Kenichi Fujii: Evolving Units—The First Revision of the Kilogram Definition in 130 Years

Do you find yourself casually measuring your weight, body temperature, or waistline on a daily basis? (Some of you might be measuring quite carefully for the sake of a diet). When you discuss those measurement results with family or doctors, you need "units."

A unit is a scale that represents the magnitude of a physical quantity; therefore, a physical quantity is expressed as the product of a numerical value and a unit. Since the method of representing numerical values using the decimal system is already unified, as long as the units are unified, people can correctly understand the magnitude of physical quantities across national borders. This is important not only for science and technology but also for commerce, industry, and trade. For this reason, several basic units have been used since ancient times, but today, a global standard called the International System of Units (SI) is used.

The SI has seven base units. For example, the "meter" was defined around the time of the French Revolution as one ten-millionth of the length of the meridian from the North Pole to the Equator. Later, with the advent of the theory of relativity, it was redefined as the distance light travels in a specific amount of time, utilizing the law that the speed of light is constant. The "second" was also previously defined by the period of the Earth's rotation or revolution, but it is now defined by the vibration period of a cesium atomic clock. The "candela," whose name is derived from the word for candle, was once based on the brightness of a single candle, but is now defined in terms of the energy of electromagnetic waves.

In this way, physical quantities of a magnitude that can be perceived by the human five senses were chosen for SI units, but as science and technology progressed, their definitions underwent repeated transitions, evolving into definitions with higher universality.

However, the "kilogram," the unit of mass, had not changed once since it was defined in 1889 by a physical artifact—a weight known as the International Prototype of the Kilogram. The mass standards of various countries were maintained by the International Bureau of Weights and Measures (BIPM) in the suburbs of Paris, which periodically calibrated the kilogram prototypes (copies of the international prototype) distributed to member states of the Metre Convention against the international prototype.

However, as an artifact, there are limits to its stability. Comparisons between the international prototype and national prototypes over the past 100 years revealed that the mass of the prototypes gradually increased due to surface contamination and other factors, and that the stability as a unit was limited to about 5 parts in 100 million. For this reason, research to change the definition using modern methods has been underway for quite some time.

Even so, the revision of the kilogram's definition did not materialize for a long while. It could be said that the stability of the mass of the platinum-iridium alloy, forged using vacuum metallurgy—the cutting-edge technology of 130 years ago—was just that excellent. Engineers at the time even stated that if this alloy were used, its mass would likely not change even after 10,000 years. Consequently, until very recently, it was impossible to measure physical constants such as the Avogadro constant or the Planck constant with a precision exceeding that stability. In the 2012 issue of the scientific journal "Nature," the revision of the kilogram's definition was listed as one of the five major unsolved challenges in physics, alongside the detection of gravitational waves.

In recent years, however, measurements with precision exceeding this became possible. At the General Conference held in November 2018 based on the Metre Convention, it was adopted to simultaneously revise the definitions of the kilogram, ampere, kelvin, and mole using the Planck constant, elementary charge, Boltzmann constant, and Avogadro constant, respectively. The new definitions went into effect on World Metrology Day, May 20, 2019.

When I was in the university's Faculty of Engineering, the world was in the midst of the oil crisis. That triggered my interest in energy conservation research, and I conducted research under Professor Koichi Watanabe (now Professor Emeritus) of the Department of Mechanical Engineering to improve energy efficiency by precisely measuring the thermal properties of substances. However, the measuring equipment used for that purpose was expensive, so I could not receive research funds without sufficiently explaining the necessity.

Around that time, I learned that there was a research institution in Tsukuba called the National Research Laboratory of Metrology (now the National Metrology Institute of Japan at the National Institute of Advanced Industrial Science and Technology), and thinking that I could perform measurements with the highest precision there, I went for a job interview in the summer of 1983. At that time, I happened to meet a certain researcher in the laboratory's cafeteria. He said he was conducting research to change the definition of the kilogram. It was then that I first learned that the definition had not changed since it was defined by an artificial weight called the International Prototype of the Kilogram at the end of the 19th century.

Immediately after joining, I participated in research to remeasure the density of water. Water is used when measuring the density or volume of other substances, but its value had not been measured since the end of the 19th century. Therefore, I conducted research to precisely remeasure the density of water using the volume of a quartz glass sphere as a reference, measuring its diameter with a laser interferometer.

Around this time, it became possible in Japan to polish silicon crystals into spheres. To measure the Avogadro constant using a method called the X-ray crystal density method and realize a new definition of the kilogram from the number of atoms, precise values for density are required in addition to the lattice constant (interatomic distance) and molar mass (isotopic abundance ratio) of the silicon crystal. For this reason, I, who had already developed a laser interferometer to measure the diameter of quartz glass spheres, was put in charge of measuring the density of silicon crystal spheres. In 1988, the NRLM Avogadro Group was formed.

At the time, we started with five people measuring the lattice constant and density of silicon crystals. We had the enthusiasm to achieve something with our own hands that no one had been able to do for 100 years, but measuring the number of atoms with a precision exceeding the stability of the prototype was difficult, and the project even faced a crisis. The leader at the time even told an interviewer from the National Museum of Nature and Science, "It will probably be impossible to change the definition of the kilogram while we are alive."

A few years later, we succeeded in measuring the Avogadro constant, but prospects for improving precision were hard to come by. At that time, the limit of the precision for the silicon crystal density measurement I was in charge of was 9 parts in 100 million. We were unable to break the wall of 5 parts in 100 million, which was the stability of the prototype. There was also a period when I sought other methods, stayed at the National Institute of Standards and Technology (NIST) in the United States—our rival—and challenged myself to realize a new definition of the kilogram using the Planck constant.

The turning point came in 2002 after I returned to Japan. We received an invitation from a German research group conducting similar research. They asked if we would like to try enriching the isotopes of silicon used as the crystal material. I intuitively felt that if we could do this, we could improve precision all at once, but such enrichment requires a massive amount of money, comparable to making an atomic bomb. It was also technically difficult and required enrichment using Russian nuclear technology. However, we gradually gained the understanding of the institute, and this isotope enrichment project began in 2004. From around this time, I served as a coordinator for international projects with Germany, Italy, and the BIPM, and aimed for further precision improvement as a project leader within AIST.

Subsequently, this international project proceeded smoothly, and in 2007, a crystal enriched only with silicon of mass number 28 (²⁸Si) was obtained. From this crystal, two 1-kilogram crystal spheres were polished, and we developed a laser interferometer (photo) capable of measuring their diameters with a precision nearly equal to the interatomic distance. We then newly developed surface analysis technology and succeeded in improving the measurement precision of crystal density to 2 parts in 100 million. We had finally reached the precision capable of changing the definition of the kilogram.

In 2011, the first measurement results for the Avogadro constant with a precision surpassing the stability of the prototype were obtained. We continued to make improvements, and several sets of data with sufficient precision to convince the world were obtained.

In 2017, an adjustment of physical constants was conducted by the Committee on Data for Science and Technology (CODATA) to determine the value of the Planck constant to be used for the new definition of the kilogram. Ultimately, eight sets of data were selected. Four of them were values of the Avogadro constant measured jointly by AIST and research institutions in Germany and Italy, converted into the Planck constant, and one of those was the measurement result from AIST alone. Japan left an achievement that contributed greatly to the first revision of the kilogram definition in 130 years. This was the first time in history that Japan played a decisive role in defining the International System of Units.

Then, in November 2018, the revision of the kilogram's definition was adopted at the General Conference on Weights and Measures held in Versailles. This was exactly 30 years after I began this research.

The greatest benefit brought by the revision of the kilogram's definition is that anyone with the technology will be able to have a mass standard based on the Planck constant, without relying on the prototype stored at the BIPM near Paris. This is the same as how the definition of length was replaced by the speed of light, allowing anyone to have a length standard as long as they can measure the frequency of light.

Furthermore, with the previous definition, the minimum mass that could be measured was limited to about 1 microgram. Since the new definition does not require reliance on a weight, if new measurement technologies linked to the Planck constant are developed, it will become possible to measure mass in even smaller regions. Such measurement technologies will contribute widely to biotechnology, nanotechnology, and other fields through, for example, the development of new drugs, measurement of fine particles in the environment, inkjet technology, and mass measurement of semiconductor devices.

History shows that new definitions of units create several breakthroughs and have the effect of encouraging the emergence of newer technologies. I hope that more stakeholders will understand the importance of supporting such long-cycle basic research.