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Isotopic homogeneity of “AVO28” silicon crystal experimentally confirmed


In consideration of the redefinition of the SI, the goal of the Avogadro project is to re-determine the Avogadro constant with a measurement uncertainty in the range of better than 1 · 10–8. To achieve this goal, it is necessary to measure the molar mass M(Si) of silicon with a relative measurement uncertainty of < 5 · 10–9. In addition to the chemical preparation and the mass-spectrometric measurement, this value also has to take isotopic inhomogeneities into account. The systematic investigation of local variations of the molar mass in the AVO28 crystal resulted in a relative measurement uncertainty associated with the molar mass of 4.4 · 10–9. At the same time, it was possible to experimentally demonstrate the necessary homogeneity of the crystal for the first time. Because of the relevance of this work, it was included in the “Highlights Collection 2015” of the journal Metrologia.

Fig. 1. Position and identification of the individual samples investigated in the AVO28 single crystal.

Fig. 2. Molar mass M(Si) in the AVO28 silicon single crystal as a function of the location in the crystal, determined by means of 14 individual samples that originate from 3 axial positions, each of which has 4 to 5 radial positions.

Improved measurements of the molar mass of the AVO28 silicon single crystal, which exhibits a high enrichment regarding the 28Si isotope of x(28Si) > 0.9999 mol/mol, were performed by PTB Working Group 3.11 with the goal of quantifying possible local variations of the molar mass. Due to their relevance in connection with the planned redefinition of the SI units “kilogram” and “mole” (as based on fundamental constants such as the Avogadro constant, NA), a total of 14 individual samples were investigated from 3 axial positions, each of which had 4 to 5 adjacent radial positions (Fig. 1). In addition to M(Si), the amount-of-substance fractions x(iSi) of the individual isotopes 28Si, 29Si and 30Si were also determined. Various experimental improvements, together with an optimized evaluation, made it possible to reduce the measurement uncertainties for the results of an individual sample to a level previously unmatched; as a result, possible local inhomogeneities of the isotopic pattern can be resolved.

The mean molar mass across all 14 samples is M(Si) = 27.976 970 13(12) g/mol with a relative combined uncertainty of uc,rel(M) = 4.4 · 10–9 (Fig. 2). This result agrees well with results published previously by PTB and confirmed by NIST (National Institute of Standards and Technology, USA) and NMIJ (National Metrology Institute of Japan). Within the measurement uncertainties, no significant variation of the molar mass or of the amount-ofsubstance fractions of the 28Si and 29Si isotopes was found as a function of the location in the AVO28 crystal. For the 30Si isotope, minimal variations were observed just above the measurement uncertainty. Current experiments are investigating the extent to which this actually represents a property of the crystal or whether it should be attributed to experimental shortcomings.

In sum, this means that the isotopic homogeneity of the AVO28 crystal is more than sufficient for the determination of the molar mass with a relative measurement uncertainty of < 5 · 10–9, and thus for the redefinition of the Avogadro constant.