Принципы нанометрологии, страница 63

Measurements using coherence scanninginterferometry have shown typical surface roughness (Ra) values of 65 nm to85 nm for hand-polished weights, compared with 10 nm to 15 nm achievedby diamond turning [7].10.1.3 Dissemination of the kilogramThe BIPM is responsible for the dissemination of the unit of mass worldwide.Dissemination is achieved via official copies of the International PrototypeKilogram, known as national prototypes, held by all countries that aresignatories to the Metre Convention. These are periodically compared, at theBIPM, with the International Prototype.

The official copies of the kilogramare, like the original, made of platinum-iridium alloy and the final machiningand adjustment is done at BIPM. At present there are approximately ninetyofficial copies of the kilogram.Periodic verification of the national kilogram copies takes place approximately every ten years [8].

Each time the national copies are returned to theBIPM they are cleaned and washed by a process known as nettoyage-lavage[9], which theoretically returns them to a reference value. All kilograms,including the International Prototype, are subject to nettoyage-lavage prior tothe periodic verification exercise. The BIPM justify the use of this cleaningprocess because of the wide spread in the contamination levels of thereturning national prototypes and the need to return K to its reference value.Surface contamination varies between national copies and ranges from thosewhich are not used at all (some are returned to the BIPM with the seal on thecontainer still intact from the last verification) to those that are used ona regular basis and have collected many tens of micrograms worth of accretedmaterial on their surfaces.291292C H A P T ER 1 0: Mass and force measurement10.1.4 Post nettoyage-lavage stabilityAlthough the gravimetric effects of the nettoyage-lavage process have beenstudied by various NMIs [8,10,11] and the (variable) reproducibility of themethod is documented, no work has been done to link the actual effect onthe surface of the weight (measured by a reliable surface analysis technique) with either the mechanical cleaning method or the observed weightloss.

Furthermore, while the BIPM has made studies of the mass gain overthe first three months after cleaning based on the behaviour of all thenational prototypes, the return of the prototypes to their NMIs after thisperiod means no longer-term studies have been made. Only an NMI withat least three other platinum-iridium kilograms, against which the stabilityof the national prototype could be monitored, would be able to carry outsuch work and even so the stability of the other three kilograms wouldaffect the results. Due to the lack of data on the stability of nationalstandards after returning from BIPM (approximately three to four monthsafter cleaning and so relatively unstable) a wide variety of algorithms areused to predict the longer-term mass gain of the kilogram standards.

Somealgorithms are expressed as a function of time; for example, NPL has usedthe following expression to predict the value of kilogram 18 after cleaningat the BIPMMass18 ¼ 1 kg þ DV þ 0:356097t0:511678 mg(10.1)where DV is the measured difference from nominal in micrograms directly aftercleaning (as measured by the BIPM) and t is the time after cleaning in days.The most commonly used algorithm is that the national standard has thevalue assigned on leaving BIPM (approximately three months after cleaning)plus 1 mg per year. Some NMIs modify this by using a 0.22 mg per month gainfor the first two years.

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.