Changing the mass standard

For more than a century, the base SI unit for mass was defined by a material artefact.

Originally, 1 kilogram was defined as the mass of 1000 cm³ of water at 4°C. Based on this, the international prototype kilogram (IPK) was made in the 1880s from an alloy of 90% platinum and 10% iridium. Six official copies were also made. The platinum-iridium alloy is very hard, corrosion resistant and of high density – twice that of lead – and its cylindrical shape, with its height equal to its diameter (3.917 cm), allows for a minimum surface area to be exposed to the air. Since it was cast, the IPK has been stored in a triple-locked vault 8 metres below the offices of the International Bureau of Weights and Measures (BIPM) in Paris.

Problems with the IPK

Despite the strong historical attachment to the IPK, its continued use as the mass standard came with a number of practical problems:

• The IPK is used to calibrate six official ‘sister’ copies of the kilogram. The sisters are used to calibrate the copies owned by national institutes, which, in turn, calibrate stainless steel standards used by other member nations. This long chain of mass measurement and calibration inevitably results in a loss of accuracy.
• Although the IPK and its copies are housed under nested glass bell jars with a carefully controlled atmosphere, their masses have diverged – the differences have been as much as 50 micrograms over the last 120 years. As weighing technologies have advanced, this lack of stability has caused issues.
• Cleaning and washing the IPK requires multiple, careful steps.
• If the IPK is damaged in any way, by definition, the mass of the universe changes, which is a rather absurd situation.

These issues prompted the international metrology community to begin searching for a suitable replacement standard based on fundamental constants that do not change over time. Work began in earnest in the 1970s, and in more recent years, it focused on the use of Planck’s constant (h) – a term that links the amount of energy a photon carries with the frequency of its electromagnetic wave. Developing measurement systems that could measure h with sufficient accuracy took extensive work and multiple independent experiments from international metrology laboratories.

Two very different methods were found to give close agreement, leading to their acceptance at the General Conference on Weights and Measures in 2018. On 20 May 2019, the kilogram was formally redefined in terms of Planck’s constant, meaning that the IPK could be retired.

Silicon sphere

The X-ray-crystal-density (XRCD) method is based on the idea that the mass of a pure substance can be determined by measuring the number of elementary entities (such as atoms) in the substance. This requires an understanding of the distances between atoms to a high degree of accuracy. This only works if your substance is a perfect crystal with no defects or other elements present. It’s possible to grow very large and very pure single crystals of silicon – they look like a highly reflective solid sphere – so they are the most popular crystal used in the XRCD method. The mass of this sphere can be first expressed in terms of the mass of a single silicon atom, and X-ray imaging is used to determine the actual number of atoms present in the crystal. By fixing the value of h (= 6.626 070 15 x 10^–34 kg m² s^–1), mass can be determined via constants of nature.

These measurements were first used to determine the value of the Avogadro constant (N^A), the number of elementary entities per mole of substance, but in the new SI, the value of N^A has been fixed, which means that the definition of the mole is now independent of the kilogram.

The Kibble balance

A Kibble balance relates mechanical power to electrical power by comparing the gravitational force on a mass with the electromagnetic force on a current-carrying coil in a magnetic field. Bryan Kibble, a British metrologist, first proposed this system in 1975, though he called it the watt balance. It was renamed in Bryan’s honour after his death in 2016.

A Kibble balance has two measurement modes – the weighing mode and the moving mode. In weighing mode, the balance uses electromagnetic forces, via a current flowing in a wire coil that is suspended in a strong magnetic field, to balance a physical mass. In moving mode, the same coil is moved vertically through the magnetic field, which creates a voltage in the coil.

Comparing the results of these two measurements leaves metrologists with a simple equation whereby all of the terms can be linked back to natural constants such as the elementary charge (e) and the speed of light (c). The voltage and current measurements made in the Kibble balance can be directly linked to Planck’s constant (h), allowing the system to relate mass to h with incredible accuracy.

Scientists from the Measurement Standards Laboratory have come up with a uniquely Kiwi solution for redefining the kilogram – a ‘desktop’ version of the Kibble balance that is predicted to measure mass with an accuracy approaching 20 parts per billion.

Planck’s constant

In 1900, German physicist Max Planck discovered a relationship between the radiation emitted from a hot object and its temperature. This led Planck to propose that the energy emitted by a hot object comes in very small packets of energy called quanta.

The relationship linking the energy of a given packet and the frequency of its radiation is E = hf, where:

• E is the energy of the packet
• f is the frequency of the radiation
• h is Planck’s constant.

Like the speed of light (c), Planck’s constant (h) is a fundamental physical constant:

• c = 299,792,458 m s^-1
• h = 6.626 070 15 x 10^–34 kg m² s^-1