Probing the homogeneity of the isotopic composition and molar mass of the ‘Avogadro’-crystal

Abstract

Improved measurements on silicon crystal samples highly enriched in the 28 Si isotope (known as 'Si28' or AVO28 crystal material) have been carried out at PTB to investigate local isotopic variations in the original crystal. This material was used for the determination of the Avogadro constant N A and therefore plays an important role in the upcoming redefinition of the SI units kilogram and mole, using fundamental constants.

Improved measurement results for the Avogadro constant using a28Si-enriched crystal

“…The experimental design for this study called for 5 adjacent radial samples (each with a mass of approximately 300 mg) to be taken from three distinct longitudinal positions (parts 4, 7, and 9) of the original crystal ingot (figure 1 in [12]) and analyzed for their molar mass. A de-tailed description of this study will be published elsewhere [18]. However, given that this homogeneity study incorporated most of the state-of-the art improvements in the measurement of Si isotope-amount-ratios developed since 2011, the average and individual molar masses as well as the Si isotope amount fractions derived from these data are presented in tables 1 and 2.…”

The Avogadro Constant for the Definition and Realization of the Mole

“…The enrichment of the 28 Si isotope was almost 100%: x( 28 Si) = 0.99995752 (12). [67] However, also the composition of the remaining two isotopes 29 Si and 30 Si had to be measured to obtain a value of the molar mass M with an associated uncertainty of u rel (M) ࣘ 2 × 10 −8 . This was the intended upper limit of u rel (M), because one of the prerequisites for a revised definition of the kilogram and the mole was an uncertainty u rel (N A ) ࣘ 2 × 10 −8 , implying that all relevant quantities necessary to determine N A via the XRCD method exhibit associated uncertainties of the same or even smaller size.…”

“…This was the intended upper limit of u rel (M), because one of the prerequisites for a revised definition of the kilogram and the mole was an uncertainty u rel (N A ) ࣘ 2 × 10 −8 , implying that all relevant quantities necessary to determine N A via the XRCD method exhibit associated uncertainties of the same or even smaller size. [67] When measuring the respective isotope ratios related to the isotope with the highest abundance 28 Si, extremely small isotope ratios far from unity will result: R = x( 29 Si)/x( 28 Si) = 4.14 × 10 −5 mol mol −1 and R = x( 30 Si)/x( 28 Si) = 1.12 × 10 −6 mol mol −1 . The amount of substance fractions of the two minor isotopes in the first enriched silicon crystal were x( 29 Si) = 4.136(11) × 10 −5 mol mol −1 and x( 30 Si) = 1.121(14) × 10 −6 mol mol −1 .…”

Realization of the kilogram by the XRCD method

“…The samples of the first enriched Avogadro crystal (Si28-10Pr11) were cut in the vicinity of the two spheres ('AVO28-S5' and 'AVO28-S8'). A 'homogeneity' study concerning local variations of the molar mass has been carried out on 14 samples of the Si28-10Pr11 crystal originating from three different axial positions of parts 4, 7 and 9 [52]. For each of these three positions, four or five adjacent samples were cut from a crystal bar in order to get information about the effects of the radial position.…”