The Avogadro constant: Counting atoms in a single-crystal 28 Si sphere

Transcription

1 The Avogadro constant: Counting atoms in a single-crystal 28 sphere Peter Becker Physikalisch-Technische Bundesanstalt Braunschweig The new SI Royal Society London, Jan 2011

2 Our Intention: Replace the International kg Prototype K with uncertainty 0 by a definition based on a fundamental constant with an uncertainty < Alea iacta est: Proposal and Recommendation CPIM 2010: The kilogram, kg, is the unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be equal to exactly X 10 4 when it is expressed in the unit s 1 m 2 kg, which is equal to J s. N A h = (57) x Js/mol, with relative uncertainty of (correct?) Why we can contribute!

3 Way to the realization of a measurement of h by N A (the silicon route ) uncertainty of Equal volumes of all gases at the same temperature and pressure contain the same number of molecules Amadeo Avogadro ( ), Thesis 1811

4 How to count 10 2 bottles in a regular stack? 1. Stack volume of boxes 2. Volume of box. Number of bottles 4. Volume of bottle N all = V stack v bottle Regular=perfect Stack=crystal Box=unit cell Bottle=atom

5 How to count 10 2 atoms in a regular crystal? 1. volume of sphere 2. Volume of unit cell. Number of atoms 4. Volume of atom N A V = v sphere atom M m mol sphere = m V sphere sphere M mol 8 d 220

6 IAC 200 nat CODATA 2006

7 IAC for M improvement M V N = sphere A 8 d m 220 sphere 2009 sphere lica layer

8 IAC : 99,9957% A N = M 8 d V 220 m IAC 2008

9 N A = M 8 d V 220 m > % conventional Molar Mass Determination 28 Isotope ratios nat. 28 R 28/ /28 R 29/ R 0/ % % Technical limit of MS, Risk of contamination gnals : 0 : 5 mv 29 : 46 mv 28 : 1000 V!!!

10 N A = M 8 d V 220 m New concept of 28 Molar Mass Determination M() 29 and 0 impurities Classical Concept Novel Concept R VE R 29 0 modified IDMS: virtual element IDMS R R 70 w(ve) IDMS (isotope dilution mass spectrometry )

11 N A = M 8 d V 220 m Molar mass NEPTUNE MC-ICP-MS Multi Collector Inductively Coupled Plasma Mass Spectrometer multi collector IDMS, virtual element: 29 and 0 crystal aequeous sol. aerosol IDMS (isotope dilution mass spectrometry ) Repetitions at NIST, NRC and IMR-Beijing

12 N A = M 8 d V 220 m Molar mass M /(g/mo ol) PTB (Feb. 2010) part 5 PTB (Nov. 2009) part 4 PTB (Oct. 2009) part 9 PTB (Feb. 2010) part 8 PTB average (part 4, 5, 8, 9) PTB: + u (mean) PTB: - u (mean) Experiment M = (18) g/mol u r (M):

13 How perfect/regular are silicon crystals? Natural licon Enriched crystal 28 : 92,2% 29 : 4,67% 28 : 99,9957% 29 : 0,0042% 0 :,10% 0 : 0,0001% Impurities (in cm - (2x10-8 )) C: O: 1, B/P: 0,00 Vac: 0, Impurities (in cm - (2x10-8 )) C: 0,1 O: 0,2 0,4 B/P: 0,02.0, Vac: 0,

14 N A = M 8 d V 220 m Lattice parameter Analyzer displacement up to 50 mm (~10 7 lattice planes) Feedback loops provide: picometer positioning nanoradian alignment Sub-nanometer movements Exact displacements sensed via additional laser interferometry and via capacitors 28 interferometer, analyzer crystal 50mm copper block for temperature

15 N A = M 8 d V 220 m Lattice parameter variations of the (220) lattice-plane spacing along the 50 mm, 5 mm from top u r (d 220 ):.6 x 10-9 No lattice strain within the ± survey resolution.

16 Surface characterization m = m core + m layer V = V core + V layer X-ray reflectometry (XRR) at BESSY II for calibration XRFluorescence for contamination Spectral ellipsometry (SE) for mapping XPhotoSpectroscopy for stoichiometry d / nm Thickness topography on by spectral ellipsometry (SE)

17 All CSIRO/ACPO polished spheres are contaminated at the outer surface with µg strongly bonded Cu and Ni. Surface characterization This x-ray fluorescence spectrum evidences the removal of the contamination by Ni and Cu.

18 Surface layer characterization d SL (nm) m SL (µg) Sphere 2.91(4) 2.72() 224(16) 215(16) AVO28-5 AVO28-8 u r (SL):

19 N A = M 8 d V 220 m Mass determination at the BIPM: different densities and surface areas Sartorius CCL 1007 mass comparator with its vacuum transfer system Air buoyancy artefacts V = 8 cm Surface artefacts S = 186 cm 2 P residual =1mPa 8 stations Standard deviation < 0.1 µg

20 N A = M 8 d V 220 m Mass comparison in air and under vacuum on the 28 sphere S5 Mass (value-1kg g) (µg) PTB air (hydrostatic department) NMIJ air (mass department) BIPM air PTB air (mass department) IAC vacuum (Weighted mean) NMIJ air (hydrostatic department) NMIJ vacuum BIPM vacuum PTB vacuum (mass department) IAC air (Weighted mean) u r (m): 5, Values in air are corrected by the amount of water adsorbed The error bars represent the combined uncertainty (k=1) 02/ / / /2008 0/ / / / / /2010 date (Month/Year)

21 N A = M 8 d V 220 m Volume: interferometer for spheres Optical interferometer with flat etalons Active radiation shield for thermal uniformity Volume determination from 770 directions u (D) = 1 nm

22 N A = M 8 d V 220 m Volume: interferometer for spheres PTB s sphere interferometer with spherical symmetry PTB s sphere interferometer enables complete topographies of spheres, n diameter The radius uncertainty is 0.8 nm u r (V): Radius topography of 28 -sphere S8. Peak to valley deviations from roundness amount to 99 nm.

23 M N M V = sphere A 8 d m 220 sphere d 220 m sphere V sphere value consistency N A = (18) 10 2 mol -1 More: Nature 467 (2010) 892 PRL 106, (2011) Metrologia 2011 special issue Avogadro

24 Avogadro constant determinations 6, constant in 10 2 mol -1 6, , NIST 2007 NPL 2010 Avogadro 2010 Avogadro 6, , , Measurement N A h = (57) x Js/mol, with relative uncertainty of

25 Uncertainty budget Quantity Relative uncertainty 10-9 Contribution % Molar mass 8 7 Sphere mass 5 Surface Sphere volume Lattice parameter Point defects 4 2

26 Future work Remeasurement of repolished spheres Thermal oxidation of spheres Remeasurement of molar mass at NIST, NRC, NIM Coordination of project by CCM WGAC New partner NIM Target 2012: 1 x 10-8! Support of BIPM kg mise en pratique

27 Acknowledgements IAC: B. Andreas 1, Y. Azuma 2, G. Bartl 1, H. Bettin 1, M. Borys 1, I. Busch 1, M. Gray, P. Fuchs 4, K. Fujii 2, H. Fujimoto 2, E. Kessler 5, M. Krumrey 1, U. Kuetgens 1, N. Kuramoto 2, G. Mana 6, P. Manson, E. Massa 6, S. Mizushima 2, A. Nicolaus 1, A. Picard 7, A. Pramann 1, O. Rienitz 1, D. Schiel 1, S. Valkiers 8, and A. Waseda 2 1 Physikalisch-Technische Bundesanstalt PTB, Bundesallee 100, 8116 Braunschweig, Germany. 2 National Metrology Institute of Japan NMIJ, Umezono, Tsukuba, Ibaraki , Japan. National Measurement Institute NMI-A, Bradfield Road, Lindfield, NSW 2070, Australia. 4 Bundesamt für Metrologie METAS, Lindenweg 50, 00 Bern-Wabern, Switzerland. 5 National Institute of Standards and Technology NIST, 100 Bureau Drive, Gaithersburg, MD 20899, USA. 6 Istituto Nazionale di Ricerca Metrologica INRIM, str. delle cacce 91, 1015 Torino, Italy. 7 Bureau International des Poids et Mesures BIPM, Pavillon de Breteuil, 9212 Sèvres cedex, France. 8 Institute for Reference Materials and Measurements IRMM, Retieseweg 111, B-2440 Geel, Belgium. 28 material: H-J Pohl 2, A K Kaliteevski, O N Godisov, M F Churbanov 4, G G Devyatykh 4, A V Gusev 4, A D Bulanov 4, S A Adamchik 4, V A Gavva 4 ; I D Kovalev 4, N V Abrosimov 5, B Hallmann-Seiffert 5, H Riemann 5, S Valkiers 6, P Taylor 6, P De Bièvre 7, E M Dianov 8 2 VITCON Projectconsult GmbH, Dornbluthweg 5, D-0774 Jena, Germany Science & Technical Center «CENTROTECH», Prospekt Stachek 47, RU St. Petersburg, Russia (CT) 4 Institute of Chemistry of High-Purity Substances RAS, Tropinina Street 49, RU Nizhny Novgorod, Russia (IChHPS) 5 Institute for Crystal Growth, Max-Born-Strasse 2, D Berlin, Germany (IKZ) 6 Institute for Reference Materials and Measurements, EC-JRC, Retieseweg, B-2460 Geel, Belgium (IRMM) 7 Independent Consultant on Metrology in Chemistry, B-2460 Kasterlee, Belgium 8 Institute of General Physics of RAS, RU Moscow, Vavilov Street 8 (GPI)

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