## 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 Avogadro approach

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 = (M _{m}/N_{A})·(V/v_{0})*

where | m |
is the calculated mass of the sphere | |

M_{m} |
is the molar mass of the silicon isotopes measured by spectrometry | ||

N_{A} |
is the Avogadro constant | ||

V |
is the volume of the sphere measured by interferometry | ||

v_{0} |
is the volume occupied by a silicon atom |

To calculate *v _{0}* 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 N

_{A}, 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 Au^{197} 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 = ½n _{1}n_{2}m_{a}*∫

*f(t')dt'*, with the integral between

*t' = 0 → t*

where n and _{1}n_{2 } |
are integers | |

m_{a} |
is the atomic mass of gold | |

f(t') |
is the frequency of the microwave radiation irradiated onto the Josephson junction | |

m_{a} |
197 u, for gold isotope Au^{197}, where u is the atomic mass (equal to 1/12 of the mass of C^{12}) |

### 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 10^{8} 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

**Last Updated: 25 Mar 2010**

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