METROLOGY FOR NON-METROLOGISTS -...

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METROLOGY FOR

NON-METROLOGISTS

Rocío M. Marbán

Julio A. Pellecer C.

2002

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To contact the authors:

2001 Producción y Servicios Incorporados S.A.Calzada Mateo Flores 5-55, Zona 3 de MixcoGuatemala, Centro AméricaTel.: (502)431-0662Fax: (502)434-0692email: [email protected]

ISBN 99922-770-1-7© OAS, 2002

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This English version of the second revised edition is pub-lished under the sponsorship of SIM.

The Interamerican Metrology System , SIM (SistemaInteramericano de Metrología, Normalización, Acreditacióny Calidad) is the regional organization for metrology inAmerica, comprising national metrology institutes from the34 member nations represented at the Organization of theAmerican States, OAS, which acts as its Executive Sec-retariat.

The opinions stated in this document are not necessarilyopinions of the OAS, its bodies or its staff.

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CONTENTS

Acknowledgements ixPresentation xi

Introduction 1What we measure and how 11

Characterization of metrology 19Vocabulary 21

Applications - what is measured andwhat for 27

Length 27Mass 28Temperature 29Time and frequency 30Electricity and magnetism 31Photometry and radiometry 32Acoustics and vibrations 33Ionizing radiation 34Chemistry 35

Standards and reference materialsIntroduction 37Length 39Mass 45

1

INTRODUCTION

The initial concept of metrology derives from itsetymology: from the Greek metros - measure, andlogos - treaty. This concept is certainly as old ashuman beings: “I have nothing”, “I have something”,“I have much”; these expressions reflect a primi-tive comparison that is still valid and presently wecan say that metrology is the science of mea-surements and that to measure is to compare withsomething (a unit) which is taken as the basis forcomparison.

Measurements for primitive human beings beganwith the ideas of: near-far, fast-slow, light-heavy,clear-dark, hard-soft, cold-hot, quiet-noisy. Atfirst these were personal perceptions, but experi-ence and life in common gave rise to comparisonsbetween persons and, through the ages, to gener-ally accepted bases for comparison.

Thus, after several millennia, it is easy to think ofbases for comparison of personal concepts - inother words: measurements and their units.

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Some of these measurements and units are basic:

MEASURE UNIT

length metre (meter)mass kilogramtime secondtemperature kelvinintensity of light candelaelectric current ampereamount of substance mol

For other purposes, not covered by the above, it isoften necessary to use other measurement units,called derived units because they use or are basedon the base units. That is, using mathematical al-gorithms, a unit is expressed algebraically in termsof other units.

To enter the realm of units based on one or morefundamental units, is to enter a world of scientificalgorithms for specific purposes, which is why de-rived units are more numerous.

A unit is a value in terms of which a quantity maybe described. It must be stressed that, qua unit, itmust not be broken down into its elements. Mul-

Metrology for non-metrologists

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tiples and sub-multiples are used to express quan-tities larger or smaller than those of the unit per se.We will see later on that in the International Sys-tem of Units multiples and sub-multiples are deci-mal, that is, they use powers of 10.

We mentioned using something with which to com-pare; this something is known as a measurementstandard or simply a standard.

Originally, a standard was considered to be a rep-resentation or physical embodiment of a unit. It wasnecessary to stress that the standard was a trust-worthy representation of the unit only under a setof precisely defined conditions, to make sure it wasindependent of environmental influences such astemperature, humidity, atmospheric pressure, etc.Because of their characteristics, physical standardswere not used to directly take measurements. In-stead they were the basic reference point for themanufacture and calibration of the instruments thatare used for such purposes.

Today, thanks to scientific advances, we have moreexact and reliable definitions for the units, basedon universal physical constants, and now a stan-dard can be defined as: a materialized measure,

Introduction

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measurement instrument, reference material ormeasurement system, whose purpose is the defi-nition, materialization, conservation, or reproduc-tion of a unit, or one or several known values of aquantity, for transmission by comparison to othermeasurement instruments (2).

It is also important that the procedure used to mea-sure give reproducible results and, in fact, thereare precise instructions on how to carry out the pro-cedure, which units to use and which standard.

In the real world, we usually measure following thissequence:

- we decide what we are going to measure,- we select the unit according to the measure,- we select the measuring instrument (calibrated),- we apply the accepted procedure.

Before going into details of the main measures, letus have a brief, very brief look, at the history ofmeasurement.

Archeological finds show that very ancient civiliza-tions had well-defined concepts of weighing andmeasuring. Trade, land division, and taxation,


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among others, must have required very soon theuniformity of measurements.

The appearance of weights and measures systemsgoes far back into time. We know little of what wasdone in the Far East; however, there is no doubtthat they existed in the Mesopotamian civilizationsand - clearly - it is obvious that the construction ofpyramids in Egypt (3000 to 1800 BC) requiredelaborate systems of measurement.

We know, and in some countries we still use, someof the linear measurements of current usage inancient Egypt (the span, the foot, the pace, thefathom, the cubit).

Also in Egypt, scales were used to weigh preciousmetals and gems. Later on, when coins began tobe used as elements of trade, they were simplypieces of gold or silver, stamped with their weight.They gave birth to a monetary system that spreadthroughout the whole Mediterranean area.

The way we measure time is based on thesexagesimal system developed in Mesopotamia,and our calendar is derived from the original 365days Egyptian calendar.

Introduction

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Roman conquest of a large part of the Europeancontinent contributed to disseminate the systemsof weights and measures.

By the beginning of the second millennium AD, thedifferent measures in use had mutiplied uncontrol-lably. There were, for instance, different measuresfor capacity according to the product, be it wine orbeer, wheat or barley. Measures could also varyfrom province to province or from town to town.

England used Anglo-Saxon measures and gradu-ally tried to improve and simplify its system. Formany centuries, the pound-foot-second systemwas the preferred system in English-speaking coun-tries as well as worldwide for some commercial andtechnical uses; to date it has not been totally dis-carded and is still used for many activities in manycountries.

France created and developed a simple and logi-cal system, based on the most advanced scientificprinciples known at the time (the end of the eigh-teenth century) - the decimal metric system,which first came in use during the French Revolu-tion. It owes its name to the use of the decimalsystem for multiples and sub-multiples and to its


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base unit: the metre, mètre in French, which is it-self derived from the Greek metron, meaning mea-sure. In its first version, the metre was defined asone ten-millionth of the length of a quadrant of theearth’s meridian (i.e. one ten-millionth of an arcrepresenting the distance between the Equator andthe North Pole) and it was determined by measur-ing an arc of meridian between Dunkerque, inFrance, and Barcelona, in Spain. The history, vi-cissitudes, development and application of this sys-tem are amply documented (1,18).

Metrologists are very active and there are con-stantly important changes and improvements in allaspects of measurements. Growing cooperationbetween metrologists from different countries is alsohelping to establish internationally accepted workprocedures. There are now uniform methods ofmeasurement so we can all work on the basis ofthe same known quantity or unit, and the results ofany calibration, verification and test, in any labora-tory or enterprise, are a guarantee of compatibilityand quality.

In consonance with the global approach, more andmore countries are adopting the International Sys-tem of Units (SI) based on the decimal metric sys-

Introduction

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tem, with the subsequent adoption of the corre-sponding standards and measurements tech-niques.

Forty-eight countries have subscribed the MetreConvention, that adopted the International Systemof Units (SI). The Convention gives authority to theConférence Générale des Poids et Mesures(CGPM - General Conference on Weights and Mea-sures), the Comité International des Poids etMesures (CIPM - International Committee onWeights and Measures) and to the Bureau Inter-national des Poids et Mesures (BIPM - InternationalOffice of Weights and Measures), to act interna-tionally in matters pertaining to metrology.

CGPM is constituted by representatives of themember countries and it holds meetings every fouryears in Paris, France for: discussion and exami-nation of agreements for the improvement and dis-semination of the International System of Units (SI),validation of advances and results of new funda-mental metrological determinations, scientific inter-national resolutions, and decisions pertaining to theorganization and development of the BIPM.


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In search of a world-wide unification of physicalmeasurements, the BIPM:

- establishes fundamental standards andscales for the main physical quantities,

- carries out and coordinates determinationsrelated to physical constants,

- preserves international prototypes,- coordinates comparisons with standards

kept at the National Laboratories ofMetrology,

- ensures coordination of the measurementtechniques.

Introduction

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WHAT WE MEASURE AND HOW

The units of the International System of Units (SI)are established by the General Conference onWeights and Measures (CGPM) with authority overthe International Office of Weights and MeasuresBIPM, with headquarters in France. In what follows,the international definitions for the units are thosepublished by BIPM, as of June 2002.

CGPM decided to base the SI on seven well-de-fined units. These are known as base units andthey are listed in Table 1.

Originally, the base or fundamental units were socalled because they were considered to be mutu-ally independent and because, from them, all otherunits could be derived. The corresponding stan-dards were material embodiments, kept in agreedlocations, under strictly determined conditions.Thanks to scientific and technical advances, andthe availability of more exact instruments, the baseunits, with the single exception of the kilogram, arenow defined differently, based on physical experi-ments. It can be argued that in some cases baseunits are no longer mutually independent. For

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TABLE 1

Base Units of the SI

Quantity Symbol Unit

length m metre

mass kg kilogram

time s second

electric current A ampere

thermodynamictemperature K kelvin

amount ofsubstance mol mol

luminousintensity cd candela


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instance, the metre is no longer definedagainst the former prototype metre - an iri-dium-platinum bar - and the current defini-tion involves the concept of second, anotherbase unit. Similarly, the candela, the baseunit for luminous intensity, is defined in termsof the hertz (s-1) and the watt (m2.kg.s3), bothderived units, and of the steradian, a supple-mentary non-dimensional unit.

However, taken as the set of both base and de-rived units, the SI is considered to be a coherentsystem because:

- the base units are defined in terms of physical constants (Appendix 1), with the sole exception of the kilogram, defined in terms of a prototype,- each quantity is expressed in terms of a single unit, obtained by multiplication or division of the base units and of the non- dimensional derived units,- multiples and sub-multiples are obtained by multiplication by an exact power of ten,- derived units can be expressed strictly in terms of the base units, that is, they have no numerical factor other than the number 1.

What we measure

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The work that is being done for the definition andthe improvement of SI units always strives to haveunits consistent with those that already exist.

As we mentioned before, the base units give riseto a large number of other units; Appendix 2 listssome of those considered SI derived units.

Two derived units, known formerly as “supplemen-tary” units, deserve special mention. They are theradian (rad), used to measure plane angles, andthe steradian (sr), used to measure solid angles.They are also called non-dimensional units. Theneper and the bel, of accepted use although theyare not integrated into the SI, are also non-dimen-sional units.

The SI also has a set of rules and conventions thathave to do with the use of mixed units, how to se-lect and identify prefixes, the use of multiples andsub-multiples, spelling conventions, use of capitali-zation, use of singulars and plurals, how to groupdigits of numerical values, decimal marker, round-ing out of numerical values, etc.(16,30,37)

These rules are not yet uniformly applied; for in-stance, in several countries of America, the dot and


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not the comma is used as the decimal sign ormarker. In any case, it is important to be aware ofthese rules and for more detailed information onthe subject we recommend consulting some of thereferences (16,37,40,46).

There are also some units that do not belong tothe SI but that are accepted for use with it. Theyare sometimes called additional units and are listedin Table 2.

Some of those are accepted temporarily, until theiruse is no longer necessary and they are substi-tuted by the approved units; in some cases theiruse is limited to specialized fields, as for examplethe carat (ct) in jewelry. There are other units, out-side the SI(40,46), still in use in some countries andsome contexts, such as the dyne and the stokes.

If we now look at the hierarchical structure of mea-surement standards, we see we can describe it asa pyramid. At the top, we have the set of standardsthat corresponds to the SI base units, of which wehave already spoken.

The second position is taken up by the set of na-tional standards.

What we measure

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At the next level, we find the reference standardsthat will be used to prepare the working standardsto be used in turn for operational work.

The set of operational standards (working stan-dards) is the base of the pyramid.

The chain of organizations in charge of the opera-tion of the SI, is headed by the BIPM, followed bythe National Metrology Institutes, the CalibrationLaboratories and, finally the working Laboratories.

The national metrology institutes have custody ofthe national standards, and the responsibility fordissemination of the SI units to accredited calibra-tion laboratories in their respective countries.

The calibration laboratories are in charge of verify-ing that measuring equipment as well as referenceand working standards comply with the nationalstandards.

The testing and assay laboratories, at the opera-tional level, are in charge of evaluating conformityfor the products that are to be certified. To do this,they use reference standards, calibrated using thenational standards of the upper level.


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TABLE 2

Additional units accepted for use with the SI

Name Symbol Expression in terms of SI units

Time:minute min 1 min = 60 shour h 1 h = 60 min = 3600 sday d 1 d = 24 h = 86 400 s

Plane angle:degree o 1o = (π/180) radminute ’ 1’ = (1/60)o = (π/10 800) radsecond ” 1”= (1/60)’ = (π/648000) rad

Volume:liter l, L(a) 1 L = 1 dm3 = 10-3 m3

Mass:ton,metric ton t 1 t = 103 kg

a) The alternative symbol for the liter, “L”, was adopted by the CGPM inorder to avoid the risk of confusion between the letter l and the number1. The script letter is not approved for the liter.

b) Other additional units are: the electronvolt (eV), the unified atomic massunit (u), and the astronomical unit (ua).

What we measure

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Finally, we find those organizations and entitiesworking with operational or working standards,used by industry and others, and that are normallycalibrated against reference standards, which, inturn, have been calibrated using national standards.

An important concept in metrology is that of trace-ability. It refers to the property of a measurementor of the value of a standard, to be related to es-tablished references, normally national or interna-tional standards, through a continuous chain ofcomparisons, all of them with known uncertainties.The possibility of determining traceability in anymeasurement relies on the concept and the actionsof calibration and on the hierarchical structure ofthe standards we have already mentioned.

For metrologists, calibration is: a set of operationsthat establish, under specified conditions, the rela-tion between the values shown by a measuring in-strument, a measuring system, the values repre-sented by a materialized measure or by a refer-ence material, and the corresponding values of thequantities established by the standards. The termis sometimes misapplied to a process of compari-son or verification that is used to verify that be-tween the values shown by a measuring instrument


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or system and the known values of the measuredquantity, the differences are below the maximumtolerance (2).

On the other hand, metrologists usually take intoconsideration the main causes of errors in mea-surements; they may or may not be known andcontrollable and can be due to factors of the envi-ronment where the measurements are taken, todefects of construction or calibration of the instru-ments, to operator mistakes, to the interpretationitself of the data, or simply to fortuitous factors.

CHARACTERIZATION OF METROLOGY

For convenience, a distinction is often made be-tween the several fields of application of metrol-ogy, into: Scientific Metrology, Legal Metrology, andIndustrial Metrology.

Scientific metrology

This is the set of actions taken to develop primarystandards of measurement for the base units andthe derived units of the International System of Units(SI).

What we measure

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Legal metrology

According to the International Organization for Le-gal Metrology (OIML) “legal metrology is the en-tirety of the legislative, administrative and techni-cal procedures established by, or by reference topublic authorities, and implemented on their behalfin order to specify and to ensure, in a regulatory orcontractual manner, the appropriate quality andcredibility of measurements related to official con-trols, trade, health, safety and the environment”.

Industrial metrology

The function of industrial metrology is mainly theproper calibration, control and maintenance of allmeasuring equipment used in production, inspec-tion and testing. The purpose is to guarantee thatthe products will comply with quality standards. Theequipment is controlled at set times and in such away that the uncertainty of the measurements willbe known. Calibration is done against certifiedequipment, with a known valid relation to standardssuch as, for instance, the national reference stan-dards.


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VOCABULARY

To understand each other, metrologists use an in-ternationally approved vocabulary, the InternationalMetrology Vocabulary (VIM)(54); some of the mostcommon definitions follow:

Quantity (measurable)attribute of a phenomenon, body or substance thatmay be distinguished qualitatively and determinedquantitatively.

Base quantityone of the quantities that, in a system of quantities,are conventionally accepted as functionally inde-pendent of one another.

Derived quantityquantity defined, in a system of quantities, as a func-tion of base quantities of that system.

Dimension of a quantityexpression that represents a quantity of a systemof quantities as the product of powers of factorsthat represent the base quantities of the system.

What we measure

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Quantity of dimension one, dimensionless quantityquantity in the dimensional expression of which allexponents of the dimensions of the base quanti-ties reduce to zero.

Unit (of measurement)particular quantity, defined and adopted by conven-tion, with which other quantities of the same kindare compared in order to express their magnitudesrelative to that quantity.

Base unit (of measurement)unit of measurement of a base quantity in a givensystem of quantities.

Value (of a quantity)magnitude of a particular quantity, generally ex-pressed as a unit of measurement multiplied by anumber.

Measurementset of operations having the object of determininga value of a quantity.

Measurandparticular quantity subject to measurement.


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Accuracy of measurementcloseness of the agreement between the result ofa measurement and a true value of the measurand.

Repeatability (of results of measurements)Closeness of the agreement between the resultsof successive measurements of the samemeasurand carried out under the same conditionsof measurement.

Reproducibility (of results of measurements)closeness of the agreement between the results ofmeasurements of the same measurand carried outunder changed conditions of measurement.

Uncertainty of measurementparameter, associated with the result of a measure-ment, that characterizes the dispersion of the val-ues that could reasonably be attributed to themeasurand.

Material measuredevice intended to reproduce or supply, in a per-manent manner during its use, one or more knownvalues of a given quantity.

What we measure

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Measurement standard, etalonmaterial measure, measuring instrument, referencematerial or measuring system intended to define,realize, conserve or reproduce a unit or one or morevalues of a quantity to serve as a reference. Stan-dards may be international (recognized throughinternational agreement) or national (recognized bynational agreement).

Primary standardstandard that is designated or widely acknowledgedas having the highest metrological qualities andwhose value is accepted without reference to otherstandards of the same quantity.

Secondary standardstandard whose value is assigned by comparisonwith a primary standard of the same quantity.

Reference standardstandard, generally having the highest metrologi-cal quality available at a given location or in a givenorganization, from which measurements madethere are derived.


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Working standardstandard that is used routinely to calibrate or checkmaterial measures, measuring instruments or ref-erence materials.

Transfer standardstandard used as an intermediary to compare stan-dards.

Traceabilityproperty of the result of a measurement or the valueof a standard whereby it can be related to statedreferences, usually national or international stan-dards, through an unbroken chain of comparisonsall having stated uncertainties.

Reference material (RM)material or substance one or more of whose prop-erty values are sufficiently homogeneous and wellestablished to be used for the calibration of an ap-paratus, the assessment of a measurementmethod, or for assigning values to materials.

Certified reference material (CRM)Reference material, accompanied by a certificate,one or more of whose property values are certifiedby a procedure which establishes traceability to an

What we measure

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accurate realization of the unit in which the prop-erty values are expressed, and for which each cer-tified value is accompanied by an uncertainty at astated level of confidence.

Note: because not all countries use the same sys-tem to write numbers, it must be stated that in thisdocument we use the comma as the decimalmarker and an “x” for the multiplication sign. Thus,for instance, we shall write 6,023 x 1023 and not6.023 x 1023. Most English-speaking countries usethe period or full stop as the decimal marker.


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APPLICATIONS

A possible question is: what do we measure for?Without going into details and without any pretenseat being exhaustive, let us look at some answers,restricted to main aspects.

As can be expected, different applications requiredifferent actions which are done with different lev-els of reliability; in metrology this is known as “un-certainty”, an interval of confidence in the resultsof the measurements.

Length

Measurement of length, or the determination of dis-tance, is used in dimensional measurements suchas: areas, volumes, capacities, speed and veloc-ity, roundness. Length is present in the definitionof the radian and the steradian, the non-dimen-sional units used to measure angles. In general,we could say that it is used in any determination ofthe shape of an object.

Many fields of human endeavor require dimensionalmeasurements: geodesy, real estate and the prop-erty and use of land, construction and maintenance

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of roads, highways, streets and avenues, buildingof dwellings, all manufacturing industry, machinetools, odometers to calculate charges for car rent-als, many commercial aspects. It is probably in themanufacturing industry where the influence of goodlength measurements is more striking. The indus-tries of apparel, furniture, automotive, accessories,home appliances, scientific and medical instru-ments, electronic equipment and many more, re-quire parts that must fit properly into each other, aswell as exact measures in the final consumer prod-ucts.

Mass

The need to know mass quantitatively is present inmost human activities. This explains the wide rangeof standards and instruments used to determinemass. Without going into details we can mention:industry - administration (purchasing, storehouses,etc.), production (processes and control), sales(orders and shipments); laboratories (research andcontrol); trade (all transactions); science (even intheoretical occupations). The amounts to be deter-mined can go from the mass of the electron to themass of the universe, through that of mosquitoes,hamburgers, human beings, vehicles, etc.


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Normally, everything that is produced, sold or ex-changed, is related, directly or indirectly, to mass;which is why we can say that application of metrol-ogy in its mass aspect is omnipresent at all levelsin everyday life.

Temperature

The sensation of heat or cold is a common one forliving beings and the concept of temperature andits measurement are present in countless humanactivities.

Our first contact with scientific measurement of tem-perature is usually the home thermometer. We thusthink immediately of medical applications and, par-ticularly, measurement of body temperature in sickpeople, with the importance it can have for the evo-lution of some ailments. But correct temperaturemeasurements are also required for the manufac-ture of pharmaceuticals, the use of diagnosis tech-niques, clinical analysis, sterilization of clinical andhospital materials.

Food preparation and the techniques for its con-servation require temperature measurements;

Applications

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these can be empirical for home use but industrydemands accuracy in its measurements.

Dyeing of fabrics, manufacture of all types of ce-ramics, paints and enamel for home appliances andfor vehicles, generation of energy, refrigeratedtransport, air conditioning, and many more humanactivities, require correct determinations of tem-perature.

Time

Measurement of time is useful not only to makesure we are punctual or to determine the winner ina race! There are obvious applications in daily life(getting up at a certain time; buses, trains and air-planes being on time, control of working hours forpayment of salaries, control of time for telecom-munication charges, etc.). There are also manyindustrial processes, many medical techniques, thatrely on exact measurements of time.

Other applications include the use of taximeters(based on time only, or on a combination of timeand distance), timekeepers, speedometers.


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Synchronization of activities such as those on thestock exchange and the military, launching andcoupling of spacecraft, etc. demand exact measure-ments of time.

In general terms, we can speak of watches andchronometers (either of type I with digital electroniccircuits, or of type II with analog mechanisms orsynchronous motors) as well as other timepiecessuch as those used in vehicle parking meters, au-tomatic car washers, or the timers of home appli-ances such as washing machines, dryers, micro-wave ovens.

Electricity and magnetism

The last two centuries have given birth to count-less advances toward our current modern devel-opment; electric motors were built and these con-tributed to industry, transport and all activities thatrequire some type of movement. With incandes-cent bulbs, artificial light radically changed all ofman’s nocturnal activities.

To try to enumerate all current applications of elec-tricity, properly offered and used, would mean list-ing all of mankind’s activities for which electricity

Applications

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has to be controlled (i.e. measured), a control thatdemands reliable apparatus and systems with aknown accuracy.

Electricity is fundamental for communications, beit telephones, radio, television, satellite operation.But, what metrology guarantees with its standardsand its procedures for electricity and magnetism,is really the reliability in the handling and use ofthis resource, rather than the availability itself ofsuch a resource. During design, many problems ofreliability come up, and the ability to rely on sys-tems that can ensure the proper behavior of equip-ment, within set limits, is what makes it possible todesign, plan and implement complex projects.

Also, all of electronics demands reliable (exact, tothe layman) measurements, and this reliability andreproducibility are due in great part to the advancesin metrology.

Photometry and radiometry

Man has developed many apparatus and devicesthat allow him to see no matter what the naturalconditions are and, what is more, that can give himlight intensities that would be difficult to find in na-


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ture. All these apparatus demand reliable measure-ment techniques to ensure that the intensity re-quired is effectively being obtained.

But, even more important, the techniques for physi-cal and chemical analysis are very often based onextremely exact measurements of light or radia-tion. Absorption photometers, black body photom-eters, photoelectric instruments, spectrophotom-eters and radiation measurement apparatus relyfor their accuracy on careful calibrations, based onaccepted standards.

Photodynamic therapies are currently being usedfor some ailments, ultraviolet light is used industri-ally, certain wavelengths of radiation are used fortheir germicidal properties while others are usedfor plant growth, etc.; all these applications needreliable measurements.

Acoustics and vibration

Exact acoustic measurements are crucial for ap-plications such as the design of theaters andauditoria, telecommunications, radio, the manufac-ture of musical instruments and of sound repro-duction and transmission devices (including pho-

Applications

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nographs, microphones, amplifiers), the eliminationof bothersome or dangerous sounds (in offices,production areas, land and air transport), the de-sign of warning systems such as ambulance andfiremen sirens and certain industrial indicators,sonar, petroleum exploration, seismographs,echocardiograms and ultrasound in chemistry andin medicine for diagnosis and treatment, in indus-trial applications such as welding.

Ionizing radiation

Medical applications of ionizing radiation are pos-sibly the better known, under the form of X rays fordiagnosis, and the use of radioactive isotopes forradiotherapy and as tracers in medical and bio-chemical research.

Among industrial applications, we can mention theactivation of vitamins, chemical synthesis (such asthat for ethyl bromide), polymerization (polystyrene,polyethylene), rubber vulcanization, polymerizationof methylmetacrylate, textile finishes for permanentpress fabrics and garments, food processing (cook-ing, drying, pasteurization, etc.), preservation andsterilization of foods, control of germination and of


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insect infestations in stored grains, “curing” or so-lidification of finishes in paints and inks, metallurgy,geochemistry, archeology (C14), thickness measure-ments, electric power generation.

Chemistry

In scientific and technical activities it is always ofimportance to be able to know on which basis tocalculate which and how much of several sub-stances should be used.

An obvious case is that of the laboratory, clinical orindustrial, but this can also be said of all types ofindustrial processes; some, because they handlevery large volumes and small variations can implylosses of tons; others, because they use very smallamounts and minimal variations can be crucial.

That is to say, the use of standards and referencematerials is the basis for successful production andthe guarantee of quality. As a simple example, theproduction and marketing of pharmaceuticals is ahuge field for the application of metrology.

Applications

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STANDARDS AND REFERENCEMATERIALS

INTRODUCTION

Standards and reference materials are the subjectsto be treated in the next sections, in accordancewith the following scheme: general considerationsof what we measure, the definition of the measure-ment unit, primary standards, accuracy and uncer-tainty, and measuring instruments.

On the subject of uncertainty, it should be notedthat there are two schools among metrologists(2).One of them looks at uncertainty as an element todenote uniformity of the results in repeated mea-surements. The other school uses the term to meanthat we are determining differences among the re-sults. In both cases, we must remember that un-certainty is simply an interval of confidence in theresults of the measurement. Both points of vieware valid considering the field of application,whether operational or national metrology labora-tories. National and secondary laboratories shouldapply the 1993 ISO “Guide to the expression ofuncertainty in measurement”(28).

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In the Western Hemisphere, the Inter-AmericanSystem of Metrology, SIM, through the work it isdoing, is striving to obtain the highest possible in-tegration and coherence in metrology aspectsamong its members. In 1999, SIM authorities dida strategic planning exercise. One of the aspectsstudied was the determination of which areasshould be the subject of regional and of nationalactions. These areas turned out to be: length, mass,temperature, time and frequency, electricity andmagnetism, photometry and radiometry, acousticsand vibration, ionizing radiation, and chemistry.


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LENGTH

What do we measure

We all know intuitively what length is. In practice,what we really measure is the distance or separa-tion between two points and, given that the currentdefinition of standards is nowadays oriented to theuse of physical constants, we must be consciousthat length implies distance.

There are estimates that around 80% of the mea-surements done in industry have to do with dis-placements and thus with length. In the year 1800,an accuracy of 0,25mm was considered proper forlength measurements; today(18) we speak of re-quired intervals that range from the field ofnanotechnology up to that of geophysics.

International definition of the unit for mea-surement of length

History

Originally, the metre was defined as one ten-mil-lionth of the length of a quadrant of the earth’s

Standards and reference materials

40

meridian (i.e. one ten-millionth of an arc represent-ing the distance between the Equator and the NorthPole) and it was determined by measuring an arcof meridian between Dunkerque, in France, andBarcelona, in Spain, cities both at sea level. Thefirst physical embodiment of the metre, the so-calledmètre des Archives, was built in 1799 on this ba-sis. Later, with the approval of the “Convention ofthe Metre” in 1875, a copy of this prototype be-came, in 1889, the international prototype of themetre. This prototype metre, an iridium-platinumbar which is still kept in Paris, was considered stableand precise, as well as its copies, and they wereused until 1960, when the definition was replacedby one based on the wavelength of a given orange-red line of the spectrum of the isotope krypton-86.In 1983, the 17th General Conference on Weightsand Measures modified it to the current definitionwhich is related to the speed of light in vacuum(299 792 458 metres per second).

Definition

The metre (symbol m) is the length of the pathtraveled by light in vacuum during a time intervalof 1/299 792 458 of a second.


41

Standards

For the measurements of length to be practical, itis necessary to transfer from a standard expressedin terms of the velocity of light, to a physical deviceor standard.

For measurements of the order of the metre, inter-ferometric methods are used. The method consistsof a comparison between the length to be measuredand the wavelength λ of a luminous radiation whosefrequency f has been previously determined withgreat accuracy. The reference used is the wave-length of the radiation produced by a laser, stabi-lized either in frequency or in wave-length(43).

For instance(43), with an helium-neon laser, stabi-lized in a methane chamber, wavelengths of3 392,231 397 327 nm can be measured with arelative uncertainty of 3 x 10-12; with an argon la-ser, stabilized in a iodine chamber, wavelengths of514,673 466 4 nm, can be measured with a rela-tive uncertainty of the order of 2,5 x 10-10.

There are currently portable models of stabilizedlasers, and with these it has been possible for BIPMto compare and calibrate in situ in a region without


42

the requirement of several national metrology labo-ratories having to take their apparatus to Paris forcalibration(19). Thanks to these laser-based cali-brations, the countries can have their own nationalstandards.

By following the chain we have already seen, cali-bration standards as well as testing and operationalstandards can be derived from these national stan-dards, and they may include measuring tapes, rul-ers and all other devices used in everyday life tomeasure length.

In addition to the methods based on light sources,standard gauge blocks are also used. These arehighly polished, metallic or ceramic blocks, whoseedges have a very high-quality parallelism, and thatcan be combined in the required number to obtainthe desired length, with an accuracy according totheir intended use, whether for calibration or op-erational work.

The gauge blocks, calibrated by interferometry, maythemselves constitute the physical embodiment ofthe standard, and, through mechanical compari-son, secondary standards may be derived fromthem.


43

Uncertainties

As mentioned before, stabilized laser standards canoffer relative uncertainties for the measurement oflength of the order of 10-9 and of 10-12.

Measuring instruments

Length, width, height, thickness, diameter, all theseare linear measurements and many instrumentsand devices have been developed so they can bemeasured simply and with the required accuracy.

We thus find, among others: rulers (wood, metal,fiberglass or plastic, rigid or folding), tape rulers (ofmetal, plastic or fabric), calipers and dividers (high-precision, for nuts and screws, for gears), microme-ters, verniers, gauge blocks, depth and anglegauges, protractors, interior and exterior diametertapes, roundness or surface gauges, roughnesstesters, etc.

These instruments may be based on mechanical,pneumatic, optical or electronic methods. Accuracytolerances are established in accordance with thetype of instrument and its intended use.


44


45

MASS

What do we measure

The mass of a body can manifest itself in two ways:one is by a change in its state of motion (inertia)and the other by its attraction to other bodies.

Let us suppose an imaginary vacuum tunnel, wherewe have a perfectly lubricated plane surface so that,if we place an object on this surface, there is nofriction whatsoever between the surface and theobject. If the object is at rest and we want it tomove, the effort required to move it is an indica-tion of the mass of the object.

In the same tunnel, under the same conditions, ifwe remove the plane surface, the object falls down,attracted by planet Earth, and this is another mani-festation of its mass.

In both cases, we would have the measure of themass of the object: in the first, by the measure ofthe effort to move the object, and in the second, bythe measure of its fall.


46

In other words, mass is the quantity of matter con-tained in a given body while weight is the result ofthe attraction of planet Earth on that body.

International definition of the unit for mea-surement of mass

History

The mass unit, the kilogram, was originally definedas the mass of one liter of water at a temperatureof 4o C. This definition was later modified in view ofthe practical difficulties of obtaining pure water, andbecause the definition involved another quantity:temperature.

It could be argued that the kilogram is really a mul-tiple of the gram and that it is the gram that shouldbe the unit. This has been studied by metrologistsbut, for practical reasons, it was agreed to continueconsidering the kilogram as the mass unit.

With present knowledge, it has not yet been pos-sible to define the mass unit in terms of universalphysical constants; thus, based on the agreementsat the 1st and 3rd General Conferences on Weights


47

and Measures in 1889 and in 1901 respectively, itis currently still defined in terms of a device or pro-totype. However, the 21st General Conference onWeights and Measure, in October 1999(13), “recom-mends that national laboratories continue their ef-forts to refine experiments that link the unit of massto fundamental or atomic constants with a view toa future re-definition of the kilogram”.

Definition

The kilogram (symbol kg) is the unit of mass; itis equal to the mass of the international proto-type of the kilogram.

Standards

The international prototype is a cylinder, thirty-ninemillimetres high and thirty-nine millimetres wide,made from an alloy of ninety percent platinum andten percent iridium. It has an approximate densityof twenty-one and one half grams per cubiccentimetre. It is considered the sole primary stan-dard for the kilogram. The original prototype -kilogramme des Archives, manufactured at the


48

same time as the mètre des Archives, is consid-ered to be the historical prototype.

From a single smelt, in 1889, were prepared: theinternational kilogram, four witnesses, and nationalprototypes (originally 40 of them to fill the needs ofthe countries then signatories of the Convention ofthe Metre). These, and those subsequently manu-factured by BIPM, are sometimes known as “Noxkilogram”, where “x” is the identification number ofone of these standards.

Because the definition and construction of the unitare based on an artifact, the unit can never be trans-ferred more accurately than allowed by mass com-parison with the international mass prototype.

Taking into account the limitations of the compari-sons, a hierarchy of the mass standards has beenset up, with the following obligatory characteristics:


49

INTERNATIONAL PROTOTYPE KILOGRAM Material: Platinum-Iridium; Density: 21,5 g cm-3

PRIMARY STANDARDS OF THE BIPM Material: Platinum-Iridium.

NATIONAL PROTOTYPE KILOGRAMMaterial: Platinum-Iridium.

PRIMARY NATIONAL STANDARDS Material: Steel (Brass) Density: 8,0 g cm-3 (8,4 g cm-3)

SECONDARY NATIONAL STANDARDSMaterial: Steel (Brass)

REFERENCE STANDARDS

WORKING STANDARDS


50

Accuracy

With the current kilogram standard it is possible tomeasure mass with an accuracy of 1 in 108.

The purpose of standards is to be able to measureexactly the mass of bodies; this requires multiplesand sub-multiples of the kilogram so that massescan be exactly determined.

The sets of multiples and sub-multiples of the kilo-gram must also be represented in the form of massstandards and compared with one or more kilogramstandards. To do so, multiples and sub-multiplesare grouped in decades related to at least 4 stan-dards; the most common representation is 1 2 2 5;thus, a one kilogram mass, m

1kg, can be determined

as:

m100

+ m200

+ m200

+ m500

where:

m100

= mass of the 100 grams standard.m

200 = mass of the 200 grams (NO 1) standard.

m200 = mass of the 200 grams (NO 2) standard.m

500 = mass of the 500 grams standard.


51

Clearly, an analytical laboratory balance requiresa different degree of accuracy than a truck weightcontroller scale. Accuracy of mass standards canbe categorized as E

i , F

i , M

i with values going usu-

ally from one milligram to 50 kilograms. High accu-racy masses correspond to class Ei , fine accuracyto class F

i , and medium accuracy to class M

i .

When studying the accuracy of m1kg

, the first com-position to estimate variability would be:

m1kg

- (m100

+ m200

+ m200

+m500

) = x

where m1kg

is the one kilogram mass standard andthe value of x can belong to any of the E, F or Mclasses.

OIML Recommendation R111(41) gives the differenttolerance levels for accuracy of different standardsmasses for classes E

i , F

i y M

i. Quality of measure-

ment will be characterized by its uncertainty.


The beam balance is the oldest known instrumentto have been used to measure mass. As long asthe definition of the kilogram remains unchanged,


52

we can only compare mass, never measure it di-rectly. With contemporary techniques it is possibleto build countless numbers and capacities of in-struments, adequate for their intended use, be thatin laboratories, industries, commerce, governmentagencies, etc. Basic requirements for balances arethat they be stable, exact, sensitive and subject tocalibration.

High accuracy metrology uses mass comparators.The mass comparator for a national standard musthave a limited interval and good sensitivity (for in-stance, 1 microgram).

In the past, we spoke of simple balances, with equalor unequal arms, with or without gliding weights,combination balances, platform-scales, romanscales, crane scales, deflection balances, springbalances and automatic balances with multipleequilibrium positions; today we also use electro-mechanical scales which send electrical signals todetermine weight. In view of all possible combina-tions, we nowadays speak of weighing instruments,without making distinctions between, for instance,a balance and a scale.


53

TEMPERATURE

What do we measure

In the case of measurements of what we call tem-perature, what we are looking for is an indicator ofthe heat of a given body. But heat is not the sameas temperature. We can define heat as a form ofenergy associated with and proportional to the mo-lecular motion. What we know as temperature isreally the value of a reading on a measuring de-vice such as a thermometer. For this reason, wesay that temperature is a manifestation of heat.

International definition of the unit for mea-surement of temperature

History

The definition of the measurement unit for tempera-ture has a long and complex history. As early as1742, Anders Celsius proposed a centigrade scaleof temperature, based on water, with zero at thefreezing point and a value of 100 at the boiling point.BIPM(19) has compiled the history of the unit, start-ing from the normal scale of hydrogen of 1878 up


54

to the current international temperature scale (ITS-90 or EIT-90) of 1990. It is however interesting tonote that a whole century went by until, in 1954,the 10th CGPM (General Conference on Weightsand Measures) adopted the proposal made in 1854by William Thomson Kelvin, of defining the unit forthermodynamic temperature (presently named af-ter him) in terms of the interval between absolutezero and a single fixed point. The current definitionwas approved by the 13th General Conference onWeights and Measures, in 1967.

Definition

The kelvin (symbol K), unit of thermodynamictemperature, is the fraction 1/273,16 of the ther-modynamic temperature of the triple point of wa-ter.

The triple point of water is the point where it is pos-sible to have equilibrium or coexistence of the sub-stance - water in this case - in its three states: solid,liquid and gaseous.

When speaking of temperature scales, it is commonto find references to the thermodynamic tempera-


55

ture, to which the international definition refers, and,also, to the practical scale of temperature.

The practical scale or Celsius scale, known beforeas centigrade, is the most commonly used. Its zerois the freezing point of water, and the boiling pointis defined as 100 oC, both measured under speci-fied conditions. Under zero of this scale, tempera-tures have a negative value; which is why we com-monly say that in a harsh winter, temperature maygo down to minus forty degrees (Celsius degrees).

On the other hand, the thermodynamic tempera-ture scale is expressed in kelvin by definition, andhas its zero at what is called absolute zero, equiva-lent to -273,16 oC. Thus, this scale has no nega-tive values and its intervals are the same as thoseof the Celsius scale.

Experts in thermometry usually express tempera-tures below 0 oC in kelvin, and those higher than0 oC in Celsius degrees. They also insist on thefact that the freezing point of water, 0 oC, at normalatmospheric pressure, occurs really at 273,15 Kwhile the triple point of water occurs at 273,16 K,equivalent to 0,01 oC.


56

Standards

The standard for the temperature unit is the physi-cal embodiment of the international temperaturescale ITS-90. Its purpose is to specify proceduresand practical thermometers, internationally ap-proved, that allow national laboratories to do directrealizations of the scale and to determine highlyreproducible values.

This direct realization is done by means of a seriesof sealed cells that contain a pure substance; thesubstance is in a state that corresponds to a giventemperature which, in turn, represents a fixed defi-nition point. The fixed definition points were origi-nally selected so that they would correspond asclosely as possible to the thermodynamic scale.

The data is compiled in the legal document knownas ITS-90. In October 1999(13), the 21st GeneralConference on Weights and Measures, invited theInternational Committee to work towards extend-ing the ITS-90 below its present lower limit of 0,65K.

There are many fixed points of definition for theITS-90 scale. Some are shown in Table 3.


57

TABLE 3

Some fixed points of definitionfor the ITS-90 scale

Temperature Substance State

T90/K t90/oC

from 3 to 5 from - 270,15 Saturated vaporto - 268,15 He - Helium pressure

83,805 8 - 189,344 2 Ar - Argon Triple point

234,315 6 - 38,834 4 Hg - Mercury Triple point

273,16 0,01 H2O - Water Triple point

302,914 6 29,764 6 Ga - Gallium Melting point

429,748 5 156,598 5 In - Indium Solidification point

505,078 231,928 Sn - Tin Solidification point

692,677 419,527 Zn - Zinc Solidification point

933,473 660,323 Al - Aluminium Solidification point

1 234,93 961,78 Ag - Silver Solidification point

1 337,33 1 064,18 Au - Gold Solidification point

1 357,77 1 084,62 Cu - Copper Solidification point


58

Uncertainties

With the sealed cells it is possible to calibrate tem-perature measurement devices with a relative un-certainty of the order of 10-6.


The first thermometer of which we have any refer-ence was built by the Italian scientist Galileo Galilei,around 1593. Today, there are several types ofsensors to measure temperature, and all of theminfer temperature through some change in a physi-cal characteristic (42).

The artifacts most commonly in use are: change-of-state devices, liquid-expansion devices, thermo-couples, resistive devices and thermistors, opticaland infrared radiators, bimetallic devices, pyrom-eters.

The change-of-state devices are indicating labels,pellets and crayons, lacquers, liquid crystals, grainsand cones, that change their appearance when agiven temperature is reached. They are normallyused for temperatures between 38 oC and 1 780 oC.The change due to the temperature is permanent


59

so that they cannot be used over again, their re-sponse time is relatively slow and their accuracy isnot very high, but they are useful for industrial ap-plications such as soldering or in ceramic ovens.

The home thermometer is the best known repre-sentative of the fluid-expansion devices. Thesethermometers can use mercury or an organic liq-uid such as alcohol, and some use a gas. Theycan work by partial, total or complete immersion.They can be used repeatedly, they do not requirea source of energy, but the data they give cannotbe directly recorded or transmitted.

Thermocouples are built from two pieces, made ofdifferent metals, joined at one end, and with a volt-meter; they are accurate, robust, reliable, and theirprice is relatively low. Their measurement intervaldepends on the metals used and usually is between- 270 oC and 2 300 oC.

Resistive devices (also known as RTDs) are basedon the principle that a change in temperature bringsabout a change in the electrical resistance. Whenusing metals, the resistance increases with a tem-perature increase; on the contrary, with thermistors,the electrical resistance of the ceramic semicon-


60

ductor diminishes with an increase of temperature.These are stable devices but they have a draw-back; because they work based on the flow of cur-rent through a sensor, a certain amount of heat isgenerated and can influence their accuracy. RTDswork at temperatures between -250 oC and 850 oC;thermistors between - 40 oC and 150 oC.

Optical pyrometers or sensors rely on the fact thatlight emitted by a hot body is related to its tem-perature; they work between 700 oC and 4 200 oC.Infrared pyrometers or sensors measure theamount of radiation emitted by a surface; they areappropriate for temperatures around 3 000 oC. Theyare more expensive but both have the advantageof not having to be in direct contact with the sur-face whose temperature is to be measured.

Bimetallic devices are based on the different ther-mal expansion of different metals. Two pieces ofdifferent metals are joined together; upon beingheated, one piece will expand more than the otherwhen exposed to the same change of temperature,and the generated motion is transmitted to an indi-cator on a temperature scale. They have the ad-vantage of being portable and of not requiring asource of energy.

Metrology for non-metrologistsMetrology for non-metrologists

61

Other temperature measurement devices used inmetrology are the standard platinum resistancethermometer, SPRT, the constant volume gas ther-mometers, CVGT, the radiation thermometers.(55)

Specifications and tolerances are set in accordancewith the type of temperature measurement artifact,its intended use, and the temperature interval of itsreadings. For instance, in industry, between 0 oCand 100 oC, an accuracy of 1 oC is considered nec-essary; above 100 oC, the required accuracychanges to 5 oC (6).


62


63

TIME AND FREQUENCY

What do we measure

The concept of time has always drawn the interestof philosophers and physicists. Aristotle and New-ton, among many others, tried to define time(44) and,more recently, Hawking(17) speaks of real time andimaginary time.

For practical purposes, time is a concept related tothe order and duration of events; if two events donot occur simultaneously in a given space, theyoccur in a given order and with an interval betweenthem(9). For primitive man, the first intimation of theflow of time must have been the daily cycle of dayand night, with the visible movements of the stars.We may reasonably suppose that longer durationswere later conceived through observation of lunarphases and of the seasons.

History

Time intervals were initially measured based on theposition of celestial bodies. One of the first artifactsmust have been the sun-dial, based on the obser-vation that the length of shade changes during the


64

day; it consists of a rod (called style or gnomon),parallel to the axis of the Earth, that projects itsshade on a quadrant. It is believed to date as farback as 579 BC and is attributed to Anaximanderor to Thales of Miletus.

Fire clocks were used to measure time during thenight, in closed rooms, or during sunless days, andwere nothing more than knotted ropes, markedcandles or a certain amount of oil. Later on, therewere water clocks of which a very ancient model isknown, with a float, built in China, but whose bestrepresentative is the clepsydra, perfected inGreece. This instrument was used by Assyrians,Egyptians, Greeks and Romans, and its use con-tinued well into the Renaissance. It is based on theassumed regularity of the flow of water through anorifice, and the better models used different diam-eters at different levels. The clepsydra in turn origi-nated the well-known and distinctive sand glass orhourglass.

Mechanical clocks are believed to have their originin China; they came to Europe around the thirteenthcentury. The first clock moved exclusively byweights, for which we have a description, was builtin 1364 by Henri de Vick, a German watchmaker,


65

for King Charles V of France. We owe the pendu-lum clock to Huygens, in 1657; he also developedthe mechanisms that would make pocket watchespossible. A Nuremberg locksmith, Peter Henlein,created the spiral or royal spring and by the seven-teenth century, the mechanisms were mostly springand balance. Clocks often had additional soundsystems of bells, carillons or “cuckoo”. All of thesegave rise to an important industry and real worksof art.

In 1855, E.D. Johnson built the chronometer. Al-ready in 1780, Louis Recordon had invented theautomatic chain for pocket watches but it was notuntil 1924 when John Harwood used it in wrist-watches. In the twentieth century, electric watchesand alarm clocks became very common, but thewidespread use of watches really came about whenbattery-operated watches became available on themarket; they were originally called digital watchesalthought there are also analog models. Presently,very accurate quartz watches are being manufac-tured.

The high degree of accuracy for time measure-ments which can be obtained today is possible withatomic clocks, used in science - particularly in me-


66

trology. They are stable because the frequenciesproduced are only very slightly influenced by ex-ternal factors such as temperature, pressure orhumidity.

International definition of the units formeasurement of time [13th General Confer-ence on Weights and Measures, 1967], andof frequency

Formerly, the definition referred to what we mightcall the astronomical second, nowadays we referto the atomic second.

The second, (symbol s), is the duration of 9 192631 770 periods of the radiation corresponding tothe transition between the two hyperfine levels ofthe ground state of the caesium 133 atom.

where 9 192 631 770 is the frequency of the en-ergy involved in said caesium transition; the groundstate is considered to be the state where electronsare at their lowest energy level; the hyperfine lev-els represent the smallest energy increase that theycan undergo in that state (6).


67

The derived unit for frequency is the hertz.

The hertz (symbol Hz) is the frequency of aperiodic phenomenon, the period of which isone second.

The hour (symbol h) and the minute (symbol min),are not decimal multiples of the second and thusare not SI units. However, their use is so wide-spread that they are considered units accepted foruse with the SI (see Table 3). In some cases, it isalso necessary to refer to larger time intervals suchas the week, the month and the year.

Standards

Practical realization of the definition of the secondis done using a caesium atomic clock. It is basedon the fact that atoms, under diverse excitements,emit monochromatic radiations and can thus gen-erate a period (the duration of an oscillation) whichcan be defined very accurately.

Other standards use other sources of frequencies,such as the hydrogen maser, rubidium standards,


68

commercial caesium standards, etc. They are suf-ficiently accurate for most applications, and theyare considered secondary standards.

It is not sufficient to be able to measure time inter-vals accurately; there must also be a world-widescale for comparisons and precise relations; airtransportation timetables are a good example ofthe importance of this synchronization.

This demands permanent maintenance of the samecontinuous temporal reference as an element inthe practical realization of the standard.


69

Atomic caesium clock(43)

Internal energy of an atom (electrons+nucleus) as-sumes values which correspond to the diverse quantum statesot the atom.

The atom has the possibility of carrying out a transi-tion between one level of energy E

A and another level of en-

ergy EB, with emission or absorption of radiation. Frequency

ν of the radiation is determined by the relationship:

h.ν = | EB - E

A |

where h is Planck’s constant.The transition adopted to define the second was se-

lected not only because of its own properties (monochroma-tism of the radiation which implies a well-defined frequency,with slight sensitivity to external perturbations), but also dueto technical reasons (among others, the transition frequencyis in a domain of frequencies accessible to current electronicinstruments, ease of use of caesium to obtain an atomic beamand for detection of ionization).

The caesium clock uses a very precise quartz oscilla-tor whose frequency is verified by generation of an electro-magnetic radiation which illuminates a cloud of caesium at-oms. If the radiation frequency is precisely 9 192 631 770cycles per second, the caesium atoms become polarized andcan be detected by a magnetic field. If the frequency deviatesslightly, the number of polarized atoms diminishes and thisgenerates a signal for correction to keep the oscillator’s fre-quency at its nominal value.


70

Time scales(19)

The International Atomic Time (TAI) scale, is calcu-lated at the BIPM. In 1999 it was obtained from data fromsome two hundred atomic clocks in nearly fifty national me-trology laboratories. To keep the scale unit of TAI as closeas possible to the SI second, BIPM uses data from thosenational laboratories which maintain the best primary cae-sium standards.

TAI is a uniform and stable scale which does not, there-fore, keep in step with the slightly irregular rotation of theEarth. For public and practical purposes it is necessary tohave a scale that does so in the long term. Such a scale isCoordinated Universal Time (UTC), which is identical withTAI, except that, from time to time, a leap second is addedto ensure that, when averaged over a year, the Sun crossesthe Greenwich meridian at noon UTC to within 0,9 second.When fractions of a second are not important, the well-known“Greenwich Meridian Time or Greenwich Mean Time, GMT”is practically equivalent to UTC. However, it is recommendednot to use the term GMT but instead to always use the termUTC.

Diffusion of the scale is done through severalmeans and may require special reception instru-ments.


71

It can de done by:

- telephone access to a time service, with an ac-curacy of up to 50 ms,

- coded hourly signals (for instance, 3 MHzto 30 MHz short wave, with an accuracy of10 ms(36), 1350 KHz modulated frequency, etc.)with accuracies of milliseconds,

- accuracies of 10 ns by reception of televisionsignals using GPS, Global PositioningSystem, based on artificial satellites.

Uncertainties

Current time standards work with relative uncer-tainties of the order of 10-14 and, in some cases, upto 10-15.

It has also been calculated that, in a million yearsof use, the atomic time scale TAI will differ from theideal scale by less than a second.

More than the accuracy, that may not be constant,the most important characteristic of a UTC scale(generated at national laboratories) is its stability.


72


Usual measurements of time are done with diversetypes of timepieces (such as clocks, watches andchronometers) with a greater or smaller accuracyaccording to the needs, calibrated with the UTC orTAI scales. Time interval counters and quartz os-cillators are also used.

For their part, measurements of frequencies requirevery high accuracies in applications such as digitalcommunication and global positioning systems(GPS).


73

ELECTRICITY AND MAGNETISM

What do we measure

Some materials, known as conductors, have freeelectric charges that can move, such as electronsin metals and ions in salt solutions. In these mate-rials, in the presence of an electric field, a stableflow is produced in the direction of the field; such aflow is an electric current.

Ohm’s Law relates the three basic elements of elec-tricity with the equation:

E = IR

where E is the electric potential, commonly calledvoltage, I is the electric current, and R is the resis-tance.

Based on this law, the electricity unit could havebeen defined through any one of these three ele-ments. It was decided to define it in terms of elec-tric current, leaving electric potential and resistanceas derived units.


74

Electric current is a property of matter that produceselectric and magnetic effects. In an isolated sys-tem, it is constant and produced in packets. Thesmallest isolated charge is that of the electron. Asimple manifestation of electric current is obtainedby rubbing with a silk cloth two spheres, of amberfor instance, suspended in a non-conductor mate-rial; the spheres repel each other because theyhave the same electric charge. If the spheres areof different materials, such as one of amber andthe other of glass, they attract one another becausethey have different charges(1).

We can visualize the behavior of electricity and theinterdependence of its characteristics through thefollowing similarity.

If we have a pipe carrying water, we can charac-terize it by the amount of water that flows throughthe pipe, the pressure at which it flows, and theproperties of the pipe itself. In electricity, the waterpressure would be equivalent to the electric poten-tial, expressed in volts (V); the amount of waterwould be the electric current expressed in amperes(A); and the friction due to the pipe material wouldbe equivalent to the electric resistance in ohms (Ω).


75

History

Nearly 2 600 years ago, Thales of Miletus notedthat when amber was rubbed with wool or leather,it attracted small pieces of hay or feathers.

Some 250 years later, Aristotle commented on the(electric) discharges produced by a fish - a varietyof eel.

The poet Lucretius described 2 100 year ago themagnet stone found in the region of Magnesia.

In 1 600, William Gilbert made a clear distinctionbetween electric and magnetic phenomena; the firstmachine to produce electricity through friction wasbuilt 63 years later.

Nowadays, the phenomenon is well known al-though complex, and closely related to quantummechanics.

Appendix 4 lists some of the scientists who havecontributed to the development of knowledge onelectricity.


76

International definition of the units formeasurement of electricity and magnetism[9th General Conference on Weights andMeasures, 1948]

The ampere (symbol A) is that constant currentwhich, if maintained in two straight parallel con-ductors of infinite length, of negligible circularcross-section, and placed one metre apart invacuum, would produce between these conduc-tors a force equal to 2 x 10-7 newtons per metreof length.

The main derived units are the volt and the ohm.

The volt (symbol V) is the potential differencebetween two points of a conducting wire carryinga constant current of one ampere, when the powerdissipated between these points is equal to onewatt.

Metrology for non-metrologistsMetrology for non-metrologists

77

The ohm (symbol Ω) is the electric resistance be-tween two points of a conductor when a constantpotential difference of one volt, applied to thesepoints, produces in the conductor a current of oneampere, the conductor not being the seat of anyelectromotive force.

Standards

The principles and devices used in a standard re-flect scientific development and the technical fa-cilities available. Formerly, electric current balanceswere used for the ampere, but they had a high un-certainty. Presently, better results are obtained us-ing the ohm and the quantized volt, and Ohm’s Law.

Practical realization of the unit is done with a sys-tem that is itself a standard. The Josephson effectis used for the reference unit of the volt and theHall effect for the resistance. The work carried outin the realization procedure is complex and requiresspecialized apparatus and instruments as well ashighly qualified personnel.

Standards and reference materialsStandards and reference materials

78

Uncertainty

Measurement uncertainty of the electric potential(volt) in an array of Josephson junctions is of a fewparts in 1010 and for the resistance standard withthe Hall effect of a few parts in109.

The high reliability in the transportation of the Jo-sephson and quantized Hall systems has given asa result that national laboratories can have inter-nationally comparable standard systems.


With current technology it is possible to build ana-log and digital devices to measure electric current.As in all scientific work, use of computers facili-tates, speeds up and gives higher certainty of re-sults. Measurement work uses extensively digitalprocessing and knowledge of quantum mechan-ics, making this high technology work even if theresults are in popular use in apparatus such as am-pere meters, voltmeters and resistance meters. Wemust also make a distinction between measure-ments of high resolution/low uncertainty - standardsand reference systems - and those for practical ap-plications.


79

LIGHT(PHOTOMETRY AND RADIOMETRY)

What do we measure

The different forms of radiant energy include cos-mic rays, gamma rays, X rays, ultraviolet rays, lightvisible to man, infrared, microwave, electric and ra-dio waves (hertzian).

In the case of photometry, we are primarily inter-ested in the phenomenon called light, one of theforms of radiant energy, that is energy as electro-magnetic waves, emitted as photons, and with a setfrequency and wavelength. From the point of viewof the spectrum visible to man, light for him has beenmostly sunlight and its substitutes through the cen-turies: fire, torches, candles, and all the lamps: oil,kerosene, gas; electric lighting in the form of incan-descent carbon filament, tungsten filament, sodium,neon, fluorescent, vapor of mercury, etc.

History

The study of light goes way back into history. Fourcenturies before Christ, Euclides worked on his


80

Optica, however the mechanism of vision was notidentified until the beginning of the seventh cen-tury. Other researchers have studied intensively thisphenomenon: Ibn al-Haitham in the eleventh cen-tury, Galileus in 1610, Kepler in 1611 with his Diop-trics, Descartes in 1637 when he discovered thelaw governing refraction, Newton in 1704 with histreaty on Opticks(53). Later on, Huygens, Fresnel,Maxwell, Michelson and many more have contrib-uted to this field of study.

For practical purposes, photometry tries to expressthe visual impression of an “average observer”. Dif-ferent people have different visual perceptions; forthis reason, the International Commission on Lightdid a series of measurements in a large number ofpersons, in order to be able to somehow definethis “average observer”.

Because human visual response varies with thewavelength, and the human eye does not perceiveinfrared and ultraviolet radiation, work is done onmeasuring physical quantities - in this case the en-ergy characteristics of radiation - and this is thefield of radiometry. Thus, although photometry andradiometry are two different fields, they are veryclosely related.


81

International definition of the unit for mea-surement of light

History

The unit and its standard have an uneven history(31).The candela was originally defined in the eighteenthcentury; it was based on burning elements and thushad a very low reproducibility. It was later modified(Carcel 1800, Hefner 1884) but working conditionsstill were a critical factor. In 1880, Violle suggestedusing a piece of platinum at a temperature corre-sponding to the transition point between the solidand the liquid states. There were problems derivedfrom the purity requirements of platinum andBlondel suggested in 1896 the use of a black bodythat would keep a constant high temperature; in1930, Burgess placed the platinum in a thorium cru-cible inside an induction furnace. Due to the diffi-culties for realization of the photometric unit, sev-eral congresses modified the Violle candle, in 1884,1889, 1909, 1921, 1933, 1937, 1938 and 1954 -when the candela was recognized as the sixth baseunit, after the metre, the kilogram, the second, the


82

ampere and the kelvin - up to the current definitionapproved by the 16th General Conference onWeights and Measures, in 1979.

International definition of the units of mea-surement in photometry and radiometry[16th General Conference on WeightsMeasures, 1979].

The candela (symbol cd) is the luminous inten-sity, in a given direction, of a source that emitsmonochromatic radiation of frequency 540 x 1012hertz and that has a radiant intensity in that di-rection of 1/683 watt per steradian.

The following working units are derived from thecandela.

The lumen (symbol lm) is the luminous flux emit-ted in a unit solid angle of one steradian by a uni-form point source having a luminous intensity ofone candela.


83

The lux (symbol lx) is the illuminance of a sur-face receiving a luminous flux of one lumen, uni-formly distributed over one square metre of thesurface.

The candela per square metre (symbol cd.m-2)is the luminance perpendicular to the plane sur-face of one square metre of a source of which theluminous intensity perpendicular to that surfaceis one candela.

In photometry, we use: luminous flux (lm), luminousefficiency (lm.W-1), luminous intensity (cd), lumi-nance (cd.m-2), illuminance (lx).

In radiometry, the units are: the energy flow rate,or heat flow rate, or power (W), the energy inten-sity or radiant intensity (W.sr-1), the energy lumi-nance or radiance (W.m-2.sr-1), the energy illumi-nance also known as irradiance or thermal flow den-sity (W.m-2).


84

Standards

Presently, maintenance of photometric and radiomet-ric standards no longer emphasizes photometricmethods, but rather radiometry based on detectors.The primary standard at the BIPM relies on a com-mercial cryogenic substitution electric radiometer, con-sidered to be one of the most accurate radiometersavailable. In addition, when the highest degree of ac-curacy is not required, there are sets of silicon photo-diodes that are used as working and transfer stan-dards. Transfer to national or other standards is alsodone using lamps, calibrated by comparison.

Uncertainties

The candela standard is realized with a relative un-certainty of 3 x 10-3.


In photometry and radiation, the following are used:radiometers; absorption, black body, polarization, elec-tric, and photoelectric photometers; integrators, colo-rimeters, spectrophotometers, spectroradiometers, andradiation measurers; also, cryogenic radiometers (de-tector-based radiometers) for standards.


85

ACOUSTICS AND VIBRATION

What do we measure

With the exception of people deaf from birth, hu-man beings intuitively perceive the concept ofsound. For all animals, sound is an important partof the environment. For man, particularly, soundsare involved in communications with others and inthe awareness of external circumstances eithernatural or man-made (music, the noise of machinesworking, warning bells and sirens, etc.)

Sound can be defined as a mechanical alteration,such as a change of density, or of particle displace-ment or velocity, in an elastic medium such as airor water. We consider a medium to be elastic if itcan go back to its original shape and size once thealteration that provoked the tension, shear or com-pression, has ceased.

Based on this definition, we can in turn define asound field as an elastic medium where a mechani-cal alteration, such as a change of density, or ofparticle displacement or velocity, is produced andpropagated.


86

In acoustics, we study and measure basic proper-ties of sound:

- intensity or loudness, determined by thewave amplitude

- pitch, determined by the frequency or numberof vibrations

- timbre, determined by the additionalvibrations (harmonic sounds) together withthe fundamental vibration

A normal human being cannot hear sounds of afrequency lower than 16 Hz (infrasounds) or higherthan 20 kHz (ultrasounds or supersonics).

Quantitative measurements of sound began in thenineteenth century, but it was really in the twenti-eth century, particularly its last 20-30 years, whenstudies have been done on the nuisance and thehazards of noise on the human auditory system(29).Recently, in 1999, the CIPM created a Consulta-tive Committee on Acoustics, Ultrasound and Vi-bration.


87

The International Standardization Organization,ISO, has established several standards, strictly inthe field of acoustics, that include aspects such as:standard tuning frequency, methods to calculateloudness levels, reference quantities for acousticlevels, etc.; and an even larger number of stan-dards in related fields. For its part, the InternationalElectrotechnical Commission, IEC, has been stan-dardizing aspects related to microphones and theircalibration, sound level meters, sound intensity, hu-man ear simulators, etc.

For metrological purposes, the most common mea-surements in acoustics are: the magnitude of asound field and the strength of a sound source.

In practice(29), to measure the strength of a soundfield, we use the sound pressure because it is theeasiest to transform from a form of energy (particlealteration in the elastic medium) to another equiva-lent form that is the one usually measured (for ex-ample, pascal, Pa, equivalent to newtons persquare metre, N/m2).

In the case of a source of sound, characterizationis done by its power.


88

Both the sound pressure and the power of asource of sound are measured in relative deci-bels at 20 µPa and 1 pW respectively.

Definition of the units for measurements in acousticsand vibration

We are familiar with watts in terms of illumination -we know that we can read comfortably when usinga light bulb of 100 W, while a 25 W bulb will give avery dim light. In the case of light, this is an arith-metical relation.

In comparison, sensibility to sound is different.Sounds of an ordinary conversation are around1 mW, which we can express as 1000 microwatts(µW), but soft sounds fall to fractions of 1 mW.

The human ear perceives differences in intensityexponentially. Thus, if 2000 µW “sound” a certainamount louder than 1000 µW, then we need 4000 µWinstead of 3000 to perceive the same amount ofincrease and, in turn, 8000 µW are necessary forthe perception of the same increase starting from4000 µW. The ratios 2000/1000, 4000/2000, 8000/


89

4000, are all equal, thought the differences betweenvalues are not, and it is by ratios that the ear judges.

When a sound has 10 times the power of a secondsound, the ratio is 10, whose logarithm is 1. In thiscase, we say that the difference in sound intensityis one bel (so called after Alexander Graham Bell).Similarly, if a sound is 100 times stronger than an-other, it is 2 bels stronger; if it is 1000 times stron-ger, it is 3 bels stronger. This type of unit reflectsthe logarithmic way the ear works.

Because the bel turns out to be too large a unit forusual measurement needs, we use the decibel.Thus, a sound will be one decibel stronger thananother when it is 1,26 times stronger, because0,1 is nearly the logarithm base 10 of 1,26.

This non-dimensional derived unit “one” has beenused to express logarithmic values such as thelogarithmic decrease, the pressure level or thepower level, in acoustics and electrotechnics.

We use the name bel (symbol B) and its commonlyused sub-multiple the decibel (symbol dB) whenusing logarithms of base ten; we speak of the neper


90

(symbol Np) when using natural or neperian loga-rithms. Acceptance of these units is still under studyby the CGPM.

Standards

The basic quantity for all measurements in acous-tics is the sound pressure. There is no practicalway to obtain a reference source that would gen-erate a sound pressure of one pascal, and workcontinues to find a way of generating or measuringa sound field in such a way it can be used as areference standard. Up to the present, accuracy ofmeasurements relies on the use of accurately cali-brated microphones.

For measurement purposes, the acoustic signal isconverted to an electric signal, using a condenseror electrostatic microphone. In this type of micro-phone, a diaphragm acts as one of the plates ofthe capacitor; the vibration produces changes in


91

the capacitance and these, in turn, producechanges in the output voltage.

The International Electrotechnical Commission,IEC, has a set of specifications for standard micro-phones, both for laboratory and for field work.

Calibration is done using sound calibrators with areference sound source. The IEC has establishedspecifications for calibration using the reciprocitytechnique(29), based on condensing microphones.This technique was selected for its uncertainty leveland has been internationally approved for the real-ization of the primary reference standard; it is be-ing refined through studies and world-wideintercomparisons.

Uncertainties

The minimum sound pressure difference that thehuman ear can perceive is 1 dB (one decibel).However, for many applications, such as thosehaving to do with the determination of noise and,particularly, that of aircraft, certification requiresmeasurements on the order of 0,1 dB; thus, pri-


92

mary references for measurement must have anuncertainty of around 0,05 dB.


Other measuring instruments are used in additionto microphones.

To determine pressure in continuous sounds, anexponential-averaging meter is used, and the val-ues are expressed in decibels as a sound pres-sure level. For discrete sounds, it is an integrating-averaging sound level meter, and the value is ex-pressed in decibels as an equivalent continuoussound pressure level.

Intensity of sound is a measure of the magnitudeand direction of the flow of sound energy. It is usu-ally measured using two microphones and thesound intensity level is expressed in decibels rela-tive to 10-12 Wm-2. With measurement of sound in-tensity, it is possible to determine the power of asource without the need for specialized environ-ments, but the method is not yet widespread.


93

IONIZING RADIATION

What do we measure

We call ionizing radiations those highly penetrat-ing electromagnetic radiations of extremely shortwavelength, at least as energetic as X-rays, whoseradiation is strong enough to remove or add elec-trons from matter, thus producing ions.

Among ionizing radiations we have: those that pro-duce charged particles such as α and β radiationsand the proton radiations; those that produce non-charged particles such as γ rays and x-rays (bothliberate photons) and the neutron radiations.

These radiations may be natural or artificially pro-duced in particle accelerators such as cyclotrons,betatrons, synchrotrons or linear accelerators.

History

X-rays were discovered by Wilhelm KonradRöntgen en 1895. In 1896, Antoine Henri Becquerel(whose name has been given to the radioactivematerial disintegration unit) discovered radioactiv-ity in an uranium salt. Pierre and Marie Curie


94

showed that all uranium salts were radioactive, aswell as thorium salts, and they also discovered theradioactive elements polonium and radium, presentin the mineral called pitchblende. Radioactive emis-sions are not homogeneous and Ernest Rutherford,in 1899, classified them according to their chargesand their penetrating power, and gave them thenames of alpha, beta and gamma radiations.

Definition of the measurements units for ionizing ra-diation

The nucleus of a radionuclide can be transformedor disintegrated spontaneously (see Appendix 5).Activity is characterized by the average number ofdisintegrations per second, and is measured witha unit called the becquerel.

Another important measurement is the absorbeddose, the quantity of energy imparted by ionizingradiation to a unit mass of matter, and it can beconsidered the fundamental unit in dosimetry.

The SI does not have base units for ionizing radia-tion, but it recognizes the becquerel and the gray


95

as derived units; in their simplest form they can bestated as follows.

The becquerel (symbol Bq) is the activity of aradioactive source in which one disintegration isproduced per second.

The gray (symbol Gy) is the dose of ionizing ra-diation uniformly absorbed by a unit mass of mat-ter, at a rate of 1 joule per kilogram of its mass.

Standards

Because of the variety of emitted particles and ofthe alterations suffered by the radioactive sources,there is no single primary standard for thebecquerel.

Primary references are set up as a blend of instru-ments and measurement methods, specific to eachtype of radionuclide.

As an example, for α emissions, (plutonium 239and plutonium 240 for instance) a silicon detector


96

is used as a counter in a defined solid angle. Acounter in a sodium iodide crystal well is used for γemissions (iodine 123 or iridium 192, for instance).

Similarly, there is no single standard for the gray indosimetry. In this case, the methods are based oncolorimetry, ionometry (with highly sensitive instru-ments that can be used for all radiations), Frickedosimetry, thermoluminescence (in radioprotectionand radiotherapy), electronic paramagnetic reso-nance (for industrial radiations).

Uncertainties

Uncertainties in measurements, both for thebecquerel and the gray, are on the order of 10-2 to10-3.


As for the setting up of standards, measurementinstruments are detectors, counters, dosimeters,calibrators for α and γ rays, ionization chambers,calorimeters, extrapolation chambers (variable ion-ization), etc.


97

CHEMISTRY

What do we measure

Stoichiometry is the branch of chemistry and chemi-cal engineering that deals with the quantities of sub-stances that enter into, and are produced by chemi-cal reactions. Every chemical reaction has its char-acteristic proportions; they are determined fromchemical formulas, equations, atomic weights andmolecular weights, and from determination of whatand how much is used and produced - that is, theamount of matter involved. All of stoichiometry isbased essentially on the evaluation of the numberof moles of substances, as a precise indicator ofthe amount of substance.

In chemistry, particularly in analytical chemistry, theamount of matter in a given sample is crucial infor-mation. It is also an important element in other as-pects such as concentration of solutions, the de-termination of pH, etc. In chemical industry, it isnecessary to know the amount of substances usedin the diverse reactions and in the products obtainedfrom them.


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History

Chemistry can be said to have been “studied” sincethe most remote ages. Metal work (copper, goldand silver, bronze, iron), ceramics, enamels, pig-ments, etc., all involve chemical processes to somedegree and this requires a certain amount of knowl-edge, even if at first this knowledge was eminentlypractical.

Around 1460, there was in Florence, Italy, a manu-script with fourteen treatises, allegedly written by apossibly fictitious person, Hermes Trismegistus,and known as the Corpus hermeticum. It is be-lieved to date back to years 100-300 although, inview of some references to Egypt, some believepart of its contents to go as far back as 2500 BC;this would make it the earliest known recordedknowledge of chemistry.

Empedocles (500 BC), whom we know throughAristotle, believed there are four elements in na-ture: fire, earth, air, and water. The first “atomic”theory (matter is made up of atoms, infinitely smalland indivisible) of which we have notice is due toLeucippus (around 475 BC) and his discipleDemocritus. It was taken up by Epicurus (341 BC),


99

the Latin poet Lucretius (De rerum natura), and inhis time, by Aristotle who taught that all matter iscomposed of mixtures of these four elements andthat they are not permanent but can change oneinto another. This led to the belief that it was pos-sible to transmute bodies, such as base metals,into others, such as gold.

The first “chemist” may well have been Jabir al-Hayian (also known as Jabir or Geber) of the courtof Harun al-Rashid (circa year 786), who studiedGreek documents and to whom a large amount ofwritten texts is attributed. He is believed to havemastered the techniques of practical chemistryknown at the time. He based his work on sulfur,mercury and salt, and wrote instructions on how tocarry out the manipulations.

There is material on chemistry written during theeighth century in Northern Africa and, with the avail-ability in Europe of translations from the Arab inthe twelfth and thirteenth centuries, there existrecords of the work performed by the alchemists.

In the fourteenth century one of them, NicolasFlamel, is reputed to have been able to succeed inproducing gold; what we know he did produce was


100

a gold fever, during the fifteenth and sixteenth cen-turies: a fever for alchemy, that hermetic and eso-teric world, to which scientists such as RobertBoyle, John Locke and Isaac Newton were not im-mune.

But alchemy, more than a simple search for theproduction of gold, began to be a science. It seri-ously studied chemical reactions, contributed tomany discoveries and new knowledge (for instance:distillation of aqua vitae or ethanol, preparation ofaqua regia, nitric acid, sulfuric acid, many salts),and generated countless controversies.

As an example, Robert Boyle in his book The Scep-tical Chymist (1661) refuted the chemical theoriesbased on the four elements and on the alchemisttrio (mercury, sulfur and salt), arguing they couldnot explain the results of experiments.

For our purposes, possibly the most importantchemist must have been Antoine Laurent Lavoisierwho, in 1789, published his Traité élémentaire dechimie. Lavoisier always insisted on the fact thatmeasurements were important in chemistry; quali-tative observation was not sufficient, it was neces-sary to work quantitatively.


101

Later, in 1811, Amadeo Avogadro stated the prin-ciple known by his name: equal volumes of gas atthe same temperature and pressure contain thesame number of molecules regardless of theirchemical nature and physical properties. This num-ber, the Avogadro number, is 6,023 x 1023; it is thenumber of molecules of any gas present in a vol-ume of 22,41 liters and is the same for the lightestgas (hydrogen) as for a heavy gas such as carbondioxide or bromine. Avogadro’s number is one ofthe fundamental constants of chemistry.

International definition of the unit for mea-surement in chemistry [14th General Confer-ence on Weights and Measures, 1971].

History

Formerly, the mole was defined as the molecular weightof a substance expressed in grams. Presently, andalthough this is not obvious from the way the unit isexpressed, the term is applied to an amount of 6,023x 1023 (Avogadro’ number) of chemical entities; thus,we can speak of a mole of atoms, a mole of ions, ofradicals, of electrons, of quanta. Nowadays, when the


102

mole is used, the elementary entities must be speci-fied and these may be atoms, molecules, ions, elec-trons, other particles or specified groups of such par-ticles.

The mole (symbol mol) is the amount of substanceof a system which contains as many elementaryentities as there are atoms in 0,012 kilogram ofcarbon 12.

The recent adoption of a derived unit, by the 21st Gen-eral Conference on Weights and Measures in 1999(13),is based on a recommendation for the use of SI unitsin medicine and biochemistry due to the importance ofavoiding the results of clinical measurement beinggiven in various local units.

The katal (symbol kat) is the mole per second unit, foruse in medicine and biochemistry for the expression ofcatalytic activity.


103


There is as yet no unique primary standard realizationfor the mole although work is being done towards hav-ing reliable standards.

Working standards in chemistry consist of a set of meth-ods, called primary, together with chemically pure sub-stances, with a defined titer, and in a known matrix,the reference materials.

The Consultative Committee on the Amount of Sub-stance (Comité Consultatif sur la Quantité de Matière- CCQM) of the CIPM has recommended several meth-ods as having a high potential for their recognition asprimary methods; among them we have:

Primary methods of direct measurement:

Electrochemistry:

- coulometric titration- pH measurements- electrolytic conductivity


104

Methods of classical analytical chemistry:

- gravimetry- titrimetry

Primary correlation methods of measurement:

- isotopic dilution with mass spectrometry- nuclear magnetic resonance- differential calorimetry

As to the materials to be used, let us recall here thedefinitions for reference material and for certified ref-erence material.

Reference material: material or substance one or moreof whose property values are sufficiently homogeneousand well established to be used for the calibration ofan apparatus, the assessment of a measurementmethod, or for assigning values to materials.

Certified reference material: Reference material, ac-companied by a certificate, one or more of whose prop-erty values are certified by a procedure which estab-lishes traceability to an accurate realization of the unitin which the property values are expressed, and for

105

which each certified value is accompanied by an un-certainty at a stated level of confidence.

An example of these is the usual certified referencematerials used in laboratories to calibrate instruments,and to verify methods and reagents.

Uncertainties

In chemistry, uncertainties of results vary according tothe element to be quantified and its concentration. How-ever, we can speak of levels from 10-3 to 10-4.


All determinations involve analytical techniques andinstruments for those methods considered to be pri-mary and they have already been mentioned.

107

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108

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References

116

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-62x10

Reproduced by authorization of the BIPM

Appendix 1

Fundamental physical constants and theirrelationship to the base units


117

C

Appendix 1

m12

c speed of light in vacuum

h Planck’s constant

α fine structure constant

R gas constant

k Boltzmann’s constant

Kj

Josephson’s constant

Kj-90

conventional value of

Josephson’s constant

Rk

von Klitzing’s constant

Rk-90

conventional value of

von Klitzing’s constant

e elementary charge

NA

Avogadro’s number

G gravitational constant

mass of carbon 12

me

electron mass

R∞ Rydberg’s constant

118


Ap

pen

dix

2

So

me

SI d

eriv

ed u

nit

s

Der

ived

SI d

eriv

edN

ame

Exp

ress

ion

inE

xpre

ssio

n in

qu

anti

tyu

nit

term

s o

f o

ther

term

s o

f S

I

SI u

nit

sb

ase

un

its

plan

e an

gle

radi

an (a

)ra

dm

·m-1 =

1 (b

)

solid

ang

lest

erad

ian(a

)sr

(c)

m2·m

-2 =

1 (b

)

freq

uenc

yhe

rtz

Hz

s-1

forc

ene

wto

nN

m·k

g·s-2

pres

sure

, str

ess

pasc

al P

aN

/m2

m-1·k

g·s-2

ener

gy, w

ork,

quan

tity

of h

eat

joul

eJ

N·m

m2·k

g·s-2

pow

er, r

adia

ntflu

xw

att

WJ/

sm

2·k

g·s-3

elec

tric

cha

rge,

quan

tity

of e

lect

ricity

coul

omb

Cs·

A

119

Appendix 2

elec

tric

pot

entia

ldi

ffere

nce,

elec

trom

otiv

efo

rce

volt

VW

/Am

2·k

g·s-3

·A-1

capa

cita

nce

fara

dF

C/V

m-2·k

g-1·s

4·A

2

elec

tric

res

ista

nce

ohm

ΩV

/Am

2·k

g·s-3

·A-2

elec

tric

con

duct

ance

siem

ens

SA

/Vm

-2·k

g-1·s

3·A

2

mag

netic

flux

web

erW

bV

·sm

2· k

g·s-2

·A-1

mag

netic

flux

dens

ityte

sla

TW

b/m

2kg

·s-2·A

-1

indu

ctan

cehe

nry

HW

b/A

m2· k

g·s-2

·A-2

Cel

sius

tem

pera

ture

degr

ee°C

KC

elsi

us(d

)

lum

inou

s flu

xlu

men

lmcd

·sr

(c)

m2·m

-2·c

d =

cd

illum

inan

celu

xlx

lm/m

2m

2·m

-4·c

d =

m-2·c

d

activ

ity (

refe

rred

toa

radi

onuc

lide)

becq

uere

lB

qs-1

120


abso

rbed

dos

e, s

peci

ficen

ergy

(im

part

ed),

kerm

a, in

dex

ofab

sorb

ed d

ose

gray

Gy

J/kg

m2 ·s

-2

dose

equ

ival

ent,

pers

onal

dos

e eq

uiva

lent

,

orga

n eq

uiva

lent

dos

esi

ever

tS

vJ/

kgm

2 ·s-2

(a)

The

rad

ian

and

ster

adia

n m

ay b

e us

ed w

ith a

dvan

tage

in e

xpre

ssio

ns fo

r de

rived

uni

tsto

dis

tingu

ish

betw

een

quan

titie

s of

diff

eren

t nat

ure

but w

ith th

e sa

me

dim

ensi

on.

(b)

In p

ract

ice,

the

sym

bols

rad

and

sr

are

used

whe

re a

ppro

pria

te, b

ut th

e de

rived

uni

t “1”

is g

ener

ally

om

itted

.(c

)In

pho

tom

etry

, th

e na

me

ster

adia

n an

d th

e sy

mbo

l sr

are

usu

ally

ret

aine

d in

exp

res-

sion

s fo

r un

its.

(d)

Thi

s un

it m

ay b

e us

ed in

com

bina

tion

with

SI p

refix

es, e

.g. m

illid

egre

e C

elsi

us,

m°C

.

121

Appendix 3

Ap

pen

dix

3

Mo

st c

om

mo

n m

ult

iple

s an

d s

ub

mu

ltip

les

for

use

wit

h S

I

Fac

tor

P

refix

S

ymbo

l F

acto

r in

wor

ds

1 00

0 00

0 00

0=

109

giga

Gon

e th

ousa

nd m

illio

ns

1 00

0 00

0=

106

meg

aM

one

mill

ion

1 00

0=

103

kilo

kon

e th

ousa

nd

0,00

1=

10-3

mili

mon

e th

ousa

ndth

0,00

0 00

1=

10-6

mic

roµ

one

mill

iont

h

0,00

0 00

0 00

1=

10-9

nano

non

e th

ousa

nd m

illio

nth

0,00

0 00

0 00

0 00

1=

10-1

2pi

cop

one

billi

onth

122

Appendix 4

Scientists who have worked with electricity

Epicurus (342-270 BC). First hypothesis on magnetism

Roger Bacon (1214-1294). Magnetic repulsion

Peter Peregrinus (1269). First text on magnetism

Cornelius Gema (sixteenth century). Attraction betweenlines of force

G. Cardan (1501-1576). Differences between electric and magnetic phenomena

Nicolo Cabeo (1585-1650). Repulsion

William Gilbert (1540-1603). First electroscope

S. Gray (1696-1736). Classification of bodies that can be electrified by rubbing

F. Hauskbee (seventeenth century). Superficial distribution of electricity


123

Appendix 4

C. Du Fay (1698-1739). Electric fluids, good and bad conductors

Benjamin Franklin (1706-1790). Lightning as an electric phenomenon

H. Cavendish (1731-1810). Dielectric constant, electric capacity and potential

Charles A. Coulomb (1736-1806). Quantitative law of attraction between two poles

Georg Simon Ohm (1789-1854). Fundamental law of electricity

Alessandro Volta (1745-1827). Voltaic pile

G. Green (1793-1841). Concept of potential in electrostatics

J. Karl F. Gauss (1777-1855). Terrestrial magnetism

M. Faraday (1791-1867). Dielectric constant and magnetic lines of force

Wilhelm Weber (1804-1890). Permanent dipoles

124


Hans C. Oersted. (1770-1851). Magnetism is a manifestation of electricity in motion

M. Ampere (1775-1836). Two parallel currents are attracted if they flow in the same sense, and repelled if in opposite senses

Pierre S. Laplace (1749-1836).

Jean B. Biot (1774-1862).

J. Henry. (1797-1878). Induced electromotive force

James Clerk Maxwell (1831-1879). Light is an electromagnetic phenomenon

H. R. Hertz (1857-1894). Verification that the speed of electromagnetic waves equals the speed of light

Ernest Rutherford (1871-1937). Theory of the nuclear atom

Edwin H. Hall (1855-1938). When a magnetic field is applied perpendicular to a current-carrying strip, a potential difference appears across the width of the strip

125

Leon N. Cooper (in 1956). In the ground state, at 0 K, with no external field and no current flowing, all the electrons form Cooper pairs in which two electrons have opposite momenta and spin

Briand David Josephson (1940- ). Cooper pairs can tunnel through a thin (1 nm) insulating barrier separating two superconductors; since each pair carries a charge of 2e, a supercurrent is created in the absence of any applied potential difference

Appendix 4

126


Appendix 5

Radionuclides - basic concepts(50)

Atoms of the same element always have the samenumber of protons in their nuclei but they can havedifferent numbers of neutrons. Those with differentnumbers of neutrons belong to different varietiesof the same element and are called its isotopes.They are usually distinguished by the total numberof particles in their nuclei. Thus, uranium-238 has92 protons and 146 neutrons while uranium-235has the same 92 protons but only 143 neutrons.Atoms thus characterized are called nuclides.

Some nuclides, the minority, are stable or producesuch low radiation that they can be consideredstable.

In those that are unstable, every transformationfrees energy and there are many variations forthese sequences of transformation or decay as itis called. The whole transformation process is calledradioactivity and the unstable nuclides are calledradionuclides. The average number of transforma-

127

Appendix 5

tions that take place each second in an amount ofradioactive material is called its activity. The activ-ity is measured in becquerels, after the man whodiscovered the phenomenon. The transformationsmay be natural or man-made by, for instance, neu-tron bombardment of stable nuclides.

The diverse forms of radiation are emitted with dif-ferent energies and penetrating power. Alpha (α)radiations can be stopped by a sheet of paper andthey barely penetrate the outer layers of the skin;however, they are extremely damaging when theyget into the body through an open wound, or whenthey are eaten or breathed in. Beta (β) radiationscan penetrate through a couple of centimetres ofliving tissue and gamma (γ ) radiations are stoppedonly by thick slabs of lead or concrete.

It is the energy of α radiation that does the dam-age. The amount of radiation deposited in livingtissues is called the absorbed dose and it is mea-sured with a unit called the gray.

128

On the other hand, a dose of α radiation is moredamaging (20 times more so) than the same doseof β or γ radiation; for this reason, the damage po-tential is taken into account in what is known asthe dose equivalent which is measured in sieverts.


viii

Temperature 53Time and frequency 63Electricity and magnetism 73Photometry and radiometry 79Acoustics and vibrations 85Ionizing radiation 93Chemistry 97

References 107

Appendix 1Fundamental physical constants and theirrelationship to base units 116

Appendix 2Some derived SI units 118

Appendix 3Multiples and submultiples of commonuse with SI 121

Appendix 4Scientists in the field of electricity 122

Appendix 5Radionuclides - basic concepts 126

ix

ACKNOWLEDGEMENTS

Several people and organizations have helped tomake this publication possible. The Organization ofthe American States, OAS, and the German Coop-eration for Development, GTZ, were the first to be-lieve that such a document could be of use.

For the help received, the authors wish to thank theBureau International des Poids et Mesures (BIPM);Dr. Gérard Geneves at the Laboratoire Central desIndustries Eléctriques du Bureau National deMétrologie in France (BNM-LCIE); Dr. Duncan Jarvis,Acoustical and Noise Standards, of the NationalPhysical Laboratory of the United Kingdom (NPL,UK); Dr. Hans-Jürgen von Martens, “Acceleration”section of the Physikalisch-TechnischeBundesanstalt (PTB) in Germany, Ing. LesterHernández from COGUANOR in Guatemala. For itspart, the National Institute of Standards and Tech-nology in the USA, NIST, through its Director for In-ternational Affairs, Dr. Steve Carpenter, made freelyavailable copies of its specialised publications.

The authors are particularly indebted to the scientificexcellence of the Centro Nacional de Metrología deMéxico (CENAM) and the contribution of its Director,Dr. Héctor Nava Jaimes, and the professional staff

Acknowledgements

x

of that organization; all of them shared fully and un-reservedly their knowledge and their work practices.Several changes in this second edition were sug-gested by CENAM personnel. We are particularly in-debted for their valuable comments to Dr. IsmaelCastelazo Sinencio, Director of Tecnological Servicesand M.Sc. Rubén Lazos, Scientific Coordinator, bothat CENAM, and to Dr. Luis Mussio, Head of Metrol-ogy at the Laboratorio Tecnológico del Uruguay(LATU).

The authors would also like to thank Mr.HermonEdmonson and Mr. Allan Foreman of the Bureau ofStandards of Jamaica for their help with the Englishversion of this publication.

Responsibility for the contents of this publication liessolely with the authors.

July 2002

xi

PRESENTATION

The aim of this book is to make available, to thosewho are not themselves metrologists, a scientificallyand technically sound document as an introduction tothe main aspects of Metrology in the hope that it willhelp them understand its importance.

A study of history shows that the progress of nationshas always been related to their progress in measure-ments. Metrology is the science of measurements andmeasurements are a permanent and integral part ofour daily lives, a fact we often disregard. Metrologyblends tradition and change; measurement systemsreflect a people’s traditions, but at the same time weare always seeking new standards and ways of mea-suring as part of our progress and evolution.

Thanks to our measurement instruments and appara-tus, tests and assays can be done to establish if aproduct or service conforms to existing quality stan-dards and this, in turn, gives an assurance of qualityof those products and services offered to consumers.

Because they facilitate and regulate commercial trans-actions, correct measurements are fundamental forgovernments, for enterprises and for the population atlarge. Very often, the amounts and characteristics of aproduct are the result of a contract between the client(consumer) and the provider (manufacturer); measure-ments contribute to this process and thus influence

Presentation

xii

quality of life for the population by protecting the con-sumer, helping to preserve the environment, and con-tributing to a rational use of natural resources.

Metrology related activities in a given country are usu-ally the responsibility of one or several bodies, autono-mous or governmental and, according to their scopeand their field of application, they are characterized asScientific, Legal or Industrial Metrology.

Scientific metrology is responsible for the researchneeded to produce standards with a sound scientificbasis, and it promotes their acceptance and interna-tional equivalence. Legal and industrial metrology re-late to the national use of the standards in commerceand in industry.

The field of Legal metrology relates to commercial trans-actions; it seeks to ensure, at all levels, that the clientwho buys something is effectively receiving the amountagreed upon. For its part, the aim of Industrial metrol-ogy is to promote competitiveness in manufacturing andservice industries, through permanent improvement ofthe measurements that influence quality.

As a result of the current dynamics of world commerce,metrology has become even more important, with astronger emphasis on the relationship between metrol-ogy and quality, measurements and quality control,calibration, laboratory accreditation, traceability, andcertification. Metrology is the basic core for these func-


xiii

tions and, when carried out coherently, it can bring or-der and contribute to the final aim of improving andguaranteeing quality in products and services.

In every country, Metrology plays a singular role, re-lated to Government, Enterprises and Population, a re-lationship known as the GEP model.

From the Government point of view, this model is es-sential to fully understand the purpose of the infrastruc-ture required to support the establishment of policiesand regulations for manufacturing products and forservices, both those produced locally and those im-ported from other countries.

Government must also be aware that the measurementcapabilities of a country are a measure of its level oftechnological development in several fields, includingmanufacturing and services (such as health, educa-tion, etc.), and that they directly influence competitive-ness of enterprises. Internationally, enterprises, and notgovernments, are the ones who compete, and one ofthe pillars of international competitiveness is quality; itmust be recognized that metrology is a necessary (al-beit insufficient by itself) condition for quality.

The capacity of an enterprise to innovate is one of thefactors of the competitiveness of the enterprise. Inno-vation may be applied to production or managementprocesses, to products, to services, or to any other func-tion of the enterprise. Permanent improvement of quality

Presentation

xiv

requires continuous improvement of activities; continu-ous improvement requires procedures that use mea-surement parameters, so that the newly implementedprocedures may be compared with what had been usedbefore. Measurements are, therefore, an integral partof the innovation process. Change is the only constantin an environment of continuous improvement. For en-terprises, the purpose of continuous improvement isgenerally to win markets and expand production facili-ties that, in turn, will open new avenues for growth andthe creation of new jobs.

Metrology is essential to support the control of the prod-ucts being manufactured and their impact on the wellbeing of the Population. Communities consume nationaland foreign products, and Metrology is called upon todetermine that these products are in accordance withhealth and safety standards and specifications.Metrology’s relationship with population is twofold: withits influence on the development of enterprises, it indi-rectly contributes to the creation of new jobs, but it alsohelps to protect people by watching over the contents,the quality and the safety of consumer products as wellas the impact of these products on the environment.

Worldwide open commerce has meant a growing inter-dependence among nations. More and more often,countries find themselves signing bilateral or regionalagreements and treaties. These involve different sec-tors (industry, commerce, health, defense, environment,etc.) and enterprises are then faced with operational


xv

international rules that apply to manufacture, buying ofraw materials, marketing, etc. If we add to this the factthat consumers are ever more influenced by globalpatterns of consumption, it is easy to see how essen-tial it is to have a technical infrastructure that can actas the framework for global coordination and order.

A primary requirement for this order is the adoption andrecognition of an international system of measurementunits. The first serious formal step for an internationalorder on measurements was the international MetreConvention or Treaty of the Meter (May 20, 1875), whichgave birth to the BIPM (Bureau International des Poidset Mesures - International Office of Weights and Mea-sures). In October 1995, the 20th General Conferenceon Weights and Measures (Conférence Générale desPoids et Mesures - CGPM) asked the InternationalCommittee on Weights and Measures (Comité Inter-national des Poids et Mesures - CIPM) to carry out astudy on international needs related to Metrology, soas to be able to direct and establish the respective rolesof BIPM, the National Institutes of Metrology and theRegional Metrology Organizations.

In the Western Hemisphere, the national metrology or-ganizations of 34 countries are associated in the Inter-American Metrology System, known as SIM. SIM co-ordinates its functions based on an organization of fivesub-regions that correspond to the five main economicand commercial groups of the Western Hemisphere.These metrology groups are: NORAMET (North

Presentation

xvi

America), CAMET (Central America), CARIMET (theCaribbean), ANDIMET (Andean Group), andSURAMET (South America).

Because of the recognized importance of Metrology andbecause of the importance of its being better under-stood by different groups of specialists, this publicationis addressed, as its title clearly shows, to those whosespecialty is not Metrology. The first chapter is a gen-eral introduction, the second tries to explain what ismeasured and why, the third strives to underline theimportance of this field of endeavor with a very briefdescription of some applications, the fourth chapterdetails the measurement standards and the referencematerials currently used for the main units of the Inter-national System of Units (SI). Our hope is that readingthis publication will help to gain easily a better under-standing of current Metrology.

Oscar HarasicRegional Coordinator of the Project Inter-American Systemfor Metrology, Standardization, Accreditation and Quality ,Organization of the American States, OAS.


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