A new 28Si single crystal: counting the atoms for the new kilogram definition

A new single crystal from isotopically enriched silicon was used to determine the Avogadro constant NA by the x-ray-crystal density method. The new crystal, named Si28-23Pr11, has a higher enrichment than the former ‘AVO28’ crystal allowing a smaller uncertainty of the molar mass determination. Again, two 1 kg spheres were manufactured from this crystal. The crystal and the spheres were measured with improved and new methods. One sphere, Si28kg01a, was measured at NMIJ and PTB with very consistent results. The other sphere, Si28kg01b, was measured only at PTB and yielded nearly the same Avogadro constant value. The mean result for both 1 kg spheres is NA = 6.022 140 526(70) × 1023 mol−1 with a relative standard uncertainty of 1.2 × 10−8. This value deviates from the Avogadro value published in 2015 for the AVO28 crystal by about 3.9(2.1) × 10−8. Possible reasons for this difference are discussed and additional measurements are proposed.

[1]  Michael Borys,et al.  State-of-the-art mass determination of 28Si spheres for the Avogadro project , 2011 .

[2]  Naoki Kuramoto,et al.  Realization of the kilogram by the XRCD method , 2016 .

[3]  Frank Scholze,et al.  A quarter‐century of metrology using synchrotron radiation by PTB in Berlin , 2009 .

[4]  A. H. Wapstra,et al.  The AME2012 atomic mass evaluation (II). Tables, graphs and references , 2012 .

[5]  D. B. Newell,et al.  A summary of the Planck constant measurements using a watt balance with a superconducting solenoid at NIST , 2015, 1501.06796.

[6]  Peter J. Mohr,et al.  CODATA Recommended Values of the Fundamental Physical Constants (version 4.0) , 2003 .

[7]  A Picard,et al.  Mass determinations of a 1 kg silicon sphere for the Avogadro project , 2006 .

[8]  G. Mana,et al.  A finite element analysis of surface-stress effects on measurement of the Si lattice parameter , 2013 .

[9]  M. Seah,et al.  Ultrathin SiO2 on Si. I. Quantifying and removing carbonaceous contamination , 2003 .

[10]  Lulu Zhang,et al.  Realization of the Kilogram Based on the Planck Constant at NMIJ , 2016, IEEE Transactions on Instrumentation and Measurement.

[11]  Gerhard Bönsch,et al.  Absolute volume determination of a silicon sphere with the spherical interferometer of PTB , 2005 .

[12]  Naoki Kuramoto,et al.  Determination of the Avogadro constant by the XRCD method using a 28Si-enriched sphere , 2017 .

[13]  G. Mana,et al.  Purity of (28)Si-Enriched Silicon Material Used for the Determination of the Avogadro Constant. , 2016, Analytical chemistry.

[14]  C. A. Sanchez,et al.  A summary of the Planck constant determinations using the NRC Kibble balance , 2017 .

[15]  Yasushi Azuma,et al.  Surface layer determination for the Si spheres of the Avogadro project , 2011 .

[16]  D. B. Newell,et al.  Measurement of the Planck constant at the National Institute of Standards and Technology from 2015 to 2017 , 2017, 1708.02473.

[17]  R. Fliegauf,et al.  Quantitative surface characterization of silicon spheres by combined XRF and XPS analysis for the determination of the Avogadro constant , 2017 .

[18]  K. Fujii,et al.  Molar-mass measurement of a 28Si-enriched silicon crystal for determination of the Avogadro constant , 2014 .

[19]  Physikalisch-Technische Bundesanstalt History and progress in the accurate determination of the Avogadro constant , 2001 .

[20]  S. Mizushima,et al.  Establishment of the platinum–iridium kilogram mass standards at NMIJ after the Extraordinary Calibrations , 2016 .

[21]  I Busch,et al.  Improved measurement results for the Avogadro constant using a 28Si-enriched crystal , 2015, 1512.05642.

[22]  G. Mana,et al.  A More Accurate Measurement of the 28Si Lattice Parameter , 2015 .

[23]  G. Mana,et al.  Quantification of the Void Volume in Single-Crystal Silicon. , 2016, Analytical chemistry.

[24]  G. Mana,et al.  Measurement of the 30Si Mole Fraction in the New Avogadro Silicon Material by Neutron Activation and High-Resolution γ-Spectrometry. , 2017, Analytical chemistry.

[25]  Stuart Davidson,et al.  A report on the potential reduction in uncertainty from traceable comparisons of platinum-iridium and stainless steel kilogram mass standards in vacuum. , 2004 .

[26]  L. Colombo,et al.  Density functional theory calculations of the stress of oxidised (1 1 0) silicon surfaces , 2016, 1608.01885.

[27]  L. Colombo,et al.  Lattice strain at c-Si surfaces: a density functional theory calculation , 2014, 1412.3301.

[28]  Z. Mester,et al.  Determination of the atomic weight of 28Si-enriched silicon for a revised estimate of the Avogadro constant. , 2012, Analytical chemistry.

[29]  B. Beckhoff,et al.  Experimental verification of the individual energy dependencies of the partial L-shell photoionization cross sections of Pd and Mo. , 2014, Physical review letters.

[30]  S Mizushima,et al.  Determination of the amount of gas adsorption on SiO2/Si(100) surfaces to realize precise mass measurement , 2004 .

[31]  B. Taylor,et al.  CODATA Recommended Values of the Fundamental Physical Constants: 2010 | NIST , 2005, 1203.5425.

[32]  Hans-Ulrich Danzebrink,et al.  Oxide layer mass determination at the silicon sphere of the Avogadro Project , 2008, 2008 Conference on Precision Electromagnetic Measurements Digest.

[33]  Kenichi Fujii,et al.  Volume measurements of 28Si spheres using an interferometer with a flat etalon to determine the Avogadro constant , 2011 .

[34]  Lulu Zhang,et al.  Thickness Measurement of Oxide and Carbonaceous Layers on a 28Si Sphere by XPS , 2017, IEEE Transactions on Instrumentation and Measurement.

[35]  Naoki Kuramoto,et al.  Improvements to the Volume Measurement of 28Si Spheres to Determine the Avogadro Constant , 2015, IEEE Transactions on Instrumentation and Measurement.

[36]  D. Briggs,et al.  Practical surface analysis: By auger and x-ray photoelectron spectroscopy , 1983 .

[37]  Arnold Nicolaus,et al.  Volume determination of two spheres of the new 28Si crystal of PTB , 2017 .

[38]  Giovanni Mana,et al.  Measurement of the {2 2 0} lattice-plane spacing of a 28Si x-ray interferometer , 2010, 1010.3088.

[39]  Kenichi Fujii,et al.  Mass measurement of 1 kg silicon spheres to establish a density standard , 2004 .

[41]  M. Borys,et al.  The Correlation of the NA Measurements by Counting 28Si Atoms , 2015, 1512.06138.

[42]  Sabine Zakel,et al.  A new generation of 99.999% enriched 28Si single crystals for the determination of Avogadro’s constant , 2017 .

[43]  Michael Stock,et al.  Calibration campaign against the international prototype of the kilogram in anticipation of the redefinition of the kilogram part I: comparison of the international prototype with its official copies , 2015 .

[44]  Matthieu Thomas,et al.  A determination of the Planck constant using the LNE Kibble balance in air , 2017 .

[45]  M. Milton,et al.  Calibration campaign against the international prototype of the kilogram in anticipation of the redefinition of the kilogram, part II: evolution of the BIPM as-maintained mass unit from the 3rd periodic verification to 2014 , 2016 .

[46]  H. Fujimoto,et al.  Homogeneity characterization of lattice spacing of silicon single crystals by a self-referenced lattice comparator , 2011, 29th Conference on Precision Electromagnetic Measurements (CPEM 2014).

[47]  P. Becker,et al.  Silicon lattice parameters as an absolute scale of length for high precision measurements of fundamental constants , 1990 .

[48]  Chi Chen,et al.  Application of ellipsometry for the accurate oxide layer measurement on silicon spheres , 2017 .

[49]  Naoki Kuramoto,et al.  Volume measurements of 28Si-enriched spheres using an improved optical interferometer for the determination of the Avogadro constant , 2017 .

[50]  D. Schiel,et al.  Infrared spectrometric measurement of impurities in highly enriched ‘Si28’ , 2011 .

[51]  P. Becker,et al.  History and progress in the accurate determination of the Avogadro constant , 2001 .

[52]  Kenichi Fujii,et al.  Phase corrections in the optical interferometer for Si sphere volume measurements at NMIJ , 2011 .

[53]  Impurities in a 28Si-Enriched Single Crystal Produced for the Realization of the Redefined Kilogram. , 2017, Analytical chemistry.

[54]  M. Krumrey,et al.  Thickness determination for Cu and Ni nanolayers: Comparison of completely reference-free fundamental parameter-based X-ray fluorescence analysis and X-ray reflectometry , 2005 .

[55]  Yasushi Azuma,et al.  Counting the atoms in a 28Si crystal for a new kilogram definition , 2011 .

[56]  B. Beckhoff,et al.  Determination of SiO2 and C layers on a monocrystalline silicon sphere by reference-free x-ray fluorescence analysis , 2017 .

[57]  D. Schiel,et al.  Novel concept for the mass spectrometric determination of absolute isotopic abundances with improved measurement uncertainty: Part 1 – theoretical derivation and feasibility study , 2010 .

[58]  Martin P. Seah,et al.  Ultrathin SiO2 on Si II. Issues in quantification of the oxide thickness , 2002 .

[59]  G. Turk,et al.  Absolute silicon molar mass measurements, the Avogadro constant and the redefinition of the kilogram , 2014 .

[60]  A. Pramann,et al.  Determination of the isotopic composition and molar mass of a new 'Avogadro' crystal: homogeneity and enrichment-related uncertainty reduction , 2017 .

[61]  Naoki Kuramoto,et al.  Uniformity Evaluation of Lattice Spacing of 28Si Single Crystals , 2017, IEEE Transactions on Instrumentation and Measurement.

[62]  Michael Krystek,et al.  Volume determination of the Avogadro spheres of highly enriched 28Si with a spherical Fizeau interferometer , 2011 .

[63]  Arnold Nicolaus,et al.  Optical simulation of the new PTB sphere interferometer , 2017 .

[64]  B. Taylor,et al.  CODATA Recommended Values of the Fundamental Physical Constants: 2010 | NIST , 2007, 0801.0028.

[65]  M. Seah Summary of ISO/TC 201 Standard: ISO 14701:2011 – Surface chemical analysis – X‐ray photoelectron spectroscopy—measurement of silicon oxide thickness , 2012 .

[66]  A. Pramann,et al.  Probing the homogeneity of the isotopic composition and molar mass of the ‘Avogadro’-crystal , 2015 .

[67]  Naoki Kuramoto,et al.  Homogeneity Characterization of Lattice Spacing of Silicon Single Crystals , 2015, IEEE Transactions on Instrumentation and Measurement.

[68]  Tongxiang Ren,et al.  Measurement of the molar mass of the 28Si-enriched silicon crystal (AVO28) with HR-ICP-MS , 2015 .

[69]  G. Mana,et al.  A new analysis for diffraction correction in optical interferometry , 2017 .

[70]  Naoki Kuramoto,et al.  Surface Layer Analysis of a 28Si-Enriched Sphere Both in Vacuum and in Air by Ellipsometry , 2017, IEEE Transactions on Instrumentation and Measurement.

[71]  Arnold Nicolaus,et al.  The coefficient of thermal expansion of highly enriched 28Si , 2009 .