Traceability in Chemical Measurement

Paul De Bièvre · Helmut Günzler (Eds.)

123

Traceability inChemical Measurement

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Prof. Dr. Paul De BièvreDuineneind 92460 KasterleeBelgium

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Preface

Not many terms covering concepts in measurement have cir-culated over the last ten years in the chemical measurementcommunity around the world so intensely as the term �trace-ability�. It appears in the title of CITAC (Cooperation on In-ternational Traceability in Analytical Chemistry) since 1993.It is addressed almost yearly in Workshops of EURACHEM(A Focus for Analytical Chemistry in Europe). Documents ofILAC (International Laboratory Accreditation Cooperation)require it to be used in the process of accreditation. Stan-dards and Guides of ISO (the International Organisation forStandardization) mention them frequently and insistingly.

In short, everybody talks and writes about �traceability�(because everybody talks and writes about �traceability�?).

The 2nd edition of the International Vocabulary of Generaland Basic Terms in Metrology, VIM2, (1993) de�nes it as the�property of the result of a measurement or the value of astandard whereby it can be related to stated references, usu-ally national or international standards, through an unbrokenchain of comparisons all having stated uncertainties�.

Over the years the problem had arisen that the term �trace-ability� became more and more ambiguous because it wasused for many different traceability concepts such as trace-ability of a sample (sample traceability), traceability of a doc-ument (document traceability), traceability of an instrument(instrument traceability) or -most important- traceability of ameasurement result (measurement traceability). The VIM2de�nition clearly meant it to be related to a measurementresult.

The revised edition of the VIM (VIM3), will probably�ne-tune the term for traceability of a measurement result tobe named �metrological traceability�. It is also likely thatthis de�nition is improved to read something like �propertyof a measurement result relating the result to a stated metro-logical reference through an unbroken chain of calibrationsor comparisons each contributing to the stated measurementuncertainty�.

Metrological traceability of chemical measurement re-sults means the establishment of a relation to a stated metro-logical reference (a �trace�). This can be the de�nition ofa measurement unit which, of necessity, must go througha practical realization or (better: an embodiment) of that

de�nition. But in case of operationally de�ned measurands(no units), metrological traceability can be to the result ofan (internationally) agreed measurement procedure, or tothe quantity value1 carried by a measurement standard suchas a certi�ed reference material. All of these metrologicaltraceabilities must be realized through an �unbroken chainof calibrations or comparisons�. The chain ensures that themetrological traceability of a measurement result has beenestablished to a metrological reference which must be stated.Only when measurement results are �traceable� to a commonmetrological reference, is their direct metrological compara-bility possible, i.e. is their ability assured to be comparable.

This anthology contains 56 outstanding papers on thetopic �Traceability�, published in the Journal �Accreditationand Quality Assurance� since its inception, but mostly in theperiod 2000�2003. They re�ect the latest understanding ofthe concept �measurement traceability� -or lack thereof- andpossibly some rationale(s) for the answer to the question whyit is important to integrate the concept of measurement trace-ability into the standard measurement procedures of everyanalytical laboratory.

For one thing, the wide variety of opinions re�ected in thepapers demonstrates that we have not yet achieved a commonunderstanding of the concept �traceability� and therefore notyet international understanding based on a concept which isunambiguously understood in the same way by everybody.Thus the international discussions will (have to) go on forsome time because agreement must be reached. Measure-ment traceability (metrological traceability) is a cornerstoneproperty of any measurement result. Only measurement re-sults which are traceable to a stated common metrologicalreference (such as a measurement unit), are directly �compa-rable�. �Comparability� of results is essential in any border-crossing context, whether that is the estimate of the monetaryvalue of goods, based on measurement results, or the rejectionof goods based on measurement results for toxic substancescontained in the goods, or when comparing results of clinical

1quantity (German: �Messgr ¤osse�, French: �grandeur de mesure�, Dutch:�meetgrootheid�) is not used here in the meaning �amount�, but as the genericterm for the quantities we measure: concentration, volume, mass, tempera-ture, time, etc., as de�ned in the VIM.

VI Preface

measurements in case of international business and leisuretravel. At least as important is the fact that proper evaluationof measurement uncertainty is only possible after metrolog-ical traceability has been established, i.e. after the �trace�or �track� has been decided by the analyst along which (s)hewill organize the plan of the measurement in order to makesure that metrological traceability to a common metrologi-cal reference would be in place. That is needed because themeasurement uncertainty in a measurement result can onlybe evaluated by combining the uncertainty contributions gen-erated by every step along the metrological traceability chain.

This anthology hopefully is of bene�t to both the pro-ducers and the users of results of chemical measurements:the basic concepts and the basic thinking in measurement arethe same for both. Only their measurement uncertainty willdiffer.

Prof. Dr. P. De BiŁvreEditor-in-ChiefAccreditation and Quality AssuranceKasterlee 2004-04-02

Contents

Measurement principles for traceability in chemicalanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Protocols for traceability in chemical analysis. Part I:De�nitions and terminology . . . . . . . . . . . . . . . . . . . . . . . . . 12

Protocols for traceability in chemical analysis. Part II:Design and use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Metrological traceability in laboratory medicine . . . . . . . 29

Traceability and analytical chemistry . . . . . . . . . . . . . . . . . 36

Do interlaboratory comparisons provide traceability? . . 45

From total allowable error via metrological traceabilityto uncertainty of measurement of the unbiased result . . . 50

Practical considerations on the traceability toconventional scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Traceability of (values carried by) reference materials . . 64

What can we learn from traceability in physicalmeasurements? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

How to achieve international comparability forchemical measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

The key elements of traceability in chemicalmeasurement: agreed or still under debate? . . . . . . . . . . . 79

The practical realization of the traceability of chemicalmeasurements standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Link to the SI via primary direct methods . . . . . . . . . . . . . 93

The role of reference materials . . . . . . . . . . . . . . . . . . . . . . 97

The measurement assurance concept in calibration andtraceability at NBS/NIST . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Lifetime of the traceability chain in chemicalmeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Pro�cienc y evaluation as a traceability link inchemical metrology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Achieving traceability in chemical measurement � ametrological approach to pro�cienc y testing . . . . . . . . . 114

Traceability issues in measurement . . . . . . . . . . . . . . . . . 121

Comparative study of the presentations at the CCQMworkshop on traceability . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Traceability in laboratory medicine . . . . . . . . . . . . . . . . . 128

Testing for foods derived from modern biotechnology:opportunities and limitations for metrology . . . . . . . . . . 134

A national traceability system for chemicalmeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Establishing measurement traceability in clinicalchemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Clinical laboratory reference networks . . . . . . . . . . . . . . 160

One way of disseminating reference values withdemonstrated traceability and demonstrateduncertainty to �eld laboratories: IMEP . . . . . . . . . . . . . . 166

Implementation of traceability � needs and perspectiveof the in-vitro-diagnosticum industry . . . . . . . . . . . . . . . . 175

Improvements in ef�cienc y of production andtraceability for certi�cation of reference materials . . . . 177

Traceable measurement in clinical laboratories . . . . . . . 184

A traceability protocol to the SI by gravimetric analysis 192

Reference samples for analysis of gas impurities inaluminium and titanium alloys: Features ofproduction, certi�cation and usage to ensuretraceability of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

The use of certi�ed reference materials in theRomanian traceability scheme . . . . . . . . . . . . . . . . . . . . . . 199

Traceable measurements of pH . . . . . . . . . . . . . . . . . . . . . 206

The development of gas standards and calibrationtechniques for measurements of vehicle, aircaft andindustrial emissions, natural gas, occupationalexposure and air quality . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

Problems of traceability of total protein andcatecholamine determinations in human urine . . . . . . . . 222

VIII Contents

Traceability in routine chemical measurements: anexample of application in the determination of CO2 atatmospheric concentration . . . . . . . . . . . . . . . . . . . . . . . . . 226

Traceability of measurement results of the effectiveacquisition time in gamma-ray spectrometryimplemented by the pulser method . . . . . . . . . . . . . . . . . . 230

Practical ways in establishing traceability in chemicaland other measurements in Mexico . . . . . . . . . . . . . . . . . 239

Bene�ts of the implementation of a metrologicalstructure for water analyses . . . . . . . . . . . . . . . . . . . . . . . . 245

Validation steps for traceability of linear calibratedchemical measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

Traceability, is it what we really want in our chemicalmeasurements? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

Traceability in measurement � time for an update? . . . . 260

On the existence of primary methods of measurement . 262

Traceability and uncertainty � A comparison of theirapplication in chemical and physical measurement . . . . 264

Traceability and its role in interlaboratory comparisons(pro�cienc y testing programmes), modeled on traceelement determination in biological materials . . . . . . . . 267

Traceable property values of in-house referencematerials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

Primary reference materials and traceability chain forgas compositon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

Traceability to units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

Traceability without uncertainty: current situation inpharmaceutical industry . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

The role of reference materials in analytical chemistry 279

Meeting ISO/IEC 17025 Traceability Requirements: ANew Guide with Worked Examples . . . . . . . . . . . . . . . . . 284

UK delivery of traceable chemical measurements inthe 21st century: building on the foundation of theVAM programme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Disseminating traceability in chemical measurement:Principles of a new EURACHEM/CITAC guide . . . . . . 290

CITAC Position Paper: Traceability in chemicalmeasurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

Glossary of analytical terms . . . . . . . . . . . . . . . . . . . . . . . . 295

Contributors

Hassan Y. Aboul-EneinBiological and Medical Research Department,MBC-03, P.O. Box 3354, Riyadh 11211, Saudi Arabia

Freddy C. AdamsDepartment of Chemistry, University of Antwerpen(UIA), Universiteitsplein 1, B-2610 Wilrijk, Belgium

Des AlphonsoCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

Elena Amico di MeaneIstituto di Metrologia �Gusta vo Colonnetti� delC.N.R., Strada delle Cacce 75, I-10137 Torino, Italy

Boris AnisimovThe National Physical Laboratory of Israel (INPL),Givat Ram, Jerusalem, 91904, Israel

V. P. AntipinAll Russia Institute for Light Alloys, Bldg. 2,Gorbunova Street, 121596 Moscow, Russia

Paul ArmishawNational Analytical Reference Laboratory, AGAL,Clive Road 3, Cottesloe, 6011 Western Australia,Australia

Charles M. Beck IINational Institute of Standards and Technology,Gaithersburg, MD 20899, USA

Brian BelangerVisiting Committee on Advanced Technology(Retired), National Institute of Standards andTechnology, Gaithersburg, MD, 20899�1004, USA

William BellCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

Chris BrookesCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

Lutz Brüg gemannDepartment of Analytical Chemistry, UFZ Centre forEnvironmental Research, Leipzig-Halle,Permoserstrasse 15, 04318 Leipzig, Germany

Mirella BuzoianuNational Institute of Metrology, Sos.Vitan-Bârzesti 11, 75669 Bucharest, Romania

Philippe CharletBureau National de MØtrologie� Laboratoire Nationald�Essais, 1 rue Gaston Boissier, 75724 Paris Cedex 15,France

Ludmila DabrowskÆNational Institute of Public Health, �robÆrova 48,100 42 Praha, Czech Republic

Paul De BiŁvreInstitute for Reference Materials and Measurements,European Commission � JRC, B-2440 Geel, Belgium

Hansa D�SouzaCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

Steluta DutaNational Institute of Metrology Sos.,Vitan-Barzesti 11, 75669 Bucharest, Romania

RenØDybkaerDepartment of Standardization in LaboratoryMedicine, Frederiksberg Hospital, H:S CopenhagenHospital Corporation Øster Farimagsgade 5, DK-1399Copenhagen, Denmark

Steve L. R. EllisonLGC Limited, Teddington, Middlesex, TW11 0LY, UK

John FlemingLGC Limited, Queens Road, Teddington, Middlesex,TW11 0LY, UK

D. Glavi�c-Cindro�Jo �zef Stefan� Institute, Jamova 39, 1000 Ljubljana,Slovenia

X Contributors

Irena GoldfeldThe National Physical Laboratory of Israel (INPL),Givat Ram, Jerusalem, 91904, Israel

Brian GoodyCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

A. A. GrigorievaAll Russia Institute for Light Alloys, Bldg. 2,Gorbunova Street, 121596 Moscow, Russia

Bernd GüttlerPhysikalisch-Technische Bundesanstalt (PTB),Bundesallee 100, 38116 Braunschweig, Germany

Gill HolcombeLGC Limited, Queens Road, Teddington, Middlesex,TW11 0LY, UK

Paul E. HollandCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

Lars JorhemNational Food Administration, Box 622,751 26 Uppsala, Sweden

Robert KaarlsNetherlands Measurements Institute, AR, 2600 Delft,The Netherlands

Mary M. KimberlyDivision of Laboratory Sciences, National Center forEnvironmental Health, Centers for Disease Controland Prevention, Atlanta, GA 30341�3724, USA

Barnard KingAnalytical Measurement Consultant, 25 BoltonGardens, Teddington, Middlesex, TW11 9AX, UK

B. KingNational Analytical Reference Laboratory, 1 SuakinStreet, Pymble, NSW 2073, Australia

Matjaz Korun�Jo �zef Stefan� Institute, Jamova 39, 1000 Ljubljana,Slovenia

Jan Ku�ceraNuclear Physics Institute, 250 68 �Re�z u Prahy, CzechRepublic

Ilya KuselmanThe National Physical Laboratory of Israel (INPL),Givat Ram, Jerusalem 91904, Israel

Richard LawnLGC Limited, Queens Road, Teddington, Middlesex,TW11 0LY, UK

Wang LinzhenNational Research Center for Certi�ed ReferenceMaterials, 100013 Beijing, People�s republic of China

Markus LippMonsanto Company, 800 North Lindbergh Boulevard,St. Louis, Missouri, 63167, USA

Randie R. LittleDepartments of Child Health and Pathology,University of Missouri School of Medicine, Columbia,MO, 65212, USA

M. MÆriÆssySlovak Institute of Metrology, KarloveskÆ63,842 55 Bratislava, Slovakia

A. MarschalBureau National de MØtrologie� Laboratoire Nationald�Essais, 1 rue Gaston Boissier, 75724 Paris Cedex 15,France

A. MathiasovÆSlovak Institute of Metrology, KarloveskÆ63,844 55 Bratislava, Slovakia

Roderick G. MillarNational Analytical Reference Laboratory, AGAL,Clive Road 3, Cottesloe, 6011, Western Australia,Australia

Martin MiltonCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

Yoshito MitaniCentro Nacional de Metrologia, Mexico, Col. Centro,Apdo. Postal 1-100, QRO. 76000 Queretaro, Mexico

Mathias M. MüllerInstitute of Laboratory Diagnostics, Kaiser Franz JosefHospital, Kundratstrasse 3, 1100 Vienna, Austria

Gary L. MyersDivision of Laboratory Sciences, National Center forEnvironmental Health, Centers for Disease Controland Prevention, Atlanta, GA 30341�3724, USA

Bernd NeidhartPhilipps-Universität Marburg,Hans-Meerwein-Strasse, 35032 Marburg, Germany

Ioannis PapadakisInstitute for Reference Materials and Measurements,Joint Research Centre � European Commission,Retieseweg, B-2440 Geel, Belgium

H. Steffen PeiserNational Institute of Standards and Technology 638,Blossom Drive, Rockville, MD, 20850, USA

Alejandro Perez-CastorenaCentro Nacional de Metrologia, Mexico, Col. Centro,Apdo. Postal 1-100, QRO. 76000 Queretaro, Mexico

Margherita PlassaIstituto di Metrologia �Gusta vo Colonnetti� delC.N.R., Strada delle Cacce 73, I-10136 Torino, Italy

Contributors XI

Gary PriceP.O. Box 57, Menai, NSW 2234, Australia

Han QiaoNational Research Center for Certi�ed ReferenceMaterials, 100013 Beijing, People�s republic of China

Paul QuinceyCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

Stanley D. RasberryNational Institute of Standards and Technology,31 Longmeadow Drive, Gaithersburg, MD, 20899,USA

William P. ReedNational Institute of Standards and Technology,Gaithersburg, MD, 20899, USA

Wolfgang RichterPhysikalisch-Technische Bundesanstalt (PTB),Bundesallee 100, 38116 Braunschweig, Germany

Rod RobinsonCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

Mike SargentLGC Limited, Queens Road, Teddington, Middlesex,TW11 0LY, UK

Michela SegaIstituto di Metrologia �Gusta vo Colonnetti� delC.N.R., Strada delle Cacce 73, I-10135 Torino, Italy

Lothar SiekmannInstitut für Klinische Biochemie, Universitätsklinikumder Universität Bonn, Sigmund-Freud-Str. 25,53127 Bonn, Germany

Ilona �perlingo vÆNational Institute of Public Health, �robÆrova 48,100 42 Praha, Czech Republic

Peter SpitzerPhysikalisch-Technische Bundesanstalt,Bundesallee 100, 38116 Braunschweig, Germany

Christoph TauschPhilipps-Universität Marburg,Hans-Meerwein-Strasse, 35032 Marburg, Germany

Philip TaylorInstitute for Reference Materials and Measurements,European Commission � JRC, B-2440 Geel, Belgium

Miloò TichýNational Institute of Public Health, �robÆrova 48,100 42 Praha, Czech Republic

Ian UprichardCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

B. Vodenik�Jo �zef Stefan� Institute, Jamova 39, 1000 Ljubljana,Slovenia

Emil Völk ertChairman of EDMA WP Standardisation, RocheDiagnostics GmbH, Sandhofer Str. 116,68305 Mannheim, Germany

L. Vysko�cilSlovak Institute of Metrology, KarloveskÆ63,842 55 Bratislava, Slovakia

Andrew WallardBureau International des Poids et Mesures, Pavillon deBreteuil, 92312 SŁvres, France

Wolfhard WegscheiderInstitute of General and Analytical Chemistry,University of Leoben, Franz-Josef Strasse 18,8700 Leoben, Austria

Alexander WeismanChemagis Ltd., P.O.Box 9091, Tel-Aviv 61090, Israel

R. WennrichDepartment of Analytical Chemistry, UFZ Centre forEnvironmental Research, Leipzig-Halle,Permoserstrasse 15, 04318 Leipzig, Germany

Alex WilliamsChairman EURACHEM Working Group onMeasurement Uncertainty, 19 Hamesmoor Way,Camberley, Surrey, UK

Peter T. WoodsCentre for Optical and Environmental Metrology,National Physical Laboratory, Teddington, Middlesex,TW11 0LW, UK

Adolf ZschunkeBundesanstalt für Materialforschung und-prüfung (BAM), Richard-Willstätter -Strasse 11,12489 Berlin, Germany

Accred Qual Assur (1996) 1 :3–13Q Springer-Verlag 1996 GENERAL PAPER

P. De BièvreR. KaarlsH. S. PeiserS. D. RasberryW. P. Reed

Measurement principles for traceability

in chemical analysis

Abstract By the definition of themole as a base unit for amount-of-substance measures within the In-ternational System of Units (SI),chemists can make chemical meas-urements in full compliance withestablished metrological principles.Since the mole requires exactknowledge of the chemical entity,which is often neither available norof practical relevance to the pur-pose of the measurement, the SIunits of mass or length (for vol-ume) are unavoidable in the ex-pression of results of many chemi-cal measurements. Science, tech-nology, and trade depend upon ahuge and ever increasing numberand variety of chemical determina-tions to quantify material composi-tion and quality. Thus, internation-al harmonization in the assess-ments of processes, procedures,and results is highly desirable andclearly cost effective. The authors,with relevant experience and re-

sponsibilities in Europe and Amer-ica, have found some consensus inthe interpretation of the metrologi-cal principles for chemical measur-ements, but believe open discus-sion should precede wide imple-mentation by chemical communi-ties. In fostering this dialogue, thispaper shows, for instance, thatmore precise interpretation of thedefinitions for “traceability,” “cali-bration,” and “validation” isneeded for present-day chemicalmeasurements. Problems that facescientists in making measurementsdo not all vanish just by adherenceto the SI. However, such com-pliance can improve communica-tion among chemists and metrolog-ists.

Key words Traceability 7 Mole 7Definition 7 Measurements 7Chemical metrology 7 Calibration 7Validation 7 Reference materials

Received: 30 June 1995Accepted: 30 June 1995

This publication is not subject to copy-right; it includes contributions from theNational Institute of Standards and Tech-nology, an agency of the U.S. Govern-ment.

Paul De Bièvre (Y)Institute for Reference Materials andMeasurements, European Commission –JRC, B-2440 Geel, Belgium

Robert KaarlsNederlands Meetinstituut,NL-2600 AR Delft, The Netherlands

H. Steffen Peiser638, Blossom Drive, Rockville,MD 20850, USA

Stanley D. Rasberry and William P. ReedNational Institute of Standardsand Technology, Gaithersburg,MD 20899, USA

Introduction

Science, technology, and commerce require rapidly ris-ing numbers and types of measurements that for goodreasons can be trusted [1–4]. Worldwide acceptance ofmeasurement results requires reliable, traceable, andcomparable measurements for reduction of costs, effi-cient production processes, subsequent use of measure-ment data, realization of fair-trade conditions, and forinternationally recognized and accepted laboratory ac-creditations. Physical measurements made in accor-

dance with the International System of Units (SI),which was introduced under the Convention of the Me-ter (with status of an International Treaty), have satis-fied many of these needs [5, 6]. Such measurementstypically rely on a comparison of the measured quantityin the item concerned with the same quantity in a“standard.” Chemical measurements are usually notmade by comparison with an equivalent chemical“standard.” Chemical measurements are not yet widelymade in terms of the SI unit of amount of substance,the mole [7]. This paper will explore the possibilities

2 P. De BiŁvre et al.

for bringing a stronger metrological foundation tochemical measurements and will specifically describe arole for reference materials in the traceability of chem-ical measurements to the SI [8].

Amount-of-substance measurements

Most chemists will agree that the majority of chemicalmeasurements are, or could be, expressed as amount-of-substance measurements. When appropriate, theywill in this paper be so described. However, whereasmass or length (volume) measurements at the smallestattainable uncertainty do not generally require a de-tailed understanding of the material whose property isquantified, amount-of-substance measurements requirereference to the exact composition of the measured en-tity, to interfering impurities, and to the material – bycomposition, mass, or volume – within which that entityis measured.

In many chemical measurements one neither knowsnor, at the time of measurement, wishes to know theexact composition of the matrix. To give an example, ametallurgical firm will receive ore shipments measuredby mass in kilograms. Representative samples in theseller’s and receiver’s laboratories are measured forquality by the amount of substance of a specified metalelement or compound per given mass of ore. It is unne-cessary and far too complex to attempt amount-of-sub-stance measurements on all components of the bulk. Inexactly the same way, a food laboratory might measurethe amount of substance (say lead) in orange juice inmilligrams per liter (per cubic decimeter). The charm ofthe SI system lies in a coherence, which makes it possi-ble to express all measured quantities in a combinationof base and derived units [9].

Thus, whereas chemists have historically expressedanalyses mostly by mass per mass, or as convenient per-centages, or by mass per volume, they could expresstheir measurements in amount of a specific substanceper mass (mole per kilogram) or per volume. In casessuch as pure materials and gases, mole per mole can beused. A percentage statement, or one in parts per thou-sand, million, or billion, is possible, though not recom-mended. In the SI system, as originally visualized, suchdimensionless numbers as results of measurements arenot favored. The quantitative result of any measure-ment should be expressed by a number “multiplied” bythe appropriate unit associated with the measuredquantity. As is further discussed below, this originalpreference proposed for the International System doesnot fit well with much of current practice in chemicalmeasurements.

Towards harmony in amount measurements

There is no doubt that chemical measurements are andmust be widely used in science and research, technolo-gy, engineering, and agriculture, as well as in regulatoryissues, including boundary crossings, health control, en-vironmental assessment, and commerce. A vast numberof chemical measurements is made every year. Evermore will be needed for reasons of increasing complex-ities in human interactions with the environment [4, 10,11]. For many measurements worldwide – such asozone levels in cities and the upper atmosphere – it isnecessary to maintain anchor points with long-term sta-bility. More generally, all equivalent measurementsshould be made in harmony with each other [2], evenwhen the practically needed and achievable reproduci-bility [9] has to be superior to the best attainable uncer-tainty in measurement relative to “true value.” The re-lation to true value, however, remains the ultimate testfor quality of a measurement [12]. At present it is arather widely accepted opinion that, even when the re-lation to the true value is elusive, chemists in differentlaboratories equipped to make repeatable measure-ments can still make them comparable to one anotherby the use of a reference material (RM) [13–15]. Thecorrectness of this concept will be discussed later.

The use of the mole

We seek to understand the reasons why chemists tendnot to express their measurements by the mole, the SIunit of amount of substance, which is said to have beenintroduced at their request and which is appropriate formany chemical measurements. Some of the backgroundhas been discussed previously [7, 16, 17]. Here we hopeto discuss:1. Why and to what extent we advocate a coherent im-

plementation of a wider use of “amount of sub-stance” by chemists

2. Why the use of the mole itself does not solve press-ing common problems in chemical measurements

3. Why certified reference materials can meet many,but not all, needs of chemists

4. How we hope a consensus either exists or can beachieved regarding the traceability of measurementsto SI

5. Why RMs are necessary to promote harmony amongchemical measurements worldwide.

The nature of chemical measurements

Measures of a mass, a length, or a time are not depend-ent on the composition and constitution of the material.By the definition of the mole, need exists for amount-

Measurement principles for traceability in chemical analysis 3

of-substance measurements to specify the entity amongpossibly many types of entities in the material underconsideration. Amount-of-substance measurements arehighly dependent on the composition and constitutionof the material. Chemical measurements fall into fourgroups:1. Measurements that can be expressed as a mole/moleratio, the most basic measurements in chemistry, aretypified by processes which react, interact, blend, or re-place a described amount of substance A with a de-scribed amount of substance B. Included are solutionconcentration measurements when all solutes areknown in a known solvent. Note especially that thesemeasurements are independent of the magnitude of theunit mole. Note also that if these measurements aremade by mass or volume determinations, the uncertain-ties in the corresponding atomic or molecular mass val-ues must be taken into account.2. Measurements that can be expressed as a mole/kilo-gram or mole/liter ratio are the most commonly madeand are typified by a described amount of substance ofcompound A in an unspecifiable amount of substanceB. Note that for these measurements the uncertainty ofand relation to the unit mole, just as those applicable tothe kilogram or meter, are involved.3. Measurements that can only be expressed as kilo-gram/kilogram or kilogram/liter are unusual becausethey involve amounts of substances of unknown com-position. Instances of this type are not really rare. Ex-amples are particulates in air and condensed-ring com-pounds in tar. Chemists can be reassured that no men-tion of the mole is made or needed for expressing theresults of such measurements.4. Measurements that are described directly in terms ofmultiples and submultiples of the kilogram, the liter, orthe mole are the measurements that provide the under-pinning of chemical measurements in science, technolo-gy, and trade. They are typified by calibrations or vali-dations of values of weight sets, reference materials, orinstruments, as well as by determinations of the magni-tude of the unit mole of a specifie compound (from thequotient of that compound’s mass divided by that of asingle 12C atom), or of the Avogadro Constant.

Measurements for which reproducibility is more easilyobtained than accuracy

Practical chemical measurements are commonly moreprecise than accurate. By that statement, we mean thatthe uncertainty of a measurement relative to the truevalue expressed, in either the mole or the kilogram, isgreater than the range for repeated measurements inthe same or even different laboratories at differenttimes or by different operators under different environ-ments.

1 The use of “in the field” is intended without detriment to meas-urements made in laboratories other than those whose main con-cern is the traceability link to the true value and the SI.2 Although for physical measurements one often speaks of var-ious kinds of “standards,” there is a functional difference, but nosharp distinction, in current usage between, say, a transfer stand-ard and an RM.

By contrast, satisfactory practical mechanical, elec-trical, optical, and thermal measurements are oftenmade adequately for the purpose at hand, even if lessaccurate than corresponds to the optimum achievableuncertainty relative to “true value” expressed under SI.Routine measurements in these fields can thus be ex-pressed conveniently in terms of the relevant SI unit toan uncertainty determined principally by the uncertain-ty of the practical measurement in the “field.” 1 Harmo-ny among most physical and engineering measurementscan be achieved to the uncertainty of the measurementin the field by traceability of all measures to the SI unitwithout invoking an intermediate “standard” 2 or RM.

In physical science there are occasionally instanceswhere measurements need to be more reproduciblethan the lowest achievable uncertainty relative to thetrue value in SI units. Chemists, not just occasionallybut as a rule, must achieve traceability of measure-ments by use of some standard, a reference material, areference instrument, or a reference method [18]. Thespread of these measurements made in different labo-ratories is often required to be smaller than the uncer-tainty with respect to true value. Nevertheless, oneshould state any such measurement in moles along withan assessment of the quality of its reproducibility. Sucha statement will be different depending on its applica-bility within a laboratory, between laboratories, for agiven method and environment, or in relation to anRM. When an RM is used, one must also include itsoften larger uncertainty of traceability to the SI unit.This uncertainty of the value of the RM must be in-cluded in the total uncertainty of the unknown.

Some important issues in all metrologyy

When discussing traceability of both physical andchemical measurements, one must be clear from theoutset on the following conditions applicable to anymeasurement or measurement capability.

The type of measurement

First, we must specify the type of quantity: a base quan-tity such as temperature (a property that is coupled to abase unit within the SI), a derived quantity such aspressure (a property coupled to a derived unit, being

4 P. De BiŁvre et al.

the quotient of two or more base units within the SI),or even a quantity such as a hydrogen-ion concentra-tion (a property that by convention is not commonlycoupled to the SI, although perhaps it should be).

The relevant range of measurement

Measurements are needed over a total of many moreorders of magnitude of a quantity than any one meas-urement methodology or instrument can achieve. Forelectric current, the measurement in a nerve fiber near1 nA will differ from one applicable to a gigantic TAcurrent in a magnet laboratory. At the two ends of themeasurement range there is a non-trivial need to relateany “standard” in the smallest or highest range to theapplicable SI unit itself. Needed amount-of-substancemeasurements, too, may range over more than 12 or-ders of magnitude.

The uncertainty statement

The uncertainty applicable to a measurement containscomponents for repeatability and reproducibility [9, 19,20], caused in part by variability of measurement-rele-vant parameters. The uncertainty also depends on theindividual making the measurement, the laboratory fa-cilities used, and the environment during the measure-ment. Without some quality control over measure-ments, statements on relevant traceability can have lit-tle meaning. Such controls provide a laboratory withconfidence in its operators and credibility to the out-side.

Often of general interest is the reproducibility ofmeasurements when operator, equipment or environ-ment is not the same. One must commonly distinguishclearly between uncertainties applicable to measure-ments at different times (called repeatability [9]) andthose made in different places (called reproducibility).A statistical analysis of homogeneity may be neededwhenever a measurement is made on a representativesample from the object to be evaluated.

The similarity principle of metrology

In metrology in general, the closer the similarity be-tween two specimens, the smaller the relative uncer-tainty of the measured difference between them andthe easier it is to make a reliable measurement. Thus,by the use of suitable “standards,” measurements in the“field” can become highly reliable and far less demand-ing and costly.

By this similarity principle it is possible to measureprecisely and relatively easily small differences from an

amount, or ratio of amounts, given by a “standard.”RMs thus become very attractive vehicles for measure-ment traceability and quality. However, there is an as-sociated problem: good reproducibility of comparisonsbetween pairs of similar specimens is liable to misleadand, in practice, often causes underestimations of totaluncertainties through failure to consider additional,large error sources.

Fitness for purpose

The achievement of smaller uncertainties than neededis usually uneconomical. In a practical way, realistic un-certainty assessments in relation to true requirementslead to economically sound planning for measurementsto be fit for their intended purpose.

The classical measurement pyramid

A simple view of measurement services pictures the In-ternational Bureau of Weights and Measures (BIPM)with its international prototype kilogram and the seem-ingly perfect constants of physics at the peaks of hugepyramidal systems for all types of measurements, eachwith many levels. The first level below the apex lists therealizations of units at a number of national metrologyinstitutes, passing on slightly more uncertain measure-ments to a much larger number of laboratories, whichin turn service lower-tier measurement laboratories,until at the very bottom of the broad-based pyramidsthe workbenches receive calibrations that have becomea little more uncertain at every intervening level. Thatsystem is simple to understand and works well for mostindustrial and legal services and for the control ofsmall-scale markets, for which the step-by-step lossesfrom impressive accuracies near the appropriate apexlevel are tolerable. An inverted pyramid may also be-come useful for illustrating traceability [7].

For chemical measurements, a possibly preferablesystem is illustrated in Fig. 1. Various possible forms ofrealization of traceability are given. They range fromvirtual lack of traceability to a fully “SI-bonded” meas-urement. The authors tentatively use the term “SI-bonded” to indicate a direct realization of the SI unit,as opposed to being traceably linked by way of mea-sured values. Any user laboratory must seek a refer-ence laboratory that is capable of providing measure-ment links of the adequate uncertainty and that pro-vides the direct bond to the SI, if that is needed. Thereference laboratory can in turn choose the traceabilityquality that it wishes to maintain, with the responsibili-ty of fulfilling the corresponding competence require-ments.

Measurement principles for traceability in chemical analysis 5

Fig. 1 Traceability Schemesfor Field Measurement values(FM)

M p Measurement values

In modern high-technology situations, however, veryhigh reproducibilities are frequently required. A goodmetrological system must provide means whereby anymeasurement station can have access to the highestneeded level of the system.

Some important issues for the wider introduction ofmetrological concepts into chemistry

The above features are common to all measurements.However, some chemical considerations do not have aclear equivalent in physical measurements.

The diversity of chemical measurements

Whereas the types of measurements in physics and en-gineering do not exceed the numbers of base and de-rived units of the SI, chemical measurements are vir-tually infinite, equal to the number of chemical ele-

ments and compounds. Whereas the magnitude of, say,mass is defined independently of the entity for which itis measured, the amount-of-substance determination ismade specifically relative to one entity. This situationshould not lead to confusion, but some chemists fearthat it might. For instance the “mole of nitrogen” is notdefined until it is said whether reference is made to N2

or N.

The word “mole”

Other potential difficulties for chemists arise from dif-ferences among molecular, molar, and the historicmeaning of “mole” in chemistry [16, 17]. Some find themole unsuited as a base unit in SI because, they argue,it is just a number of entities. Others find the use of“amount of substance” awkward, especially when theentity – for instance an ion – is not generally regardedas a substance. However, true and relevant some ofthese objections to current nomenclature and defini-

6 P. De BiŁvre et al.

tions are, a consensus is most unlikely to be reached onany related change in the foreseeable future. Discus-sion on such a change here is therefore not relevant tomore immediate opportunities for a useful consensus inamount-of-substance measurements.

The matrix effect

Whereas the measurement of, say, mass depends littleon the character (e.g., density) of the object for which itis made, the measurement of amount of substance isstrongly dependent on the matrix in which the entityresides. Chemists have always been concerned with in-terferences, but the general problem has become moreimportant with the introduction of many powerful ana-lytical-chemical instruments, the performance of whichdepends not only on specific physical properties of theentity to be measured, but also on the matrix withinwhich the entity is contained. Chemists may wish forRMs for all entities to be measured in all kinds of ma-trices of interest to technology or trade. However, theproduction of every RM is a time-consuming expensiveprocess. Chemists are thus faced with the unendingproblem of available resources imposing severe practi-cal limits to the number of RMs that can be producedin conflict with the wide range of matrices of interest.Consequently, a most important contribution that basicchemical science must make is in the development ofmatrix-independent methods of measurement [21]. Thechallenge is to separate the one entity to be measuredfrom the influence of all other entities in a mixture. Bywidespread abilities to do so, metrology in chemistrywill reach its most desirable aim to make accurateamount measurements related to the mole unit. In thefuture, chemical metrology should be directed at thebasic science on RMs whose link to SI is strong and atfield methods whereby specimens can be compared re-liably with the RMs, independent of matrix [7, 22].

SI recognizes derived units (products or quotients ofbase units)

Whereas the measurement of, say, mass can be statedas a fraction of a total mass (e.g., mass of a sample in abottle), the amount of substance of a given entity canusually not be stated as a fraction of all amounts of sub-stance in a material. One typically does not even knowor care about all the other entities, and one certainlydoes not generally wish or need to analyze the materialin terms of all its constituents. The SI system permitsand widely encourages coherently associated units. Thesubstance of interest should, where possible, be ex-pressed in the SI unit, the mole. The other substances,the amounts of which are of no immediate interest to

3 By contrast, many measurements are initially additive, as is truefor mass, time interval, and length.

the determination, are quantified in terms of SI unitssuch as the kilogram that do not distinguish entities.

Do physicists use the mole?

Geophysicists generally describe the composition of theuniverse or of the earth by mass percentages. Theycould use the mole, the amount of terrestrial substanceof, say, aluminum. In the very processes leading to thebirth of the elements, amount ratios are of prime inter-est. The end amount of Al would be expressed in moleper average terrestrial kilogram.

Measurement by ratio

Proponents of the SI for chemistry must consider thatproportionality is deeply embedded in chemical think-ing.3 Many of the potentially most reliable analyticaltechniques – for instance isotope-dilution mass spec-trometry – yield ratios in the first place. In complex se-ries of ratio measurements the uncertainty propagationis more straightforward than when sums and differ-ences from standards – such as for mass determinations– are involved. Consistent with the use of SI, the valueof a ratio is called a “measurement” when numeratorand denominator are multiplied by a unit and the re-lated uncertainties have been evaluated.

Uncertainty about the nature of the entity to bemeasured

Chemists may not exactly know what is the entity theywish to measure in a material. A common example ismoisture, say in grain. There are known to be contin-uous levels of strengths of chemical bonding of the wa-ter molecule in products. Mass loss on heating is rou-tinely used to determine moisture in grain, but maycause error by including in the measured loss volatilecompounds other than water and will also depend onthe method used, principally on the temperature andtime of drying. In giving the result in mole of H2O perkilogram, one cannot assure that it was free water inthe grain, where some of it was present as a differentchemical entity. The same may apply to a metal ele-ment, say aluminum in an alloy. The user may well beinterested in whether a mole of Al per kilogram refersto total aluminum or just the metallically bound – asopposed to oxide – aluminum. The result obtained in ameasurement will then depend on the measurement

Measurement principles for traceability in chemical analysis 7

method that is used. The use of amount-of-substancemeasurements can neither help nor hinder the chem-ist’s need to carefully distinguish significant entity dif-ferences such as those due to chemical bonding andmolecular association in a material.

Some vague usages of terms in measurementprocesses [23]

It is quite common for the chemical community nowad-ays to use the terms “calibrate” and “calibration” forany process that converts an observed value into amore reliable result, which is then called “corrected,”“true,” or “calibrated.” We must also concede thatRMs are sometimes used that do not have a matrixclosely similar to that of the sample. To make mattersworse, uncertainties associated with that situation aregenerally ignored. Insofar as the chemical community isaware of these problems, the call goes out for more andmore RMs in appropriate matrices beyond available ca-pabilities to produce reliable RMs. In order to arrive atrational conclusions on these issues, it is necessary toexamine closely and to understand the proper role of“calibration” and “validation” procedures. In the fol-lowing paragraphs we describe our views and hope thatothers will endorse them.

What constitutes a measurement?

A measurement of a specified property in an “un-known” material is a quantitative comparison by ratioor difference made of that property between a refer-ence standard or reference material and the unknownor between relevant settings in an instrument, prefera-bly in the appropriate unit for the quantity under inves-tigation, provided:a. Measurements of the relevant type and range, at thesite where the measurement is made, are subjected toreliable uncertainty assessment.b. The result (difference or ratio) is proven to be aknown function of the true difference or ratio, or ap-propriately corrected for non-linearity, usually bymeans of a set of RMs.c. The comparison applies only to a constituent part ofeither or both the RM and the “unknown,” and thecomparison is:i. proven to be independent of the matrices,ii. based on knowledge that the matrices are preciselysimilar, oriii. quantitatively evaluated for variability with matrixd. The result is given with its uncertainty includingthose caused by possible lack of linearity and by theabove criteria applied to RMs involved.

Under these conditions, the comparison constitutes ameasurement, and the value given of the property inthe “unknown” has been determined.

Chemists will have an important reservation con-cerning this understanding of what constitutes the un-certainty of a measurement. Physicists and engineersmay not, but chemists often are subjected to majorsampling, stability, blank, and contamination errors.Chemists should include them in their total uncertaintyestimates. The distinction between the measurementuncertainty and the degree to which the measured sam-ple fails to represent the relevant larger bulk needs tobe debated and discussed for consensus and under-standing.

What is a calibration?

Let us begin with the ISO definition [9]: A calibrationis a “set of operations that establish, under specifiedconditions, the relationship between values of quanti-ties indicated by a measuring instrument or measuringsystem, or values represented by a material measure orreference material, and the corresponding values real-ized by standards.” Applied to amount measurements,the “standards” would then be the values assigned tothe RMs (of defined composition) at the stated uncer-tainty relative to the true value of the property, ex-pressed in SI units, or relative to an internationally re-cognized, certified standard RM for the relevant prop-erty, range, and matrix composition.

An instrument or system is said to be calibrated foramount measurements only if, within a specified range,a value versus signal (response) curve has been evalu-ated against RMs including two near the ends of therange. At the present time, it is unfortunately quitecommon to use the term “calibration” to describe anyprocess which converts a single observed measurementinto a more reliable result.

What is a “validation”?

An RM can validate a measurement procedure (includ-ing the measurement instrument) [13] if, prior to its usefor an unknown sample, it has been shown to give:1. A quantitative response for the quantity (in the rele-

vant range) to be measured2. A response with a defined and acceptable repeata-

bility3. A response with a defined and acceptable reproduci-

bility over changing times and measurement condi-tions

4. A defined and acceptable estimate of their overallintrinsic uncertainty

8 P. De BiŁvre et al.

Traceability for chemical measurements

ISO in its vocabulary for metrological terms [9] definestraceability as follows: “property of the result of ameasurement or value of a standard whereby it can berelated to stated references, usually national or interna-tional standards, through an unbroken chain of com-parisons all having stated uncertainties”. Thus, the termdoes not apply directly to laboratories, but should beapplied to the results of chemical amount-of-substancemeasurements. Every link in the traceability chainshould consist of comparisons that are measurements inaccordance with the above proposed meanings, whichinclude the validation of measurement procedure byRMs. A measurement therefore often has strong linksto internationally accepted RMs, but may be onlyweakly connected to the SI unit. For comparabilityamong measurement laboratories, the strength of thelink must be adequate to assure equity in trade. Weak-ness of the relation to SI may thus be acceptable, butthe metrologically minded chemist will be disposed toaim for strongly linked reference measurements, meth-ods, and instruments. They are based on simpler con-cepts with greater permanence and would be more eas-ily understood by the wider public. Other definitions oftraceability have been described [24–26].

Not all chemical measurements are, or should be,traceable to the mole. We have seen instances wherethe unit of mass was the proper SI unit for a quantita-tive measurement of a material of unspecified entities.There are chemical measurements that are not, butprobably should be, referred, and preferably be tracea-ble, to the SI unit. Color is used either simply as a qual-itative attribute not subject to a measurement, or it ismeasured quantitatively by some spectrometry, whereit may inevitably be subject to high uncertainties fromboth the measurement itself as well as from theory,such as the Lambert-Beer Law, but well understood inrelation to SI.

The description of the relation of a measurement toan SI unit encounters a basic difficulty when the de-sired meaningful measurement result is a ratio, as inmany chemical determinations. The magnitude of theunit then becomes irrelevant. Chemists err when theyclaim that the inaccuracy of their weight set relative tothe international prototype is a component in their un-certainty budget. The self-consistency of their weightset is of course of paramount importance. Since thatwould include tareweights, internal balance weights,and sensitivity weights, the advice to use weights cali-brated against the international kilogram is still gener-ally good.

The quality of ratio measurements seems not to beconcerned directly with the SI unit. The only essentialcondition is that the unit for the numerator be the sameas that for the denominator. Traceability requirements

for many amount-of-substance measurements, there-fore, appear to concern not the unit mole, but a stand-ard measured ratio, preferably between pure definedsubstances in one RM. Nevertheless, the authors pro-pose that by consensus it shall be a rule for all measur-ements, where a choice could be made, that it shall fallon the SI unit.

Unusual are measurements for which a direct link tothe mole is useful. We should probably not talk abouttraceability in that connection, because that term is de-fined as a relation between measured values. An ac-ceptable chain of measurements for compound X of es-tablished purity, containing element E that has isotopeiE and that would establish a link to the mole, thenwould take one of the following general routes: theamount of substance n(X)]n(E)]n(iE)]n(12C); orn(X)]n(E)]n(C)]n(12C). The ratio of atomic massesm(iE)/m(12C) is also involved in the definition, but thatratio is known with a negligible uncertainty comparedwith the other links in the chain. Clearly, only in a fewinstances will laboratories attempt to execute such achain of measurements for a link to the SI unit. Is itfear that such a difficult process is involved in everychemical analysis that has kept so many chemists fromusing the mole as the way to express chemical measure-ment values? Or is it just habit and the convenience ofa balance that subconsciously links amount of sub-stance to amount of mass?

Laboratory accreditation

For laboratory accreditation, based on ISO guide 25[27] and the EN 45001 standard, as well as for certifica-tion, based on the ISO 9000 series of standards [1], it isrequired that measurement and test results be traceableto international, defined, and accepted physical andphysicochemical standards [28]. This requirement in-cludes the use of conventionally expressed quantitiesand units in conformity with the SI [29]. It also includesthe proper use of the concept of measurement uncer-tainty. All these are necessary conditions for relianceon the measurement results of another laboratory. Ac-creditation is granted when a laboratory has demon-strated that it is competent and capable of working inthe above-mentioned sense. Technical trade barriersthen fall away, and the needs and requests from indus-trialists, traders, and the general public can be met inthe interest of open and fair trade, health, safety, andthe environment.

For amount-of-substance measurements we includekilogram mass units, which are linked to the amount-of-substance unit in SI by the atomic-weight values.The latter differ greatly in uncertainty for differentchemical entities, but are always available, with the bestestimates by current knowledge of their uncertainties,

Measurement principles for traceability in chemical analysis 9

through the International Union of Pure and AppliedChemistry [30, 31].

Reference materials

In the above sections we have already illustrated someof the characteristics and uses of RMs. A more formaldefinition of RM by ISO is [9]: “material or substanceone or more of whose property values are sufficientlyhomogeneous and well established to be used for thecalibration of an apparatus, the assessment of a meas-urement method, or of assigning values to materials.”Extraordinary care in the production of RMs [15] is es-sential for effective, harmonized chemical measure-ments. Special features of certified RMs are carefullyexplained by that ISO document [9, 15] and their desig-nation as measurement standard specifically author-ized.

One may be inclined to suppose that for each type ofchemical measurement there is a need to build a meas-urement system based on the pyramid concept [7, 32].For the practicing chemist, however, this would be seenonly as an unhelpful imposition. Previously discussedlimitations of such a pyramid system would applyequally to the use of RMs. In addition, there is a majordifficulty due to the previously discussed differencesbetween RM matrix and sample matrices. Whereas forextrinsic measurements the composition of an RM orother traveling standard is of little or no concern, in-trinsic amount-of-substance measurements are general-ly affected by the internal composition, structure, andtexture of the RM.

The limited number of reliable RMs that can be pre-pared and made available leads to the use of possiblyinappropriate RMs. When the matrix in a sample dif-fers from that of the RM, reliable comparison may bevery difficult. A provision for the support of criticallyimportant and accurate bench level measurements isneeded. In such situations there is a better alternative:from the bench level a specimen with typical matrixproperties is sent to a laboratory having competenceappropriate for providing a “reference measurement.”That value is communicated back to the “bench” whereit provides a certified value – a kind of in-house RM –for comparison with routine sample measurements.Thus, the concept of reference measurement emergesas being equally as important as that of the RM. Chem-ical science has no other choice, since the combinedoutput of RM-producing institutions could not possiblyaccommodate all the rapidly diversifying demands forall measurands in all matrices of interest.

In order to establish traceabilities of measurements,we advocate the structure shown in Fig. 1 where manytypes of linkage can be found, including but not limitedto those terminating in SI.

Table 2 Classes of reference materials determined by their tra-ceability

Class Description and criteria in terms of traceability to SI

0 Pure specified entity certified to SI at the smallestachievable uncertainty

I Certified by measurement against class 0 RM or SIwith defined uncertainty by methods without measura-ble matrix dependence

II Verified by measurement against class I or 0 RM withdefined uncertainty

III Described linkage to class II, I, or 0 RM

IV Described linkage other than to SI

V No described linkage

Table 1 Categories of reference materials, determined by theirchemical nature

Category Kind ofmaterial

Description and criteria in terms ofmateiral composition

A Highpurity

Pure specified entity (isotope, ele-ment, or compound) stoichiometri-cally and isotopically certified asamount of substance, with total im-purities~10 mmol/mol

B Primarychemicals

As above, but with limits of~100 mmol/mol

C Pure One constituent`950 mmol/mol

D Matrix Matrix with one or more major con-stituents`100 mmol/mol

E With minorconstituents

Minor constituents in matrix~100 mmol/kg

F With traceconstituents

Trace constituents~100 mmol/kg

G With ultratraceconstituents

Ultra trace constituents~100 nmol/kg

H Undefined Entities unspecified or undefinable

A system for describing types of candidate chemicalmaterials for RMs

We would also advocate the optional use of a descrip-tive materials system for candidate RMs. Firstly, weshould have categories depending on the chemical na-ture of the materials (Table 1). Secondly, we shouldagree on RM classes dependent upon their degree oftraceability (Table 2).

The isotopic composition of an element in a speci-men can be established and expressed in abundances –that is amount-of-substance fractions or moles of iso-

10 P. De BiŁvre et al.

tope per mole of element – by comparison to syntheticmixtures of enriched isotope class 0 RMs of that ele-ment.

Certification of an elemental class 0 RM can be per-formed by metrology laboratories having the bestscientific procedures for the establishment of traceabili-ty routes to the SI system. For every such RM the costin facilities and experts’ time is very high and in prac-tice cannot easily be balanced against sales. Only a longhistory of the laboratories’ reliability and their free andopen discussions of problems, coupled with energeticself-criticism, will reassure the scientific and technologi-cal communities. Metrological quality, not cost andeconomy, should be the prime concern of operatorswithin such laboratories.

All other classes of RMs are needed in much greaternumber and diversity. They are therefore of muchgreater potential interest commercially. Intercompari-son between similar RMs is always helpful. Only oneclass IV or class V RM should be made available byconsensus for a certain purpose, so that all laboratoriesare encouraged to make their measurements compara-ble to others through just one RM.

Validation of a measurement procedure including aninstrument can be performed with an RM of class 0, I,or II, but only if differences in matrix or impurities arespecified, small, and of proven limited influence on theuncertainty. The uncertainty of the RM relative to truevalue or the mole may be larger than the link betweenthe measurements on the material and the RM. Tracea-bility between measurements can be achieved with the

help of all classes of RMs, but requires a clear state-ment on uncertainty. Traceability to the mole, if not bydirect realization of the mole, can be established onlyby class 0 RMs. Their relation to the unit mole must beestablished by way of atomic-weight determinations orby direct atomic mass comparisons with carbon 12atoms.

An example of a class I RM is an RM for which theamount of substance of an element has been measuredby isotope dilution against a class 0 RM, provided themeasurement has been shown to be in accordance withbasic laws [7, 22, 33] of chemistry and physics.

Conclusions

Reliable chemical measurements in future will dependon more RMs with direct links to the SI as well as onRMs of greater diversity than are available now. Chem-ical science will be assisted by clear consensus defini-tions of traceability, certification, and validation, aswell as by a widely accepted system for describing RMsby material composition, degree of traceability, uncer-tainty, quality, and purpose. Ultimately, chemists, phy-sicists, and engineers benefit from adherence to thewell-grounded and well-established discipline of metro-logy under a coherent system of units.

Acknowledgement The authors thank two reviewers of themanuscript, Robert Watters and Walter Leight, who provided nu-merous valuable suggestions.

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Measurement principles for traceability in chemical analysis 11

27. General requirements for the compe-tence of calibration and testing labo-ratories (1990) ISO Guide 25, 3rdedn, Geneva

28. Cigler JL, White RV (eds) (1994) Na-tional Institute of Standards andTechnology Handbook 150

29. Quantities and units (1993) ISOStandards Handbook, Geneva

30. Atomic weight of the elements 1993(1994) Pure and Appl Chem66:2433–2444

31. De Laeter JR, De Bièvre P, PeiserHS (1992) Mass Spectrom Rev11 :193–245

32. Taylor JK (1993) National InstituteStandards and Technology SpecialPublication 260–100, pp 1–102

33. De Bièvre P (1990) Fresenius J AnalChem 337 :766–777

Accred Qual Assur (1997) 2 :168–179Q Springer-Verlag 1997 REVIEW PAPER

Paul de BièvreRobert KaarlsH. Steffen PeiserStanley D. RasberryWilliam P. Reed

Protocols for traceability in chemical

analysis

Part I: Definitions and terminology

Received: 12 January 1997Accepted: 31 January 1997

P. De Bièvre (Y)Institute for Reference Materials andMeasurements, European Commission –JRCB-2440 Geel, BelgiumTel.: 32-14-571-605; Fax: 32-14-591-978

R. KaarlsNetherlands Measurements Institute,2600 AR Delft, The Netherlands

H. S. Peiser, retired fromNational Institute of Standards andTechnology, 638, Blossom Drive,Rockville, MD 20850, USATel.: 1-301-762-6860; Fax: 1-301-762-1173

S. D. Rasberry 7 W. P. Reed, retired fromNational Institute of Standards andTechnology, Gaithersburg, MD 20899,USA

Abstract The authors propose def-initions and terminology for proto-cols on traceability links, generallyto the international system of units,for specific chemical-analyticalmeasurements in accordance withrecognized principles of science.These definitions and terms couldbe useful in science, technology,commerce or law. A chain of suchlinks leads from a measurand in asample up to a unit in the Interna-tional System of Units or, if un-available, to a value on an interna-tionally recognized measurementscale. The quality of such a chain isquantified by combining all recog-nized uncertainties estimated forall its links. These uncertainties of

the measured values arise frommany potential error sources. Theprotocols should give details ofspecific uses of reference materials,measuring instruments and stand-ard measurement methods.

Introduction

This publication is the second of three contributions ontraceability in chemical analysis. The first was pub-lished in this Journal [1] and deals with the generalprinciples, whereas the third is planned chiefly to pres-ent examples, but also to suggest implementation pro-cedures, to assess comments from chemical groups andto introduce possible modifications of concepts anddefinitions [2, 3].

The second contribution we present in two parts. Inthis first part we discuss definitions and terminology,mostly from recognized sources [2–9]. Some ideas inthis article go beyond established international under-standings; they are introduced for debate and possiblerefinement. The terms used here are responsive to thefundamental concepts under which chemical analystscan formally substantiate and record a traceability link.A chain of such links should lead from the value of aquantity in a sample up to a unit in the International

System of Units (SI) [5] or, where that is not possible,up to a unit on an agreed and conventional measure-ment scale.

We address chiefly individuals or groups of analystswho aim to originate a protocol, that is a document re-cording the procedures for a specific link. That protocolestablishes scientifically reliable measurements for thebenefit of equity in trade and industry, as well as forlegal interpretations of scientific realities.

A protocol must deal with the quality of the linkbased upon carefully estimated uncertainties [6, 7] fromall foreseen error sources that remain after due precau-tions have been taken and after significant correctionshave been applied where possible. The combined un-certainties of all links in the chain of links will then de-fine the quality of a link to SI1 or to some other rele-

1 As has become customary [4], we use “the traceability (or thelink) to SI” meaning “the traceability (link) to an appropriateunit or units in the SI”

Protocols for traceability in chemical analysis. Part I: De�nitions and terminology 13

2 Traceability is defined as follows [2]: “property of the result of ameasurement or the value of a standard whereby it can be relatedto stated references, usually national or international standards,through an unbroken chain of comparisons all having stated un-certainties”3 When using “quantity” [3] we will refer to a property, such asmass, length, amount of substance, or speed of light. We will notuse “quantity” for describing a portion or bulk of a material, achemical, or a sample, but rather consistently use “amount” of asample or of rubber etc. Furthermore, we will try to distinguishsuch a general use of “amount” from “amount of substance”which is an SI base quantity requiring specificity of entity in termsof its chemical formula

Fig. 1 Schematic of typical chemical analysis

4 An elaboration on how a duly recorded traceability protocolmight be used outside the professional chemical arena is not thesubject of this paper5 Questions of chain of custody of samples or “trackability”, aterm recently proposed [11], and due representation of the popu-lation are not addressed in this article

vant scale unit. This quantitative assessment of qualityof traceability to SI from combined uncertainties is notinconsistent with the metrological term of “accuracy”[2, 6]. It differs from popular meanings of “accurate”such as “free from error” and “highly exact”. A tracea-ble measurement may be adequate for its intended pur-pose, yet be inferior compared with the optimumachievable.

Fundamental understandings

By “protocol for traceability” [2]2 we here mean a doc-umented record of a relationship, consisting of a “link”,or chain of links, emanating from the value of a quanti-ty3. The value is obtained by a measurement applicableto the measurand, the property of an entity in a samplewhich may consist of a pure material or incorporate theentity in a matrix. Each such traceability link is estab-lished for a stated chemical purpose and asserted byvirtue of that measurement, which relates the foremen-tioned value to another value in a reference material(see Fig. 1 for an outline of the use of RMs in typicalchemical analyses) or to the response of a calibratedinstrument (see Fig. 2). This measurement is carriedout in a responsible laboratory using planned and de-scribed procedures, in a validity interval (time period)for a specific type of quantity (such as a concentrationor other material property), within a limited range ofmagnitude of the quantity measured. The measurementis characterized, in part, by an observed repeatabilityand invariably by a substantiated estimated uncertainty[6] (including especially any arising from matrix ef-fects), which is the sole indication of quality of the tra-ceability relationship for each link or, when duly com-bined, for a chain of links. Thus, the uncertainty be-comes the quantified indication of quality for the mea-sured value itself. Wherever possible, the value of thatmeasurement is ultimately made traceable to an SI unit(or units) [2, 5, 8], through realizations of those units. Ifnot possible, the final link is made to a unit in an inter-nationally recognized scale.

Underlying concepts and definitions

The record

The record of a traceability protocol is a written docu-ment that may serve: in science and technology as ref-erence; in product control as procedural “written stand-ard”; in environmental comparisons as precept [10]; intrade and industry as basis for agreement, especiallywhere border crossings are involved; and in courts oflaw as a means to judge whether specified limits aremet4.

The sample

For a chemical measurement the history and homo-geneity of the sample must be established. Subsamplesfrom the original sample are drawn for measurement.Although the selection of a sample in the “field” is im-portant and often of concern to analysts, this paperdeals only with the sample as delivered to the laborato-ry5. Two kinds of questions there can profoundly affectthe uncertainty associated with the measurement [12]:

14 P. De BiŁvre et al.

Fig. 2 Instrument calibrationfor analytical measurements

6The meaning of “stable” as here intended does not always indi-cate constancy of value. For radioactive materials, for example, aquantified change with time is here understood to be “stable”

1. Is the sub-sample on which the measurement ismade representative of the undivided sample?

2. Does the measurement of the intended quantitymeet the measurement objective?An important issue, for example, may be whether

the measurement value is to apply to a specific sampleor to the bulk of its source material. When surface con-tamination is the purpose of the measurement, totaltrace-element measurements could be misleading.Thus, surface sampling may have to be part of the pro-tocol. Conversely, measurement methods that give re-sults preferentially for surface layers may not be repre-sentative of the bulk of the subsample.

The measurand

The measurand is the selected property to be quanti-fied by measurement of a constituent in a sample. Formost analytical measurements, one prefers to select aquantity that is invariant on division of the material.Mass, amount of substance, volume etc. do not remaininvariant on division and so are unsuitable for the char-acterization of a material.

Temperature remains invariant on division, but isunsuitable for characterizing a material because of thedependence of that base SI quantity on the external en-vironment. To a lesser extent, external temperatureand pressure conditions affect volume, too. In chemis-try, the commonly used ratio of amount of substance(of a stable6 entity) to mass of the material, in which itis uniformly contained, is not only invariant to contam-ination-free division, but is also independent of exter-nal environmental conditions, as long as they ensurethe stability of the entity. In this respect amount-of-substance concentration per mass of material is suitable

for characterizing a material, but not unique. Mass perheat capacity has similar invariance on division of thematerial and independence upon the environment.Concentration by mass per amount of substance has theadditional unique property for a pure substance thatthese two base quantities are related by the molar massof the entity. Thus, the analyst has the option of meas-uring either of the base quantities and from it derivingthe other base-quantity value and hence the concentra-tion with an appropriate increase in uncertainty.

Issues involved in the choice of measurand may berelated to the purpose of measurement, which shouldbe precisely and unequivocally identified and stated inthe protocol.

The measurement

The measurement – a quantified comparison by differ-ence or ratio between two values of the same quantity –shall conform to well-accepted principles of the chemi-cal profession and good measurement practice [12–14].

The value

The value is the numerically expressed magnitude of aquantity either in a material or indicated by a cali-brated instrument (see Fig. 2). An uncertainty must beassociated with every value. Its important estimation isdiscussed in detail in the section “The uncertainty” be-low (see also [6, 8]).

Wherever possible, every value and every uncertain-ty that is cited in a protocol or quoted in the implemen-tation of a protocol shall be expressed in a unit of theSI (with or without prefix) associated with a numbercommonly called the numerical value [5]. Thus, the val-ue and its uncertainty are multiples or fractions of thatSI unit. If an SI unit for the relevant quantity is not in

Protocols for traceability in chemical analysis. Part I: De�nitions and terminology 15

7 In fact, the kilogram is the SI unit most likely to be redefined inthe near future. If so, it will be in terms of an atomic-scale massrather than by an artifact

Table 1 Frequently used ratios of SI units

Quantity Amount ofsubstance

Volume Mass

Symbol of quantityName of SI unit

Symbol of SI unit

nmole

mol

V(derived)cubic meter(derived) m3

mkilogram

kg

mol/unit ofquantity

m3/unit ofquantity

kg/unit ofquantity

Unit of quantity/molUnit of quantity/m3

Unit of quantity/kg

mol/molmol/m3

mol/kg

m3/molm3/m3

m3/kg

kg/molkg/m3

kg/kg

common use, the value could be associated with an in-ternationally accepted measurement scale or on thescale of a written procedure, perhaps involving an in-laboratory prepared reference material that is properlyidentified. In some cases, even a commercially availablestock solution may serve this purpose. The long-termconstancy of such values is an important issue, to beconsidered in the use of any reference (see section“The validity interval” below). Possible non-negligibleinstabilities of a reference value used in a protocol mustbe mentioned and appropriately taken into account.

The unit

In the physical and engineering sciences, the metric In-ternational System of Units for measurements [5] hasbecome widely accepted throughout the world. An in-tended characteristic of all SI units is their unsurpassedstability and their independence of location and time.That characteristic of the SI contributes decisively itsunique appeal to measurement science and technology.In technology, the use of SI is gradually gaining accept-ance over many customary, especially non-metric, units.Chemists have no problem in using SI for mass compar-isons, because of the convenience and sensitivity ofanalytical balances and the universal acceptance of thekilogram as the unit for mass7. Chemists also use SIunits for measurements of volume, temperature, andsome other quantities, but tend to avoid the use of themole for amount-of-substance measurements, evenwhen the chemical entity is well defined and althoughthat quantity is the most meaningful for the considera-tion of chemical formulae, reactions, kinetics, and ener-gy. In such situations the use of the mole in protocolsshould be expected. Traceability to SI, however, can beclaimed relative to any SI unit that is appropriate forthe measured quantity. That SI unit can be a base or aderived unit, or even a unit temporarily accepted foruse within SI. When traceability is planned to derivedunits or composed of products or quotients of other SIunits, it is often operationally necessary to achieve tra-ceability to these SI units separately. This is the situa-tion for the quantity of greatest interest for characteri-zation of any material by chemical measurement: con-centration measured in mole per kilogram or mole percubic meter. Most laboratories may routinely maintaintraceability to the SI units of mass and length at loweruncertainties than is needed for many protocols forchemical analytical measurements.

Whereas mass can be quantified irrespective of theintrinsic nature of a sample, amount-of-substance quan-

tification requires the explicit chemical description ofthe entity pertaining to the measurand [15]. A descrip-tion in mole units may be inappropriate for specificpurposes when the composition of the chemical entitylacks specificity and would impose an objectionablemolar mass or volume uncertainty. This limitation ap-plies frequently in quantifications for purposes of trade,such as when describing amounts of polymers (withlarge uncertainty of molar mass and additional difficul-ty in defining its mean), a lithium compound (of varia-ble isotopic composition), sodium carbonate (of unde-fined hydration), iron oxide (of undefined Fe valency),chlordane (composed of several molecules), nutritionalfibers (vague definition), and numerous other sub-stances.

The mole is associated with a specific chemical enti-ty as defined by its chemical formula [15]. Its structuralformula, isotopic composition, isomeric form, crystalstructure, or chirality may have to be given in order tocompletely specify the entity of interest. The achievableuncertainty of amount-of-substance measurement islimited by that of its apparent molar mass. This consid-eration affects not only measurements on entities withvariable molar mass, but those on pure substances. It isrelated to the traditional and important concern aboutpurity.

Ratio measurements in analytical chemistry will oft-en relate values in different units for the numerator anddenominator. The most commonly used ratios betweenSI units are summarized in matrix form in Table 1 (ad-apted from [5]). Confusion may result when values arestated in different SI quantities. The pharmaceutical in-dustry, for example, is careful to distinguish values inmg/g from values in mmol/g. It is important to retainthe two units used in expressing a ratio such as mol/g.Differential measurements are often made, obtaining aratio of ratios for which the numerator and denomina-tor are generally expressed in multiples of identicalpairs of units, e.g. (g/L)/(g/L). For such a ratio of ratiosno great harm is done by stating, for instance: “the con-

16 P. De BiŁvre et al.

centration in the numerator equals a (dimensionless)number of times the concentration in the denomina-tor.” An unlike pair of units for a ratio of ratios shouldbe avoided, otherwise it becomes imperative to identifyexplicitly all four units for a meaningful description ofthe measurement.

On some occasions, protocols may involve SI unitsof time, electric current, thermodynamic temperature,or luminous intensity. These units are also base units ofthe SI. Traceability to SI can even refer to realizationsof derived SI units, such as those for energy, pressure,and amount of electricity. Solubility per unit pressuremay be quoted in (mol/m3)/(m7s2/kg) or in (mol/m3)/Pa, but should not be written as mol7s2/(m27kg) [5, 20],that is: not in reduced form relating to units of quanti-ties not actually measured.

There are chemical measurements for which the de-cision to use the kilogram or the mole as SI unit de-pends on the type of deduction that is intended to bemade from the measurement. Such examples could ar-ise in polymer studies, in alloying, in isotropic displace-ments, in assessing electronically active impurities, ineffects from variations in isotope abundances, or inthose arising from chemical binding states. When docu-menting a formulation for an industrial reaction pro-cess, the use of mass proportions is appropriate evenwhen an entity is known, because weighing devicesalone are likely to be available for preparing theneeded mixture. In ionic crystals and the alumino-sili-cates of the earth’s crust, especially when dealing withtheir solid solutions, the concept of a molecular entityhas little relevance. Although quantification underthose circumstances is best achieved in terms of mass,certain amount-of-substance ratios represent importantfeatures of such materials. For instance the ratio ofquadrivalent to trivalent ions in feldspars gives mean-ingful descriptions of attributes of rocks. For abun-dance of the elements on earth or in space, the com-mon use of kilogram per tonne should with advantagebe replaced by the amount of substance per kilogramor by the less common ‘Cosmic Abundance Units’(atoms per 106 Si atoms).

The dalton is not accepted within SI [9]. It is per-ceived as a molecular mass of a specific species. In pro-tocols, molar mass, relative molecular mass or unifiedatomic mass units should be substituted. The last ofthese, in conjunction with the SI mass unit, is currentlyacceptable with an added relative standard uncertaintyof 10P6.

Realization of an SI unit

A value – whether based on a specific material or onthe output of a detector – when traced by a single linkto a multiple or submultiple of an SI unit, at a stated

Table 2 Categories of reference materials, determined by theirchemical naturea

Cate-gory

Kind ofmaterial

Description and criteria in terms ofconstituent(s) certified

Single major constituent

A High purity Pure specified entity (isotope, element, orcompound) stoichiometrically and isoto-pically certified in amount-of-substanceratios with total impurities ~10 mmol/mol

B Primarychemicals

As above, but with limits of~100 mmol/mol

C Definedpurity

As above, but with limits of~50 mmol/mol

Maxtrix types

D With majorconstituents

Major constituents (in matrix)`100 mmol/kg or `100 mol/L

E With minorconstituents

Minor constituents (in matrix)~100 mmol/kg or ~100 nmol/L

F With traceconstituents

Trace constituents~100 mmol/kg or ~100 mmol/L

G With ultratraceconstituents

Ultra trace constituents~100 nmol/kg or ~100 nmol/L

Undefined

H Undefined Entities unspecified or indefinable

a A similar table was originally published [1] as basis for discus-sion. The version here presented incorporates significant changes.Further suggestions for improvements are welcome. – The pro-posed limits of the concentrations are arbitrary, and, for instance,preclude RM’s for most organic entities in category A. Chemistsmay well use and state their own RM category designations

low uncertainty, without requiring intermediate stand-ards, reference materials, or significant empirical cor-rection factors, is a realization of that SI unit. The con-ditions that are involved in a realization of an SI unitinclude all those involved in the recently proposed def-inition of a primary method of measurement [4]. Meas-urements made by a primary method are in principlerealizations of an SI unit. For other realizations of anamount of substance, the entity must be defined andthe purity of the material containing the entity must bedetermined. Conceptually, every entity might bedeemed to require its specific realization of its mole.

Reference materials (RMs)

In all but a very few chemical measurements, use ismade of reference materials (RMs) with appropriatepedigrees [17–19] (Fig. 1). Analytical-chemical RMs aregenerally certified by properties (such as concentra-tions) of entities and by values with their uncertainties,and are sometimes provided with limit values [17–19].These values within their uncertainty ranges remain in-

Protocols for traceability in chemical analysis. Part I: De�nitions and terminology 17

Table 3 Classes of reference mateirals, determined by the lengthand strength of their traceabilityb

Class Description and criteria in terms of traceability toSI

0Primary

Pure specified entity certified to SI at the smallestachievable uncertainty

I Certified by measurement against class 0 RM or SIwith defined uncertainty (no measurable matrix de-pendence)

II Verified by measurement against class I or 0 RMwith defined uncertainty

III Described linkage to class II, I, or 0 RM

IV Described linkage other than to SI

V No described linkage

b This, like the preceding Table, was originally offered for discus-sion [1]. Currently it is not widely adopted. The authors welcomeproposals for changes

Fig. 3 Issues arising whenconsidering the meaning of acertified value and its uncer-tainty in a certified referencematerial

variant on division into subsamples. RMs are widely re-garded and used in chemical analysis, just as are travell-ing and transfer standards in engineering and physicspractice.

Tentative attempts have been made to categorizechemical RMs in terms of their material composition(Table 2) and to classify them by the length andstrength of their traceability chain (Table 3). This clas-sification might in future be generalized and expandedin terms of ranges of relative uncertainties.

Whereas an individual value, the result of a meas-urement, can be said to be “verified” by another meas-urement, a chemical method or procedure should be“validated”, generally by success in application of thatmethod to a certified RM. Validation remains unde-fined in the ISO vocabulary of terms in metrology [2].A definition along the following lines is under discus-sion within EURACHEM/EUROMET: “A validationis a set of operations that establishes, under specifiedconditions and for a specific range, the suitability of agiven measurement instrument, measurement proce-dure, or measurement method for a measurement of aspecified quantity at a stated level of uncertainty.” Val-idation usually is accomplished with the help of RMsand gives an opportunity to forge a link (see next sec-tion), but does not verify a given value or its uncertain-ty.

By one convention, illustrated in Fig. 3, the valida-tion of a measurement method, as replicated in thefield, succeeds if the certified value of an appropriateRM falls within the estimated measurement uncertaintywhen the RM is measured using the method. That defi-nition of validation does not require a mutual confor-mance condition in which the two values (that deter-

18 P. De BiŁvre et al.

mined at the “field” laboratory and that given by thelaboratory establishing the protocol) must both lie ineach others uncertainties8.

The values in a sample can be linked to the values inRMs in several ways (see Fig. 1) [14, 16–19]. This rela-tionship can, for example, be established:1. Directly by a controlled comparison of values from

measurements on a sample with certified values foridentical entities in closely similar RMs9, or

2. Indirectly through an instrument calibration estab-lished for values for identical entities in closely simi-lar RMs8

3. In conjunction with a specified method (or proce-dure) of measurement [8]

4. To confirm the sensitivity of an instrument or meth-od to detect a trace impurity or contamination.

The link

A trace (“traceability” by definition [2]) is establishedby a link or an unbroken, single-path (compare foot-note 18) chain of links that connects by measurementtwo or more values of the same indicated quantity in aunidirectional order of authority. One of these valuesusually refers to a sample that is representative of a ma-terial embodying the measurand. The other value maybe of that quantity in a reference material, or indicatedby an instrument reading, or that of an SI unit (see sec-tions “The value” and “The unit” above (to be contin-ued in the next issue)). Links in a chain, as here dis-cussed, can be thought of as having direction, emanat-ing from a sample and leading progressively throughhigher levels of authority and perceived expertise to theSI. Each link could then be likened to a vector with themagnitude of its uncertainty. Links without directional-ity, between laboratories at equal level (see Fig. 1 in[1]), are of great importance to a successful measure-ment network but are not further discussed in this arti-cle. The chain link with the largest uncertainty is theweakest in that chain. It is not exceptional in measure-ment practice for the link connecting the value in ameasurand to the reference chain to be stronger thanthe rest of the chain is to SI.

The values associated with an established traceabili-ty link are given as a difference or ratio and must havean associated uncertainty. This, combined with the un-certainty of the higher link, determines the uncertaintyof the value at the lower end of the link.

The responsible laboratory

For every link there is a qualified analyst or team ofchemical specialists operating within a laboratory ac-cepting personal and institutional responsibilities forthe end result and its uncertainty, in full knowledge ofthe technical aspects further outlined below [12, 13].

The chemical analyst

In various sections of this paper, the authors appro-priately emphasize the needed professional knowledge,experience, integrity and responsibility of the analyst.The handling of samples, the estimation of uncertain-ties, and the vigilance for unexpected errors also re-quire some familiarity with statistics and possibly thehelp of a statistician as a consultant. However, the finalassignment of uncertainties is the responsibility of theanalyst who has actually performed the analyses.

The all-important manipulative skill of the analysthas yet to be underscored. No automated instrumenta-tion or computer software can substitute for the ana-lyst’s dexterity and alert observation. Nevertheless, itmust be understood that a disparity in this regard existseven between competent analytical analysts. No shameis attached to acknowledging a greater uncertainty in agiven analysis than is achieved by the most experiencedand the most skilled. During implementation of a pro-tocol, an analyst, estimating a higher uncertainty for hisown measurements than indicated in that document,may be demonstrating trustworthiness rather thandoubt in his measurements.

Under the enormous ever-growing volume ofneeded analyses for production controls, environmen-tal needs, and medical test programs, protocols have tobe designed to be executed reliably by trained techni-cians. That protocol development, however, is and mustbe understood to be exclusively the proper role of theanalytical chemist.

The validity interval

The validity interval is the time period during whichrelevant measurement operations are maintained incontrol with acceptable repeatabilities by each labora-tory involved. This important limitation of validity of atraceability link is provided by design or could be im-

8 An initially failed validation calls for repeat measurements or areassessment in order to ascertain whether the uncertainties inthe “field” were underestimated. Larger uncertainties may be ac-ceptable for the purpose of the measurement. If so, the originalmeasurement itself may be acceptable9 Even minor differences in matrices, however, will require deter-mination of the significance of such differences and their effect onthe uncertainties involved

Protocols for traceability in chemical analysis. Part I: De�nitions and terminology 19

10 “Repeatability” [2] is defined as the: “closeness of the agree-ment between the results of successive measurements of the samemeasurand carried out under the same conditions of measure-ment.” Repeatability should be distinguished from “reproducibil-ity” for which the closeness of the agreement concerns the resultsof measurements (of the same measurand) that are not necessar-ily made successively and not under the same conditions, by thesame method, or in the same laboratory

posed from neglect. In order to assign a value to anRM, for example, a laboratory has to work within thevalidity interval for maintaining all relevant compe-tences and procedures, such as to determine homo-geneity and constancy of that RM. Thereafter, howev-er, the measured, preferably certified, value of the RMremains valid, subject only to a validity period based onthe RM’s stability and requirements for its storage.These should be part of the RM’s certificate with theaim of protection against contamination, temperatureextremes etc. [18, 19].

The range

The range of values of the measured quantity is definedby the upper and the lower value for which the recordis valid. At and between these extremes repeat measur-ements may not differ by more than an indicated uncer-tainty (see below). A zero should not be used to specifythe lower end of a range. For small values of a meas-urand, a protocol may indicate the needed repeatabili-ty10 of measurement or specify the smallest requireddetectable value.

Traceability to the SI

Wherever possible, a traceability chain of measuredvalues terminates in an SI unit. When the base unit formass is appropriate, this relationship is readily achievedthrough a mass standard, calibrated in terms of thekilogram prototype. The concept of traceability to SIhas to be more carefully considered when conformity toSI depends on the SI concepts in the definition of theSI unit itself.

Basic to chemistry is the numerically simple (stoi-chiometric) proportion of entities in reaction and informulae of compounds. The chemical analysts’ pur-poses are therefore well served by comparing numbersof defined entities. The numerical value (see sect. entit-led “The measurement” above) for the SI measure-ment of the amount-of-substance quantity fits thosepurposes. Historically, however, few were the analyti-cal-chemical methods by which entities could becounted or counts of different entities could even becompared. With the nearly correct assumption that mo-

lar masses of the elements from terrestrial sources areconstants of nature, chemistry made spectacular pro-gress by measuring mass and converting to amount ofsubstance by the factor of Avogadro’s constant. Theirmeasurements were thereby burdened by the uncer-tainty in that constant – which for many purposes can-cels – as well as by the uncertainties in the molarmasses – which do not cancel and which become signif-icant as the total uncertainty of a measured value is re-duced. For good measurement practice, protocolsshould therefore prefer traceability to the mole, as isstated in sects. entitled “The value” and “The unit”above.

The SI traceability statement for a chemical compo-sition of a material cannot be completed by the tracea-bility to the mole of one entity. The statement must in-clude reference to another quantity, which could be amass, a length, some other quantity, or even an amountof substance of another entity. Examples of such tra-ceability statements for chemical composition couldrefer to a mole and the kilogram for the concentration,say, of a known element in an ore. The source of theelement in that ore is then described in terms of theratio of SI units mol/kg. Similarly by the SI units ofmole and meter one could designate the solution of adefined organic compound, that is in mol/L. For someimportant chemical measurements we need to find tra-ceability to SI for the mole of one entity as well as themole of another entity. These moles are not identicaland need separate traceability chains (see next para-graph). Measurements by mol/mol ratios are appro-priate, for instance, for a trace impurity of known com-position in a pure compound, or for an amount of iso-tope-to-element substance ratio (abundance).

The ratio measurement between the numbers of twoentities establishes an amount-of-substance ratio thatmight satisfy the principal purpose of a chemical meas-urement. In measurement science, however, under theSI system, relative quantities do not fully satisfy theconcepts. There remains an underlying requirement forall values to be individually traceable to the appro-priate SI unit. For amounts of substance that unit is it-self a number, the number of carbon-12 atoms of mass0.012 kg. The magnitude of a given amount of sub-stance, that is the numerical value of the SI quantity, isthe number of defined entities divided by the SI unitnumber. It follows that equality of amount of substanceis equality of the numbers of the two relevant entities.

If, in a ratio of amounts of substance, both of thetwo numbers of entities are traceable to numbers ofcarbon-12 atoms, and if the ratio between the entities isobtained by an appropriate measurement, the measure-ment is perfectly true to the concept of that SI unit.Calling that relationship traceable to SI is thereby rea-soned and should be considered correct. Just as formass measurements, the realization of amounts of sub-

20 P. De BiŁvre et al.

stance to SI could be left as a prime responsibility tonational measurement laboratories.

That realization will often have larger uncertaintythan relative measurements of entities by analysts. Thisshould not surprise; similar conditions commonly applythroughout metrology. One can link the value of agood-quality gram standard to another similar standardwith smaller uncertainty than that with which either canbe linked to the international prototype kilogram. Thedesigner of the protocol must carefully consider to whatextent uncertainties in the realization of the SI unitcancel for the purpose of a given measurement. Not thecalibration, but only the self-consistency of a mass-piece set, built-into – or external to – a balance, mayenter into the uncertainty of a mass ratio. Similarly, theamount-of-substance ratio may have an uncertaintypartially independent of that of the realization of the SIunit.

Summing up conclusions in this section: traceabilityof chemical measurements to SI involves concepts oth-er than a direct comparison with a physical standard.Uncertainties may relate principally to values producedin the laboratory. The uncertainties of the links of twovalues of the same quantity to the SI unit may be largerthan the uncertainty of the link between these valuesmade in accord with the concepts of the SI.

The repeatability of a measurement

All uncertainty estimates start with that associated withthe repeatability of a measured value obtained on theunknown. It is neither required for the sake of qualitycontrol, nor could it always be economically justified, tomake redundant determinations of each measured val-ue, such as would be needed for complete statisticalcontrol. Repeat measurements of a similar kind underthe laboratory’s typical working conditions may havegiven satisfactory experience regarding the range ofvalues obtained under normal operational variations ofmeasurement conditions such as: time intervals, stabili-ty of measurement equipment, laboratory temperatureand humidity, small disparities associated with differentoperators, etc. Repeatability of routine measurementsof the same or similar types is established by the use ofRMs on which repeat measurements are made periodi-cally and monitored by use of control charts, in order toestablish the laboratory’s ability to repeat measure-ments (see sect. entitled “The responsible” laboratoryabove). For this purpose, it is particularly importantnot to reject any outlier, unless cause for its deviationhas been unequivocally established as an abnormalblunder. Rejection of other outliers leads a laboratoryto assess its capabilities too optimistically. The repeata-bility in the “field” of a certified RM value representsthe low limit of uncertainty for any similar value meas-ured there.

When fewer than about 100 measurements of thesame type are needed, the use of control charts be-comes impractical. A few repeat measurements madewithin the routinely encountered range of relevant val-ues is sufficient to estimate the repeatability of a singlemeasurement. Difficulty arises only when a measure-ment type or procedure is inordinately time-consumingor costly to replicate. Relevant examples are: the meas-urement of an unusual trace constituent in a sample ofminimal size, and a lengthy isotope dilution mass-spec-trometric determination. The analyst is then requiredto depend on general experience of reliability of amethod and would be wise to estimate the uncertaintywith special care.

Just as the value obtained by measurement of a sam-ple carries an uncertainty, so does the laboratory ‘in-field’ realization of the certified value of an RM. If thepurpose of the measurement is to validate (Fig. 3) aprocedure or instrument calibration, the measurementuncertainty estimated by the laboratory should includethe certified value of the RM. If the measurement inthe laboratory consists of determining the difference ofthe value in an unknown with that in an RM, the latteris taken as the reference value. Only when evaluatingthe uncertainty of the unknown to SI, the RM’s certif-ied uncertainty must be combined with that of the in-laboratory measurement of the unknown.

The uncertainty

Central to the protocol is the uncertainty11, symbol u,or, if expanded, U, and uc or Uc when combined [6]. Itis expressed in the same SI units as the value V towhich it refers. For propagation of uncertainties bymathematical formulae, relative uncertainties, such asU/V, are often needed.

All uncertainties are estimated and necessarilythemselves uncertain. They should not be given tomore than two significant figures; that is, to at most 1%of the total uncertainty. Individual smaller uncertain-ties thus become neglected. Uncertainties are generallygiven to be symmetric for positive and negative devia-tions from the evaluated best value12.

11 The importance of reliable uncertainties in protocols cannot beoverstressed; they distinguish between insignificant differencesand dangerous discrepancies12 On occasions, chemists designing a protocol recognize goodreasons for expecting an asymmetry of likely deviations, such asfor analyses of trace constituents that cannot be less than zero, ofpure chemicals that cannot be more than 100%, or the molarmass of hydrogen gas (obtained by electrolysis) that cannot haveless than zero content of deuterium. Under such circumstances,well-reasoned asymmetries of uncertainties may be introducedinto a protocol