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## How might the definition of the kilogram change in the future? (FAQ - Mass & Density)

For the last 20 years there has been a considerable amount of work undertaken looking for an alternative, more fundamental, definition for the SI unit of mass - the kilogram - because of limitations in the stability, realisation and dissemination of the present kilogram artefact (see section above and [4] below). In other areas of metrology, SI base units have been redefined as better techniques became available - such as using a laser to realise the unit of length - and either in step with or ahead of needs. But unfortunately in mass metrology no such opportunities exist and the new approaches to a fundamental re-definition are being forced by necessity.

Other base units have simpler definitions, essentially based on one measurement (such as the wavelength of light for the metre) but unfortunately no comparably straight-forward definitions are in sight for the re-definition of the kilogram; they all involve a number of complicated measurements. At present four methods are being investigated for their potential to provide a new fundamental definition for the SI unit of mass - the kilogram.

### The Watt balance

The first proposal for re-defining the kilogram was to link it via the SI unit for power - the Watt (equal to one joule per second). Bryan Kibble of NPL proposed using the current balance [5] - that had formerly used to define the ampere - to relate the kilogram to a value for Planck's constant. The fundamental measurements necessary for the definition of the kilogram by this method are the volt (via the Josephson junction) and the ohm (via the quantised Hall effect). Measurements of length, time and the acceleration due to gravity are also necessary. There are currently four NMIs working on the Watt balance project; NPL in the UK [6], The National Institute of Standards and Technology (NIST) in the USA [7], METAS in Switzerland [8] and BNM-LNE in France.

The internationally coordinated Avogadro project will attempt to define a kilogram based on a fixed number of atoms of silicon [9-10]. The mass of a sphere of silicon will be related to its molar mass and the Avogadro constant by the equation:

m = (Mm/NA)·(V/v0)

 where m is the calculated mass of the sphere Mm is the molar mass of the silicon isotopes measured by spectrometry NA is the Avogadro constant V is the volume of the sphere measured by interferometry v0 is the volume occupied by a silicon atom

To calculate v0 the lattice spacing of a silicon crystal must be measured by x-ray interferometry [11]. The practical realisation of this definition relies on the calculation of a value for NA, the Avogadro constant, from an initial value for the mass of the sphere [12]. This value is then set and used subsequently to give values for the mass of the sphere, m. An added complication with this definition is the growth of oxides of silicon on the surface of the spheres - the thickness of the layer needs to be monitored (probably by elipsometry) and used to correct the value of mass m.

### Ion accumulation approach

This third approach to the re-definition of the kilogram involves the accumulation of a known number of gold atoms [13, 14]. Ions of Au197 are released from an ion source into a mass separator and accumulated in a receptor suspended from a mass comparator. The number of ions collected is related to the current required to neutralise them - supplied by an irradiated Josephson junction voltage source. The mass of ions M is then given by the equation:

M = ½n1n2maf(t')dt', with the integral between t' = 0 → t

 where n1 and n2 are integers ma is the atomic mass of gold f(t') is the frequency of the microwave radiation irradiated onto the Josephson junction ma 197 u, for gold isotope Au197, where u is the atomic mass (equal to 1/12 of the mass of C12)

### Levitated superconductor approach

Like the 'Watt' balance project, this method relates the kilogram unit to electrical quantities defined from the Josephson and quantised Hall effects [15]. In this technique a superconducting body is levitated in a magnetic field generated by a superconducting coil. The current required in the superconducting coil is proportional to the load on the floating element and defines a mass (for the floating element) in terms of the current in the superconducting coil [16, 17, 18].

Even from these brief descriptions of the four methods, it can be seen that the present approaches to the redefinition involve a number of demanding measurements. Almost all of these measurements must be performed at uncertainties which represent the state of the art (and in some cases much better than those currently achievable) to realise the target overall uncertainty of 1 part in 108 set for this work. The absolute cost of the equipment also means that the ultimate goal of all national measurement institutes being able to realise the SI unit of the kilogram independently will, on purely financial grounds, not be achievable.

All four approaches require traceability to a mass in vacuum, both for their initial determination and for dissemination.

### Finally...

Any better ideas on a postcard please.

### Notes and references

 4 Downes S, Present status of the different approaches to the re-definition of the kilogram, NPL Report CMAM 11, (1998) 5 Kibble B, Robinson I, Belliss J, A realization of the SI watt by the NPL moving-coil balance, Metrologia, 27, 173-192, (1990) 6 Robinson I, Kibble B, The NPL moving-coil apparatus for measuring Planck's constant and monitoring the kilogram, IEEE Trans. Instrum. Meas. 46, 2, 596-600, (1997) 7 Newell D, Steiner R, Williams E, Picard A, The next generation of the NIST watt balance, NIST Report MOPB4-3, 108-109, (1998) 8 Richard P, The OFMET Watt balance, EUROMET Mass and Derived Quantities, 7, 11-13, (1999) 9 Rottger S, Paul A, Keyser U, Spectrometry for isotopic analysis of silicon crystals for the Avogadro project, IEEE Trans. Instrum. Meas., 46, 2, 560-562, (1997) 10 Gonfiantini R, De Bievre P, Valkiers S, Taylor P, Measuring the molar mass of silicon for a better Avogadro constant, IEEE Trans. Instrum. Meas., 46, 2, 566-571, (1997) 11 Becker P et al., Absolute measurement of the (220) lattice plane spacing in a silicon crystal, Phys. Rev. Lett., 46, 1540-1544, (1981) 12 Seyfried P, Becker P, et al. A determination of the Avogadro constant, Z. Phys. B - Condensed Matter, 87, 289-298, (1992) 13 Glaeser M, Ratschko D, Knolle D, Accumulation of ions - an independent method for monitoring the stability of the kilogram, Proc. IMEKO TC3, 14, 7-12, (1995) 14 Ratschko D, Knolle D, Glaeser M, Accumulation of gold ions on a gold coated quartz crystal, Proc. IMEKO TC3, 19, 237-240, (2000) 15 Kibble B, Realizing the ampere by levitating a superconducting mass - a suggested principle, IEEE trans. On Inst. & Meas., Vol. IM32 No. 1, 144, (1983) 16 Fuji Y, Miki Y, Shiota F, A new superconducting levitated-mass system, Proc. IMEKO TC3, 19, 63-74, (2000) 17 Fujii K, Tanaka M et al., Absolute measurements of the density of silicon crystals in vacuo for a determination of the Avogadro constant, IEEE Trans. Instrum. Meas., 44, 2, 5542-545, (1995) 18 Frantsuz E, Khavinson V, Geneves G, Piquemal F, A proposed superconducting magnetic levitation system intended to monitor the stability of the unit of mass, Metrologia, 33, 189-196, (1996)
Last Updated: 25 Mar 2010
Created: 8 Oct 2007

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