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Determination of the Avogadro Constant

Working Group 1.83

Publications (selection)

2015

Azuma, Y.; Barat, P.; Bartl, Guido; Bettin, Horst; Borys, Michael; Busch, Ingo; Cibik, Levent; D'Agostino, G.; Fujii, K.; Fujimoto, H.; Hioki, A.; Krumrey, Michael; Kuetgens, Ulrich; Kuramoto, N.; Mana, G.; Massa, E.; Meeß, Rudolf; Mizushima, S.; Narukawa, T.; Nicolaus, Arnold; Pramann, Axel; Rabb, S.A.; Rienitz, Olaf; Sasso, C.; Stock, M.; Vocke Jr, R.D.; Waseda, A.; Wundrack, Stefan; Zakel, Sabine: Improved measurement results for the Avogadro constant using a 28Si-enriched crystal. Metrologia 52 (2015), No. 2 [open access], 360-375, dx.doi.org/10.1088/0026-1394/52/2/360, IOP. ISSN 0026-1394 (print) ; ISSN 1681-7575 (online)

2014

Borys, Michael; Mecke, Michael; Kuetgens, Ulrich; Busch, Ingo; Krumrey, Michael; Fuchs, Peter; Marti, Kilian; Bettin, Horst: The growth of the oxide layer on silicon spheres and its influence on their mass stability. Joint IMEKO International TC3, TC5 and TC22 Conference 2014 (2014), 3 to 5 February 2014, Cape Town, Republic of South Africa

A. Nicolaus, H. Bettin, M. Borys, U. Kuetgens, A. Pramann: Revision of the SI: The determination of the Avogadro constant as the base for the kilogram. Key Engineering Materials 613 (2014) 3-10

2013

A. Nicolaus, H. Bettin, M. Borys, U. Kuetgens, A. Pramann: Revision of the SI: The determination of the Avogadro constant as the base for the kilogram. Proc. 11th ISMTII, July 1st to 5th, 2013. (International Symposium on Measurement Technology and Intelligent Instruments) 6 pp.

Horst Bettin, Kenichi Fujii, John Man, Giovanni, Mana, Enrico Massa, Alain Picard: Accurate measurements of the Avogadro and Planck constants by counting silicon atoms. Annalen der Physik, 525, No. 8-9 (2013) 680-687

R. A. Nicolaus, G. Bartl, H. Bettin, M. Borys, M. Firlus, I. Busch, A. Felgner, R. Krüger-Sehm, M. Krumrey, M. Krystek, U. Kuetgens: Current State of the Avogadro 28Si sphere S8. IEEE Trans. Instrum. Meas. 62 (June 2013) 1499-1505

H. Bettin, C. Jacques, Z. Zelenka, K. Fujii, N. Kuramoto, K.-H. Chang, Y. J. Lee, L. O. Becerra and N. Domostroeva: Final report on CCM key comparison CCM.D-K2: Comparison of liquid density standards, Metrologia Techn. Suppl. 50 (2013) 07006

2012

R. A. Nicolaus, G. Bartl, H. Bettin, I. Busch, M. Borys, R. Krüger-Sehm, M. Krumrey, U. Kuetgens: State of the Avogadro 28Si spheres. CPEM 2012 digest

H. Baumann, H. Bettin, F. Bielsa, A. Eichenberger, G. Genevès, N. Kuramoto, G. Mana, E. Massa, F. Pereira dos Santos, A. Picard, P. Pinot, A. Schindler: Realization of the Anticipated Definition of the Kilogram. CPEM 2012 digest

2011

Metrologia Special Issue “International determination of the Avogadro constant”, Vol. 48, No. 2 April 2011

B. Andreas et al: Counting the atoms in a 28Si crystal for a new kilogram definition. Metrologia 48 (2011), S1–13

S. Zakel, S. Wundrack, H. Niemann, O. Rienitz and D. Schiel: Infrared spectrometric measurement of impurities in highly enriched ‘Si 28’. Metrologia 48 (2011), S14–19

A. Pramann, O. Rienitz, D. Schiel, J. Schlote, B. Güttler and S. Valkiers: Molar mass of silicon highly enriched in 28Si determined by IDMS. Metrologia 48 (2011), S20–25

S. Valkiers, G. Mana, K. Fujii and P. Becker: Si primary standards for the calibration of ion-current ratios in the molar-mass measurement of natural Si single crystals. Metrologia 48 (2011), S26-31

E. Bulska, M. N. Drozdov, G. Mana, A. Pramann, O. Rienitz, P. Sennikov and S. Valkiers: The isotopic composition of enriched Si: a data analysis. Metrologia 48 (2011), S32–36

E. Massa, G. Mana, U. Kuetgens and L. Ferroglio: Measurement of the {2 2 0} lattice-plane spacing of a 28Si x-ray interferometer. Metrologia 48 (2011), S37–43

E. Massa, G. Mana, L. Ferroglio, E. G. Kessler, D. Schiel and S. Zakel: The lattice parameter of the 28Si spheres in the determination of the Avogadro constant. Metrologia 48 (2011), S44–49

L. Ferroglio, G. Mana and E. Massa: The self-weight deformation of an x-ray interferometer. Metrologia 48 (2011), S50–54

H. Fujimoto, A. Waseda and X. W. Zhang: Homogeneity characterization of lattice spacing of silicon single crystals by a self-referenced lattice comparator. Metrologia 48 (2011), S55–61

I. Busch, Y. Azuma, H. Bettin, L. Cibik, P. Fuchs, K. Fujii, M. Krumrey, U. Kuetgens, N. Kuramoto and S. Mizushima: Surface layer determination for the Si spheres of the Avogadro project. Metrologia 48 (2011), S62–82

N. Kuramoto, K. Fujii and K. Yamazawa: Volume measurement of 28Si spheres using an interferometer with a flat etalon to determine the Avogadro constant. Metrologia 48 (2011), S83–95

G. Bartl, H. Bettin, M. Krystek, T. Mai, A. Nicolaus and A. Peter: Volume determination of the Avogadro spheres of highly enriched 28Si with a spherical Fizeau interferometer. Metrologia 48 (2011), S96–103

B. Andreas, L. Ferroglio, K. Fujii, N. Kuramoto and G. Mana: Phase corrections in the optical interferometer for Si sphere volume measurements at NMIJ. Metrologia 48 (2011), S104-111

A. Picard, P. Barat, M. Borys, M. Firlus and S. Mizushima: State-of-the art mass determination of 28Si spheres for the Avogadro project. Metrologia 48 (2011), S112–119

 

A. Pramann, O. Rienitz, D. Schiel, B. Güttler and S. Valkiers: Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty: Part 3 - Molar mass of silicon highly enriched in 28Si. Int. J. Mass Spectrom. 369 (2011), 3925-3935

A. Pramann, O. Rienitz, D. Schiel and B. Güttler: Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty: Part 2 – Development of an experimental procedure for the determination of the molar mass of silicon using MC-ICP-MS. Int. J. Mass Spectrom. 299 (2011), 78–86

Axel Pramann, Olaf Rienitz, Detlef Schiel, Bernd Güttler, Staf ValkiersP. Becker and H. Bettin: The Avogadro constant: determining the number of atoms in a single-crystal 28Si sphere. Phil. Trans. R. Soc. A (London) 369 (2011), 3925-3935

H. L. Hall: Learning from the time and length redefinitions, and the metre demotion, Phil. Trans. R. Soc. A (London) 369 (2011), 4090-4108

B. Andreas et al.: A determination of the Avogadro constant by counting the atoms in a 28Si crystal, Phys. Rev. Lett. 106 (2011), 030801-1-4

 

2010

O. Rienitz, A. Pramann and D. Schiel: Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty: Part 1 – theoretical derivation and feasibility study. Int. J. Mass Spectrometry 289 (2010), 47-53

G. Mana, O. Rienitz and A. Pramann: Measurement equations for the determination of the Si molar mass by isotope dilution mass spectrometry. Metrologia 47 (2010), 460-3

G. Mana and O. Rienitz: The calibration of Si isotope ratio measurements. Int. J. Mass Spectrometry 291 (2010), 55-60

G. Mana, E. Massa, S. Valkiers and G.-D. Willenberg: Uncertainty assessment of Si molar mass measurements. Int. J. Mass Spectrometry 289 (2010), 6-10

E. Massa, G. Mana, U. Kuetgens and L. Ferroglio: Calibration of a silicon crystal for absolute nuclear spectroscopy. J. Appl. Cryst. 43 (2010), 293-296

G. Mana, J. Krempel and L. Ferroglio: Estimation of the centre of a diffraction peak by triggering the goniometer-angle readings via photon detection. J. Appl. Cryst. 43 (2010), 83-88

C. Palmisano and M. Guida: Two-wave approximation in surface effects in asymmetric Laue crystals. Acta Cryst. A66 (2010), 470-8

G. Bartl, M. Krystek, A. Nicolaus and W. Giardini: Interferometric determination of the topographies of absolute sphere radii using the sphere interferometer of PTB. Meas. Sci. Technol. 21 (2010), 115101-1-8

G. Mana, E. Massa and S. Valkiers: Uncertainty assessment of Si molar mass measurements, Int. J. Mass Spectrom. 289 (2010), 6-10

 

2009

P. Becker: Determination of the Avogadro Constant – A contribution to the new definition of the mass unit kilogram. Eur. Phys. J. Special Topics 172 (2009), 343-352

P. Becker and A. Nicolaus: The marathon race to a new atomic kilogram. Europhysicsnews 40 (2009), 23-26

A. Picard, N. Bignell, M. Borys, S. Downes and S. Mizushima: Mass comparison of the 1 kg silicon sphere AVO#3 traceable to the International Prototype K. Metrologia 46 (2009), 1-10

P. Becker, H. Friedrich, K. Fujii, W. Giardini, G. Mana, A. Picard, H.-J. Pohl, H. Riemann and S. Valkiers: The Avogadro constant determination via enriched silicon-28. Meas. Sci. Technol. 20 (2009), 092002-1-20

E. Massa, G. Mana and U. Kuetgens: Comparison of the INRIM and PTB lattice-spacing standards. Metrologia 46 (2009), 249-253

E. Massa, G. Mana, U. Kuetgens and L. Ferroglio: Measurement of the Lattice Parameter of a Silicon Crystal. New J. Phys. 11 (2009), 053013-1-12

E. Massa, G. Mana and L. Ferroglio: Observation of a Bent Crystal-Lattice by X-Ray Interferometry. Optics Express 17 (2009), 11172-11178

I. Busch, H.-U. Danzebrink, M. Krumrey, M. Borys and H. Bettin: Oxide layer mass determination at the silicon sphere of the Avogadro project. IEEE Trans. Instrum. Meas. 58 (2009), 891-896

G. Bartl, A. Nicolaus, E. Kessler, R. Schödel and P. Becker: The coefficient of thermal expansion of highly enriched 28Si. Metrologia 46 (2009), 416-422

G. Bartl and A. Nicolaus: Influence of the distribution of measuring points on the mean diameter determination of the Avogadro project's silicon spheres. Meas. Sci. Technol. 20 (2009), 065104-1-6

A. Nicolaus and G. Bartl: lnvestigations on diameter measurements of the Avogadro silicon sphere dependent on the position in the field of view of the interferometer optics. IEEE Trans. Instrum. Meas. 58 (2009), 919-23

A. Nicolaus and G. Bönsch: Aperture correction for a spherical interferometer. Metrologia 46 (2009), 668-73

M. Jentschel, J. Krempel and P. Mutti: A validity test of E = mc2. Eur. Phys. J. 172 (2009), 352-62

 

2008 and earlier

P. Becker and A. Nicolaus: Hat das Urkilogramm bald ausgedient? Physik in unserer Zeit 39 (2008), 164-65

P. Becker: Towards an atomic realization of the kilogram: The measurements of NA and NAh. European Physical Journal 163 (2008), 127-39

P. Becker, P. DeBièvre, K. Fujii, M. Gläser, B. Inglis, H. Lübbig and G. Mana: Consideration on future redefinitions of the kilogram, the mole, and of other units. Metrologia 44 (2007), 1-14

P. Becker, M. Jentschel, G. Mana and G. Zosi: Towards an atomic realization of the kilogram: the measurement of NA and NA h. Proceedings of the International School of Physics, E. Fermi: Metrology and Fundamental Constants, Course CLXVI, Varenna, Italy 18th - 28th July 2006, ed. by S. Leschiutta, T. Hänsch, and A. Wallard, North-Holland, 2007

P. Becker, D. Schiel, H.-J. Pohl, A. K. Kaliteevski, O. N. Godisov, G. G. Devyatykh, A. V. Gusev, A. D. Bulanov, S. A. Adamchik, V. A. Gavva, I. D. Kovalev, N. V. Abrosimov, B. Hallmann-Seiffert, H. Riemann, S. Valkiers and P. Taylor: Large scale production of highly isotopic enriched 28Si for precision determination of the Avogadro constant. Meas. Sci. Technol. 17 (2006), 1854-1860

K. Fujii, A. Waseda, N. Kuramoto, S. Mizushima, P. Becker, H. Bettin, A. Nicolaus, U. Kuetgens, S. Valkiers, P. Taylor, P. De Bievre, G. Mana, E. Massa, R. Matyi, E. Kessler, M. Hanke: Present State of the Avogadro Constant Determination From Silicon Crystals With Natural Isotopic Composition, IEEE Trans. Instrum. Meas. 54 (2005), 854-859

P. Becker, H. Bettin, H.-U. Danzebrink, M. Gläser, U. Kuetgens, A. Nicolaus, D. Schiel, P. DeBievre, S. Valkiers and P. Taylor: Determination of the Avogadro constant via the silicon route. Metrologia 40 (2003), 271-287

P. Becker: History and progress in the accurate determination of the Avogadro constant. Rep. Prog. Phys. 64 (2001), 1945-2008

P. Seyfried, P. Becker, A.Kozdon, F. Lüdicke, F. Spieweck, J. Stümpel, H. Wagenbreth, D. Windisch, P. De Bièvre, H. H. Ku, G. Lenaers, T. J. Murphy, H. S. Peiser and S. Valkiers: A determination of the Avogadro Constant. Z. Phys. B – Condensed Matter 87 (1992), 289-298