We need a new definition for the kilogram! The present

definition was sanctioned by the first General Conference on Weights and Measures (CGPM, Conférence Général des Poids et Mesures) in 1889, with a minor revision to the words in 1901, and remains unchanged after 116 years. It is the

only base unit of the International System of Units (the

SI) that is still defined in terms of a prototype artifact,

the International Prototype of the Kilogram (IPK), which is kept in a safe at the International Bureau of Weights and Measures (the BIPM, Bureau International des Poids et Mesures) in Sèvres, near Paris

Mills, Ian

English

Mills,  I.

Central Archive at the University of Reading

An update on the kilogram

g12 CHEMISTRY International    September-October 2005by Ian MillsWe need a new definition forthe kilogram! The presentdefinition (see highlightbelow) was sanctioned by the firstGeneral Conference on Weights andMeasures (CGPM, ConférenceGénéral des Poids et Mesures) in1889, with a minor revision to thewords in 1901, and remainsunchanged after 116 years. It is theonly base unit of the International System of Units (theSI) that is still defined in terms of a prototype artifact,the International Prototype of the Kilogram (IPK),which is kept in a safe at the International Bureau ofWeights and Measures (the BIPM, Bureau Internationaldes Poids et Mesures) in Sèvres, near Paris.The definitions of the base units play a key role inmodern metrology, a subject of ever greater impor-tance in our society. International trade, macro-engi-neering such as the construction of aircraft wingsmade in Britain to fit a hull made in France, micro-engineering such as the manufacture of integratedelectronic chips with many thousands of elements, themeasurement of drug concentrations in medicine, themeasurement of pollutants in the environment—allthese, and many more, demand reliable measurementsto an appropriate level of accuracy for the purposeconcerned, and with a known and appropriate uncer-tainty. In defining the units of the SI upon which thissubject is built, we endeavor today to choose defini-tions that are referenced to quantum properties ofatoms or to fundamental constants, a subject knownas quantum metrology. Thus, our unit of length (themetre) is defined in terms of the speed of light, andour unit of time (the second) in terms of the period ofthe hyperfine frequency of a caesium atom. These arebelieved to be “invariants of nature,” available to any-one, anywhere, at any time, and thus are appropriatereferences for the internationally agreed units of oursystem. The present definition of the kilogram in terms of theIPK does not fulfill this requirement, and moreoverthere are good reasons for believing that the mass ofthe IPK, along with all its official copies, may be “drift-ing” in relation to a true invariant such as the mass of acarbon atom, by perhaps as much as 100 µg (0.1 ppm,or a part in 107) over 50-year periods. The IPK, a cylin-der of platinum-iridium alloy measuring 39 mm high by39 mm diameter, has been weighed against its variouscopies three times since it was made: in the 1890s, inthe late 1940s, and most recently in the late 1980s. Theconclusion from these periodic reviews is that the var-ious kilogram artifacts may well be changing in mass.This is believed to be due to surface contamination(they are stored and weighed in air), wear and tearfrom handling, and the possible leaching out of gasesoccluded in the artifact when it was manufactured. We would like a new definition, and we would likeone that would fix the kilogram in terms of what webelieve to be an invariant of nature, such as a funda-mental constant or the mass of an atom. Draft word-ing for two possible new definitions of the kilogramthat have been discussed for the past fifteen years ormore are shown below. It may not be obvious that fixing the value of thePlanck constant defines the kilogram: it does so,because h = 6.626... J s = 6.626... kg m2 s-1, and sincethe metre and the second are already defined in termsof invariants, the value of the kilogram is fixed oncethe numerical value in this expression is fixed. Similarlym(12C) = (0.012 / 6.022... x 1023) kg, and fixing thenumerical value in this expression has the effect ofdetermining the value of the kilogram in the secondalternative definition. There are two experiments that are relevant to thesetwo alternative definitions. The first is the watt balanceexperiment, in which a weight is measured against theelectrical force generated by a coil carrying a currentAn Update on the Kilo ramPresent definition of the kilogram: The kilogram is the unit of mass; it is equal to themass of the international prototype of the kilogram.First alternative—draft definition of the kilogram to fixthe Planck constant h:The kilogram is the mass of a body at rest such thatthe value of the Planck constant h is exactly 6.626 069 311 x 10-34 joule second.Second alternative—draft definition of the kilogram to fixthe mass of the carbon 12 atom m(12C), and also to fixthe atomic mass constant mu and the value of theAvogadro constant NA:The kilogram is the mass of exactly (6.022 141 527x 1023 / 0.012) unbound carbon 12 atoms at rest andin their ground state.suspended in a magnetic field. The electrical measure-ments are made using the Josephson and quantum halleffects. The second is the X-ray crystal density experi-ment, in which a perfectly spherical single crystal of sil-icon (see photo on cover of this issue) is weighedagainst a kilogram standard, andits lattice spacing is measured byX-ray diffraction, allowing a cal-culation of the number of atomsin the crystal from its diameter.The watt balance leads to ameasurement of the Planck con-stant h in terms of the kilogram,and the X-ray crystal densityexperiment leads to a measure-ment of the Avogadro constantNA in terms of the kilogram.However, if we were to fix thevalue of h, it would define thekilogram, and the watt balancecould then be used to realize thedefinition. Similarly, if we were tofix the value of NA it woulddefine the kilogram, and the sili-con crystal density experimentcould be used to realize the def-inition. Both experiments are complex, and both areexpensive and difficult to perform with high accuracy.The present relative uncertainty of measurement inthese experiments is about 0.08 ppm for the watt bal-ance experiment, and about 0.4 ppm for the X-raycrystal density experiment.Either of the two alternatives would give us a defi-nition referenced to an invariant of nature, in place ofthe somewhat uncertain platinum-iridium prototypeused in the present definition. Either could be realizedby the experiments described in the previous para-graph, and would also give us a reference available toanyone, anywhere, at anytime, unlike the prototypereference that remains locked in a safe in Sèvres.However, a recent paper by Mills, Mohr, Quinn, Taylor,and Williams, Metrologia 2005, 42, 71–80, has drawnattention to the fact that there are further importantconsiderations involved in changing the definition.All mass measurements are relative. We measurethe mass of one object against another. Our ability tomake such measurements has improved dramaticallyin the last 100 years, and even during the last 10 years.To discuss the uncertainties in such experiments wehave to consider two distinctly different kinds of massmeasurement. On the one hand, we may be concernedwith measuring the mass of macroscopic objects,measured in grams or kilograms, usually using a bal-ance of some kind. This, to most of us, is the kind ofmass measurement that immediately springs to mind;we might call it “macroscopicmass metrology.” The referencestandard for such measure-ments is (at present) the proto-type kilogram—the IPK—used inthe current definition of the kilo-gram. The IPK has proved a con-venient reference for makingmacroscopic mass measure-ments, and even if we changethe definition to one of the alter-natives, it is likely to remain animportant intermediate step inrelating mass standards aroundthe world for macroscopic massmeasurements.On the other hand, physicistsand chemists are concernedwith the masses of atoms andfundamental particles, whichmay be compared with eachother by mass spectrometry, for example. The refer-ence standard for these measurements is the unifiedatomic mass unit, symbol u, defined as one-twelfth ofthe mass of a carbon 12 atom, also known as theatomic mass constant mu.* We might call such meas-urements “microscopic mass metrology.” It is also afact that the best estimates of the values of many ofthe fundamental constants of physics, such as thePlanck constant h and the elementary charge e arestrongly correlated with the atomic masses, so thatwhenever we discuss the masses of the atoms wehave also to consider the values of the fundamentalconstants.The present situation is that relative mass measure-ments within either the field of macroscopic or micro-scopic masses can be made with very much higherprecision than that with which we are able to comparemasses between the two fields. For example, it is pos-sible to compare the mass of two kilogram artifacts,13CHEMISTRY International    September-October 2005*This unit is also known as the dalton, symbol Da. Thelatter name and symbol is widely used by biochemistsand others concerned with the mass of large mole-cules that may be measured in kilodaltons, kDa, ormegadaltons, MDa. Thus 1 Da = 1 u = mu = m(12C) / 12.The kilogram, kept by the BureauInternational des Poids et Mesures.14 CHEMISTRY International    September-October 2005using the best modern balances, to better than a partin 109, a relative uncertainty of less than 0.001 ppm, orless than a microgram in a kilogram. Similarly, themass of an electron me can be determined relative tothe unified atomic mass constant mu with a relativeuncertainty of 4.4 parts in 1010, 0.00044 ppm.However, when it comes to measuring the mass of anyof the fundamental particles in terms of the present SIkilogram, the uncertainty is about 2 parts in 107, 0.2ppm, a relative uncertainty more than two orders ofmagnitude greater. Such measurements are depend-ent on either the watt balance or the silicon crystaldensity experiment. The present uncertainty in ourbest measurement of me/kg, for example, is 0.17 ppm,and there is a similar uncertainty in all atomic and par-ticle masses when they are expressed in the present SIkilogram. Moreover, most of the fundamental con-stants of physics depend on the kilogram (see tableabove). The best estimates of these constants arerevised at intervals by the CODATA (Committee onData for Science and Technology) task group estab-lished for this purpose. The most recent 2002 revisionwas published earlier this year (Mohr and Taylor, Rev.Mod. Phys. 2005, 77, 1–107). This review shows thatthe present relative uncertainties in the fundamentalconstants, when expressed in SI units, are mostlyaround 0.2 ppm. In every case the dominant contribu-tion to this uncertainty is simply the uncertainty inrelating atomic or particle masses to the macroscopicreference kilogram, the IPK.The present situation regarding redefining the kilo-gram is, therefore, as follows. If we were to change toa new definition using a fundamental constant or anatomic mass as a reference, it would follow immedi-ately that all particle masses and fundamental con-stants would be known with an uncertainty reducedby two orders of magnitude—because their valuesexpressed in SI units would no longer involve a knowl-edge of the bridge between macroscopic and micro-scopic masses. Both the elementary charge e and theJosephson constant KJ would also be more accuratelyknown by a similar factor, so that all electrical meas-urements made using these constants would be simi-larly improved. These are important advantages. Theeffect on the values of the fundamental constants isillustrated in the table on page 15. However, the massof the IPK would no longer be 1 kg by definition, butwould have to be determined by experiment.Although the constant appearing in the new definitionwould be chosen so that the mass of the prototypewould initially still be exactly 1 kg, it would be subjectto the uncertainty of about 0.2 ppm that applies to allatomic masses under the present definition, and it isalso possible that future measurements would lead usto revise the mass of the IPK so that it might beslightly different from 1 kg. Although it is unlikely thatthis change would ever be greater than 0.2 ppm, thisis seen as a disadvantage of changing the definition bythose concerned with macroscopic mass metrology.Mills et al. suggest that, after changing the definition,macroscopic mass measurements could continue tobe made in terms of the mass of the IPK, with a cor-rection factor being applied in those rare occasionswhen it is really necessary.If, however, we retain the present definition, thenthe values of the fundamental constants expressed inSI units will remain uncertain to about 0.2 ppm, just asthey are at present. The mass of the IPK will remainequal to 1 kg by definition—although this would notdispel doubts arising from the uncertainty of the massof the IPK compared to an invariant of nature. Themagnitude of this uncertainty is not known, but it isbelieved to be of the order 0.05 ppm, or possibly asmuch as 0.1 ppm. In this brief review it is not possible to cover all theproblems of redefining the kilogram, and readers arereferred to the paper by Mills et al. for further details.However, there is one further point to note here, whichconcerns the timing of any possible change. Changesto the base units of the SI are made by the CGPM, onthe advice of the CIPM (International Committee forWeights and Measures) and its various consultativecommittees. The CGPM meets at four-year intervals,Atomic mass constant muElectron mass mePlanck constant hAvogadro constant NAElementary charge eJosephson constant KJProton gyromagnetic ratio γpFaraday constant FBohr magneton µBNuclear magneton µNSome of the fundamental constants whose values depend on the kilogramAn Update on the KilogramThere is little doubt that thedefinition of the kilogram willeventually be changed to one of thetwo alternatives . . .15CHEMISTRY International    September-October 2005and the next two meetings will be in October 2007and in October 2011. There is little doubt that the def-inition of the kilogram will eventually be changed toone of the two alternatives, but there are differentopinions about when to make the change. The argument for making the change as soon aspossible is that once we change to one of the pro-posed alternative definitions, we shall know the valuesof the fundamental constants with much reduceduncertainty, and, moreover, future CODATA reviewscan only lead to zero or very small changes in theirvalues. We shall also be using a kilogram defined byreference to an invariant of nature. This has to be setagainst the fact that improved watt balance results ina few year’s time might perhaps lead to small changesin our estimate of the mass of the IPK, which willalmost certainly continue to be used as an intermedi-ate reference standard in macroscopic mass measure-ments. But such changes are unlikely to be greaterthan the believed uncertainty arising from the drift inthe mass of the IPK compared to a true invariant.On the other hand, the possible advantage in post-poning the change is that new watt balance results inthe next few years cannot lead to any change in themass of the IPK, which will always be 1 kg by definition,although, of course, doubts about the drift of its truemass will remain. However, we would lack the advan-tage of lower uncertainties in the fundamental con-stants, and new watt balance measurements mightlead to significant changes in the fundamental con-stants in future CODATA reviews. This would be aninconvenience to atomic and molecular physicists, andto electrical metrologists who make use of theJosephson constant and the elementary charge. Thechoice is between redefining the kilogram now—sothat it is referenced to an invariant of nature, and thefundamental constants are more exactly known andwill not be subject to significant future changes—orpostponing the decision until new experiments havereduced the uncertainty in the relation between theatomic masses and the IPK to some chosen value, per-haps 2 or 3 parts in 108, and putting up with the dis-advantages in the meantime.In writing this short article, I have tried to presentthe various arguments objectively, without takingsides. However, I must conclude by saying that I per-sonally find the arguments for making the change assoon as possible to be compelling. I would also preferthe new definition chosen to fix h rather than NA,although the difference is small, because of the centralplace that the Planck constant has as the fundamentalconstant of quantum physics. Ian Mills <i.m.mills@reading.ac.uk> has been the IUPAC Representative on BIMPsince 1996. He is a professor at the University of Reading. Key to Definitionsa. m(K) fixed (present definition)b. h fixed (first alternative definition)c. NA fixed (second alternative definition)valuerelative uncertaintymass of international prototype m(K )a. 1.000 000 00 kg (exact)b. 1.000 000 00 0.17 ppmc. 1.000 000 00 0.17 ppmPlanck constant ha. 6.626 069 3 x 10-34 J s 0.17   ppmb. 6.626 069 311 (exact)c. 6.626 069 311 0.0067 ppmAvogadro constant NAa. 6.022 141 5 x 1023 mol-1 0.17   ppmb. 6.022 141 527 0.0067 ppmc. 6.022 141 527 (exact)electron mass mea. 9.109 382 6 x 10-31 kg 0.17    ppmb. 9.109 382 551 0.0067  ppmc. 9.109 382 551 0.00044 ppmelementary charge ea. 1.602 176 53 x 10-19 C 0.085  ppmb. 1.602 176 532 0.0017 ppmc. 1.602 176 532 0.0050 ppmValue and relative standard uncertainty, for the massof the IPK, m(K), and for a small selection of funda-mental constants, for three different definitions of thekilogram (abstracted from Mills et al., Metrologia 2005):An Update on the Kilogram

An update on the kilogram

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