Text 2. The century-old artifact that defines the kilogram, the fundamental unit of mass, is to be replaced by a more accurate standards based on an invariant property of nature

Weighty Matters. By: Robinson, Ian, Scientific American, 00368733, Dec2006, Vol. 295, Issue 6

In an age when technologies typically grow obsolete in a few years, it is ironic that almost all the world's measurements of mass (and related phenomena such as energy) depend on a 117-year-old object stored in the vaults of a small laboratory outside Paris, the International Bureau of Weights and Measures. According to the International System of Units (SI), often referred to as the metric system, the kilogram is equal to the mass of this “international prototype of the kilogram” (or IPK) – a precision-fabricated cylinder of platinum-iridium alloy that stands 39 millimeters high and is the same in diameter.

The SI is administered by the General Conference on Weights and Measures and the International Committee for Weights and Measures. During the past several decades the conference has redefined other base SI units (those set by convention and from which all other quantities are derived) to vastly improve their accuracy and thus keep them in step with the advancement of scientific and technological understanding. The standards for the meter and the second, for example, are now founded on natural phenomena. The meter is tied to the speed of light, whereas the second has been related to the frequency of microwaves emitted by a specific element during a certain transition between energy states.

Today the kilogram is the last remaining SI unit still based on a unique man-made object. Reliance on such an artifact poses problems for science as measurement techniques become more precise. Metrologists (specialists in measurement) are therefore striving to define mass using techniques depending only on unchanging properties of nature. Two approaches seem most promising – one based on the concept underlying the Avogadro constant, the number of atoms in 12 grams of carbon 12, and the other involving Planck's constant, the fundamental value physicists use, for example, to calculate a photon's energy from its frequency. Because scientists measure constants in SI units (including the kilogram), any drift in the IPK's real mass will give rise to a drift in the value of a measured constant – a seeming paradox for what is commonly considered an immutable phenomenon. In the process of more accurately redefining the kilogram independently of the IPK, however, scientists will choose a best estimate of the constant's value and thus “fix” it.

Check your comprehension

~ What natural phenomena are the standards for the meter and the second based on?

~ Which SI units are based on unique man-made objects?

Web of Measurements

THE PRESENT DEFINITION of the kilogram requires that all SI mass measurements carried out in the world be related to the mass of the IPK. (“Mass” is commonly equated with “weight,” but technically the “mass” of an object refers to the amount of matter in it, whereas its “weight” is caused by the gravitational attraction between the object and the earth.) To forge this link, metrologists remove the IPK from its sanctuary every 40 years or so to calibrate the copies of the IPK that are sent to the International Bureau of Weights and Measures by the 51 national signatories of the “Meter Convention” – the treaty that governs the SI. Once equilibrated, these copies are used to calibrate all other mass standards of the member states in a long, unbroken sequence that propagates down to the weighing scales and other instruments employed in laboratories and factories around the globe.

It makes economic sense to have a stable, unchanging standard of mass, but evidence indicates that the mass of the IPK drifts with time. By observing relative changes of the other mass standards fabricated at the same time as the IPK and by analyzing old and new measurements of mass-related fundamental constants (which are thought not to change significantly over time), scientists have shown that the mass of the IPK could have grown or shrunk by 50 micrograms or more over the past 100 years. The drift could have been caused by such things as accumulated contamination from the air or loss from abrasion. Because the base units of the SI underpin worldwide science and industry (via the national standard calibration chains), ensuring that they do not vary with time is critical.

Based on Nature

THE SAME INCONSTANCY that plagues the definition of the kilogram previously affected the second and the meter. Scientists once defined the second in terms of the rate of rotation of the earth. In 1967, however, they redefined it to be “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.” Metrologists introduced this change because the rotation rate of our planet is not constant, whereas the wavelength of the radiation emitted by cesium 133 during a specific transition – that is, the ticking of an atomic clock – does not alter with time and the measurement can be reproduced anywhere in the world.

Although the definition of the second is not based on an artifact, it suffers from its dependence on a particular transition of a specific atom, which unfortunately turns out to be more sensitive to electromagnetic fields than is desirable. The definition may need to be changed in the future to accommodate the even more precise optical clocks that physicists are now developing.

The definition of the meter, on the other hand, is firmer. The SI originally based the meter on an artifact – the distance between two lines inscribed on a highly stable platinum-iridium bar. In 1983 the meter definition was switched to “the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.” This definition should also be resilient because it fixed the value of a key physical constant, the speed of light, at exactly 299,792,458 meters a second. Thus, progress in the control and measurement of the frequency of electromagnetic radiation (the number of sinusoidal vibrations a second) will merely improve the accuracy with which scientists can measure the meter – with no change in the unit’s definition required.

Check your comprehension

~ What is the difference between the notions of “mass” and “weight”?

~ What could cause drift of the mass of the IPK with time?

~ What influences a particular transition of a specific atom (the cesium 133 atom)?

Atomic Accounting

TO REDEFINE THE KILOGRAM in terms of a physical constant, metrologists measure the value of the constant as accurately as possible using the existing definition of the mass unit. This number can then be incorporated into the new definition to ensure a seamless transition between the old and new ones. Researchers can then employ the measurement method, in conjunction with the now fixed value of the constant, to determine mass according to the new definition.

One promising approach relates the kilogram to the mass of an atom by quantifying the kilogram as the mass of a certain number of atoms of a selected element. This route would fix the value of the Avogadro constant, which is defined as the number of atoms of a specific element in a mole – about 6.02 x 10²³ atoms. (A mole is the amount of an element that has a mass in grams equal to the element's atomic weight; a mole of carbon 12 has a mass of 12 grams.) The problem with this strategy, however, is that it requires one to count enough atoms to make a weighable quantity of material for comparison with a kilogram mass. Because several physical effects limit the accuracy and resolution of balances to around 100 nanograms, a minimum of five grams of material would be needed to approach the target accuracy of approximately two parts in 100 million. Sadly, physicists cannot count out atoms rapidly enough; even if a counter capable of tallying individual atoms at a rate of one trillion a second could be produced, the device would take about seven millennia to tally enough carbon 12 atoms.

Scientists could, however, determine the number of atoms in a perfect crystal by dividing the volume of the crystal by the volume occupied by a single atom. If the crystal is then weighed and the mass of the atomic species that makes up the crystal is known relative to that of carbon 12, they can calculate the Avogadro constant from these data, thereby providing a path to the redefinition of the kilogram.

This more practical method, which is now being pursued, first measures the volume occupied by an atom by determining the regular spacing of atoms within a nearly perfect crystal (with a known number of atoms per unit cell) of known weight, close to one kilogram. Then, by determining the dimensions of the crystal, scientists can find the total volume, from which the mass of an atom in the sample can be calculated. The Avogadro constant, which is calculated from the ratio of the molar mass of an element to the mass of an atom, could then be derived from the results.

Although this plan is simple in concept, researchers have difficulty implementing it because of the extreme degree of precision it entails. Indeed, the high complexity and cost of this project mean that no one facility can hope to carry it out alone. Consequently, the load is being shared among a consortium of laboratories in Australia, Belgium, Germany, Italy, Japan, the U.K. and the U.S. – the International Avogadro Coordination. For this technique to work, the crystal must have an almost perfect structure; it must contain few voids or impurities. Project scientists chose to make the crystal out of silicon because the semiconductor industry has studied it closely and has developed procedures to grow large, practically perfect, single crystals. Once researchers had completed all the measurements of the crystal, they could relate the results to the carbon 12 definition of the mole using the extremely precise relative atomic masses of silicon and carbon obtained from mass spectrometers.

Check your comprehension

~ How is the Avogadro constant defined?

~ Why was it necessary to establish the International Avogadro Coordination?

To begin the procedure, they cut several samples from a raw crystal. One was polished to form a one-kilogram sphere to measure. Planners selected a rounded shape because a ball has no corners that could get knocked off and because craftsmen already knew how to hone silicon into a close approximation of a perfect sphere. Australian technicians fabricated a sphere with a diameter of 93.6 millimeters that departs from the ideal by no more than 50 nanometers. If each silicon atom were the size of a large marble¹ (about 20 millimeters across), the sphere would equal the approximate size of the earth, and the distance between the highest and lowest “altitude” on its surface would be about seven meters (about 350 marbles in length).

To find the volume of the silicon sphere, researchers had to determine its average diameter to within the diameter of an atom. They first carefully reflected laser light of a known frequency off opposite sides of the sphere in a vacuum and gauged the difference in light paths (in wavelengths) with the sphere present and absent. This step enabled them to find its diameter in meters, as the wavelength of the light is equal to the (fixed) speed of light divided by the known laser frequency. Scientists then calculated the volume from the diameter, together with a few small corrections related to the slightly imperfect shape of the crystal and the optical properties of the surfaces.

Researchers obtained the volume occupied by one atom using combined x-ray and optical interferometry to find the distance between atomic planes in a sample cut from the raw crystal. Technicians machined several slots into the sample so that one part of the crystal could be moved reproducibly with respect to the rest of it while maintaining the angular alignment of the atomic planes. The sample was placed in a vacuum and illuminated with x-rays having a wavelength small enough to reflect easily from the atomic planes in the crystal. They then used the strength of this reflection, which varies according to the relative position of the atomic planes in the moving and stationary parts of the crystal, to count the number of plane spacings the repositioned part of the crystal had shifted. Scientists simultaneously measured the translation distance using a laser interferometer that used light of a known frequency. This technique determined the interplane spacing in meters. Using knowledge of the crystal structure, they then found the volume occupied by an atom.

Metrologists ascertained the mass of the crystal sphere by “substitution weighing” using a conventional balance and a “tare mass,” whose mass must be stable but need not be known. They placed the sphere on a balance and compared it against a separate one-kilogram tare mass sitting on the other arm of the balance. They then substituted the sphere with a mass known in terms of the IPK mass standard and repeated the weighing process. Because the substitution was carried out so that the balance remained unaffected by the switch, the difference in the two readings gave the difference in mass between the sphere and the mass standard, which revealed the mass of the sphere. This method eliminated error arising from factors such as unequal lengths of the balance arms.

The researchers also analyzed other samples of the silicon material to establish the relative abundance of the various isotopes to account for their differing contributions to the molar mass of the sphere. To accomplish this task, they had to determine the proportion of the three isotopes – silicon 28, silicon 29 and silicon 30 – present in the natural silicon crystal. For this step they used mass spectroscopy, which separates charged isotopes according to their different charge-to-mass ratios.

The IAC has nearly completed work on the natural silicon spheres, having thus determined the number of atoms in a one-kilogram sphere with an accuracy close to three parts in 10 million. But this accuracy is not good enough. To achieve higher levels, the group is producing a sphere that consists almost entirely of a single isotope, silicon 28. Making such an object will cost between $1.25 million and $2.5 million. Gas centrifuges in Russia that were once employed to refine weapons-grade uranium are purifying the material for the new sphere. The consortium is aiming for an uncertainty in the final result of about two parts in 100 million.

Check your comprehension

~ How did scientists define the volume of the silicon sphere?

~ How “substitution weighing” was conducting?

~ How will the accuracy of determining the number of atoms in a one-kilogram sphere increase after gas centrifuges in Russia have been used?