The Avogadro constant — Recent results on the molar volume of silicon

Abstract-Opitcal interferometry of an Silicon lattice period is an important link between macroscopic and microscopic lengths as well as between low-energy and high-energy spectroscopies. An evident discrepancy between two pre-1982 measurements has limited the effective application of these results. Very recent results, reported here in a preliminary way, appear to further understanding and removing this discrepancy. I. BACKGROUND AND MOTIVATIONM EASURE M E NTS linking local networks of secondary standards occurring in different spectral regions are important throughout the entire electromagnetic spectrum. The story is particularly well known to this conference in the case of the microwave-to-optical connection where the realization of a frequency synthesis chain, together with the availability of narrow-line optical oscillators, has permitted effective unification of these two regions. The situation arising when one attempts to continue this progession to the X-and -y-ray regions is perhaps less widely known but presents also some serious challenges and offers, as well, interesting rewards for successfully overcoming the evident difficulties. Although there are procedures involving many relatively small steps through the UV -and X-ray region these are not capable of giving accurate results largely because of the absence of narrowband oscillators in the intermediate (X-ray) region. To some extent, perfect monocrystalline lattices offer an alternative to sharp lines, at least in the region between 0.1 and 1.0 nm, but these are not fully equivalent to narrowline oscillators even over the limited band in which they are available. Once one reaches the region of intense nuclear -y-rays (ca 100 ke V and above), sharp lines are again available but the problem of linking these to visible light is formidable.In recent years a practical procedure has emerged for covering the 18 octaves between red light and 400 ke V (the local standard lamp for -y-ray people). In the first step of this procedure, the lattice period of a perfect monocrystalline silicon slab is determined by simultaneous Xray and optical interferometry of a common baseline. A

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“…[1]. Besides this, one can measure optical transitions in one-and two-electron ions and muonic atoms to test basic theory.…”

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confidence: 99%

Remeasurement of a Silicon lattice period

Deslattes

Tanaka

Greene

et al. 1987

IEEE Trans. Instrum. Meas.

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“…This drift can be eliminated by an interpolation of subsequent measurements of the same sample. In equation (10), the mean expansion coefficient γ ml can be used instead of γ 1 if the temperature is nearly constant (e.g.,…”

Section: Basic Equations Of the Pressure-of-flotation Methodsmentioning

confidence: 99%

“…Starting from a first flotation, the temperature is changed deliberately by a small amount and then the sample is again brought into the flotation state by adjusting the pressure. With equation (10) and ρ/ρ = 0, the compressibility of the liquid is yielded…”

Section: Basic Equations Of the Pressure-of-flotation Methodsmentioning

confidence: 99%

“…Also three very small spheres (diameters: 16 mm, 20 mm and 23 mm) were measured with standard uncertainties below 0.5 ppm, which are used for the calibration of the PTB magnetic flotation apparatus [29]. The main uncertainty contribution in this case is due to an adsorption effect in the measuring liquid that results in apparent density differences by different volume-to-surface ratios, even if the samples originate from the same homogeneous crystal [10,11,19].…”

Section: Applicationsmentioning

confidence: 99%

“…By varying the temperature or pressure in the liquid its density can be controlled to get different samples (subsequently) into the floating state [5,6] and calculate their density differences from the temperature or pressure differences, if the thermal expansion coefficients and compressibilities of liquid and sample are known. The method of flotation by temperature variation was used to determine the density differences of LiF crystals [5,7], diamonds [8] and silicon samples [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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Solid density determination by the pressure-of-flotation method

Bettin¹,

Toth²

2006

Meas. Sci. Technol.

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After a short overview of flotation methods and experiments, basic equations for the pressure-of-flotation method are given including a temperature and composition dependence of the liquid's thermal expansion and compressibility. Then, the pressure-of-flotation experiment of PTB is described. A new calibration procedure using doped silicon samples is presented. Now, density comparisons of silicon samples can be performed with an uncertainty less than 0.1 ppm for density differences up to 10 ppm, i.e. for practically all undoped silicon samples. Current applications of the method and an outlook to future developments are discussed. Relative uncertainties of the order of 10−9 seem to be possible and would allow new applications.

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Electromagnetic Quantities, Basic, Measurement of

Kibble

2003

Digital Encyclopedia of Applied Physics

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The Avogadro constant — Recent results on the molar volume of silicon

Cited by 26 publications

References 11 publications

Remeasurement of a Silicon lattice period

Remeasurement of a Silicon lattice period

Solid density determination by the pressure-of-flotation method

Electromagnetic Quantities, Basic, Measurement of

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