Instrumentation & Measurement Magazine 24-3 - 5

Realizing the Kilogram from
the Planck Constant: The Kibble
Balance and the Electrical Units
Carlos Sanchez

he international System of Units (SI) was redefined
in 2018 [1]. This historical event implemented a beautiful idea-a system of units defined entirely by
constants of nature. The most notable modification to the SI
involved abandoning the artifact definition of the kilogram
in favor of fixing the numerical value of the Planck constant.
Apart from its physical and mathematical elegance, the new SI
solves the problem of providing an absolute reference for the
kilogram. But, how do we understand the link between the kilogram and the Planck constant? And, how can we realize the
kilogram now, using the new definition? This paper attempts
to give a simple answer to these complicated questions.
For 129 years the kilogram was defined by the mass of the
International Prototype of the Kilogram (IPK), a cylindrical
mass of Pt-Ir stored in a vault at the Bureau International des
Poids et Mesures (BIPM), in Sèvres, France. The IPK was adopted in 1789 along with the International Prototype of the
Meter, a bar of Pt-Ir which defined the unit of length. At this
time the second was defined by the duration of the solar day.
Arguably these definitions and artifacts constituted the
best system of units at the time. The SI units could be disseminated to any part of the world through the use of artifacts
which had to be calibrated against the mass and length prototypes at the BIPM and could be used anywhere to perform
quantitative measurements that could be compared with measurements made anywhere else.
Maxwell was the first scientist to propose that constants of
nature could be used as the basis for a system of units (instead
of artifacts). This was a remarkably visionary idea. After all, an
ideal system of units should remain unchanged over time, be
accessible to anyone, anywhere, and allow for measurements
of sufficient accuracy and precision to satisfy the most demanding technological applications.
The first step toward the implementation of this idea came
about with the invention of atomic clocks and the redefinition
of the second in 1967, based on the absorption frequency associated with specific energy levels of the cesium133 atom ΔνCs.
Later, in 1983, following the development of the laser interferometer, the meter was redefined by fixing the numerical value
May 2021

of the speed of light c. However, the idea of an SI based entirely
on constants of nature could not be fully implemented until
2019, when the kilogram was redefined by fixing the numerical value of the Planck constant h.
The motivation to redefine the kilogram was more than a
purely philosophical one. The previous definition relied on the
stability of the mass of the IPK, and while this is believed to be
an extremely stable quantity, nobody knows for sure just how
stable it is. We do know that the IPK is likely to have changed
by a few parts in 108 since its adoption in 1889, based on historical measurements of a group of nominally identical masses
(witnesses), which were made alongside the IPK, using the
same source material and the same process, and which are
stored with the IPK, under the same conditions. Fig. 1 shows
the measured mass of the witnesses relative to the IPK over a
period of more than 120 years. Apart from the relative changes
which are evident in this plot, it is possible for the whole group
to have an absolute drift which could be comparable to the relative changes observed in the data.
Metrologists and scientists from many different countries
worked for over 30 years to develop methods to link the kilogram with constants of nature, and finally, by 2017, a few
groups had achieved uncertainties below 2 parts in 10 8, a
threshold which was deemed necessary to satisfy the needs of
mass metrologists.
Two methods are currently capable of producing this
level of accuracy. The first one, the X-ray crystal density
method, consists essentially in counting the number of atoms in a nearly perfect silicon sphere and relating the mass of
the sphere to the Avogadro constant through atomic mass ratios [3]. The number of atoms in the sphere is calculated by
measuring the volume of the sphere with an optical interferometer and the lattice spacing with a combined optical/x-ray
interferometer. This effort was led by the International Avogadro Cooperation (IAC), a partnership of National Metrology
Institutes (NMI) from various countries, notably the Physikalisch-Technische Bundesanstalt (PTB) in Germany, the Istituto
Nazionale di Ricerca Metrologica (INRIM) in Italy and the National Metrology Institute of Japan (NMIJ).

IEEE Instrumentation & Measurement Magazine 5
1094-6969/21/$25.00©2021IEEE

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