Redefining the Base Unit of Mass

A new definition of the kilogram is required, an international team of scientists contends. The current one is imprecise, they say, because it is not linked to an unvarying property of nature. The imprecision injects uncertainties in measurements and physical constants used in calculations and calibrations. They urge a redefinition based on a specific value of either the Planck constant or the Avogadro constant.

The kilogram is the base unit of mass in the International System of Units (SI). At present, the unit is defined as the mass of the international prototype of the kilogram--a plum-sized cylindrical artifact made from an alloy of platinum and iridium by Johnson Matthey in 1885. The prototype is kept in a safe, with six official copies, in a vault at the International Bureau of Weights & Measures (BIPM) at Sèvres, on the outskirts of Paris. It was designated as the unit of mass in the metric system in 1889 and has been weighed against its copies three times in the past 100 years--in 1890, 1948, and 1992.

"The previous definition of the kilogram was the mass of the cubic decimeter of water," notes Ian M. Mills, emeritus professor of chemistry at the University of Reading, in England. "The standard was difficult to reproduce accurately because of impurities and air dissolved in water and the variation of density with temperature. BIPM therefore established the kilogram in terms of the prototype."

Mills points out that copies of the artifact calibrated against the prototype at BIPM are available to countries that have signed a diplomatic treaty known as the Convention of the Metre. The convention gives authority to the General Conference on Weights & Measures (CGPM), the International Committee for Weights & Measures, and BIPM "to act in matters of world metrology, particularly concerning the demand for measurement standards of ever-increasing accuracy, range, and diversity, and the need to demonstrate equivalences between national measurement standards." The treaty has now been signed by 51 countries.

Because the international prototype at BIPM is a material artifact, it has one important limitation: It is not linked to an invariant of nature, note Mills and coauthors Terry J. Quinn, emeritus director at BIPM, and scientists Peter J. Mohr, Barry N. Taylor, and Edwin R. Williams at the National Institute of Standards & Technology (NIST) in a recent paper [Metrologia 2005, 42, 71]. They point out that the prototype is accessible only at BIPM and could be damaged or destroyed. "It collects dirt from the ambient atmosphere and must be carefully washed in a prescribed way prior to use," they observe. "It cannot be used routinely for fear of wear, and its mass may be changing with time" perhaps by 50 mg or significantly more per century.

"Unfortunately, as we have not got a more stable mass reference, any drift in mass cannot be measured directly," says Jeff Flowers, a scientist at the National Physical Laboratory (NPL), Middlesex, England.

THE KILOGRAM is one of seven SI base units. The others are the meter (base unit of length), second (time), ampere (electric current), kelvin (thermodynamic temperature), mole (amount of substance), and candela (luminous intensity). Three of these units--the ampere, the mole, and the candela--rely on the definition of the kilogram. Any uncertainty in the definition of the kilogram, therefore, propagates into these three base units. All other SI units of measurement are derived from the seven base units. Derived units such as the newton (force), the joule (energy), and the pascal (pressure) are related to the kilogram.

The kilogram is the only one of the SI base units defined by a physical artifact rather than an invariable property of nature. The meter, for example, was redefined by CGPM in 1983 in terms of a value for the speed of light, which is equal to its wavelength multiplied by its frequency.

"The meter has now been redefined as the distance light travels in a vacuum during one-299,792,458th of a second, and the second is defined in terms of natural vibrations of the cesium atom," Williams says. "The time has come for the definition of the kilogram to also be based on an unchanging natural phenomenon, either a quantity of light or the mass of a fixed number of atoms."

Mills and coauthors note that scientists and engineers use physical constants to make numerous types of calculations. The constants are also used to design and calibrate quantum-based measurement systems that are becoming important in the development of various technologies and in trade that relies increasingly on electronic testing, environmental monitoring, and quality control. A new definition of the kilogram fixed to an invariant of nature would, unlike the Paris prototype, be available to anyone at any time and in any place. The group proposes that the kilogram should be redefined so as to fix its value for all time to a specific value of either the Planck constant or the Avogadro constant, both of which are invariants of nature. The uncertainties of many of the fundamental constants would then immediately be reduced by more than a factor of 10, Mills says.

Redefining the kilogram in this way could have immediate benefits, Quinn says. "For instance, it would improve the precision of certain electrical measurements 50-fold and would enable physicists to make more precise calculations when studying the fundamental quantum properties of matter."

Scientists use the fundamental constants as part of their language to connect experiment and theory and to connect past and present data, Williams points out. "Reducing changes in the constants makes this communication easier," he says. "Artificially large uncertainties caused by the defining of the kilogram as a macroscopic artifact rather than an atomic mass or a fundamental constant could hide important future discrepancies."

The relationship between the Planck constant (h) and mass (m) is given by h = mc², where is frequency and c is the speed of light. Fixing the value of h would fix the definition of the kilogram because the SI base units of length and time are already fixed to invariants of nature.

Currently, the most advanced experimental approach for realizing the definition of the kilogram based on a fixed value of h is the moving-coil watt balance. The apparatus has a balance plate, on which an artifact to be weighed is placed, surrounded by coils of copper wire. When electricity is passed through the coils, magnetic fields that are produced offset the weight of the artifact. Because the electromagnetic forces acting on the balance are related to the force generated by the mass, the experiment links mechanical power--in terms of length, mass, and time--to electrical power, in terms of voltage and resistance. The result is an experimental determination of the mass of an unknown standard, Mills and coauthors explain.

THE MOST ADVANCED method for determining the Avogadro constant uses an X-ray crystal density (XRCD) method to measure the lattice spacing and macroscopic mass density of a single crystal of ultrapure silicon shaped to form a sphere of almost perfect roundness. The result is an experimental determination of the mass of the crystal based on a specific value of the Avogadro constant, Mills and coauthors note.

To date, the most accurate experimental value of the Avogadro constant, based on the fixed mass of the kilogram prototype in Paris, is 6.022141527 x 10²³ per mole of particles (such as atoms or molecules). Mills and coauthors suggest that, if the definition of the kilogram is fixed to the Avogadro constant, the constant should be fixed at this value. The team suggests that the kilogram prototype should be retained as a secondary standard. "Its mass, which would be determined in terms of the new definition by either the watt balance or the XRCD experiment, could then be used to calibrate mass measurements, as is done at present," Mills says. "Eventually, when the watt balance and the XRCD experiments are sufficiently accurate, the kilogram artifact will no longer be needed."

Flowers observes, however, that the silicon sphere used in the XRCD experiment is an artifact. "It will be difficult to ensure that it remains unchanged and to compare it with secondary standards," he notes in a review of atomic and quantum standards (Science 2004, 306, 1324). "Although it could be reproduced if damaged, this would require major and time-consuming effort."

Mills and coauthors note that the Planck constant could be fixed by any physical experiment that links electrical to mechanical quantities and the Avogadro constant by any experiment that counts microscopic entities. Such experiments need to be carried out with the required accuracy, however, and there lies a problem.

According to Flowers, the target accuracy for measurements to define the kilogram is one part in 10⁸. The moving-coil watt balance and XRCD experiments have yet to relate the mass of the kilogram to the Planck and Avogadro constants, respectively, at accuracies much better than one part in 10⁷. Furthermore, the difference in the results from the two approaches is almost one part in 10⁶.

"There is some support for a definition based on the atomic mass unit," Flowers tells C&EN. "Then the kilogram would be, for example, the mass of a certain number of unbound carbon-12 atoms in their ground state." By definition, the mass of 1 mole of carbon-12 atoms at rest and in their ground state is 12 g or 0.012 kg. The kilogram could then be defined as the mass of exactly 6.022141527 x 10²³ such carbon atoms divided by 0.012. The kilogram would thus become an invariant of nature, because the mass of a carbon-12 atom at rest and in its ground state and, therefore, the mass of the Avogadro number (6.022141527 x 10²³) of these atoms are invariants of nature.

"This definition has the advantage of being easily understandable: the large mass is the sum of the microscopic masses," Flowers says. "In practice, however, the watt balance is likely to prove more accurate in overall mass measurement."

THE ADVANTAGE of the watt balance-Planck constant definition is that it is based on electrical units that are exactly based on fundamental constants and on the second, which is also a fundamental constant. "This argument may well sway the metrological community," Flowers says.

Flowers proposes an interim measure in which constants such as the Avogadro constant, the atomic mass unit, the electron volt, and the Planck constant are given agreed values. "These would be additional to the kilogram artifact and not replace it," he says. "Later, when there is good experimental evidence on the situation, a redefinition could be made."

Mills and coauthors argue that redefining the kilogram should proceed without delay and that, for the time being, the artifact in Paris should be retained as a working reference for highly precise comparisons to individual countries' national kilogram standards.

A new definition fixed to the Planck constant or the Avogadro constant would be immediately beneficial, they say. "By retaining the prototype kilogram as a secondary standard, the present excellent worldwide uniformity of 1-kg Pt-Ir mass standards would be maintained, while at the same time the many benefits of having either the Planck or Avogadro constants exactly known would be realized," they suggest. "Moreover, each SI base unit would then be defined in terms of invariants."

The group hopes that the 23rd CGPM, when it next convenes in Paris in October 2007, will adopt a new definition of the kilogram based on the best available numerical values of the Planck or Avogadro constant at the time.