Принципы нанометрологии (1027623), страница 65
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Other NMIs assume that their national kilogram isperfectly stable on return from the BIPM and the mass gain is zero.10.1.5 Limitations of the current definition of the kilogramThe kilogram is unique among the seven base SI units in that it is the onlyone that is still defined in terms of a physical artefact. As an artefact definition its realization and dissemination presents a unique set of practicalproblems.While the theoretical uncertainty associated with the value of K is zero (itis, by definition, exactly 1 kg) the practical accuracy with which the kilogramcan be realized is limited by the stability of the artefact and the repeatabilityof the nettoyage-lavage cleaning process.
Although the BIPM monitor theTraceability of traditional mass measurementstability of K against a number of official copies it keeps, the practical limitof the uncertainty in its value is about 2 mg. Additionally, the value ofplatinum-iridium kilograms has been seen to drift by up to 2 mg per yearalthough K is undoubtedly more stable than this.The fact that one artefact provides traceability for the entire world-widemass scale also presents difficulties. The calibration of the national prototypes presents a problem for the BIPM as it involves a large number ofmeasurements. The use of the nettoyage-lavage cleaning process to returnthe kilograms to a ‘base value’ is not only time-consuming and arduous initself but greatly increases the number of weighings which must be made onthe artefacts.
Values of the kilograms before and after cleaning are calculated,as is the weight gain of the kilograms immediately after the cleaning process,from measurements made over a period of several weeks. Thus, not only isthe work load of the BIPM very high, but the national prototype kilograms arenot available to their NMIs for up to six months.Most NMIs around the world hold only one official copy of the kilogramand thus their entire national mass measurement system is dependent onthe value of their national prototype. This means that the handling andstorage of this weight is very important and any damage means it would atleast have to be returned to the BIPM for re-calibration and at worstreplaced.10.1.6 Investigations into an alternative definitionof the kilogramFor the last twenty years there has been a considerable amount of workundertaken looking for an alternative, more fundamental, definition for theSI unit of the kilogram [12].
This work has been driven by two mainassumptions. The limitations of the stability, realization and disseminationof the kilogram have been discussed in section 2.4. The other reason for there-definition work currently being performed is the perception of the definition using an artefact as ‘low tech’ when compared with the definitions ofthe other six SI base units. For this reason, the approaches to a fundamentalre-definition have in some ways been forced rather than being logical solutions to the problem.
The other base units have more simple definitionsbased on one measurement (such as the wavelength of light for the metre)whereas any of the current proposals for the re-definition of the kilograminvolve a number of complicated measurements. In the same way thetimescale for the re-definition of the other base units was defined bythe discovery of a suitable phenomenon or piece of equipment (for example293294C H A P T ER 1 0: Mass and force measurementthe laser used to define the metre).
A similar method for re-definition ofthe kilogram has yet to be found.At present there are four main methods being investigated with a view toproviding a new fundamental definition for the SI unit of the kilogram. Evenfrom these brief descriptions of the four approaches given in sections10.1.6.1 to 10.1.6.4, it can be seen that the present approaches to the redefinition involve a number of demanding measurements.
Almost all ofthese measurements must be performed at uncertainties which represent thestate of the art (and in some cases much better than those currentlyachievable) to realize the target overall uncertainty of one part in 108 set forthis work. The absolute cost of the equipment also means that the ultimategoal of all NMIs being able to realize the SI unit of the kilogram independently will, on purely financial grounds, not be achievable.All four approaches require traceability to a mass in vacuum both for theirinitial determination and for dissemination.
The significance of the workdescribed in this book, therefore, extends not only to improving knowledge ofthe stability of the current definition of the kilogram but also to facilitatingthe practical use of any of the currently considered methods of re-definition.10.1.6.1 The Watt balance approachThe first proposed re-definition of the kilogram was via the Watt. Bryan Kibbleof NPL proposed using the current balance [13], formerly used to define theampere, to relate the kilogram to a value for Plank’s constant.
The fundamental measurements necessary for the definition of the kilogram by thismethod are the volt (via the Josephson junction) and the ohm (via the quantized Hall effect). Measurements of length, time and the acceleration due togravity are also necessary. There are currently three NMIs working on the Wattbalance project: NPL [14], NIST [15] and METAS in Switzerland [16].10.1.6.2 The Avogadro approachThe Avogadro project will define a kilogram based on a fixed number ofatoms of silicon [17,18]. The mass of a sphere of silicon will be related to itsmolar mass and the Avogadro constant by the following equationm ¼Mm VNA v0(10.2)where m is the calculated mass of the sphere, Mm is the molar mass of thesilicon isotopes measured by spectrometry, NA is the Avogadro constant, V isthe volume of the sphere measured by interferometry and v0 is the volumeoccupied by a silicon atom.Traceability of traditional mass measurementTo calculate v0 the lattice spacing of a silicon crystal must be measured byx-ray interferometry [19] (see section 5.7.2).
The practical realization of thisdefinition relies on the calculation of a value for NA from an initial value forthe mass of the sphere [20]. This value is then set and used subsequently togive values for the mass of the sphere, m. An added complication with thisdefinition is the growth of oxides of silicon on the surface of the spheres. Thethickness of the layer needs to be monitored (probably by ellipsometry) andused to correct the value of mass, m.10.1.6.3 The ion accumulation approachA third approach to the re-definition of the kilogram involves the accumulation of a known number of gold atoms [21,22]. Ions of Au197 arereleased from an ion source into a mass separator and accumulated ina receptor suspended from a mass comparator.
The number of ions collectedis related to the current required to neutralize them supplied by an irradiated Josephson junction voltage source. The mass of ions, M, is then givenby the equationZn1 :n2 :ma tM ¼fðtÞdt(10.3)20where n1 and n2 are integers, ma is the atomic mass of gold, f(t) is thefrequency of the microwave radiation irradiated onto the Josephson junctionand ma ¼ 197 u, for gold isotope Au197, where u is the atomic mass unit(equal to 1/12 of the mass of C12).10.1.6.4 Levitated superconductor approachAs with the Watt balance approach, the levitated superconductor methodrelates the unit of the kilogram to electrical quantities defined from theJosephson and quantized Hall effects [23].
A superconducting body is levitated in a magnetic field generated by a superconducting coil. The currentrequired in the superconducting coil is proportional to the load on thefloating element and defines a mass (for the floating element) in terms of thecurrent in the superconducting coil [24–26].10.1.7 Mass comparator technologyFrom the earliest days of mass calibration, the measurements have beenmade by comparison, each weight or quantity being compared witha standard of theoretically better accuracy.
A series of comparisons wouldthus allow all measurements to be eventually related back to a primarystandard, whether it was a naturally occurring standard (such as a grain of295296C H A P T ER 1 0: Mass and force measurementwheat) or an artefact standard such as the current international prototypekilogram.Until recently these comparisons have been performed using two-panbalances. From the earliest incarnations to the present day the technologyhas relied on a balance beam swinging about a pivot normally at the centre ofthe beam.
The mechanical quality of the beam and in particular the pivot hasbeen refined until modern two-pan mechanical balances are capable ofresolutions of the order of one part in 109, equivalent to 1 mg on a 1 kg massstandard.10.1.7.1 The modern two-pan mechanical balanceTwo-pan balances consist of a symmetrical beam and three knife-edges. Thetwo terminal knife-edges support the pans and a central knife-edge acts asa pivot about which the beam swings. Two-pan balances are generally undamped, with a rest point being calculated from a series of turning points.Some balances incorporate a damping mechanism (usually mechanical ormagnetic) to allow the direct reading of a rest point.Readings from two-pan balances tend to be made using a simplepointer and scale although some use more complicated optical displays.In all cases the reading in terms of scale units needs to be converted intoa measured mass difference.
Capacities of such balances range from a fewgrams up to several tonnes. The resolution of smaller balances is limitedto the order of 1 mg by the accuracy with which the central knife-edge canbe polished.10.1.7.2 Electronic balancesElectronic balances are usually top-loading balances with the applied loadbeing measured by an electro-magnetic force compensation unit or a straingauge load cell.
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