The mole, symbol mol, is the International System of Units (SI) unit of the amount of substance which is the quantity referring to a measure of the number of specified elementary entities, such as chemical elements or compounds in a sample. In the current SI, the mole is defined by specifying the mass of carbon-12. But this base unit is not an invariant of nature because the mass is defined by the material artefact. According to efforts to define the base units in SI using true invariants of nature, the mole will be redefined by fixing the numerical value of a fundamental constant, the Avogadro constant. In the new SI, the definition of the mole can be realized through the experiments that lead to the determination of the Avogadro constant. The best experimental value of the Avogadro constant has been obtained by the X-ray crystal density experiment using silicon-28 highly enriched silicon sphere in the frame work of the International Avogadro Coordination. In this paper, the current definition of the mole and practical aspects of this unit are introduced, then the principle and technical challenges in X-ray crystal density experiment for redefinition of the mole are discussed.

The unit of the thermodynamic temperatures, kelvin, will be redefined after May of 2019, by the new process of fixing the numerical value of the Boltzmann constant. In this respect, the Boltzmann constant, which is a conversion factor between the thermal energy and the thermodynamic temperature, will be assigned as 1.380 649 × 10^-23 J K^-1 after the redefinition procedure. This paper reviews the three experiments which have contributed to the determination of the Boltzmann constant, which are namely: the acoustic gas thermometry, dielectric constant gas thermometry and the noise thermometry. By and large, the physical principles of these experiments are important even after the redefinition takes place, because they are methods used as primary thermometers for the determination of the thermodynamic temperatures. The status of the redefinition and the relation between the thermodynamic temperature and temperature scale is reviewed in this paper.

It is often overlooked that so far, there has been inconsistency between the definition of the ampere in SI units and its realization. For instance, the ampere is defined based on the classical Ampere’s law, while its representation has been made through the Ohm’s law, that is, the ratio of the Josephson voltage to the quantum Hall resistance that do not belong to the SI units. However, in the revised SI units that are slated to take effect in 2019 on World Metrology Day, 20 th of May, it is significant to note that the ampere will be defined as a flow of electrons with the numerical value of the elementary charge fixed. In this instance, all three of the electrical units, such as the current, voltage and resistance will become defined on the basis of quantum physics. As a candidate for the quantum current standard, the various types of single electron pump devices are reviewed in relation to the redefinition of the ampere.

In the current SI (International System of Units), the kilogram is defined by the mass of a material artefact. In this instance, because the artefact can be damaged during use, the present definition is inherently considered unstable. To overcome the shortcomings of the present kilogram definition, the SI will be redefined in near future. In the new SI, the kilogram will be redefined by fixing the numerical value of the Planck constant. After the kilogram redefinition, realization experiments which link the Planck constant to the mass will be necessary. In the new SI, the kilogram will be realized through experiments including the Kibble balance and the X-ray crystal density. The Kibble balance, which is named for the scientist Bryan P. Kibble, is an electromechanical device comparing mechanical power and electrical power. The electrical power is proportional to the Planck constant, because of the voltage and resistance are measured using the Josephson effect and the quantum Hall effect, respectively. The Planck constant is an invariant and not a characteristic of a man-made object, or a specific experiment. The new mass unit is more stable than the current one, and will pave the way for the advancement of precision measurement.

The International System of Units (acronym: SI) is founded on seven base units (meter, kilogram, second, ampere, kelvin, mole, and candela) corresponding to seven base quantities (length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity). SI was formally established in 1960 by the 11th CGPM. It has been revised from time to time in response to requirements of users and advances in science and technology. However, the most significant revision is going to be done in November 2018 by the 26th CGPM. Four base units (kilogram, ampere, kelvin, and mole) will be given new definitions linking them to exactly defined values of Planck constant, elementary charge, Boltzmann constant, and Avogadro constant, respectively. In this paper, historical background for the revision of SI is described and scientific principle of redefinition is explained. The procedure used to redefine meter from the speed of light in a vacuum is used as an example. After this revision, uncertainties of many other fundamental constants will be eliminated or reduced. From May 20, 2019 (World Metrology Day), the revised SI will come to practice.