Determination of the isotopic composition and molar mass of a new 'Avogadro' crystal: homogeneity and enrichment-related uncertainty reduction

Abstract

The molar mass M and isotopic composition (expressed in amount-of-substance fractions x(iSi) of the silicon isotopes 28Si, 29Si, and 30Si) of a new silicon crystal (notation: Si28-23Pr11) highly enriched in the 28Si isotope have been determined independently at PTB and NMIJ by measuring exactly the same sample solutions using both a high resolution multicollector-inductively coupled plasma mass spectrometer (MC-ICP-MS). This crystal will be used for the complementary determination of the Avogadro constant NA and thus providing one of many key parameters in the planned redefinition of the SI units kilogram and mole, using fundamental constants. Samples from three different axial positions in the crystal ingot, each divided into several radial positions were measured in order to probe possible variations of the molar mass and isotopic composition. Results obtained at PTB and NMIJ agreed within the limits of uncertainty. The application of the latest improved measurement techniques as well as an improved determination of the calibration factors (K) required to correct for mass bias effects resulted in an averaged M = 27.976 942 666(40) g mol−1 with a relative combined uncertainty uc,rel(M) = 1.4 × 10−9. The course of M as a function of the origin of the measured samples suggests no significant inhomogeneity within the limits of the claimed uncertainty throughout the crystal supporting its applicability for the determination of a new NA. This extends to x(28Si) and x(29Si). Variations in x(30Si) as a function of the sample location were observed, but a systematic relation to physical origins cannot be claimed. Compared to the previous silicon crystal (‘AVO28’, notation: Si28-10Pr11) used for the latest determination of NA, the enrichment increases from x(28Si) = 0.999 957 52(12) mol mol−1 (‘AVO28’) to x(28Si) = 0.999 984 470(39) mol mol−1 (Si28-23Pr11, discussed in this paper) which is at least in part responsible for a reduction of the associated measurement uncertainty u(M).