO): three of European association metrology institutes (EURAMET), three of Asia pacific metrology programme (APMP), two of inter-American metrology system (SIM), one of intra-Africa metrology system (AFRIMET) and one of Gulf association for metrology (GULFMET). This CIPM key comparison, was coordinated by the Physikalisch-Technische Bundesanstalt (PTB, DE) as the pilot laboratory, and Centro Nacional de Metrología (CENAM) and Istituto Nazionale di Ricerca Metrologica (INRIM) as co-pilot laboratories. The Key Comparison Reference Values (KCRVs) have been obtained for the volume and density values related to the transfer standard by the results of participants, whereby the method of least squares χ2 is estimated. The KCRVs and the corresponding uncertainties were calculated by the weighted mean in case of consistent results. Only two laboratories differed and were excluded from the analysis (En-value greater than 1). For each participant, the degree of equivalence (DoE) was determined with respect to the corresponding KCRV and between the other laboratories. 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 CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

A new high-precision density measurement method for small non-silicon samples was developed. Hydrostatic weighing (HW) and the pressure-of-flotation method (PFM) are high-precision techniques for determination solid sample densities. However, in HW, the uncertainty of the density measurement is quite large when the volume of the sample is much smaller than that of a 1 kg silicon sample owing to the uncertainty of the auxiliary weights during the measurement. Additionally, the PFM is not applicable for measuring the density of non-silicon materials. We developed a new method that combines HW and the PFM. We prepared a small 45 g Si₃N₄ sphere sample with a diameter of 30 mm. By employing two silicon discs with these masses that were nearly equivalent to the apparent masses of the sample, the same auxiliary weights were used for both the standards and the sample. The new method was validated by measuring the density of the 45 g Si₃N₄ sphere with a relative standard uncertainty of 4.6 × 10⁻⁶, which is significantly lower than that obtained by traditional HW methods. This approach demonstrates substantial improvements in the precision of small-sample density measurements, thus offering a robust alternative to conventional techniques.

This paper focuses on the relationship between decision trees, a typical machine learning method, and data anonymization. It is known that information leaked from trained decision trees can be evaluated using well-studied data anonymization techniques and that decision trees can be strengthened using k-anonymity and ℓ-diversity; unfortunately, however, this does not seem sufficient for differential privacy. In this paper, we show how one might apply k-anonymity to a (random) decision tree, which is a variant of the decision tree. Surprisingly, this results in differential privacy, which means that security is amplified from k-anonymity to differential privacy without the addition of noise.

This article describes a high-efficiency experimental configuration for a self-referenced lattice comparator with a `brush beam' of synchrotron radiation from a bending magnet and two linear position-sensitive photon-counting-type X-ray detectors. The efficiency is more than ten times greater compared with the `pencil-beam' configuration and a pair of zero-dimensional detectors. A solution for correcting the systematic deviation of d-spacing measurements caused by the horizontal non-uniformity of the brush beam is provided. Also, the use of photon-counting-type one-dimensional detectors not only improves the spatial resolution of the measurements remarkably but can also adjust the sample's attitude angles easily.

To improve the primary density standard of the National Metrology Institute of Japan (NMIJ), the absolute densities of two 1 kg silicon spheres, NMIJ-S4 and NMIJ-S5, were determined by measuring their masses and volumes. The volumes of the two spheres were measured by optical interferometry based on the primary length standard of NMIJ. For the accurate volume determination, the thicknesses of the surface layers on the spheres were determined by x-ray photoelectron spectroscopy (XPS). By combining the results of optical interferometry and XPS, the volumes of the two spheres at 20.000 °C and 0 Pa were determined with relative standard uncertainties of 3.0 × 10⁻⁸ and 2.9 × 10⁻⁸ for NMIJ-S4 and NMIJ-S5, respectively. From these results, the sphere volumes at 20.000 °C and 101.325 kPa were determined using the isothermal compressibility of silicon. The masses of the spheres in air were determined based on the national prototype of the kilogram of Japan. From the results of the volume and mass measurements, the densities of the two spheres at 20.000 °C and 101.325 kPa were determined with a relative standard uncertainty of 3.2 × 10⁻⁸. The density difference between the two spheres was estimated taking into account the correlation between the densities of the two spheres. The pressure-of-floatation method was also used to determine the density difference between the two spheres. The density differences determined by the two different methods agree with each other within their uncertainties.

The uniformity of the lattice spacing of silicon crystals was evaluated by the self-referenced lattice comparator with a resolution of 3 × 10 ^-9 . Lattice strain measurements were performed for the sample 10.5 cut from ²⁸ Si ingot (Avo28), which was used to determine the Avogadro constant. The mapping results for samples 4.R1, XINT, and 9.R1 performed in the previous works have also been re-evaluated. The 4.R1 in the seed side of the ingot and the XINT in the middle of the ingot have small distribution of lattice spacing. The standard deviations of the lattice spacing distribution for the 4.R1 and XINT were 4.8 × 10 ^-9 and 5.5 ×10 ^-9 , respectively. In contrast, the 9.R1 and the 10.5 samples cut from the tail side of the ingot have a larger distribution of lattice spacing. These lattice spacing distributions in the ingot are consistent with the impurity distribution in the ingot.

The homogeneity of the lattice spacing of silicon single crystals was characterized by the self-referenced lattice comparator. Lattice strain measurements were performed on single crystals from ²⁸ Si ingot (Avo28), which was used to determine the Avogadro constant. A curved and layered pattern was observed for the sample of 10.5 cut from the tail-side of the Avo28 ingot. The homogeneity of the lattice constant of the Avo28 was discussed.