No abstract

This paper concerns an international research project aimed at determining the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The counting procedure was based on the measurement of the molar volume and the volume of an atom in two 1 kg crystal spheres. The novelty was the use of isotope dilution mass spectrometry as a new and very accurate method for the determination of the molar mass of enriched silicon. Because of an unexpected metallic contamination of the sphere surfaces, the relative measurement uncertainty, 3 × 10−8 NA, is larger by a factor 1.5 than that targeted. The measured value of the Avogadro constant, NA = 6.022 140 82(18) × 1023 mol−1, is the most accurate input datum for the kilogram redefinition and differs by 16 × 10−8 NA from the CODATA 2006 adjusted value. This value is midway between the NIST and NPL watt-balance values.

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.

One of the most striking predictions of Einstein's special theory of relativity is also perhaps the best known formula in all of science: E=mc(2). If this equation were found to be even slightly incorrect, the impact would be enormous--given the degree to which special relativity is woven into the theoretical fabric of modern physics and into everyday applications such as global positioning systems. Here we test this mass-energy relationship directly by combining very accurate measurements of atomic-mass difference, Delta(m), and of gamma-ray wavelengths to determine E, the nuclear binding energy, for isotopes of silicon and sulphur. Einstein's relationship is separately confirmed in two tests, which yield a combined result of 1-Delta(mc2)/E=(-1.4+/-4.4)x10(-7), indicating that it holds to a level of at least 0.00004%. To our knowledge, this is the most precise direct test of the famous equation yet described.

We demonstrate a new heterodyne Michelson interferometer design for displacement measurements capable of fringe interpolation accuracy of one part in 36 000. Key to this level of accuracy are the use of two acousto-optic modulators for heterodyne frequency generation and digital signal processing demodulation electronics. We make a direct comparison of our interferometer to a commercial interferometer based on a Zeeman-stabilized laser, and show that the residual periodic errors in ours are two orders of magnitude lower than those in the commercial unit. We discuss electronically induced optical cross talk and optical feedback as sources of periodic error. Our new interferometer is simple, robust, and readily implemented.