Kilogram

The kilogram is the SI unit of mass.

At the end of the 18th century, a kilogram was the mass of a cubic decimeter of water. In 1889, the 1st CGPM sanctioned the international prototype of the kilogram, made of platinum-iridium, and declared: This prototype shall henceforth be considered to be the unit of mass.

The 3d CGPM (1901), in a declaration intended to end the ambiguity in popular usage concerning the word "weight," confirmed that:

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

The kilogram, rather than the gram, is the unit of mass due to historical accident. An early version of the metric system proposed the "grave", equal to the mass of one cubic decimeter of water, as the unit of mass. However, after the French revolution, a unit equal to one-thousandth of the "grave" was chosen, as most common commercial transactions were for weights less than one "grave". Due to the small mass of the gram, it was decided to prepare a prototype artifact of 1000 grams, or one kilogram, as the mass standard.

History of the kilogram

From the early history of humankind to modern times, mass measurements have formed the cornerstone for trade and commerce. Evidently, a reliable international standard for mass and length is indispensable. It was not until 1875 that sixteen countries signed the Meter Convention that established the foundations of the International System of Units SI that would provide uniformity in the standards of weights and measures. The foundation of the SI lies with the 1791 decision of the French National Assembly to adopt a uniform system based entirely on the unit of length, the meter, defined at the time as being equal to one ten-millionth of the length of the quadrant of the Paris meridian. The unit of mass was the mass of a cubic decimeter of water at 4 ⁰C, the temperature of maximum density.

Based on these definitions, a prototype meter and kilogram were manufactured and deposited in the Archives of the French Republic in 1799 forming the basis of the presently adopted SI. In 1875, the Meter Convention founded the Comité International des Poids et Mesures (CIPM), which took the responsibility of manufacturing replicas of the meter and kilogram prototypes, and the Bureau International des Poids et Mesures whose function was to serve as the custodian of the prototypes. In 1878, a kilogram cylinder made of 90 % platinum—10 % iridium alloy was polished, adjusted, and compared with the kilogram of the Archives. It was placed in a safe at the BIPM in 1882, and was ratified as the International Prototype Kilogram by the first Conference Generale des Poids et Mesures (CGPM) in 1889. In 1901, the third CGPM in Paris established the definition of the unit of mass: The Kilogram is the unit of mass; it is equal to the mass of the International Prototype of the Kilogram.

The unit of mass is still only available at the BIPM. Therefore, the prototypes serving as national standards of mass must be returned periodically to the BIPM for calibration either on an individual basis, which could be done anytime, or as part of a simultaneous recalibration of all the prototypes known as periodic verification. The results of the third periodic verification demonstrated a long-term instability of the unit of mass on the order of approximately 30 μg/kg over the last century; this instability is attributed to surface effects that are not yet fully understood.

To date the kilogram remains as the only SI base unit defined by an artifact and thus is constantly in danger of being damaged or destroyed. While comparisons of nearly identical 1 kg mass standards can be performed with a relative precision of 10⁻¹⁰ with commercially available balances and with 10⁻¹² with special balances, it is clear that the limitation in the field of mass metrology lies within the artifact definition itself. Therefore, the ultimate need for mass metrology is to redefine the unit of mass in terms of a fundamental constant of nature.

Current Efforts for an Alternative Definition of the Unit of Mass

Efforts to replace the artifact kilogram definition with one based on an invariant of nature have been ongoing for years and have been a challenge to the scientific community. These efforts are based on two approaches:

• mechanical electrical measurements,
• atom counting.

The mechanical electrical measurement approach, uses what has become known as a moving-coil watt balance. The main concept is to compare a power measured mechanically in terms of the kilogram, meter, and second to the same power measured electrically using the Josephson effect and quantum Hall effects. This links the kilogram to one of nature’s time invariants, the Planck constant h. One can thus consider defining the kilogram in such a way as to fix the value of h and to use a watt balance to implement the definition and to directly calibrate standards of mass.

The atom counting approach aims at relating the mass of an atom to the kilogram. Within this framework, two paths can be taken:

1. Count the number of atoms in a macroscopic object of known mass. This is the basis of the silicon project. The main concept is to relate the mass and volume of a 1 kg single crystal sphere of silicon, lattice spacing of a unit cell of the silicon crystal, mean molar mass of the silicon atoms in the sphere, number of atoms in a unit cell, and the Avogadro constant. This approach determines the Avogadro constant and hence the mass of the carbon-12 atom in kilograms.

1. Buildup a macroscopic object atom by atom while counting the number of atoms as they accumulate.

In one approach currently being pursued, gold ions from an ion beam are deposited on a target. When the total current is measured in terms of the Josephson and quantum Hall effects, and the target is weighed, the result is a value of the Avogadro constant and again the mass of the carbon-12 atom in kilograms.

None of these approaches has been able to rival the present artifact definition yet. However, competing with the present definition requires achieving a minimum level of precision on the order of 1×10⁻⁸.

References

• The name "kilogram": a historical quirk, Bureau International des Poids et Mesures.
• Unit of mass (kilogram), SI brochure, Section 2.1.1.2, Bureau International des Poids et Mesures.
• Z. J. Jabbour and S. L. Yaniv, The Kilogram and Measurements of Mass and Force, Journal of Research of the National Institute of Standards and Technology NIST vol. 106, pp. 25–46 (2001)