Absolute measurement of the density of silicon crystals in vacuo for a determination of the Avogadro constant

Fujii, K.; Tanaka, Mitsuru; Nezu, Y.; Sakuma, Akihiro; Leistner, Achim J.; Giardini, W.

doi:10.1109/19.377902

Cited by 49 publications

(29 citation statements)

References 23 publications

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“…The iso-octane is a density standard prepared by Kyoto Electronic Manufacturing, Co. [5] and is traceable to the density standard [6] of Japan; its density is 691.86 ± 0.03 kg · m −3 . From the experimental results, we have determined the mass ratio, µ, as follows.…”

Section: Results Of Calibration For Vibrating-tube Densimetermentioning

confidence: 99%

Rapid Measurements of Thermodynamic Properties for Alternative Refrigerants with Vibrating-Tube Densimeter

et al. 2005

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More than 2000 PVT data in the liquid phase, vapor phase, and at saturation boundaries have been obtained for pure compounds of several alternative refrigerants. In addition, more than 1000 liquid-density data have been obtained for several binary and ternary mixtures. The alternative refrigerants measured in the present study include CF 3 OCH 3 (trifluoromethyl methyl ether) and CF 3 CF 2 OCH 3 (pentafluoroethyl methyl ether), which are hydrofluoroethers developed by RITE (the Research Institute of Innovative Technology for the Earth, Japan), and typical hydrocarbons, such as propane, n-butane, isobutene, and their binary and ternary mixtures. The measurement uncertainties are estimated to be 3 to 7 mK for temperature, 0.26 kPa or 0.022% whichever is greater for pressure, and 0.07 kg · m −3 or 0.024% whichever is greater for density. The present measurement system took only a few minutes to get one PVT datum, and one or two days to complete all the measurements for a single fluid at temperatures from 240 to 380 K and at pressures up to 7 MPa. In addition, an empirical equation of state (EoS) for the liquid phase was developed on the basis of the present data, and the EoS nicely reproduces not only the present data but also existing data reported by other researchers.

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Section: Results Of Calibration For Vibrating-tube Densimetermentioning

confidence: 99%

Rapid Measurements of Thermodynamic Properties for Alternative Refrigerants with Vibrating-Tube Densimeter

et al. 2005

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“…The most accurate means by which the density of a crystal can be determined is by direct measurement of mass and volume (Fujii et al, 1995). A sphere is an ideal shape for the measurement of its dimensions, and hence volume.…”

Section: A New Definition Of the Kilogram?mentioning

confidence: 99%

“…The mean diameter is determined by optical interferometric length measurements, whereby a sphere is placed within a quartz etalon and a light beam from a frequency-stabilized He-Ne laser is divided into two beams pointing at opposite ends of the interferometer. From the phase difference of the interfering beams, with and without the sphere in place, a diameter can be determined (Fujii et al, 1995). The presence of a native oxide on a sphere's surface causes a phase retardation of the light beam on reflection from the oxide and a systematic difference between the observed and real diameters (Fujii et al, 1999).…”

Section: A New Definition Of the Kilogram?mentioning

confidence: 99%

Determining the crystallographic orientation of Avogadro silicon spheres

2004

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Highly polished spheres, manufactured from silicon single-crystal material, are used in the X-ray crystal density method (XCDM) to determine the Avogadro constant. If the measurement uncertainty associated with this method can be reduced to 0.01 p.p.m., it would be possible to redefine the SI unit of mass, the kilogram, in terms of a fixed number of atoms of a definite species. The spheres are manufactured with a nominal mass of 1 kg and nominal diameter of 90 mm and a surface roughness of 0.5 nm (peak to valley). A goniometer has been constructed to enable the crystallographic orientation of these spheres to be determined using the back-reflection Laue technique. Two spheres have been successfully orientated in this manner by identifying two orthogonal 〈100〉 directions.

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“…We will show that the second part in equation (4) straightforward [6]. We will apply this method for estimating the uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Evaluating uncertainty of the mean diameter of silicon sphere by Spherical Harmonics

Zhang

et al. 2010

Cpem 2010

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Considering the most accurate target of Avogadro project ever, the methods of estimating the uncertainty of average diameter by Spherical Harmonics (SH) are reevaluated, and the uncertainty component that can not be ignored is emphasized. Five thousand approximate spheres are generated to simulate the features of real sphere. It's shown that, the estimated uncertainty of the average diameter based on the N-point mean method is incomplete when considering the features of the real sphere. Besides, increasing the number of sampling points can improve the uncertainty of the average diameter.

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Absolute measurement of the density of silicon crystals in vacuo for a determination of the Avogadro constant

Cited by 49 publications

References 23 publications

Rapid Measurements of Thermodynamic Properties for Alternative Refrigerants with Vibrating-Tube Densimeter

Rapid Measurements of Thermodynamic Properties for Alternative Refrigerants with Vibrating-Tube Densimeter

Determining the crystallographic orientation of Avogadro silicon spheres

Evaluating uncertainty of the mean diameter of silicon sphere by Spherical Harmonics

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