Axel Pramann

Counting the atoms in a 28Si crystal for a new kilogram definition

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, 3 × 10−8 NA, is larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, NA = 6.022 140 82(18) × 1023 mol−1, is the most accurate input datum for the kilogram redefinition and differs by 16 × 10−8 NA from the CODATA 2006 adjusted value. This value is midway between the NIST and NPL watt-balance values.

Improved measurement results for the Avogadro constant using a 28Si-enriched crystal

New results are reported from an ongoing international research effort to accurately determine the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The surfaces of two 28Si-enriched spheres were decontaminated and reworked in order to produce an outer surface without metal contamination and improved sphericity. New measurements were then made on these two reconditioned spheres using improved methods and apparatuses. When combined with other recently refined parameter measurements, the Avogadro constant derived from these new results has a value of

Measurement equations for the determination of the Si molar mass by isotope dilution mass spectrometry

N_A = 6.022 140 76(12) \times 10^{23}

Realization of the kilogram by the XRCD method

mol

The isotopic composition of enriched Si: a data analysis

^{-1}

A More Accurate Molar Mass of Silicon via High Resolution MC-ICP-Mass Spectrometry

. The X-ray crystal density method has thus achieved the target relative standard uncertainty of

30Si Mole Fraction of a Silicon Material Highly Enriched in 28Si Determined by Instrumental Neutron Activation Analysis

2.0 \times 10^{-8}

Mass Spectrometric Investigation of Silicon Extremely Enriched in 28Si: From 28SiF4 (Gas Phase IRMS) to 28Si Crystals (MC-ICP-MS)

necessary for the realization of the definition of the new kilogram.

The pycnometer challenge

A new method applying isotope dilution mass spectrometry to determine the molar mass of a silicon sample, highly enriched with respect to 28Si, has been proposed recently. This paper describes a different way of calculating the molar mass by solving an equation linking the measurement results to the ratio between the amount-of-substance fractions of 28Si and 30Si in the sample. The mathematical model and the final measurement equation are much more straightforward than those previously reported, though fully equivalent.

Isotope amount ratio measurement challenge

When the kilogram is redefined in terms of the fixed numerical value of the Planck constant h, the x-ray-crystal-density (XRCD) method, among others, is used for realizing the redefined kilogram. The XRCD method has been used for the determination of the Avogadro constant NA by counting the number of atoms in a 28Si-enriched crystal, contributing to a substantial reduction of uncertainty in the values of NA and h to 2 parts in 108. This method can be therefore used reversely for the mass determination of a 1 kg sphere prepared from the crystal. This is realized by SI-traceable measurements of its lattice parameter, isotopic composition, volume, and surface properties. Details of the corresponding measurements are provided, as well as the concept of the XRCD method, isotope enrichment, crystal production, sphere manufacturing, and evaluation of impurities and self-point defects in the crystal, together with mass comparison with respect to the silicon sphere for disseminating mass standards.