Absolute silicon molar mass measurements, the Avogadro constant and the redefinition of the kilogram

Abstract

The results of an absolute silicon molar mass determination of two independent sets of samples from the highly 28Si-enriched crystal (AVO28) produced by the International Avogadro Coordination are presented and compared with results published by the Physikalisch-Technische Bundesanstalt (PTB, Germany), the National Research Council (NRC, Canada) and the National Metrology Institute of Japan (NMIJ, Japan). This study developed and describes significant changes to the published protocols for producing absolute silicon isotope ratios. The measurements were made at very high resolution on a multi-collector inductively coupled plasma mass spectrometer using tetramethylammonium hydroxide (TMAH) to dissolve and dilute all samples. The various changes in the measurement protocol and the use of TMAH resulted in significant improvements to the silicon isotope ratio precision over previously reported measurements and in particular, the robustness of the 29Si/30Si ratio of the AVO28 material. These new results suggest that a limited isotopic variability is present in the AVO28 material. The presence of this variability is at present singular and therefore its significance is not well understood. Fortunately, its magnitude is small enough so as to have an insignificant effect on the overall uncertainty of an Avogadro constant derived from the average molar mass of all four AVO28 silicon samples measured in this study. The NIST results confirm the AVO28 molar mass values reported by PTB and NMIJ and confirm that the virtual element–isotope dilution mass spectrometry approach to calibrated absolute isotope ratio measurements developed by PTB is capable of very high precision as well as accuracy. The Avogadro constant NA and derived Planck constant h based on these measurements, together with their associated standard uncertainties, are 6.02214076(19) × 1023 mol−1 and 6.62607017(21) × 10−34 Js, respectively.

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

“…The use of aqueous TMAH solutions, as proposed and carried out for the first time at NIST [17], has many advantages. The extreme enrichment of the 28 Si isotope in the AVO28 material leaves very little 29 Si and almost no 30 Si to be ionized and detected.…”

“…NIST analyzed 4 different crystals of the AVO28 silicon, two proximal to AVO28-S5 (5B2.1.1.3, 5B1.1.1.1) and two taken near AVO28-S8 (8A4.1.1.3, 8B1.1.1.1) [17]. All silicon samples were dissolved and diluted using TMAH and also analyzed on a commercial MC ICP-MS (Neptune™, Thermo Fisher Scientific) in high resolution mode.…”

Equivalence principles, spacetime structure and the cosmic connection

“…The silicon sphere experiment of counting atoms to determine the Avogadro constant reached 3  10 8 relative uncertainty (See, e.g., Becker [108]). In 2014, the Avogadro constant NA and derived Planck constant h based on the absolute silicon molar mass measurements with their standard uncertainties are 6.02214076(19)  10 23 mol 1 and 6.62607017(21)  10 34 J s [111]. The three measurements of NIST [111], PTB [112], and NMIJ [113] agree within their stated uncertainties and also agree with the NRC watt balance measurement with 1 .…”

“…In 2014, the Avogadro constant NA and derived Planck constant h based on the absolute silicon molar mass measurements with their standard uncertainties are 6.02214076(19)  10 23 mol 1 and 6.62607017(21)  10 34 J s [111]. The three measurements of NIST [111], PTB [112], and NMIJ [113] agree within their stated uncertainties and also agree with the NRC watt balance measurement with 1 . These experimental progresses set the stage for a new definition of kilogram using Planck constant/Avogadro number.…”

The Avogadro Constant for the Definition and Realization of the Mole

“…[74][75][76][77] Currently, a CCQM-pilot study is pending aiming at the screening of the ability of the participants of the study to measure the molar mass M of highly enriched silicon with sufficiently small associated uncertainties applying the VE-IDMS method. [74][75][76][77] Currently, a CCQM-pilot study is pending aiming at the screening of the ability of the participants of the study to measure the molar mass M of highly enriched silicon with sufficiently small associated uncertainties applying the VE-IDMS method.…”