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An artefact standard based on a naturalquantity (the weight of a cubic decimetre of water) is still used to maintainand disseminate the unit, nowadays on a global rather than a regional scale.The development of the balance as a measurement instrument has seenmodifications in the execution of the comparison technique rather than inthe technique itself. Current technology offers little improvement in terms ofresolution on the best knife-edge balances used during the eighteenth century[1]. For the last eighty years NMIs have been able to make measurements onkilogram weights to a resolution of a few micrograms [2]. Comparisons onsuch two pan balances were time-consuming and laborious and the limitedamount of data produced in turn limited the uncertainties that could beachieved.

The recent automation of mass comparators, both in terms ofcollection of data and the exchange of weights, has allowed many more1CONTENTSTraceability oftraditional massmeasurementLow-massmeasurementLow-forcemeasurementReferencesThis section follows on from the introduction to mass given in section 2.4Fundamental Principles of Engineering NanometrologyCopyright Ó 2010 by Elsevier Inc. All rights reserved.289290C H A P T ER 1 0: Mass and force measurementcomparisons of standards and unknowns to be made. The increase in datacollected allows statistical analysis and this, rather than an absoluteimprovement in the overall resolution or accuracy of the instrument, has ledto an improvement in the uncertainty with which the kilogram can bemonitored and disseminated.The current state of the art in mass measurement allows the comparisonof kilogram weights with a repeatability approaching 1 mg on mass comparators, which can reliably be used on a daily basis.

With this frequency ofcalibration, the stability of the standard weight used as a reference becomessignificant not only at the working standards level but also for nationalstandards and for the International Prototype Kilogram itself. For this reasonthere is interest both in the absolute stability of the unit of the kilogram andin the way it is defined and disseminated.10.1.1 Manufacture of the Kilogram weightand the original copiesAfter many attempts in France, Johnson Matthey of London made a successfulcasting of a 90 % platinum 10 % iridium alloy mass standard in 1879.

Threecylindrical pieces were delivered to St-Claire Deville metallurgists in Francewhere they were hammered in a press to eliminate voids, rough machined andpolished and finally adjusted against the kilogram des archives [3]. One ofthese kilograms was designated K and became the International PrototypeKilogram. Forty further kilogram weights were produced using the sametechniques and delivered in 1884. Twenty of these were allocated to thesignatories of the convention of the metre as national standards.The International Prototype Kilogram (commonly known as the (International) Kilogram or just K) is a cylinder of approximate dimensions 39 mmdiameter by 39 mm height [4] (see Figure 2.4).

The design of the artefactminimizes its surface area while making it easy to handle and machine (asphere would give the minimum surface area but presents difficulties inmanufacture and use). Platinum-iridium was chosen as the material for thekilogram for a number of reasons. Its high density (approximately 21.5 kg$m3)means that the artefact has a small surface area and, therefore, the potential forsurface contamination is minimized.

The relatively inert nature of the materialalso minimizes surface contamination and enhances the mass stability of theartefact. The high density of the material also means that it displaces a smalleramount of air than a kilogram of less dense material (stainless steel or brass forexample). The weight-in-air of the kilogram (or any mass standard) depends onthe density of the air in which it is weighed because the air (or any fluid in whichit is weighed) exerts a buoyancy effect proportional to the volume of the artefact.Traceability of traditional mass measurementMinimizing the volume of the weight minimizes the effect of changing airdensity on the weight of the artefact.

Platinum and its alloys are reasonably easyto machine [5], enabling a good surface finish to be achieved on the artefact,again reducing the effect of surface contamination. The addition of 10 %iridium to the platinum greatly increases its hardness and so reduces wear.10.1.2 Surface texture of mass standardsThe surface texture of the kilogram standards has a major effect on theirstability. Early copies of the International Prototype (and the Kilogram itself)were finished by hand polishing using gradually finer polishing grains,concluding finally by polishing with a grain diameter of 0.25 mm [6]. Morerecent copies (since 1960) have been diamond-turned, producing a visiblybetter finish on the surface.