Mass is a physical quantity which is expressed using the mass of the international prototype of the kilogram (IPK) for its unit. Many of the units of physical quantities, such as frequency, length, voltage, and resistance, can now be defined using physical laws or quantum effects which are considered to be universal and immutable. In contrast, only mass remains as the sole SI base unit which depends on an artifact made from a platinum-iridium alloy. Continuing research with the aim of changing this SI basic unit to a new definition based on a number of atoms or the fundamental physical constants is in progress at National Metrology Institutes (NMIs) in the world. The Avogadro constant is a basic physical constant which expresses the number of atoms or molecules contained in a substance of one mole. If this constant can be determined accurately, it will be possible to rewrite the present definition as, for example, "the kilogram is the mass of 5.018 ×~ 10²⁵ free ¹²C atoms at rest and in their ground state." Therefore, the National Metrology Institute of Japan (NMIJ) has been engaged in research to improve the accuracy of the Avogadro constant to a few parts in 10⁸.

The Avogadro constant N_A can be obtained as N_A = 8M/(ρa³) from the measured values of the density ρ, lattice constant a, and molar mass M of a silicon crystal. Recently technology makes it possible to produce silicon single crystals in 1 kg spheres which are extremely close to perfect spheres, and it has become possible to determine their density with an uncertainty of several parts in 10⁸ from nanometer measurement of their diameters and mass measurement (see Photo 1). Similarly, the lattice constant was measured by the x-ray interferometer with an uncertainty of a few parts in 10⁸.

In 2002, NMIJ/AIST, with the cooperation of the EU's Institute for Reference Materials and Measurements (IRMM), which is responsible for measurements of molar mass, succeeded in measuring the Avogadro constant with the smallest uncertainty achieved to date with the x-ray crystal density method. These data were adopted by the Committee on Data for Science and Technology (CODATA), which is the international committee that determines the recommended values of the fundamental physical constants, and contributed to a general revision of the fundamental physical constants published in December 2003. It is also possible to derive the Planck constant from the Avogadro constant by using a rigorous relationship between the fundamental physical constants. A comparison of the Planck constant obtained using different measurement principles is shown in Fig. 1.

The measurement accuracy of the Avogadro constant which can be achieved at present is approximately 10^-7. If this can be improved by one order, a redefinition of the kilogram will become possible. If this new definition is realized, the definition of mass will no longer depend on an artifact, but will be linked to a universal constant for the first time in history. In order to reduce the uncertainty of the molar mass measurement, which has become the limit of accuracy, an international project using single crystals of the enriched isotope ²⁸Si was launched in April 2004. In addition to the NMIJ/AIST, the participants in this project include the IRMM, BIPM (Bureau International des Pois et Mesures), and NMIs in Germany, Italy, Australia, the UK, and the US. Thus, the redefinition of the kilogram, which has been the dream of metrologists for many years, is expected to become a reality in the near future.