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Solid State Density

Working Group 1.82


Determination of density and volume of solid samples with high precision

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Cooperation in the project for the re-determination of the Avogadro constant

Volume robot

A fully automatic apparatus for the hydrostatic determination of the volume of weights is under development. Weights with masses from 0.1 g to 1000 g will be measured, with uncertainties desired in the range from 0.02 mm3 for a 0.1 g weight to 0.5 mm3 for a 1000 g weight. In this apparatus, both the weighing of the samples in a liquid (hydrostatic weighing) and their mass determination in air will be possible. For both weighings, the (apparent) weight of the samples will be measured by comparing them with calibrated weights.

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Density comparison by the pressure-of-flotation method

The pressure-of-flotation method allows investigations of very small density differences to take place by comparing measurements of two silicon samples (e. g. 1 kg silicon-28 spheres). To this end, both samples are immersed in a liquid mixture that has nearly the same density as silicon. The pressure in the liquid is adjusted in such a way that one of the two samples floats freely without rising or sinking. Currently, an apparatus for density comparisons that uses the pressure-of-flotation method is being set up; the desired relative standard uncertainty of the density comparison measurement using this apparatus is 0.01 ppm for silicon-28 spheres. To achieve this uncertainty, both a high resolution of the pressure changes and a temperature stability in the µK range are crucial.

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Magnetic flotation

The international Avogadro project has demonstrated that it is possible to realize the SI mass unit, the kilogram, by counting the atoms in silicon spheres manufactured from silicon that is highly enriched in the isotope 28Si. However, because these 28Si spheres are too expensive for the dissemination of the mass unit, the realization and dissemination of the mass unit by using spheres made of natural silicon is being investigated. The idea behind this investigation is to transfer the well-known density of a 28Si sphere to spheres of natural silicon by means of hydrostatic weighing. In a “classical” hydrostatic apparatus, the sample is connected to the balance using a thin wire. The meniscus which forms on the wire at the surface of the liquid is responsible for a major uncertainty contribution in such an apparatus. In order to enable a density transfer with the necessary relative standard uncertainty of 3 x 10–8, a magnetic suspension coupling will be used, thus transmitting the weight of the silicon spheres to the balance without a wire.

The apparatus is currently in the design stage.

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  • Measurement of the density and volume of solid samples, e. g. solid density standards, air density artifacts and weights from 1 g to 1 kg
  • Calibration of hydrometers

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Automatic hydrostatic weighing apparatus

The automatic hydrostatic weighing apparatus is used to determine the volume of solid samples with a mass of up to about 1030 g and a volume of up to 440 cm3. The measurements are performed at 20 °C. The apparatus has been included in the international CMC tables.
The following expanded measurement uncertainties (coverage factor k = 2) are accepted worldwide:
(0.15 + 0.0015 cm-3 · V) mm3 for the volume V ranging from 50 cm3  to 440 cm3.

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Mass comparison apparatus

In this apparatus, the masses of solid samples with a mass of up to about 1000 g can be compared in order to determine the density of samples.
Mass comparisons can be performed with a measurement uncertainty of 0.10 mg (for a coverage factor k = 2).
Absolute mass determinations with a lower uncertainty (i.e. traceable to the SI mass unit, the kilogram) are performed by Working Group 1.81, “Realization of Mass.”




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Calibration of hydrometers

Hydrometers for measuring densities in the range between 500 kg/m3 and 2000 kg/m3 can be calibrated with expanded uncertainties as low as 0.02 kg/m3 (coverage factor k = 2) using the Cuckow method. This is relevant for the following types of hydrometers: Alcoholometers, hydrometers for aqueous sucrose solutions, for wort, for sulpho spirit, for petroleum and for liquefied petroleum gas. The scale unit may be kg/m3, g/cm3, % mas, or % vol. The reference temperature should be in the range from 15 °C to 25 °C. The scale reading may be "in the liquid's level" or "at the upper rim of the meniscus."

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Hydrostatic determination of the density of solid samples


The density of solid samples with masses of up to about 1000 g can be determined in the temperature range from 5 °C to 80 °C by means of hydrostatic weighing.

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