Determination of the Avogadro Constant by Counting the Atoms in aSi28Crystal

Abstract

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.

Determination of the Atomic Weight of 28Si-Enriched Silicon for a Revised Estimate of the Avogadro Constant

“…In the process, n( 29 Si)/n( 30 Si) is significantly 12,13 and concluded that the solutions used to convert the crystal samples into the SiF 4 gas utilized by IRMM for their measurement protocol were contaminated with natural Si. 4 In this study, n( 29 Si)/n( 30 Si) ≈ 60 was achieved. General Remarks.…”

“…General Remarks. The atomic weight arising from this study, when incorporated with all other relevant measurements of the IAC 4 , yields an Avogadro constant that is different from the most recent IAC estimate by 6 parts in 10 8 . It is noteworthy that measurements made using silicon of natural isotopic composition reached the tipping point in 2001−2003 when the estimates of N A from the Avogadro route and watt balance disagreed by 1 part in 10 6 (Figure 4).…”

“…The atomic weight of silicon derived from material sampled from areas surrounding both spheres, AVO28-S5 and AVO28-S8, is identical to within the uncertainty of measurement, as reported earlier. 4 Evaluation of Uncertainty. Estimates of the uncertainty for the mass bias correction factors, isotope amount ratios, as well as the atomic weight of 28 Si were done in accordance with the "Guide to the expression of uncertainty in measurement".…”

“…1,2 The measurements, for a number of technical reasons, use highly polished one-kilogram spheres of silicon. 3,4 An overall relative target uncertainty of less than 2 in 10 8 is desired for the Avogadro constant to ensure a smooth transition between the definitions. 5 The project is part of an ongoing effort to redefine the kilogram in terms of a fixed value of an invariant quantity (a fundamental constant), thus abrogating the International Prototype Kilogram.…”

Isotope effect on the lifetime of the 2p0state in phosphorus-doped silicon

“…12 Because of their perfection, such 28 Si crystals are a promising candidate for the new definition of the kilogram. 13 Although the composition of natural Si (92.23% 28 Si, 4.67% 29 Si, and 3.1% 30 Si) is close to that of monoisotopic 28 Si, the isotopic composition can significantly influence the material properties. Some examples are the thermal conductivity, which increases by a factor of eight in 28 Si (Ref.…”