Measurement of the (30)Si Mole Fraction in the New Avogadro Silicon Material by Neutron Activation and High-Resolution γ-Spectrometry

The use of new silicon single crystals highly enriched in (28)Si recently produced for the upcoming redetermination of the Avogadro constant requires knowledge of their molar masses. The isotopic composition data are collected independently in different laboratories but all using the virtual element technique with multicollector inductively coupled plasma mass spectrometers. In this framework, the comparison of the results with an independent measurement of the amount of at least one of the depleted isotopes is useful to limit hidden systematic errors. To this aim, the (30)Si mole fraction of a sample of the new material was measured using a relative measurement protocol based on instrumental neutron activation analysis. The protocol is similar to that previously applied with the AVO28 silicon material used for the last determination of the Avogadro constant value with the exception that unknown and standard samples are not coirradiated. The x((30)Si) = 5.701 × 10(-7) mol mol(-1) estimate is close to the expected one and is given with a standard uncertainty of 8.8 × 10(-9) mol mol(-1). This value, if adopted, gives a contribution to the relative standard uncertainty of the Avogadro constant of 6.3 × 10(-10)

The Correlation of the NA Measurements by Counting 28Si Atoms

open12sìpartially_openembargoed_20160715Mana, G.; Massa, E.; Sasso, C. P.; Stock, M.; Fujii, K.; Kuramoto, N.; Mizushima, S.; Narukawa, T.; Borys, M.; Busch, I.; Nicolaus, A.; Pramann, A.Mana, Giovanni; Massa, Enrico; Sasso, CARLO PAOLO; Stock, M.; Fujii, K.; Kuramoto, N.; Mizushima, S.; Narukawa, T.; Borys, M.; Busch, I.; Nicolaus, A.; Pramann, A

Amount of substance and the mole in the SI

Abstract Following the revision of the International System of Units (SI), that takes effect on 20 May 2019, the unit mole is defined by using a fixed number of elementary entities. This number is the fixed numerical value of the Avogadro constant, which is the defining constant of the unit mole. This definition was made possible because the determination of the Avogadro constant had reached a level of relative uncertainty that allowed its value to be fixed and, at the same time, safeguard continuity of measurement results before and after the definition. The motivation for the revision of the SI and the mole in particular will be explained and the experimental work that allowed it is summarized

The molar mass of a new enriched silicon crystal: maintaining the realization and dissemination of the kilogram and mole in the new SI

The local distribution of the isotopic composition and molar mass M of a new silicon crystal (Si28-24Pr11) highly enriched in the 28Si isotope is reported, with focus on the experimental methods as well as on the associated uncertainties. The crystal was used in 2018 for the production of two additional silicon spheres for the realization and verification of the Avogadro constant NA using the “X-ray-crystal-density (XRCD) method” which is a primary method for the dissemination of the revised SI units mole and kilogram. 17 subsamples have been investigated (from five different axial and in several radial positions) by isotope ratio mass spectrometry using a multicollector-inductively coupled plasma mass spectrometer (MC-ICP-MS). The average molar mass of the crystal is M = 27.976 933 787(77) g/mol with a relative combined uncertainty uc,rel(M) = 2.7 × 10−9. The mean amount-of-substance fraction of 28Si is x(28Si) = 0.999 993 104 (66) mol/mol indicating that this crystal has the highest enrichment in this isotope which has ever been used for the determination of NA. No local variations in M and x(iSi) (i = 28, 29, and 30) could be identified due to material properties. The results are compared with those from two previous enriched crystals

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

A new generation of silicon crystals even further enriched in ²⁸Si (<i>x</i>(²⁸Si) > 0.999 98 mol/mol), recently produced by companies and institutes in Russia within the framework of a project initiated by PTB, were investigated with respect to their isotopic composition and molar mass <i>M</i>(Si). A modified isotope dilution mass spectrometric (IDMS) method treating the silicon as the matrix containing a so-called virtual element (VE) existing of the isotopes ²⁹Si and ³⁰Si solely and high resolution multicollector inductively coupled plasma mass spectrometry (MC-ICP-MS) were applied in combination. This method succeeds also when examining the new materials holding merely trace amounts of ²⁹Si (<i>x</i>(²⁹Si) ≈ 5 × 10^–6 mol/mol) and ³⁰Si (<i>x</i>(³⁰Si) ≈ 7 × 10^–7 mol/mol) extremely difficult to detect with lowest uncertainty. However, there is a need for validating the enrichment in ²⁸Si already in the precursor material of the final crystals, silicon tetrafluoride (SiF₄) gas prior to crystal production. For that purpose, the isotopic composition of selected SiF₄ samples was determined using a multicollector magnetic sector field gas-phase isotope ratio mass spectrometer. Contaminations of SiF₄ by natural silicon due to storing and during the isotope ratio mass spectrometry (IRMS) measurements were observed and quantified. The respective MC-ICP-MS measurements of the corresponding crystal samples show–in contrast–several advantages compared to gas phase IRMS. <i>M</i>(Si) of the new crystals were determined to some extent with uncertainties <i>u</i>_rel(<i>M</i>) < 1 × 10^–9. This study presents a clear dependence of the uncertainty <i>u</i>_rel(<i>M</i>(Si)) on the degree of enrichment in ²⁸Si. This leads to a reduction of <i>u</i>_rel(<i>M</i>(Si)) during the past decade by almost 3 orders of magnitude and thus further reduces the uncertainty of the Avogadro constant <i>N</i>_A which is one of the preconditions for the redefinition of the SI unit kilogram

Combining Isotope Dilution and Standard Addition—Elemental Analysis in Complex Samples

A new method combining isotope dilution mass spectrometry (IDMS) and standard addition has been developed to determine the mass fractions w of different elements in complex matrices: (a) silicon in aqueous tetramethylammonium hydroxide (TMAH), (b) sulfur in biodiesel fuel, and (c) iron bound to transferrin in human serum. All measurements were carried out using inductively coupled plasma mass spectrometry (ICP–MS). The method requires the gravimetric preparation of several blends (bi)—each consisting of roughly the same masses (mx,i) of the sample solution (x) and my,i of a spike solution (y) plus different masses (mz,i) of a reference solution (z). Only these masses and the isotope ratios (Rb,i) in the blends and reference and spike solutions have to be measured. The derivation of the underlying equations based on linear regression is presented and compared to a related concept reported by Pagliano and Meija. The uncertainties achievable, e.g., in the case of the Si blank in extremely pure TMAH of urel (w(Si)) = 90% (linear regression method, this work) and urel (w(Si)) = 150% (the method reported by Pagliano and Meija) seem to suggest better applicability of the new method in practical use due to the higher robustness of regression analysis