Improved measurement results for the Avogadro constant using a28Si-enriched crystal

Metrologia

Volumn 52, Issue 2, 2015, Pages 360-375

  Azuma, Y ^a   Barat, P ^b   Bartl, G ^c   Bettin, H ^c   Borys, M ^c   Busch, I ^c   Cibik, L ^c   D'Agostino, G ^d   Fujii, K ^a   Fujimoto, H ^a   Hioki, A ^a   Krumrey, M ^c   Kuetgens, U ^c   Kuramoto, N ^a   Mana, G ^d   Massa, E ^d   Meess R ^c   Mizushima, S ^a   Narukawa, T ^a   Nicolaus, A ^c   Pramann, A ^c   Rabb, S A ^e   Rienitz, O ^c   Sasso, C ^d   Stock, M ^b   Vocke, R D ^e   Waseda, A ^a   Wundrack, S ^c   Zakel, S ^c   more..

^a NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

^b PAVILLON DE BRETEUIL   (France)

^c PHYSIKALISCH TECHNISCHE BUNDESANSTALT   (Germany)

^d ISTITUTO NAZIONALE DI RICERCA METROLOGICA   (Italy)

^e NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

Avogadro constant; Enriched silicon; Interferometry; Kilogram; Lattice parameter; Molar mass; Planck constant

Indexed keywords

LATTICE CONSTANTS; MOLAR MASS; SILICON;

AVOGADRO CONSTANT; INTERNATIONAL RESEARCHES; ISOTOPICALLY ENRICHED SILICON; KILOGRAM; PARAMETER MEASUREMENT; PLANCK CONSTANTS; STANDARD UNCERTAINTY; X-RAY CRYSTAL DENSITY METHOD;

INTERFEROMETRY;

EID: 84926456246     PISSN: 00261394     EISSN: 16817575     Source Type: Journal    
DOI: 10.1088/0026-1394/52/2/360     Document Type: Article

References (69)

1. Massa E and Nicolaus A 2011 Special issue international determination of the Avogadro constant Metrologia 48 S1-119
2. 28Si crystal Phys. Rev. Lett. 106 030801 (4 pp)
3. Busch I, Azuma Y, Bettin H, Cibik L, Fuchs P, Fujii K, Krumrey M, Kuetgens U, Kuramoto N and Mizushima S 2011 Surface layer determination for the Si spheres of the Avogadro project Metrologia 48 S62-82
4. Qin M, Poon M C and Yue C Y 2000 A study of nickel silicide film as a mechanical material Sensors Actuators 87 90
5. 28Si sphere S8 IEEE Trans. Instrum. Meas. 62 1499-505
6. Meeß R, Felgner A, Hinzmann G and Lück A 2014 Surface topography of superpolished silicon spheres Proc. Int. Conf. Eur. Soc. Precis. Eng. Nanotechnol. 2 99-102
7. Bowen D K and Tanner B K 1998 High Resolution x-Ray Diffractometry and Topography (London: Taylor and Francis)
8. Stock M 2014 Revised mass values for BIPM calibrations following the extraordinary calibration campaign against the IPK correspondence BIPM December 2014
9. Itoh Y, Nozaki T, Masui T and Abe T 1985 Calibration curve for infrared spectrophotometry of nitrogen in silicon Appl. Phys. Lett. 47 488-9
10. D'Agostino G, Bergamaschi L, Giordani L, Mana G, Massa E and Oddone M 2012 Elemental characterization of the Avogadro silicon crystal WASO04 by neutron activation analysis Metrologia 49 696-701
11. 28Si single-crystal J. Radioanal. Nucl. Chem. 299 277-82
12. 28Si crystal for a new kilogram definition Metrologia 48 S1-13
13. 28Si determined by IDMS Metrologia 48 S20-5
14. 28Si-enriched silicon for a revised estimate of the Avogadro constant Anal. Chem. 84 2321-7
15. Pramann A, Rienitz O, Noordmann J, Güttler B and Schiel D 2014 A more accurate molar mass of silicon via high resolution MC-ICP-mass spectrometry Z. Phys. Chem. 228 405-19
16. 28Si-enriched silicon crystal for determination of the Avogadro constant Metrologia 51 161-8
17. Vocke R D Jr, Rabb S A and Turk G C 2014 Absolute silicon molar mass measurements, the Avogadro constant and the redefinition of the kilogram Metrologia 51 361-75
18. Pramann A, Lee K-S, Noordmann J and Rienitz O 2015 Probing the homogeneity of the isotopic composition and molar mass of the 'Avogadro-28'-crystal Metrologia in preparation
19. Rienitz O, Pramann A and Schiel D 2010 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 Spectrom. 289 47-53
20. Vocke R D Jr et al 2015 in preparation
21. Rienitz O, Pramann A, Kaltenbach A, Hinrichs J, Barnhart D and Churchill G 2015 in preparation
22. Pramann A, Rienitz O and Schiel D 2012 Silicon isotope ratios affected by sodium-induced broadband interference in high resolution multicollector-ICPMS Anal. Chem. 84 10175-9
23. 28Si: proof of concept and estimation of the achievable uncertainty Metrologia 51 354-60
24. 28Si determined by instrumental neutron activation analysis Anal. Chem. (submitted)
25. Wang M, Audi G, Wapstra A H, Kondev F G, MacCormick M, Xu X and Pfeiffer B 2012 The AME2012 atomic mass evaluation (II). Tables, graphs and references Chin. Phys. C 36 1603-2014
26. Bodnar O and Elster C 2014 On the adjustment of inconsistent data using the Birge ratio Metrologia 51 516-21
27. CCQM/13-22 2013 CCQM Guidance note: Estimation of a consensus KCRV and associated Degrees of Equivalence, KCWG, BIPM (www.bipm.org/cc/AllowedDocuments.jsp?cc=CCQM)
28. Kessel R, Berglund M and Wellum R 2008 Appplication of consistency checking to evaluation of uncertainty in multiple replicate measurements Accred. Qual. Assur. 13 293-8
29. n for measurement science Metrologia 43 S235-43
30. Robouch P, Younes N and Vermaercke P 2003 The 'Naji Plot', a simple graphical tool for the evaluation of interlaboratory comparisons Data Analysis of Key Comparisons ed D Richter et al (Bremerhaven: Wirtschaftsverlag NW)
31. 28Si x-ray interferometer Metrologia 48 S37-43
32. White D et al 2008 Uncertainties in the realisation of the SPRT subranges of the ITS-90 Report of the CCT-WG3 on Uncertainties in Contact Thermometry CCT/08-19/rev (Sèvres: Bureau International des Poids et Mesures)
33. 28Si lattice parameter J. Phys. Chem. Ref. Data accepted
34. Fujimoto H, Waseda A and Zhang X W 2011 Homogeneity characterization of lattice spacing of silicon single crystals by the self-referenced lattice comparator Metrologia 48 S55-61
35. Waseda A, Fujimoto H, Zhang X W, Kuramoto N and Fujii K 2015 Homogeneity characterization of lattice spacing of silicon single crystals IEEE Trans. Instrum. Meas. accepted
36. Becker P et al 2003 Determination of the Avogadro constant via the silicon route Metrologia 40 271-87
37. Beckhoff B, Gottwald A, Klein R, Krumrey M, Müller R, Richter M, Scholze F, Thornagel R and Ulm G 2009 A quarter-century of metrology using synchrotron radiation by PTB in Berlin Phys. Status Solidi B 246 1415-34
38. Picard A, Bignell N, Downes S and Mizushima S 2009 Mass comparison of the 1 kg silicon sphere Metrologia 46 1-10
39. Krumrey M, Gleber G, Scholze F and Wernecke J 2011 Synchrotron radiation-based x-ray reflection and scattering techniques for dimensional nanometrology Meas. Sci. Technol. 22 094032
40. 28Si spheres to determine the Avogadro constant IEEE Trans. Instrum. Meas. accepted
41. Kuramoto N, Fujii K, Nicolaus A, Bartl G, Gray M, Manson P and Giardini W 2011 Diameter comparison of a silicon sphere for the international Avogadro coordination IEEE Trans. Instrum. Meas. 60 2615-20
42. Mizushima S, Kuramoto N, Ueda K and Fujii K 2015 Mass measurement of 1 kg silicon spheres for the determination of the Avogadro and Planck constants IEEE Trans. Instrum. Meas. accepted
43. 2/Si(1 0 0) surfaces to realize precise mass measurements Metrologia 41 137-44
44. 28Si spheres using an interferometer with a flat etalon to determine the Avogadro constant Metrologia 48 S83-95
45. Andreas B, Ferroglio L, Fujii K, Kuramoto N and Mana G 2011 Phase corrections in the optical interferometer for Si sphere volume measurements at NMIJ Metrologia 48 S104-11
46. Nicolaus R A and Bönsch G 2005 Absolute volume determination of a silicon sphere with the spherical interferometer of PTB Metrologia 42 24-31
47. Bartl G, Krystek M and Nicolaus A 2014 PTB's enhanced stitching approach for the high-accuracy interferometric form error characterization of spheres Meas. Sci. Technol. 25 064002 (8 pp)
48. 28Si with a spherical Fizeau interferometer Metrologia 48 S96-103
49. th Conf. on Precision Electromagnetic Measurements (Rio de Janeiro, 25-29 Auguest 2014) pp 394-5 (Conference Digest)
50. Nicolaus R A and Geckeler R D 2007 Improving the measurement of the diameter of Si-spheres IEEE Trans. Instrum. Meas. 56 517-22
51. Collins J G, Giardini W J, Leistner A J and Kenny M J 1997 The influence of Young's modulus on roundness in silicon sphere fabrication IEEE Trans. Instrum Meas. 46 572-5
52. Boyd E J and Uttamchandani D 2012 Measurement of the anisotropy of Young's modulus in single-crystal silicon J. Microelectromech. Syst. 21 243-9
53. 28Si spheres for the Avogadro project Metrologia 48 S112-9
54. Barat P 2015 Mémoire d'ingénieur CNAM, Projet international Avogadro: Détermination de la masse de la couche d'eau chimisorbée à la surface d'une sphère en silicium naturel
55. Mizushima S, Ueki M and Fujii K 2004 Mass measurement of 1 kg silicon spheres to establish a density standard Metrologia 41 S68-74
56. Picard A and Fang H 2004 Methods to determine water vapour sorption on mass standards Metrologia 41 333-9
57. Picard A 2006 Mass determination of a 1 kg silicon sphere for the Avogadro project Metrologia 43 46-52
58. st edn (Geneva: International Organisation for Standardisation) (corrected and reprinted 1995)
59. GUM Workbench Version 1.2.11.56 '96-'99 by Metrodata GmbH
60. 28Si atoms J. Phys. Chem. Ref. Data submitted
61. Resolution 1 of the CGPM 2011 On the possible future revision of the International System of Units, the SI (www.bipm.org/en/CGPM/db/24/1)
62. Sanchez C A, Wood B M, Green R G, Liard J O and Inglis D 2014 A determination of Planck's constant using the NRC watt balance Metrologia 51 S5-14
63. Schlamminger S, Haddad D, Seifert F, Chao L S, Newell D B, Liu R, Steiner R L and Pratt J R 2014 Determination of the Planck constant using a watt balance with a superconducting magnet system at the National Institute of Standards and Technology Metrologia 51 S15-24
64. Mohr P J, Taylor B N and Newell D B 2012 CODATA recommended values of the fundamental physical constants: 2010 Rev. Mod. Phys. 84 1527-605
65. Wood B 2015 private communication
66. Schlamminger S, Steiner R L, Haddad D, Newell D B, Seifert F, Chao L S, Liu R, Williams E R and Pratt J R 2015 A summary of the Planck constant measurements using a watt balance with a superconducting solenoid at NIST Metrologia 52 L5-8
67. 28Si spheres in the determination of the Avogadro constant Metrologia 48 S44-9
68. Melis C, Colombo L and Mana G 2015 Lattice strain at c-Si surfaces: a density functional theory calculation Metrologia 52 214-21
69. Stock M, Barat P, Davis R S, Picard A and Milton M J T 2015 Calibration campaign against the international prototype of the kilogram in anticipation of the redefinition of the kilogram part 1: comparison of the international prototype with its official copies Metrologia 52 310-6