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Primary methods of measurement and primary standards

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1997 Metrologia 34 61

(http://iopscience.iop.org/0026-1394/34/1/9)

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metrologia

Primary methods of measurementand primary standards

T. J. Quinn

Abstract. The definition and concept of primary method are explained, taking examples from the fields ofthermometry and measurements of amount of substance. It is shown that although few methods can be consideredstrictly primary, small departures from the strict definition can be quantified and useful practical primary methodsare thus available. The links between primary methods of measurement, primary standards of measurement andprimary reference materials are discussed.

1. Introduction

In the field of thermometry, the concepts of primaryand secondary thermometry are well established [1, 2]and have proved useful in distinguishing the acceptedmethods for measuring temperature and describing thehierarchical relations between them. More recently,the Comite Consultatif pour la Quantite de Matiere(CCQM) adopted a general definition of a primarymethod, similar to that used in thermometry, andidentified a number of primary methods for measuringamount of substance [3]. A primary method, as definedby the CCQM and used here, is a more precisedefinition of what in the past was sometimes called anabsolute method or, in analytical chemistry, a definitivemethod [4].

The purpose of this short note is to explain theconcept of primary method of measurement and showhow it is linked to the International Vocabulary of Basicand General Terms in Metrology (VIM) definition of aprimary standard [5]. In general, although there areexceptions, a primary standard is one whose value isdetermined by a primary method.

A clear distinction must be made between primarystandards and national standards. The latter arestandards designated as such for legal and otherpurposes and they may or may not be primary standards.National standards are not considered in this note.

2. Definitions

The definition of a primary method of measurementadopted by the CCQM is the following [3, p. Q 29] :

A primary method of measurement is a methodhaving the highest metrological qualities, whose

T. J. Quinn: Bureau International des Poids et Mesures, Pavillonde Breteuil, F-92312 Sevres Cedex, France.

operation can be completely described and under-stood, for which a complete uncertainty statementcan be written down in terms of SI units, and whoseresults are, therefore, accepted without reference toa standard of the quantity being measured.

The definition of a primary standard from the VIM isthe following [5, p. 46] :

A primary standard is a standard that is designatedor widely acknowledged as having the highestmetrological qualities and whose value is acceptedwithout reference to other standards of the samequantity.

The CCQM also defined a primary reference material[3, p. Q 29] :

A primary reference material is one having thehighest metrological qualities and whose value isdetermined by means of a primary method.

3. Primary methods in thermometry and chemistry

The definition of primary method is examined first,taking primary thermometry and chemistry as examples.By beginning with primary thermometry, a concept wellestablished, the meaning of the definition can be madeclear before entering into the field of chemistry whereits application is more complicated.

3.1 Primary thermometry

A primary method of thermometry is one whoseoperation can be described completely without callingon other standards or measurements of temperature. Fora thermometer this means that the equation of state ofthe thermometric fluid can be written in a way such thatit does not include temperature-dependent constants,or functions that require access to an independenttemperature standard for their determination. For aconstant-volume gas thermometer the equation of state

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T. J. Quinn

of the thermometric fluid, i.e. the gas, may be writtenas follows :

(1)

where is the pressure, is the volume, is theamount of substance of gas in the volume andand are the temperature-dependent second andthird virial coefficients of the gas.

From the definition of primary method, it appearsthat the gas thermometer is not strictly primarysince the virial coefficients are temperature dependent.However, it is possible to use the gas thermometerwithout a knowledge of the virial coefficients ifmeasurements are carried out over a range of pressuresand the isotherm thereby obtained extrapolated to zeropressure. If the effects of the virial coefficients aresmall, it is possible to use values obtained fromanother thermodynamic experiment. In this case theuncertainty in the final result due to uncertainties in thetemperature scale of the subsidiary experiment givingthe virial coefficients may be negligible. Strictly, suchthermometry should be considered semi-primary. It mayalso be possible to determine the virial coefficientsusing the gas thermometer itself if measurements aremade in a temperature region where the temperaturedependence is weak. Finally, it may be possible to usevirial coefficients that are calculated from theoreticalknowledge of the inter-molecular potential of the gas inquestion. Gas thermometry is, therefore, considered asone of the principal methods of primary thermometry.

For a method to be considered primary it must alsohave the highest, or potentially the highest, metrologicalqualities. This implies that the measured quantity issusceptible to precise measurement and the systematicerrors which result from ignorance of the overallbehaviour of the system are small. Systematic errorsin gas thermometry, for example, result mainly fromignorance of the sorption of the gas at the walls ofthe gas bulb. Such errors are difficult to avoid and,more important, they require a great deal of effort toquantify. In total radiation thermometry, another methodof primary thermometry, the measured parameter istotal radiant power, a quantity that appears much lesseasy to measure. Here, the systematic errors are causedby the temperature dependence of the emissivity ofthe black bodies used and diffraction. In contrast togas sorption effects, however, these effects are readilyquantified. As a result, over a wide temperature range,the two methods have been used successfully withabout the same uncertainty. The determining factorin the final uncertainty budget in each method is themagnitude of the characteristic systematic error and notthe ease with which the thermometric parameter can bemeasured. Neither method is strictly primary, but thedeviations are small and, although difficult to avoid,can be reduced to quantifiable proportions. This is in

fact what is meant by “highest metrological properties”,an otherwise somewhat imprecise term.

This short discussion on gas thermometry isintended to show that it is not always straightforward tooperate a primary method of measurement in a strictlyprimary way. In thermometry there is often no cleardividing line between a primary method and one thatat least could be called semi-primary.

Among the many secondary methods of tempera-ture measurement is platinum resistance thermometry.We do not know the explicit relation between theelectrical resistance of a piece of platinum andtemperature. All that we can write down is an empiricalrelation that includes a number of temperature-dependent constants whose values must be determinedby calibration at an appropriate number of fixed pointsof temperature. The form of the empirical relation mustbe checked by comparing it with measurements madeusing a primary thermometer.

Thermometric methods are now considered to beprecise and accurate. They have reached this conditionby extended debate and experimental refinement. Asmeasurements of amount of substance are at an earlierstage in this evolutionary process, it is instructive tokeep thermometry in mind as an example of what isexpected in measurements of amount of substance.

3.2 Primary methods in chemistry

The application of the definition of a primary method tomeasurements of amount of substance is complicated.The CCQM laid down two conditions for a method tobe considered primary. First, it must be a method whichis specific for a defined substance and second, the valuesof all parameters, or corrections which depend on otherspecies or the matrix, must be known or calculablewith appropriate uncertainty. By analogy with primarythermometry, we can say that these methods must nothave chemically-dependent constants or functions thatrequire access to an independent chemical standard intheir equation of state. The methods that the CCQMidentified as having the potential to be primary are:

(a) isotope dilution with mass spectrometry;

(b) coulometry;

(c) gravimetry (with gas mixtures or gravimetric ana-lysis);

(d) titrimetry; and

(e) a group of colligative methods, including thelowering of the vapour pressure, the raising ofthe freezing point, the lowering of the boilingtemperature and the osmotic pressure, all of whichare based on the theorem that in any sufficientlydilute solution the solvent (though not the solute)behaves ideally, so that

λ λ (2)

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Primary methods of measurement and primary standards

where λ denotes absolute activity, A the solventsubstance, * “pure”, and the mole fraction ofsolute substances B, C, .

A straightforward example of amount-of-substancemeasurement is coulometry. For a univalent substancethe equation describing the measurement is

(3)

where is the electric current, is the time, is theFaraday constant and is the amount of substance.In this, as in all equations describing a primarymeasurement of whatever nature, by expressing all themeasured quantities in SI units and taking the valuesof any constants in SI units, the result is always givenin the correct SI unit. In this case, by expressing inSI amperes, in SI seconds and in its SI unit ofcoulombs per mole, is automatically given in moles.In the same way, we find in (1), that by expressing inpascals, in cubic metres and in its SI unit of joulesper kelvin mole, is automatically given in kelvins.

Similarly for isotope dilution with mass spectro-metry, we can write the measurement equation for abi-nuclidic element determination in the following way:

(4)

where represent isotope amount-of-substanceratios in the unknown sample X, the known addition Yand the blend B respectively of X and Y. The amountof substance Y, (Y), is given by (Y)/ (Y), where

is the mass of Y and is the molar mass of Y.Provided that (Y) is expressed in the SI unit of mass,the kilogram, and (Y) is expressed in kilograms permole, the quantity (X) is naturally, and correctly, givenin SI units of amount of substance, the mole. For themeasurement of amount of substance (X) of elementX to be considered primary it is clear that (Y) mustbe determined by a primary method, for example bygravimetry.

4. Primary methods in general

For each base quantity of the SI, one primary methodof measurement is often favoured for realization ofthe base unit, remembering that the unit is simply aconvenient example of the quantity in question. Butmore than one primary method may be available: theunit of length, for example, can be realized by any oneof the methods specified by the Comite Internationaldes Poids et Mesures in the mise en pratique of thedefinition of the metre. All are primary measurementsof length.

The kilogram is unique in that a material artefactdefines the standard. Primary measurements of masscould, therefore, be considered to be restricted tothose measurements made directly in terms of theinternational prototype, all other measurements being

considered secondary. This is a very restrictive inter-pretation and would not be in accord with the chainsof primary measurements described below. Primarymass measurements, however, can be understood asequivalent to the use of a device such as a beambalance to compare the mass of one artefact with thatof another. The operation of a beam balance can becompletely described in basic terms. It is necessary toknow the mass of a small calibration mass, but this, ingeneral, can be found by using the balance to calibratethat mass in terms of the reference mass. This is similarto the use of a gas thermometer to establish the valuesof the virial coefficients of a working gas.

Electrical measurements, in particular measure-ments of current, potential difference, power andcapacitance, may be primary measurements if theyare made, respectively, by direct realizations ofthe SI definitions of the unit using a so-called“current balance”, “voltage balance”, “watt balance”or calculable capacitor. These are all devices that linkmechanical to electrical quantities.

Primary measurements of frequency or time aremade using a laboratory caesium frequency standardaccording to the definition of the second.

The candela is realized today using an absolutedetector. In fact cryogenic radiometers are used almostexclusively for this purpose.

Primary measurements of the many derivedquantities of the SI are made using systems that arepractical realizations of the definition of the quantity.As an example we can take pressure. A primarymeasurement of pressure can be made using eithera mercury column manometer or a piston gauge. Inboth of these devices a force per area is measured, inthe first case by the pressure of a column of liquidmercury and in the second by loading a piston ofknown cross-sectional area with a given mass. In bothcases the value of the acceleration due to gravitymust be known. At very low pressures, for which itis not possible to use either of these methods, thequestion arises of whether it is possible to make aprimary measurement. The answer is probably yes,if the measurement is made by establishing a lowpressure by successive volume expansions starting froma pressure that can be measured by a pressure balance ormercury column. An expansion step can be considereda primary measurement. Successive volume expansionsdo not call on an independent pressure measurementand a complete measurement equation can be writtenfor each expansion step together with a completeuncertainty statement. An ionization gauge, however,cannot be considered a primary pressure measuringdevice because an explicit measurement equation cannotbe written that fully describes its behaviour.

It seems reasonable to accept that a chain ofprimary measurements can be constructed provided thata primary measurement is made at each step. Pressuremeasurement is one example; another is temperature

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T. J. Quinn

measurement in which a temperature of, say, 2000 Kcan be measured by a spectral radiation thermometer interms of a reference temperature of 1335 K which hasbeen determined by gas thermometry. The operation ofa spectral radiation thermometer is completely describedby the Planck equation and a full uncertainty statementcan be put in written form. The measurement at 2000 Kis thus considered to be a primary measurement ofthermodynamic temperature. A measurement of thesame temperature made using a thermocouple calibratedat 1335 K would not be considered primary because themeasurement equation of a thermocouple is empiricaland does not fully describe the relation betweenthermoelectric emf and temperature in terms of basicquantities.

By accepting that a chain of primary measurementscan exist, we accept that a primary measurement canuse the result of another primary measurement as areference, as in the example just given in thermometryor in isotope dilution with mass spectrometry. Tobe primary a method must not, however, call on ameasurement of the quantity being measured as anintegral part of its operation. To measure the quantity ,there must be no -dependent constants or functions inthe measurement equation, but there can be a referencevalue of if the value is obtained from a primarymeasurement chain.

5. Primary standards

The concept of a primary standard is closely linkedto that of a primary method. A primary standard isalmost always a standard whose value is determinedby a primary method of measurement. In most cases aprimary method is used to make a practical realizationof a unit of the SI. The VIM definition of a primarystandard can, therefore, be understood as defining theresult obtained from a primary measurement.

The additional requirement that a primary standardmust possess the highest metrological qualities meansthat not every standard whose value is determined bya primary method is necessarily a primary standard.An essential quality of a primary standard is intrinsic,long-term, stability. The frequency of an atomic ormolecular transition clearly possesses this quality as dothe freezing point of a pure element and the Josephsonand quantum Hall constants. These are all stable byvirtue of their direct links to atomic or quantumphenomena.

Primary standards do not necessarily have to beatomic or quantum standards. The designation of astandard as a primary standard includes, therefore, ameasure of subjective judgement as to what constitutesa standard of the highest metrological quality in aparticular field. A Pt-Ir prototype 1 kg mass standardmade and calibrated by the BIPM can be consideredsuch a primary standard. A brass 1 kg mass, thatincludes small lead makeweights to bring its mass close

to 1 kg, is clearly not a primary standard, despite thepossibility of comparing its mass directly with thatof the international prototype. A pressure standardin the high-vacuum range, obtained by successiveexpansions in known volumes, can be considered aprimary standard provided that sufficient is known aboutsuch things as gas sorption at the walls and molecularflow effects during the expansions.

In each field, an assessment must be made of thequalities a standard must possess for it to be considereda primary standard. It is not worthwhile attempting tomake a comprehensive list of the primary standards ineach field as such a list would not be static, the qualitiesrequired for such standards evolving with advances inmetrology.

In the discussion above on the application ofprimary methods, it was pointed out that the quantitybeing measured is automatically given in the correctSI unit provided that all the other quantities in themeasurement equation are expressed in the appropriateSI unit. The direct realization of an SI unit is not,therefore, a prerequisite for making measurements inSI units. In the measurement of amount of substance,a direct realization of the mole does not serve a usefulpurpose, in the same way that a direct realization ofthe kelvin serves no useful purpose in thermometry.In both these fields it is the correct application of aprimary method that provides the basis for makingmeasurements in the appropriate SI units.

In the metrology of chemistry, standard or certifiedreference materials occupy an important place. Forthis reason the CCQM adopted a definition of aprimary reference material by analogy with that ofa primary standard. An important distinction hasto be made, however, between a primary referencematerial as defined here and a reference materialwhose characteristics are established by the so-calledconsensus method. This method is based on the averageof a number of measurements made by one or moremethods that are not primary. Although every effort ismade to avoid using it, when a primary method is notavailable there is no alternative to consensus.

6. Conclusions

Implicit in the SI is the possibility of making precise,practical realizations of some base and derived unitsand using them to make accurate measurements ofthe corresponding quantities. For those units for whichdirect realization is not appropriate, the applicationof a primary method is the only way to ensurethat measurements are correctly made in SI units.Clear definitions of the concepts of primary methodand primary standard are thus useful in identifyingthose methods and standards that possess the qualitiesessential for use as the practical basis for our system ofmeasurement. The correct use of primary methods and

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primary standards is thus of direct help in making themost advantageous use of the SI.

References

1. Quinn T. J., Temperature, 2nd ed., London, AcademicPress, 1990, Ch. 1.

2. Colclough A. R., Metrologia, 1973, 9, 75-98.3. BIPM Com. Cons. Quantite de Matiere, 1995, 1.4. Cali J. P., Reed W. P., In Accuracy in Trace Analysis,

National Bureau of Standards Special Publication 422,August 1976, 41-63.

5. International Vocabulary of Basic and General Termsin Metrology, Geneva, International Organization forStandardization, 1993.

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