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Kenichi Fujii - One of the best experts on this subject based on the ideXlab platform.
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Volume Measurement of a 28 Si-Enriched Sphere for a Determination of the Avogadro Constant at NMIJ
IEEE Transactions on Instrumentation and Measurement, 2019Co-Authors: Naoki Kuramoto, Lulu Zhang, Hajime Inaba, Kazuaki Fujita, Sho Okubo, Kenichi FujiiAbstract:For a determination of the Avogadro Constant by the X-ray crystal density method, the volume of a Si sphere manufactured from a Si crystal isotopically enriched in 28Si, named Si28-23Pr11, was measured at the National Metrology Institute of Japan (NMIJ). The volume was determined on the basis of diameter measurement in 2175 directions by an optical interferometer. The surface layers on the sphere were characterized by X-ray photoelectron spectroscopy and spectroscopic ellipsometry. Taking into account the effect of the surface layers on the diameter measurement, the volume of the Si core excluding the surface layers was determined with a relative uncertainty of $2.0\times 10^{\mathbf {-8}}$ . The results were used to determine the Avogadro Constant in 2017 by the International Avogadro Coordination project, which was used as an input datum to determine the CODATA 2017 adjusted value of the Planck Constant $h$ . This $h$ value will be used in the new definition of the kilogram. This paper provides details of the measurement apparatus and the uncertainty analysis of the Si core volume measurement. In addition, an approach to reduce the uncertainty in the Si core volume determination is proposed for the accurate realization of the kilogram based on the new definition at NMIJ. Details of the approach are also provided.
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Volume Measurement of a 28 Si-Enriched Sphere to Determine the Avogadro Constant at NMIJ
2018 Conference on Precision Electromagnetic Measurements (CPEM 2018), 2018Co-Authors: Naoki Kuramoto, Lulu Zhang, Hajime Inaba, Kazuaki Fujita, Sho Okubo, Kenichi FujiiAbstract:To determine the Avogadro Constant by the International Avogadro Coordination using the x-ray crystal density method, the volume of a28Si-enriched sphere, named Si28kgOla, was measured at NMIJ. The volume was determined from the diameter measurement in 2175 directions by an optical interferometer. Taking into account the results of the surface characterization of the sphere by x-ray photoelectron spectroscopy and spectroscopic ellipsometry, the volume of the Si core excluding the surface layers was determined with a relative uncertainty of $\pmb{2\ \times\ 10^{-8}}$ . Details of the interferometer and the uncertainty analysis of the volume measurement are presented.
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Avogadro Constant measurements using enriched 28Si monocrystals
Metrologia, 2017Co-Authors: Kenichi Fujii, Naoki Kuramoto, Enrico Massa, Horst Bettin, Giovanni ManaAbstract:Since 2011, the International Avogadro Coordination has been measuring the Avogadro Constant by counting the atoms in enriched 28Si monocrystals. This communication provides guidance on how the recently published results should be used to update the values of the Avogadro Constant measured so far.
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Determination of the Avogadro Constant by the XRCD method using a 28Si-enriched sphere
Metrologia, 2017Co-Authors: Naoki Kuramoto, Akira Kurokawa, Yasushi Azuma, Lulu Zhang, Shigeki Mizushima, Hajime Inaba, Kazuaki Fujita, Sho Okubo, Kenichi FujiiAbstract:To determine the Avogadro Constant N A by the x-ray crystal density method, the density of a 28Si-enriched crystal was determined by absolute measurements of the mass and volume of a 1 kg sphere manufactured from the crystal. The mass and volume were determined by an optical interferometer and a vacuum mass comparator, respectively. The sphere surface was characterized by x-ray photoelectron spectroscopy and spectroscopic ellipsometry to derive the mass and volume of the Si core of the sphere excluding the surface layers. From the mass and volume, the density of the Si core was determined with a relative standard uncertainty of 2.3 × 10−8. By combining the Si core density with the lattice Constant and the molar mass of the sphere reported by the International Avogadro Coordination (IAC) project in 2015, a new value of 6.022 140 84(15) × 1023 mol−1 was obtained for N A with a relative standard uncertainty of 2.4 × 10−8. To make the N A value determined in this work usable for a future adjustment of the fundamental Constants by the CODATA Task Group on Fundamental Constants, the correlation of the new N A value with the N A values determined in our previous works was examined. The correlation coefficients with the values of N A determined by IAC in 2011 and 2015 were estimated to be 0.07 and 0.28, respectively. The correlation of the new N A value with the N A value determined by IAC in 2017 using a different 28Si-enriched crystal was also examined, and the correlation coefficient was estimated to be 0.21.
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Volume measurements of 28Si-enriched spheres using an improved optical interferometer for the determination of the Avogadro Constant
Metrologia, 2017Co-Authors: Naoki Kuramoto, Yasushi Azuma, Hajime Inaba, Kenichi FujiiAbstract:For the determination of the Avogadro Constant by the x-ray crystal density method, an accurate volume measurement of 1 kg Si spheres is of primary importance. For this purpose, an optical interferometer was improved and used to measure the volumes of two 1 kg silicon spheres which were manufactured from a silicon crystal highly enriched in 28Si. The apparent volumes of the spheres, which do not take into account the influence of the surface layers on the volume measurement by interferometry, were determined with a relative standard uncertainty of as small as 2.0 × 10−8. The surface of the spheres was characterized by using an improved spectroscopic ellipsometer. By considering the influence of the surface layers, the core volumes of the spheres, which exclude the surface layers, were determined. These results were used for the determination of the Avogadro Constant in 2015 as a framework organized by the International Avogadro Coordination project. This paper provides details on the measurements, the improvements made to the apparatus, the data analysis and the uncertainty evaluation.
Peter Becker - One of the best experts on this subject based on the ideXlab platform.
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The Avogadro Constant and a new definition of the kilogram
International Journal of Mass Spectrometry, 2013Co-Authors: Peter Becker, Detlef SchielAbstract:Abstract The Avogadro Constant, the number of entities in the amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck Constant is very well known via the measurement of the Rydberg Constant, the Avogadro Constant is also closely related to the Planck Constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental Constant. Here, we describe a new and unique approach for the determination of the Avogadro Constant by “counting” the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.02214084(18) × 1023 mol−1, is now the most accurate input datum for a new definition of the kilogram.
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The new kilogram definition based on counting the atoms in a 28Si crystal
Contemporary Physics, 2012Co-Authors: Peter BeckerAbstract:The kilogram is the only unit of measure still defined by a physical object. Now, a marathon effort to tie the kilogram to a Constant of nature is nearing the finish line. This paper concerns an international research project aimed at determining the Avogadro Constant by counting the atoms in an isotopically enriched silicon crystal. The counting procedure was based on the measurement of the molar volume and the volume of an atom in two 1 kg crystal spheres. The novelty was the use of isotope dilution mass spectrometry as a new and very accurate method for the determination of the molar mass of enriched silicon. Because of an unexpected metallic contamination of the sphere surfaces, the relative measurement uncertainty, , results were larger by a factor 1.5 than that targeted. The measured value of the Avogadro Constant, mol–1 is the most accurate input datum for the kilogram redefinition and differs only by from the CODATA 2010 adjusted value. This value is midway between the watt-balance values.
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The Avogadro Constant: determining the number of atoms in a single-crystal 28Si sphere
Philosophical transactions. Series A Mathematical physical and engineering sciences, 2011Co-Authors: Peter Becker, Horst BettinAbstract:The Avogadro Constant, the number of entities in an amount of substance of one mole, links the atomic and the macroscopic properties of matter. Since the molar Planck Constant—the product of the Planck Constant and the Avogadro Constant—is very well known via the measurement of the Rydberg Constant, the Avogadro Constant is also closely related to the Planck Constant. In addition, its accurate determination is of paramount importance for a new definition of the kilogram in terms of a fundamental Constant. Here, we describe a new and unique approach to determine the Avogadro Constant from the number of atoms in 1 kg single-crystal spheres that are highly enriched with the 28 Si isotope. This approach has enabled us to apply isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022 140 82(18) × 10 23 mol −1 , is now the most
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Determination of the Avogadro Constant by counting the atoms in a 28Si crystal.
Physical review letters, 2011Co-Authors: Birk Andreas, Yasushi Azuma, Horst Bettin, Peter Becker, Guido Bartl, Michael Borys, I. Busch, M. Gray, P Fuchs, Katsumi FujiiAbstract:IRMM – Institute for Reference Materials and Measurements, Retieseweg 111, B-2440 Geel, Belgium(Dated: October 13, 2010)The Avogadro Constant links the atomic and the macroscopic properties of matter. Since themolar Planck Constant is well known via the measurement of the Rydberg Constant, it is also closelyrelated to the Planck Constant. In addition, its accurate determination is of paramount importancefor a definition of the kilogram in terms of a fundamental Constant. We describe a new approach forits determination by ”counting” the atoms in 1 kg single-crystal spheres, which are highly enrichedwith the
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Status of the n a determination by counting atoms in silicon crystals
CPEM 2010, 2010Co-Authors: Peter Becker, Giovanni Mana, Kenichi Fujii, Horst Bettin, Michael Borys, I. Busch, Ulrich Kuetgens, M. Gray, Michael Krumrey, P. MansonAbstract:This paper reports the progress and the achievements of an international research project aimed at determining the Avogadro Constant by counting the atoms in enriched 28Si spheres.
S Valkiers - One of the best experts on this subject based on the ideXlab platform.
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The isotopic composition of enriched Si: a data analysis
Metrologia, 2011Co-Authors: Ewa Bulska, Giovanni Mana, Axel Pramann, M. N. Drozdov, Olaf Rienitz, Petr G. Sennikov, S ValkiersAbstract:To determine the Avogadro Constant by counting the atoms in quasi-perfect spheres made of a silicon crystal highly enriched with 28Si, the isotopic composition of the crystal was measured in different laboratories by different measurement methods. This paper examines the consistency of the measurement results.
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Uncertainty assessment of Si molar mass measurements
International Journal of Mass Spectrometry, 2009Co-Authors: Giovanni Mana, S Valkiers, Enrico Massa, G.-d. WillenbergAbstract:Abstract The uncertainty of the Si molar mass measurement is theoretically investigated by means of a two-isotope model, with particular emphasis to the role of this measurement in the determination of the Avogadro Constant. This model allows an explicit calibration formula to be given and propagation of error analysis to be made. It also shows that calibration cannot correct for non-linearity.
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The Avogadro Constant Determination via Enriched Silicon-28
Measurement Science and Technology, 2009Co-Authors: Peter Becker, Giovanni Mana, K. Fujii, H. Friedrich, W. Giardini, A. Picard, H.-j. Pohl, Helge Riemann, S ValkiersAbstract:This review describes the efforts of several national metrology institutes to replace the present definition of the kilogram by a new one based on the mass of a given number of 12C atoms. This requires the determination of the Avogadro Constant with a relative uncertainty no greater than 2 ? 10?8. Since in previous attempts the most significant limiting factor has been the measurement of the average molar mass of the natural silicon, an international collaboration has been set up to produce a 5 kg single crystal with an isotope enrichment over 99.985%. The technological steps enabling the production of this high-purity 28Si crystal are also reported.
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Present Status of the a Vogadro Constant Determination from Silicon Crystals with Natural Isotopic Composition
2004 Conference on Precision Electromagnetic Measurements, 2004Co-Authors: Kenichi Fujii, S Valkiers, Naoki Kuramoto, Horst Bettin, Peter Becker, Shigeki Mizushima, A. Waseda, Ulrich Kuetgens, Arnold Nicolaus, Philip D. P. TaylorAbstract:A determination of the Avogadro Constant from two selected silicon single-crystals with natural isotopic compositions is described. The density, molar mass, and lattice spacing of the two crystals were measured at NMIJ, PTB, IRMM, IMGC, and NIST. When all the data are combined, they lead to a value of the Avogadro Constant of 6.022 1353 (18)/spl times/10/sup 23/ mol/sup -1/ with a relative combined standard uncertainty of 3.1/spl times/10/sup -7/.
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Determination of the Avogadro Constant via the silicon route
Metrologia, 2003Co-Authors: Peter Becker, S Valkiers, Horst Bettin, Detlef Schiel, P. De Bièvre, H-u Danzebrink, M Gläser, Ulrich Kuetgens, Arnold Nicolaus, Philip D. P. TaylorAbstract:A value for the Avogadro Constant, NA, was derived from new measurements of the lattice parameter, the density and the molar mass of a silicon single crystal. The result NA = 6.022 135 3 × 1023 mol−1 has a relative measurement uncertainty and is in excellent agreement with other published data based on the x-ray crystal density molar mass method, indicating the high repeatability of these experiments. The value differs significantly from the Committee on Data for Science and Technology's most recent recommended value of 6.022 141 99 × 1023 mol−1 by more than 1 × 10−6 NA.
Naoki Kuramoto - One of the best experts on this subject based on the ideXlab platform.
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Volume Measurement of a 28 Si-Enriched Sphere for a Determination of the Avogadro Constant at NMIJ
IEEE Transactions on Instrumentation and Measurement, 2019Co-Authors: Naoki Kuramoto, Lulu Zhang, Hajime Inaba, Kazuaki Fujita, Sho Okubo, Kenichi FujiiAbstract:For a determination of the Avogadro Constant by the X-ray crystal density method, the volume of a Si sphere manufactured from a Si crystal isotopically enriched in 28Si, named Si28-23Pr11, was measured at the National Metrology Institute of Japan (NMIJ). The volume was determined on the basis of diameter measurement in 2175 directions by an optical interferometer. The surface layers on the sphere were characterized by X-ray photoelectron spectroscopy and spectroscopic ellipsometry. Taking into account the effect of the surface layers on the diameter measurement, the volume of the Si core excluding the surface layers was determined with a relative uncertainty of $2.0\times 10^{\mathbf {-8}}$ . The results were used to determine the Avogadro Constant in 2017 by the International Avogadro Coordination project, which was used as an input datum to determine the CODATA 2017 adjusted value of the Planck Constant $h$ . This $h$ value will be used in the new definition of the kilogram. This paper provides details of the measurement apparatus and the uncertainty analysis of the Si core volume measurement. In addition, an approach to reduce the uncertainty in the Si core volume determination is proposed for the accurate realization of the kilogram based on the new definition at NMIJ. Details of the approach are also provided.
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Volume Measurement of a 28 Si-Enriched Sphere to Determine the Avogadro Constant at NMIJ
2018 Conference on Precision Electromagnetic Measurements (CPEM 2018), 2018Co-Authors: Naoki Kuramoto, Lulu Zhang, Hajime Inaba, Kazuaki Fujita, Sho Okubo, Kenichi FujiiAbstract:To determine the Avogadro Constant by the International Avogadro Coordination using the x-ray crystal density method, the volume of a28Si-enriched sphere, named Si28kgOla, was measured at NMIJ. The volume was determined from the diameter measurement in 2175 directions by an optical interferometer. Taking into account the results of the surface characterization of the sphere by x-ray photoelectron spectroscopy and spectroscopic ellipsometry, the volume of the Si core excluding the surface layers was determined with a relative uncertainty of $\pmb{2\ \times\ 10^{-8}}$ . Details of the interferometer and the uncertainty analysis of the volume measurement are presented.
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Avogadro Constant measurements using enriched 28Si monocrystals
Metrologia, 2017Co-Authors: Kenichi Fujii, Naoki Kuramoto, Enrico Massa, Horst Bettin, Giovanni ManaAbstract:Since 2011, the International Avogadro Coordination has been measuring the Avogadro Constant by counting the atoms in enriched 28Si monocrystals. This communication provides guidance on how the recently published results should be used to update the values of the Avogadro Constant measured so far.
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Determination of the Avogadro Constant by the XRCD method using a 28Si-enriched sphere
Metrologia, 2017Co-Authors: Naoki Kuramoto, Akira Kurokawa, Yasushi Azuma, Lulu Zhang, Shigeki Mizushima, Hajime Inaba, Kazuaki Fujita, Sho Okubo, Kenichi FujiiAbstract:To determine the Avogadro Constant N A by the x-ray crystal density method, the density of a 28Si-enriched crystal was determined by absolute measurements of the mass and volume of a 1 kg sphere manufactured from the crystal. The mass and volume were determined by an optical interferometer and a vacuum mass comparator, respectively. The sphere surface was characterized by x-ray photoelectron spectroscopy and spectroscopic ellipsometry to derive the mass and volume of the Si core of the sphere excluding the surface layers. From the mass and volume, the density of the Si core was determined with a relative standard uncertainty of 2.3 × 10−8. By combining the Si core density with the lattice Constant and the molar mass of the sphere reported by the International Avogadro Coordination (IAC) project in 2015, a new value of 6.022 140 84(15) × 1023 mol−1 was obtained for N A with a relative standard uncertainty of 2.4 × 10−8. To make the N A value determined in this work usable for a future adjustment of the fundamental Constants by the CODATA Task Group on Fundamental Constants, the correlation of the new N A value with the N A values determined in our previous works was examined. The correlation coefficients with the values of N A determined by IAC in 2011 and 2015 were estimated to be 0.07 and 0.28, respectively. The correlation of the new N A value with the N A value determined by IAC in 2017 using a different 28Si-enriched crystal was also examined, and the correlation coefficient was estimated to be 0.21.
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Volume measurements of 28Si-enriched spheres using an improved optical interferometer for the determination of the Avogadro Constant
Metrologia, 2017Co-Authors: Naoki Kuramoto, Yasushi Azuma, Hajime Inaba, Kenichi FujiiAbstract:For the determination of the Avogadro Constant by the x-ray crystal density method, an accurate volume measurement of 1 kg Si spheres is of primary importance. For this purpose, an optical interferometer was improved and used to measure the volumes of two 1 kg silicon spheres which were manufactured from a silicon crystal highly enriched in 28Si. The apparent volumes of the spheres, which do not take into account the influence of the surface layers on the volume measurement by interferometry, were determined with a relative standard uncertainty of as small as 2.0 × 10−8. The surface of the spheres was characterized by using an improved spectroscopic ellipsometer. By considering the influence of the surface layers, the core volumes of the spheres, which exclude the surface layers, were determined. These results were used for the determination of the Avogadro Constant in 2015 as a framework organized by the International Avogadro Coordination project. This paper provides details on the measurements, the improvements made to the apparatus, the data analysis and the uncertainty evaluation.
P. De Bièvre - One of the best experts on this subject based on the ideXlab platform.
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Determination of the Avogadro Constant via the silicon route
Metrologia, 2003Co-Authors: Peter Becker, S Valkiers, Horst Bettin, Detlef Schiel, P. De Bièvre, H-u Danzebrink, M Gläser, Ulrich Kuetgens, Arnold Nicolaus, Philip D. P. TaylorAbstract:A value for the Avogadro Constant, NA, was derived from new measurements of the lattice parameter, the density and the molar mass of a silicon single crystal. The result NA = 6.022 135 3 × 1023 mol−1 has a relative measurement uncertainty and is in excellent agreement with other published data based on the x-ray crystal density molar mass method, indicating the high repeatability of these experiments. The value differs significantly from the Committee on Data for Science and Technology's most recent recommended value of 6.022 141 99 × 1023 mol−1 by more than 1 × 10−6 NA.
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A Web-based database for the international programme to improve the Avogadro Constant along the silicon route
IEEE Transactions on Instrumentation and Measurement, 2003Co-Authors: M.j. Kenny, P. De Bièvre, A. PicardAbstract:A number of measurement institutes are working together toward a determination of the Avogadro Constant with a relative combined standard uncertainty of 10/sup -8/. This will enable a definition of the kilogram based on the mass of a specific number of /sup 12/C atoms rather than an artefact. In order to bring together all the data obtained in the various laboratories and maintain accountability and traceability across the collaborating institutes, a Web-based database has been set up. This database forms part of the BIPM website, although access is currently limited to project participants. Any data used in publications on the Si-route, together with supporting evidence, can be found in this database.
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A reassessment of the molar volume of silicon and of the Avogadro Constant
IEEE Transactions on Instrumentation and Measurement, 2001Co-Authors: P. De Bièvre, S Valkiers, Kenichi Fujii, Horst Bettin, S. Pettorruso, A. Peuto, Peter Becker, Philip D. P. Taylor, R Kessel, A. WasedaAbstract:An "absolute" value for the molar volume of Si in Si single crystals is presented as 12.058 820 7(54) cm/sup 3/ mol/sup -1/ with a relative standard uncertainty of 4.5/spl middot/10/sup -7/. It is argued that the consistency of most of the molar volume determinations is useful for evaluating the quality of the Si single crystals involved. A value for the Avogadro Constant is derived as 6.022 133 9(27)/spl middot/10/sup 23/ mol/sup -1/ having a relative standard uncertainty of 4.6/spl middot/10/sup -7/.
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determination of the Avogadro Constant by accurate measurement of the molar volume of a silicon crystal
Metrologia, 1999Co-Authors: Kenichi Fujii, P. De Bièvre, M. Tanaka, Y. Nezu, K Nakayama, H Fujimoto, S ValkiersAbstract:In order to determine the Avogadro Constant by the x-ray crystal density method, the molar volume of silicon in a single crystal grown by the float-zone method was determined by absolute measurements of the density and the molar mass of the crystal. The density was directly determined by mass and volume measurements of 1 kg spheres fabricated from the crystal. For the volume determination, a scanning-type optical interferometer was developed to measure the diameters of the spheres. The molar mass measurements were calibrated using synthetic isotope mixtures prepared from enriched silicon isotopes. Two spheres for density measurements, and fourteen samples for molar mass measurements, were systematically prepared from the crystal to evaluate distributions of the density and the isotopic composition of the crystal. The results give a molar volume of 12.0588646 cm3/mol with a standard uncertainty of 0.0000026 cm3/mol, at 22.500 °C and 0 Pa after correction for impurities. When this value is combined with the lattice Constant of the crystal determined using a combined x-ray/optical interferometer, a value of 6.0221550 × 1023 mol-1 with a standard uncertainty of 0.0000016 × 1023 mol-1 is obtained for the Avogadro Constant.
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the effect of residual adsorbed gases on silicon isotope amount ratio measurements in Avogadro Constant determination
Conference on Precision Electromagnetic Measurements, 1998Co-Authors: S Valkiers, P D P Taylor, R. Gonfiantini, P. De BièvreAbstract:An adsorption model developed for molecular flow inlet system was applied successfully to remove memory effects in high accuracy isotopic measurements, especially in the Si isotopic measurements leading to improved values for the Avogadro Constant.
