The kilogram is the last SI unit to be represented by a physical artefact. But not for long.

7 mins read

A Century ago, two of the basic units of measurement – length and mass – were calibrated against physical artefacts.

In the case of length, it was a platinum-iridium bar; for mass, it was a cylinder of the same material. The second, meanwhile, was defined as 1/86,400 of a mean solar day. Today, the metre and the second are defined using physical constants: an approach that allows these units to be reproduced in labs around the world. But the kilogram is still defined by a lump of metal kept in a safe in Paris by the International Bureau for Weights and Measures, or BIPM. The question now is for how much longer? Because work by researchers around the world to find a more elegant way of defining mass is reaching the point where the artefact can finally be replaced. Why should organisations like BIPM want to get rid of what is seemingly a good idea – a lump of metal of known mass against which other masses can be compared? The answer is simple: the International Prototype of the Kilogram (IPK), to give the artefact its proper title, may be gaining or losing material. Dr Ian Robinson, an NPL Fellow who has been closely involved with the development of alternative methods to define the kilogram, said it's difficult to know whether the IPK is gaining or losing mass. "There's only one in the world and it doesn't come out very often. The more it gets used, the more it may change. Amongst the many questions that get asked is whether the kilogram is as clean as it was." Nevertheless, Dr Robinson accepts that the IPK has been useful. "It has worked for more than 100 years," he noted, "and has hung in there because it has been difficult to replace." There is much interest in the future of the kilogram. The International Committee for Weights and Measures (CIPM), recommended in 2005 that the kilogram be redefined in terms of a fundamental constant of nature and the General Conference on Weights and Measures (CGPM) has agreed in principle that the kilogram should be redefined in terms of the Planck constant. It is hoped that at CGPM's next meeting – planned for 2014 – the IPK may be retired. What stands in the way of the decision is the development of devices which can measure Planck's constant to within acceptable limits. One of the methods being refined in the pursuit of the 'virtual kilogram' is the watt balance – invented at NPL by Dr Bryan Kibble. Another approach is the Avogadro Project, which is based on counting the number of atoms in a sphere of silicon. Both are pointing at the same problem, but from different directions. The watt balance provides a means of equating electrical and mechanical power. Dr Robinson said: "Dr Kibble thought up the defining step and it's that idea that allows the watt balance to work." In theory, mass could be defined by equating the mechanical energy needed to raise a mass over a known distance to the amount of electrical energy consumed by a motor in raising the mass. But there are energy losses – friction and heat, for example – that mean the values don't equate satisfactorily. A refinement is to 'weigh' the mass against the force produced by a current flowing through a coil suspended in a magnetic field. "Because the mass doesn't move," Dr Robinson explained, "there are no relevant losses. But you do need to know the relationship between current and force and that's not easy because it depends on field strength and the length of wire in the coil." Dr Kibble's 'Eureka' moment came when he realised that if a second experiment was performed, where the mass was removed and the coil was moved through the field at a measured velocity, then the relationship between the voltage generated by the coil and the velocity was exactly the same as the relationship between the force and the current. Combining the results of the two experiments eliminates the effects of the constant field and length of wire and equates the product of voltage and current – electrical power – to the product of mass, gravity and velocity – mechanical power. If you know voltage from the Josephson effect, current from the quantum Hall effect and Josephson Effect, acceleration due to gravity from a local gravimeter and velocity from a laser interferometer, it is possible to define mass in terms of Planck's constant. "It's not easy to do," Dr Robinson said, "but it is possible to do the experiment to the level of uncertainty that you require." And it's the level of uncertainty which is holding back the move to define the kilogram in terms of physical constants. For the move to be made, the definition using Planck's constant needs to be more accurate than using the IPK. The IPK's mass has been shown to vary, as have the masses of the so called 'witnesses' – official copies held at the BIPM. While the mass of the IPK has been assigned a constant value, the witnesses – seemingly identical cylinders of the same alloy – have changed weight. And nobody knows why. "If the IPK is changing mass and you are relating fundamental constants to it, then there are problems," he contended. What's also required is a number of watt balances around the world to feed into the maintenance of a 'good average' for maintaining the mass standards of the world after redefinition. Dr Robinson explained: "It creates an egalitarian measurement system in that no one watt balance need be any better than any other." He believes that, in the long run, 'three or four' watt balances will be needed to maintain that 'good average' and to show whether one 'piece of kit' is producing discrepant results. Watt balance approach gains momentum Much of the development effort for watt balances has been contributed by NPL and by NIST in the US. "But the approach has gained momentum with addition of others, including METAS in Switzerland and LNE in France," he noted. "And BIPM is building one; if the kilogram is to be redefined, it also needs a watt balance." The watt balance is a complex piece of equipment. "They aren't small," Dr Robinson pointed out, "and they need a lot of associated equipment. They need to operate in a vacuum to remove the effect of air buoyancy on the mass and it's useful to have them on a stable base. For the NPL balance, it was also necessary to maintain the magnet at a constant temperature – within tens of µK at room temperature." More modern balances are designed to reduce this need. Even the surroundings of the building in which the watt balance is housed can contribute to measurement uncertainty. "Trees can lever against the building," Dr Robinson said, "and, when the wind blows, measurement noise can double." Beyond that, you need to bear in mind the rotation axis of the Earth – that moves around on a 15m diameter circle – barometric pressure and the acceleration due to gravity. "There are some 50 uncertainty components which you have to think about when making measurements; that's quite a lot and you have to keep them under control," Dr Robinson noted. "But we have to lock the value of Planck's constant because its recommended value changes every four years. We are trying to bring things into agreement and get a consensus value for Planck's constant that will, in future, determine mass." Once Planck's constant can be measured to within 20ppb, the kilogram can then be redefined and the uncertainty that was associated with Planck's constant will be transferred to the IPK. Dr Robinson concluded: "The IPK will still weigh 1kg, but with an uncertainty. If the kilogram was drifting before, it will stop – and that's the benefit. There will be a distributed and more robust mass system." Canada's National Research Centre makes watt balance progress Canada's National Research Centre (NRC) purchased the NPL's watt balance in 2009 and is completing a set of experiments to improve its performance. Barry Wood, an NRC research officer in electrical standards, said good progress is being made. "Our first set of experiments aimed to repeat measurements made at NPL. Having done that," he said, "we tried to validate some of the uncertainties and corrections. One modification was an attempt to eliminate mass/force exchange errors. "We then made a second set of measurements and were pleased to get results similar to the first set, but with smaller uncertainty. Our estimate of the mass exchange error was correct and the result gave us the belief that the modification had been done properly. "Further modifications have been made to address coil suspension and alignment issues – which represent the single biggest uncertainty – and we'll be starting a third set of measurements shortly." The first round showed Planck's constant was measured to an uncertainty of 68ppb, while the second round was 35ppb. "We think we can get down to approximately 30ppb in the third round," Wood added. Yet an uncertainty of 30ppb will not on its own satisfy the CPIM's most stringent requirement. The Paris based organisation is looking for one lab to measure to within an uncertainty of 20ppb and for two others to measure to within 50ppb. If the kilogram is to be redefined, CIPM has to make a recommendation to CGPM, which would have to ratify such a change. "If NRC and NIST can produce results of 50ppb or better and Avogadro (see below) can do 20ppb, this could, in principle, satisfy the conditions," Wood concluded. The Avogadro Project - counting atoms to define mass The Avogadro Project is looking to define the kilogram in terms of a fixed number of atoms of a given substance. Silicon has been suggested as a suitable material because it can be grown as a large single crystal – the silicon ingot is, of course, the foundation of semiconductor manufacturing. The project is attempting to create perfect polished spheres of 28Si. "If you can do that," said Dr Ian Robinson from the UK's NPL, "you can measure the diameter and, hence, the volume. An optical interferometer allows the diameter of the sphere to be measured to within the depth of an atomic layer. But the fact that silicon forms an oxide 'crust' is a complicating factor. "The spacing between the atoms can be determined using combined X-ray and optical interferometry and the volume occupied by an atom can be calculated. Combining the measurements gives the number of atoms in the sphere." Because the mass of the sphere can be measured, the Avogadro constant can be calculated and transformed accurately into a corresponding value of the Planck constant. This provides a powerful check on the consistency of both approaches to the redefinition of the kilogram.