neutron activation analysis: a primary method of measurement

Spectrochimica Acta Part B 66 (2011) 193–241

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Spectrochimica Acta Part B

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Review

Neutron activation analysis: A primary method of measurement☆

Robert R. Greenberg a,⁎, Peter Bode b, Elisabete A. De Nadai Fernandes c

a National Institute of Standards and Technology, Gaithersburg, MD 20899-8395, USAb Delft University of Technology, Delft, The Netherlandsc Centro de Energia Nuclear na Agricultura, Universidade de São Paulo, Piracicaba, SP, Brazil

☆ With contributions by: Richard M. Lindstrom, ElizabMárcio Arruda Bacchi.⁎ Corresponding author. Tel.: +1 301 975 6285; fax:

E-mail addresses: [email protected], [email protected]@tudelft.nl (P. Bode), [email protected] (E.A. De Na

0584-8547/$ – see front matter. Published by Elsevierdoi:10.1016/j.sab.2010.12.011

a b s t r a c t
a r t i c l e i n f o
Article history:Received 12 September 2010Accepted 23 December 2010Available online 27 January 2011

Keywords:Neutron activation analysisMetrologyPrimary method of measurementUncertainty budgetMetrological traceability

Neutron activation analysis (NAA), based on the comparator method, has the potential to fulfill therequirements of a primary ratio method as defined in 1998 by the Comité Consultatif pour la Quantité deMatière — Métrologie en Chimie (CCQM, Consultative Committee on Amount of Substance — Metrology inChemistry). This thesis is evidenced in this paper in three chapters by: demonstration that the method is fullyphysically and chemically understood; that a measurement equation can be written down in which the valuesof all parameters have dimensions in SI units and thus having the potential for metrological traceability tothese units; that all contributions to uncertainty of measurement can be quantitatively evaluated,underpinning the metrological traceability; and that the performance of NAA in CCQM key-comparisons oftrace elements in complex matrices between 2000 and 2007 is similar to the performance of Isotope DilutionMass Spectrometry (IDMS), which had been formerly designated by the CCQM as a primary ratio method.

eth A. Mackey, Rolf Zeisler and

+1 301 208 9279.reenbe.net (R.R. Greenberg),dai Fernandes).

B.V.

Published by Elsevier B.V.

Background

The Comité Consultatif pour la Quantité de Matière — Métrologieen Chimie (CCQM, Consultative Committee on Amount of Substance—Metrology in Chemistry) has defined [Minutes from the Fifth Meeting(February 1998) of the CCQM, held at the Bureau International desPoids et Mésures (BIPM), Sèvres, France] a primary method as: “Aprimary method of measurement is a method having the highestmetrological properties, whose operation can be completely de-scribed and understood, for which a complete uncertainty statementcan be written down in terms of SI units”. More specifically, a primarydirect method was defined as “a primary method of measurementthat measures the value of an unknown without reference to astandard of the same quantity”; and a primary ratio method as “aprimary method of measurement that measures the value of a ratio ofan unknown to a standard of the same quantity; its operation must becompletely described by a measurement equation.”

The draft report of a CCQM external peer review panel for theNational Institute of Standards and Technology (NIST) ChemicalMetrology Program (October 1999) stated: “… The discussion ofsources of error … provided strong evidence that, under certaincircumstances, nuclear methods have the potential to be “primary”

methods in the sense that a complete mathematical description of themethod, and a complete uncertainty budget, can be developed. Thishypothesis should be further tested at the international level, e.g.,through a series of CCQM “pilot” exercises which might eventuallylead to one or more key comparisons. In CCQM discussions of so-called “primary” methods, the only technique relevant to theproduction of certified reference materials for inorganic trace analysisis Isotope Dilution Mass Spectrometry (IDMS). There would be greatbenefit in having another method, in particular one which does notrequire prior dissolution of solid samples.”

The metrological basis for neutron activation analysis (NAA) wasfirmly established in themid-to-late 1990s, although the fundamentalresearch was largely completed earlier. NAAwas proposed by P. Bode,R. R. Greenberg and E. A. De Nadai Fernandes as a primary ratiomethod to the CCQM as part of the Primary Methods Symposium atthe April 2000 meeting of the CCQM. However, despite previouslyidentifying 5 potentially primary methods, the CCQM declined toidentify and add additional primary methods at that time. Since April2000, various forms of NAA have been used in a large number of CCQMkey comparisons and pilot studies.

In a meeting of the Inorganic Analysis Working Group (IAWG) ofthe CCQM on April 17, 2007, P. Bode, R. R. Greenberg and E. A. DeNadai Fernandes sustained their thesis that NAA based on thecomparator method has the potentials fulfilling the requirements ofa primary ratio method with evidence on the methods' metrologicalfundamentals including the measurement equation, the evaluationand quantitation of all sources of uncertainty, the aspects ofmetrological traceability and the performance of NAA in CCQM pilotstudies and key comparisons between the years 2000 and 2007.

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194 R.R. Greenberg et al. / Spectrochimica Acta Part B 66 (2011) 193–241

Subsequently, the IAWG agreed accepting the thesis and proposed theCCQM recognizing NAA as having the potentials of a primary ratiomethod. The CCQM, in its meeting of April 19, 2007, has followed thissuggestion, and in the minutes of that meeting, approved on March31, 2008, it is explicitly stated that “…The President said that althoughthe CCQM had not discussed the list of ‘potentially primary methods’

Chapter 1. Neutron activation analysis: Prin

Peter Bode ⁎

Delft University of Technology, Faculty of Applied Sciences, Department of Radiation, RadionMekelweg 15, 2629JB Delft, The Netherlands

* E -mail address: [email protected].

during recent years, it was recognised that NAA had claims to a similarstatus to that of the five methods listed originally by the CCQM andthat NAA will be added to that list….”

The considerations leading to the three presentations given onApril 17, 2007 and the thesis of NAA being a primary ratio method aredescribed in the three chapters in this paper.

ciples and analytical characteristics

uclides and Reactors, Section Radiation and Isotopes for Health, Reactor Institute Delft,

1.1. Introduction

Activation analysis is a method for the determination of elementsbased upon the conversion of stable nuclei to other, mostlyradioactive nuclei via nuclear reactions, and measurement of thereaction products. In neutron activation analysis (NAA) the nuclearreactions occur via bombarding the material to be analyzed withneutrons. The reaction products to be measured are either theradiation, released nearly instantaneously upon neutron capture; or, ifthe resulting new nuclei are radioactive, the induced radioactivity bywhich they decay. Only the latter mode will here be discussed since itis the most common way to perform NAA.

All of the stable elements have properties suitable for production ofradioactive isotopes albeit at different reaction rates. Each radionuclideis uniquely characterized by its decay constant – the probability for thenuclear decay in unit time – and the type and energy of the emittedradiation. Among the several types of radiation that can be emitted,gamma-radiation offers the best characteristics for the selective andsimultaneous detection of radionuclides and thus of elements.

The activation will result in a mixture of radioactivities, which canbe analyzed for individual contributions by two approaches:

(i) The resulting radioactive sample is decomposed, and throughchemical separations it is divided into fractions with a fewelements each: Destructive or Radiochemical Neutron Activa-tion Analysis (RNAA).

(ii) The resulting radioactive sample is kept intact, and the elementsare determined by taking advantage of the differences in decayrates via measurements at different decay intervals utilizingequipment with a high energy resolution: Non-destructive orInstrumental Neutron Activation Analysis (INAA).

A procedure in INAA is characterized by (i) activation viairradiation with reactor neutrons, (ii) measurement of the gamma-radiation after one or more decay times and (iii) interpretation of theresulting gamma-ray spectra in terms of radionuclides, associatedelements and their mass fractions.

1.2. History

After the discovery of the neutron by Chadwick in 1932, Frédéricand Irène Joliot Curie discovered in 1934 the induced radioactivity.Enrico Fermi was one of the first in the 1930s using neutrons toproduce artificial radioactive isotopes with George de Hevesyfollowing this direction of research for studies on the rare earthelements. Results of these experiments on the action of neutrons onthe rare earth elements by George de Hevesy and Hilde Levi in 1935

marked the onset of neutron activation analysis. Theymade their ownneutron source by pulverizing beryllium in an agate mortar by handand mixing it in a glass ampoule with 222Rn (half life 3.8 days) from asolution of radium salt, which was available at the cancer hospitalin Copenhagen [1]. The α particles (4He nuclei), emitted by 222Rn,cause a nuclear reaction in beryllium with the emission of neutrons:4He+9Be→12C+1n. Once they observed the large differences ininduced radioactivity between the various (pure) lanthanides, andespecially the very high induced radioactivity of dysprosium, DeHevesy realized that even the smallest amount of dysprosium mightbe detected as impurity in any other of the rare earth elements. Theproof of principle was given in their 1936 publication [2] bydemonstrating the ability of determining the dysprosium content ofyttrium preparations. This was followed by, according to Levi [1], thereally decisive analytical experiment of determining the europiumimpurities in gadolinium samples [3]. George De Hevesy and HildeLevi stated in their first publication [2]:

“… The usual chemical methods of analysis fail, as is well known, formost of the rare earth elements and have to be replaced byspectroscopic, X-ray, and magnetic methods. The latter methods cannow be supplemented by the application of neutrons to analyticalproblems by making use of the artificial radioactivity and of the greatabsorbing power of some of the rare earth elements for slow neutrons….”

In 1949 Boyd [4] suggested to term the procedure “… the methodof radioactivation analysis …”, or, more succinctly, “… activationanalysis…” and he discussed the use of the “… chain-reacting pile …”

as a source of neutrons and an example of an analysis was given. In thesame year Brown and Goldberg [5] gave a new impulse to this methodby demonstrating that with the “… neutron pile (nuclear reactor)…very high specific activities…” could be obtained – as compared withisotopic neutron sources used so far – thereby extending thecapabilities of NAA. Kohman reported already also in 1949 on errorsin the measurement of radioactivity [6], identifying problems such assample self-absorption and measurement geometries.

The potentials of NAA method were explored in the 1950s and1960s, initially by the analysis of the decay and characteristicabsorption of the radiation emitted, and/or radiochemical separations.Gamma-ray spectrometry with scintillation detectors gave a greatimpulse to the improvement of the radionuclide – and thus element –selectivity of the technique. Chemical separations of the mixture ofradioactivities were in those years still a necessity in manyapplications for selective determination of the element(s) of interest.The introduction of the semiconductor detector in the early 1960sincreased the selectivity in gamma-ray spectrometry with orders ofmagnitude, and to such an extent that the individual radionuclidescould be identified in a mixture of radioactivities directly, without the

2 When a radionuclide decays by emission of gamma-radiation in cascade andfulfills certain constraints, in principle the intensity of sum-peaks in the gamma-ray

195R.R. Greenberg et al. / Spectrochimica Acta Part B 66 (2011) 193–241

need for chemical separations. It marked the onset of INAA asprincipal form of neutron activation analysis which development wasfurther stimulated by the availability of multi-channel pulse heightanalyzers and laboratory computers.

In the 1956 bi-annual review ‘Nucleonics’ [7] of the journalAnalytical Chemistry, the first papers are cited dealing with sources oferror in activation analysis, some of them already published in 1954[8–11]. Aspects of neutron fluence rate perturbation, geometry errors,counting efficiency are discussed and it is described how to minimizeerrors. The first practical solutions to e.g. effects of neutron self-shielding and gamma-ray self-attenuation came also in the 1950s era,e.g. by the introduction of the internal standard method by Leliart et.al. [12]. In 1960, at the Vienna Radioactivation Analysis Symposium[13], Cook presented, among others, many potential sources of errorand the documented lively discussion indicates the already estab-lished quality assurance awareness.

“Errors in activation analysis” is one of the chapters in the firstbook, published in 1963, on activation analysis [14]. About a decadelater, probably the most elaborate book on this technique by De Soete,Gijbels and Hoste was published [15], with a very extensive treatmentof systematic errors in activation analysis.

The use of NAA for the development and certification of referencematerials at organizations such as the former National Bureau ofStandards (NBS, now the National Institute of Standards and Technol-ogy, NIST) and the International Atomic Energy Agency (IAEA) [16,17]has strongly contributed to the awareness and evaluation of sources oferror, the quantization of their contribution and impact, and thedevelopment of methods to minimize their occurrence. It is thereforenot surprising that the 3rd International Conference in Modern Trendsin Activation Analysis, held at the NBS in 1968, had already a session onaccuracy and precision, the predecessor on current conference sessionslike Quality Control andQuality Assurance. These terms became familiarto the community since the end of the 1970s, though they were – andstill are – often used loosely to their definition. The awareness of astructured implementation of quality assurance practices culminatinginto quality management [18] was introduced in the 1990s and manyNAA laboratories, some of them supported by the IAEA [19] havesuccessfully implemented such management systems.

All these developments contributed to the very thorough under-standing of the principles of NAA, its sources of error andmethodologies to account for them and/or quantify their contribu-tions to the uncertainty of measurement. This forms the basis of thedemonstrated capability of operating NAA at the highest metrologicallevel, as a primary ratio method of measurement.

INAA has found its usage in many fields of science. Particularlyadvantage is taken of the fact that the samples do not have to undergoany chemical treatment, neither prior, nor after the activation: INAA is‘non-destructive’.1 In addition, low atomic number elements such asH, C, N, O, Si which in many materials belong to the major matrixcomponents, do not produce radioactive products upon neutronactivation that interfere with the determination of the other activities.It enables the observation of trace elements, often at amounts in theorder of microgram to nanogram or even less in matrices composed ofthe low Z elements. The high selectivity of gamma-ray spectrometryallows for simultaneous determination of many radionuclides. Hence,INAA is a technique for multi-element determination.

The non-destructive character makes INAA attractive for applica-tion in e.g. geochemistry and related sciences. Because of the limitedsample handling operations, there is also a lower risk of contamina-tions compared to other element determination techniques in whichthe sample has to be dissolved. This advantage has been exploited in

1 The description ‘non-destructive’ is commonly used to emphasize that the testportion does not have to be dissolved prior to the analysis. As will be further describedin Sections 1.3 and 1.6, under certain conditions also in INAA the test portion may beconsidered as ‘damaged’.

many biological applications of INAA and for the analysis of minutequantities of material such as atmospheric and cosmic dust.

Since the signals in INAA are related to the properties of the atomicnucleus, the results in INAA are not affected by the chemical andphysical state of the elements.2 Themethod iswell describedbyphysicallaw and specificity is unambiguous for all elements because of thecombination of the nuclear properties (i) decay constant (oftenconverted to the half-life, i.e. — for a single radioactive decay process,the time required for theactivity todecrease tohalf its value) and (ii) theenergies and intensities of the gamma-radiation, uniquely characteristicfor each radionuclide.

Although many forms of NAA have been identified by variouspractitioners, the discussions in this presentation will be limited toonly the standard forms of INAA and RNAA for normal size samples (afew grams or less). Other forms of NAA such as prompt gamma NAA[20], epithermal NAA [21], preconcentration NAA [22], cyclic NAA[23], large sample NAA [24], molecular NAA [25], etc. are consideredbeyond the scope of this presentation since only the standard forms ofINAA and RNAA have been directly compared with other primarymethods in CCQM comparisons.

1.3. Fundamentals of neutron activation analysis

Activation

The activationwith neutrons is, upon preparation of the test portion,thefirst stage in an INAAprocedure. Its purpose is to convert someof thestable nuclei in radioactive nuclei emitting radiation that can be used foranalytical purposes. Insight into the reactions thatmay takeplaceduringactivation facilitates the identification of the relation between theobserved radioactive nucleus, its target nucleus and associated element.Insight into the reaction rates is of importance for the quantitativeanalysis and for a priori estimates of the feasibility of an analysis.

Each atomic nucleus can capture a neutron during irradiation,resulting in a nuclear reaction in which often the nuclear masschanges; immediately (typically 10−14 s) after the capture excessenergy in the form of photons and/or particles will be emitted.3 Thenewly formed nucleus may be unstable. If unstable after activation, itstarts decaying to a stable state by the emission of radiation throughone or more of the following processes: α-decay, β−-decay, electroncapture, β+-decay, or internal transition decay. In most cases γ andX-radiation will be emitted too.

The capture of a neutron by an atomic nucleus and the resultingreaction may be illustrated, in the case of a cobalt target nucleus, by

59Coþ1n→ 60Co + promptð Þγ� radiation:

The resulting 60Co nucleus is radioactive and decays (and therebyconverts) by emission of β− radiation to excited nuclear levels of thestable 60Ni nucleus, followed by the emission of γ-radiation from theinternal transition of the nucleus from these excited levels to itsground state; see Fig. 1.1. Commonly, the reaction is written in theshorthand notation as

59Co n;γð Þ60Co

in which ‘γ ’refers to the prompt emitted radiation, not to the gamma-radiation following the β− decay.

spectrum can be affected by the chemical form of the element due to perturbation ofthe directional correlation between the gamma-rays involved. The extent of this effectcan be neglected in INAA considering the way the measurements are carried-out andthe relative unimportance of sum-peaks.

3 This prompt radiation can also be used for analytical purposes. It requiresmeasurement during activation. This method is not considered here further.

Fig. 1.1. Decay scheme of 60Co [27].


The most common reaction occurring in NAA is the (n,γ) reaction,but also reactions such as (n,p), (n,α), (n,n′) and (n,2n) are important.The neutron cross section, σ, is a measure for the probability that areaction will take place, and can be strongly different for differentreaction types, elements and energy distributions of the bombardingneutrons. Some nuclei, like 235U are fissionable by neutron captureand the reaction is denoted as (n,f), yielding fission products and fast(highly energetic) neutrons.

Neutrons are produced via

– Isotopic neutron sources, like 226Ra(Be), 124Sb(Be),241Am(Be),252Cf. The neutrons have different energy distributions with amaximum in the order of 3–4 MeV; the total output is typically105–107 s−1 GBq−1 or, for 252Cf, 2.2·1012 s−1 g−1.

– Particle accelerators or neutron generators.4 The most commontypes are based on the acceleration of deuterium ions towards atarget containing either deuterium or tritium, resulting in thereactions 2H(2H,n)3He and 3H(2H,n)4He, respectively. The firstreaction, often denoted as (D,D), yields monoenergetic neutrons of2.5 MeV and typical outputs in the order of 108–1010 s−1; thesecond reaction (D,T) results in monoenergetic neutrons of14.7 MeV and outputs of 109–1011 s−1.

– Nuclear research reactors. The neutron energy distributiondepends on design of the reactor and its irradiation facilities. Anexample of an energy distribution in a light water moderatedreactor is given in Fig. 1.4 fromwhich it can be seen that the majorpart of the neutrons has a much lower energy distribution that inisotopic sources and neutron generators. The neutron output ofresearch reactors is often quoted as neutron fluence rate in anirradiation facility and varies, depending on reactor design andreactor power, between 1015 and 1018 m−2 s−1.

In the majority of INAA procedures thermal reactor neutrons areused for the activation: neutrons in thermal equilibrium with theirenvironment (see Section 1.4). Sometimes activation with epithermalreactor neutrons (neutrons in the process of slowing down after theirformation from fission of 235U) is preferred to enhance the activationof elements with a high ratio of resonance neutron cross section overthermal neutron cross section relatively to the activation of elementswith a lower such a ratio.

In principle materials can be activated in any physical state, viz.solid, liquid or gaseous. There is no fundamental necessity to convertsolid material into a solution prior to activation; INAA is essentiallyconsidered to be a non-destructive method although under certainconditions some material damage may occur due to thermal heating,

4 Neutrons at very high energies are also produced in spallation sources. Althoughmainly tuned for realizing neutron beams, some spallation sources have also facilitiesfor NAA (e.g. at Paul Scherrer Institute in Switzerland).

radiolysis and radiation tracks by e.g. fission fragments and α-radiationemitting nuclei.

During activation the material is heated by primarily theabsorption of both reactor gamma rays (uranium fission, the fissionand activation products in the construction materials) and promptgamma-rays released upon neutron capture. Radiolysis is anothereffect caused by the gamma-rays. H2, O2 and H2O2 are formed frome.g. hydrate water, proteins or other organic molecules. Fissionfragments and α-particles may produce small holes in dedicatedplastic foils; these holes can be made visible under a microscope afterchemical treatment of the foil.

Decay

Radioactive nuclei are instable and decay resulting in product(s)withmass(es) less than that of the parent. The decay involves emissionof various types of ionizing radiation towards the groundstate of a stablenucleus. Radioactive decay is a statistically random process; theprobability that a given nucleus will decay in a certain time intervaldepends only on the time of observation. It is not possible to predictwhen a given nucleus will decay, but the decay characteristics can bedescribed by the physical laws of radioactive decay, which arecomparable to first order chemical kinetics. This is further elaboratedin the paragraph on the derivation of the measurement equation.

Decay schemes provide the details of the decayof radionuclides, suchas, e.g., the energy levels and half lives involved, the transitions, spins,multipolarities and branching ratios, types of radiation emitted, relativeintensities, conversion coefficients [26]. Decay scheme data are based ondirect experimental information with full references towards theoriginal literature. An example of such a decay scheme is given in Fig. 1.1.

Measurement

The radioactivity induced is measured by the detection of theradiation, emitted during the decay of the radionuclide. In principleboth the beta radiation from the nuclear transformation and the oftenfollowing gamma-radiation from the isomeric transition to the groundstate canbeused for this;moreover, thedecay rateof the radionuclide canbe measured. In NAA, nearly exclusively the (energy of the) gamma-radiation ismeasured because of its higher penetrating power of this typeof radiation, and the selectivity that canbeobtained fromdistinct energiesof the photons — differently from beta radiation which is a continuousenergy distribution. The interaction of gamma- and X-radiation withmatter results, among others, in ionization processes and subsequentgeneration of electrical signals (currents) that can be detected andrecorded. A radiation detector therefore consists of an absorbingmaterialin which at least part of the radiation energy is converted into detectableproducts, and a system for the detection of these products.

In ionization detectors such as gas-filled detectors and semicon-ductor detectors, the ions or the electrons are collected directly byapplying an electric field over the absorbing medium and subsequentcollection of the free charge carriers on the electrodes. There are twogreat advantages of using a solid material above a gas for detection ofradiation. Firstly, radiation is much more effective being absorbed insolid than in gas due to the much higher density of the material.Secondly, the energy required to form a single ion pair in a solid isequal to the forbidden energy gap between the valence andconduction energy bands, which is usually much smaller than theionization potential of an isolated gas atom. As a result, more ion pairsare formed upon interaction and the energy resolution is improved.Solid state ionization detectors must have a very low leakage currentto make the signals from ionizing radiation detectable, and containlittle impurities that might trap the charge carriers before detection.Crystals of semiconductor materials as such best meet theserequirements. Intrinsic silicon and germanium crystals are the mostwidely applied. The detector is constructed in such away that it acts as


a diode rectifier so that a high voltage can be applied in one directionwithout discharging current. Cooling the detectors to at least −30 °C(Si) or −160 °C (Ge) reduces the leakage current.

In scintillation detectors the ionization is measured indirectlythrough the secondary detection of light scintillations to which theabsorbing material is transparent. The difference between direct andindirect detection of the ionization products results directly in aconsiderable difference in statistical distribution of the observedevents and thus of radiation energy resolution capability.

Si, and especially Ge semiconductor detectors are currently themost applied detectors in NAA because of their energy resolution,which is superior to the resolution of scintillation detectors.

The performance of the various types of semiconductor andscintillation detectors in terms of detection efficiency and energyresolution depend strongly on the size and construction of thedetector, and the energy of the radiation to be measured. The outputof a radiation detector is a current pulse. The amount of energydeposited by ionization is reflected by the integral of this pulse withtime. It is generally assumed that the shape of the output pulse of aradiation detector does not change from one event to another. Theintegral is directly proportional to the amplitude or pulse height of theoutput pulse. The relation between the energy of the incident radiationand the total charge deposited in the detector crystal or pulse height ofthe output signal is referred to as the response of the detector. Forsemiconductor detectors, the response is linear for different energies.The shape of the response function or gamma ray spectrum reflects thethree different interaction processes of photons with matter: photo-electric effect, Compton scattering and pair production. If aninteraction results in photoelectric effect, the total energy Eγ of thephoton is transferred to an atomic electron. This photoelectron willlose its energy Eγ−Eb in the absorber. During filling of the vacancy inthe electron shell, Eb is released through emission of X-rays or Augerelectrons. The energy carried by the low energy Auger electron will betransferred completely to the absorber. As a result of the subsequentprocess, the energy deposited in the absorber totals Eγ−Eb+Eb=Eγwhich becomes visible in the gamma-ray spectrumas the so-called full

Fig. 1.2. Gamma-ray spectrum of 60Co as measured with a Ge semiconductor detector showipeak, single (S.E.) and double (D.E.) escape peaks and backscatter peak. [28].

energy photopeak. Compton scattering interaction results in aphotoelectron and a scattered Compton photon, which may interactagain via one of the three interaction mechanisms. In these successivescattering processes the scattered gamma ray contains less and lessenergy until all photoelectric absorption becomes inevitable. In thatcase, the original event will again contribute to the full energyphotopeak. However, there is a distinct probability that the scatteredCompton photon will escape from the crystal, taking the remainingenergy with it. This probability depends on the size of the activevolume of the crystal and the surface area of the detector, and theenergy of the photons. The detector response to the absorption of theCompton scattered photoelectrons only is referred to as the Comptoncontinuum. Above a threshold of 1022 keV, the incident photon mayinteract with the electric field of the atomic nucleus. It results in theconversion of the photon into an electron-positron pair, and theprocess is called ‘pair production’. The photon is completely absorbedin this process. The threshold energy arises from the energy,required to create the electron–positron pair, which is equivalent to2mec

2=1022 keV. The excess energy of Eγ-1022 keV is carried by the 2electrons as kinetic energy. Initially this energy is transferred to theabsorber. When the positron has lost its kinetic energy it will meet anelectron and annihilate, resulting in two annihilation photons of511 keV each. These photons can escape or deposit their energypartially or totally in the absorber. The net energy absorbed as aconsequence of pair production is therefore:

if 1 annihilation photon escapes: Eγ minus 511 keVif 2 annihilation photons escape: Eγ minus 1022 keVif both annihilation photons undergo photoelectric effect andcomplete absorption: Eγ keV.

The peaks in the gamma-ray spectrum resulting from escape of theannihilation photons are denoted as the single and double escapepeak, respectively. An illustrative gamma-ray spectrum as measuredwith a Ge semiconductor detector is depicted in Fig. 1.2, showing thephotopeak as the result of photoelectric absorption, the ‘Compton

ng full energy photopeaks at 1173 and 1332 keV, the Compton continuum, annihilation

image of Fig.�1.2


continuum’ reflecting the distribution of the energies deposited in thecrystal after photons resulting from Compton interaction haveescaped from the crystal and the single and double escape peakswhich reflect the energy deposited in the crystal due to escape of one,or both 511 keV quanta after pair production.

Since the probabilities of all three interacting processes aredependent on the photon energy, the detection efficiency is alsoenergy dependent. The detection efficiency is the fraction of all theradiation emitted from a source which produces some recordedinteraction in the sensitive volume of the detector. The detectionefficiency is composed of the following principal factors:

(i) The interaction efficiency, �i, which is the fraction of theradiation striking the sensitive volume of the detector andproducing a recorded event.

(ii) The geometrical factor, Gf, which is the fraction of all emittedradiationwhich are emitted in the direction of the detector. Thegeometrical factor is related to the solid angle Ω: Gf=Ω /(4π).

(iii) The peak-to-total ratio, pt, which is the fraction of recordedevents, which result in the photopeak corresponding with theenergy of the emitted radiation.

In calculations of the detection efficiency also has to be included aterm for the attenuation of the radiation in the source itself, and in thematerials between source and sensitive volume of the detector.

The product of interaction efficiency and geometrical factor isdenoted as total efficiency �T : �T=�iGf while the product of totalefficiency and peak-to-total ratio results in the full energy photopeakefficiency �p : �p = �Tpt.

The energy resolution of a gamma-ray detector is a function of theenergy deposited in the detector. Fluctuations in the number ofionizations and excitations in the detector causes that the peaks in thespectrum have a finite width normally considered as a Gaussiandistribution. The probability that an incident radiation produceselectron–hole pairs and thus charges carriers is such a process that, ina first approximation, Poisson statistics can be applied. The actual widthof the peaks in the spectrum is determined by the intrinsic resolution ofthe detector — which is determined by the number and statisticaldistributionof the charge carriers, created in the crystalupon interactionof the gamma-radiation-, and the extrinsic resolution, e.g., in semicon-ductor detectors the leakage current through or around the activevolume and the broadening effects of all electronic componentsfollowing the detector. The intrinsic resolution is also related to thesize and typeof thedetector crystal, and its temperature. In addition, theactual width of the peaks depends on the type of radiation. Nuclearenergy levels involved in the emission of gamma-radiation have verysmall widths with a negligible impact on the shape of the peaks in thespectrum, differently from natural line width of X-ray emissions. Theshape of the 511 keV peak in the spectrum results from annihilationradiation, which is Doppler broadened.

The gamma-spectrum is analyzed to identify the radionuclidesproduced and their amounts of radioactivity in order to derive thetarget elements from which they have been produced and theirmasses in the activated sample. The spectrum analysis starts with thedetermination of the location of the (centroids of the) peaks.Secondly, the peaks are fitted to obtain their precise positions andnet peak areas. The positions – often expressed as channel numbers ofthe memory of a multi-channel pulse height analyzer – can beconverted into the energies of the radiation emitted; this is the basisfor the identification of the radioactive nuclei. On basis of knowledgeof possible nuclear reactions upon neutron activation, the (stable)element composition is derived. The values of the net peak areas canbe used to calculate the amounts of radioactivity of the radionuclidesusing the full energy photopeak efficiency of the detector. Theamounts (mass) of the elements may then be determined if theneutron fluence rate and cross sections are known. In the practice,

however, the masses of the elements are determined from the netpeak areas by comparison with the induced radioactivity of the sameneutron activation produced radionuclides from known amounts ofthe element of interest.

The combination of energy of emitted radiation, relative intensitiesif photons of different energies are emitted and the half life of theradionuclide is unique for each radionuclide, and forms the basis ofthe qualitative information in NAA. The amount of the radiation isdirectly proportional to the number of radioactive nuclei produced(and decaying), and thus with the number of nuclei of the stableisotope that underwent the nuclear reaction. It provides thequantitative information in NAA. This is described in more detail inSections 1.4 and 1.5.

Measurand

The measurand in NAA – the quantity intended to be measured,[29] – is the total mass of a given element in a test portion of a sampleof a given matrix in all physico-chemical states. The quantity ‘subjectto measurement’ is the number of disintegrating nuclei of aradionuclide. The measurement results in the number of counts in agiven period of time, from which the disintegration rate and thenumber of disintegrating nuclei is calculated; the latter number isdirectly proportional to the number of nuclei of the stable isotopesubject to the nuclear reaction, and thus to the number of nuclei of theelement, which finally provides information on the mass and amountof substance of that element.

Practice of NAA

In the practice, a NAA procedure consists of the simultaneousirradiation of test portions of the unknown sample and a knownamount of a comparator of the same element— serving as a calibrator,and the sequential measurements of the induced radioactivities. AnINAA procedure has the following steps:

– Preparation (e.g. drying) and weighing of test portions of sampleand comparator; no need for dissolution

– Encapsulation of the test portions in e.g. plastic foil, plasticcapsules or quartz ampoules

– Activation via simultaneous irradiation of test portions andcomparators with neutrons

– No chemical separations, material remains intact– Sequential measurements of the induced radioactivities in each test

portion and comparator by gamma-ray spectrometry after one ormore decay periods. This is illustrated in Fig. 1.3 which shows thechanges with time of the shape of the gamma-ray spectrum. Thus,complementary information on various elements can be obtained.

– Interpretation of the gamma-ray spectra towards elements andtheir masses.

Like any other analytical method, test portions of internal qualitycontrol materials (including blanks) are following the same steps asthe samples and comparators, and are simultaneously irradiated andmeasured separately.

An RNAA procedure differs from the steps in the above only by thechemical separations of the test portion of the sample after theirradiation: so the various steps are:

– Preparation (e.g. drying) and weighing of test portions of sampleand comparator; no need for dissolution

– Encapsulation of the test portions in e.g. plastic foil, plasticcapsules or quartz ampoules

– Activation via simultaneous irradiation of test portions andcomparators with neutrons

Table 1.1Example of typical ranges of experimental conditions of an INAA procedure.

Test portion mass: 5–500 mg

Neutron fluence rates available 1016–1018m−2 s−1

Fig. 1.3. Gamma-ray spectra, recorded at different intervals after neutron activation [30].


– Chemical separations of element(s) of interest (and related radio-nuclides) from other elements in the sample test portion; the testportion of the comparator (e.g. in case of a single element standard)may be left intact.

– Sequential measurements of the induced radioactivities in eachtest portion by gamma-ray spectrometry after one or more decayperiods.

– Interpretation of the gamma-ray spectra in terms of elements andtheir masses.

An example of typical ranges of experimental conditions is given inTable 1.1.

1.4. Derivation of the measurement equation

The reaction rate R per nucleus capturing a neutron is given by

R = ∫∞

0

n vð Þvσ vð Þdv ð1� 1Þ

where

v the neutron velocity (m s−1).σ(v) the neutron cross section (in m2)5 for neutrons with

velocity v;n(v)dv the neutron density (m−3) of neutrons with velocities

between v and v+dv, considered to be constant in time.The production of radioactive nuclei is described by

dNdt

= RN0−λN ð1� 2Þ

5 Inmany tabulations and for sake of simplicity, the term ‘barn’ (notation for dimension:‘b’) is still used and preferred by many practitioners; 1 barn (b)=10−28 m2.

in which

N0 number of target nuclei.N number of radioactive nuclei.λ the decay constant, s−1; λ = ln2/t1/2 witht1/2 the half-life of the radionuclide, s.

The disintegration rate of the produced radionuclide at the end ofthe irradiation time ti follows from

D tið Þ = N tið Þλ = N0R 1� e�λti� �

ð1� 3Þ

with

D disintegration rate, Bq, of the produced radionuclide,assuming that N=0 at t=0 and N0=constant

The cross section and the neutron fluence rate are neutron energydependent. In nuclear research reactors –which are intense sources ofneutrons – three types of neutrons can be distinguished (see Fig. 1.4):

(i) Fission or fast neutrons released in the fission of 235U. Theirenergy distribution ranges from 100 keV to 25 MeV with amaximum fraction at 2 MeV. These neutrons are slowed downby interaction with a moderator, e.g. H2O, to enhance theprobability of them causing a fission chain reaction in the 235U.

Irradiation Decay Measurement5–30 s 5–600 s 15–300 s1–8 h 3–5 days 1–4 h

20 days 1–16 h

image of Fig.�1.3

Fig. 1.5. Relation between neutron cross section and neutron energy for the 59Co(n,γ)60Co reaction[32].

Fig. 1.4. Schematic representation of the neutron fluence rate spectrum in a nuclearreactor [31].


(ii) Epithermal neutrons. These are neutrons in the process ofslowing down by collisions with the nuclei of the moderator.Epithermal neutrons have energies between approximately0.5 eV and 100 keV.

(iii) Thermal neutrons, i.e. neutrons in thermal equilibriumwith theatoms of the moderator. The energy distribution of thesethermal neutrons is Maxwellian, with a most probable velocityv0 of 2200 m s−1 at 20 °C, corresponding to an energy of0.025 eV.

Typically thermal neutron fluence rates in a nuclear researchreactor are in the order of 1016–1018 m−2 s−1. As can be seen fromFig. 1.4, the thermal neutrons have the highest fluence rate. Theepithermal and fast neutron fluence rates strongly depend on theconfiguration of the reactor, particularly on the choice of moderator.The epithermal neutron fluence rate in the irradiation facilities of alight water moderated reactor is typically a factor 40–50 lower thanthe thermal neutron fluence rate.

Reactions of the (n,γ) and (n,f) type have the highest cross section(typically in the order of 0.1–100 b) for thermal neutrons whereas theother reactions ((n,p), (n,α), (n,n′), (n,2n)) mainly occur with fastneutrons at cross sections 2 or 3 orders of magnitude lower. In severalcases nuclear reactions result into the conversion of a stable nucleusinto another stable nucleus.

The cross section for thermal neutrons is often inverselyproportional to the neutron velocity; in the epithermal region theneutron cross section can be very high for neutrons of a discreteenergy and the neutron cross section versus neutron energyrelationship shows ‘resonance peaks’ (see Fig. 1.5).

The dependence of the activation cross section and neutronfluence rate to the neutron energy can be taken into account inEq. (1-1) by dividing the neutron spectrum into a thermal and anepithermal region; the division is made at En=0.55 eV (the so-calledcadmium cut-off energy). This approach is commonly known as theHøgdahl convention [33]. The integral in Eq. (1-1) can then berewritten as

R = ∫vCd

0

n vð Þvσ vð Þdv + ∫∞

vCd

n vð Þvσ vð Þdv: ð1� 4Þ

The first term can be integrated straightforward:

∫vCd

0

n vð Þvdv = v0σ0 ∫vCd

0

n vð Þdv = nv0σ0 ð1� 5Þ

in which

n = ∫vCd

0

n vð Þdv ð1� 6Þ

is called the thermal neutron density and, when Φth=nv0,

Φth the ‘conventional’ thermal neutron fluence rate, m−2 s−1,for energies up to the Cd cut-off energy of 0.55 eV.

σ0 the thermal neutron activation cross section, m2, at 0.025 eV.υ0 the most probable neutron velocity at 20 °C: 2200 m s−1.

The second term is re-formulated in terms of neutron energyrather than neutron velocity and the infinite dilution resonanceintegral I0 – which effectively is also a cross section (m2) – isintroduced:

∫∞

vCd

n vð Þvdv = Φepi ∫E max

ECd

σ Enð Þd EnEn

= Φepi I0 ð1� 7Þ

with

I0 = ∫E max

ECd

σ Enð Þd EnEn

ð1� 8Þ

in which

Φepi the ‘conventional’ epithermal neutron fluence rate per unitenergy interval, at 1 eV.

From this definition of I0 it can be seen that it assumes that theenergy dependency of the epithermal neutron fluence rate isproportional to 1/En. This requirement is fulfilled to a goodapproximation by most of the (n,γ) reactions.

In the practice of nuclear reactor facilities the epithermalneutron fluence rate Φepi is not precisely following the inverseproportionality to the neutron energy; the small deviation can beaccounted for by introducing an epithermal fluence rate distributionparameter α:

I0 αð Þ = 1 eVð Þα ∫Emax

ECd

σ Enð Þd EnE 1 + αð Þn

: ð1� 9Þ

image of Fig.�1.5

image of Fig.�1.4

7 There are a few exceptions: the chemical binding, in electron capture and internalconversion decay, may have an effect to the half-life of the radionuclide since theelectron capture rate is inversely proportional to the electron density at the nucleus,which is almost entirely determined by s-electrons. If the removed or added


The expression for the reaction rate can thus be re-written as

R = Φthσ0 + ΦepiI0 αð Þ ð1� 10Þ

Expressing the ratio of the thermal neutron fluence rate and theepithermal neutron fluence rate as f=Φth/Φepi and the ratio of theresonance integral and the thermal activation cross section asQ0(α)=I0(α)/σ0, an effective cross section can be defined:

σeff = σ0 1 +Q0 αð Þ

f

� �: ð1� 11Þ

It simplifies the Eq. (1-10) for the reaction rate to

R = Φthσeff : ð1� 12Þ

This reaction rate applies to infinite thin objects. In objects ofdefined dimensions, the inside part will experience a lower neutronfluence rate than the outside part because neutrons are removed byabsorption. Corrections have to be applied for this self-shieldingto thermal and epithermal neutrons; this is further described inChapter 2.

Decay and measurement

The nuclear transformations are established by measurement of thenumber of nuclear decays. The number of activated nuclei N(ti,td)present at the start of the measurement is given by6

N ti ; tdð Þ = RN0

λ1� e−λti� �

e−λtd ð1� 13Þ

and the number of nuclei ΔN disintegrating during the measurementis given by

ΔN ti ; td ; tmð Þ = RN0

λ1−e−λti� �

e−λtd 1−e−λtm� �

ð1� 14Þ

in which

td the decay or waiting time, i.e. the time between the end ofthe irradiation and the start of the measurement

tm the duration of the measurement

Additional correction resulting from high counting rates may benecessary depending upon the gamma-ray spectrometer hardwareused. This is further elaborated in Chapter 2.

Replacing the number of target nuclei N0 by (NAvm)/M and usingthe Eq. (1-12) for the reaction rate, the resulting net counts C in a peakin the spectrum corresponding with a given photon energy isapproximated by the ‘activation formula’:

C = ΔNγε = ΦthσeffNAvθmx

Ma1−e−λti� �

e−λtd1−e−λtm� �

λΓε ð1� 15Þ

6 The representation given here is correct only for the simplest of cases.Complications may arise when the activated nucleus decays to another unstablenucleus of which the activity is measured, e.g. 46Ca(n,γ)47Ca(β−)47Sc; here 47Ca is theactivation product, but 47Sc is the radionuclide assessed.

with

C net counts in the γ-ray peak of EγNAv Avogadro's number, mol−1

θ isotopic abundance of the target isotopemx mass of the irradiated element, gMa atomic mass, g mol−1

Γ the gamma-ray abundance, i.e. the probability of thedisintegrating nucleus emitting a photon of Eγ (photonsdisintegration−1)

ε the full energy photopeak efficiency of the detector, i.e. theprobability that an emitted photon of given energy will bedetected and contribute to the photopeak at energy Eγ inthe spectrum

Although the photons emitted have energies ranging from tens ofkeVs to MeVs and have high penetrating powers, they still can beabsorbed or scattered in the sample itself depending on the samplesize, composition and photon energy. This effect is called gamma-rayself-attenuation. Also, two or more photons may be detectedsimultaneously within the time resolution of the detector; this effectis called summation. The corrections to Eq. (1-15) for gamma-ray self-attenuation and summation effects are described in Chapter 2.

Eq. (1-15) can be simply rewritten towards the measurementequation of NAA, which shows how the mass of an element measuredcan be derived from the net peak area C:

mx = Cλ

1−e−λti� �

⋅e−λtd ⋅ 1−e−λtm� �

⋅Φth⋅σeff ⋅Γ⋅ε⋅

Ma

θ⋅NAv: ð1� 16Þ

1.5. Metrology

Nuclear reaction

All possible nuclear reactions can be completely enumeratedby knowledge of the incoming particles (thermal neutrons, epithermalneutrons, and fast neutrons), their energy and the chart of nuclides.

Nuclear decay

The decay schemes of the radionuclides are well establishedand unambiguous. Gamma-ray energies, absolute decay intensities andhalf-lives are known [26]. The combination of decay scheme andhalf-lifeis a unique characteristic of each decaying radionuclide.

The decay process is a property of the atomic nucleus. The bindingelectrons, chemical species and temperature do not influence the decayprocess.7

outermost electron is in the s-state, there will be an effect on the capture rate.However, the measured effects to the decay constant are in the order of 10−2% andonly measurable for selected, metallic or crystalline chemical species [34]. Secondly,the chemical binding may also have a measurable effect to the nuclear decay if thisdecay – under very specific conditions – includes a cascade of gamma-rays along anintermediate state of nanosecond half life. Differences of 1–2% in the intensity ratiosbetween the sumpeak of the cascade and the peaks of the individual gamma-rays havebeen observed for different chemical species of 111In [35]. This phenomenon alsocauses the observed intensity of full energy photopeaks of certain radionuclides toappear less than the true intensities [36].

8 A calibrator is defined as a measurement standard used in calibration [37].


Measurand

The area of a photopeak is a measure of the current transferin the detector, resulting from interaction of gamma-radiation ofcorresponding energy in the radiation detector. The current is directlyproportional to the number of decaying radioactive nuclei.

The number of decaying radioactive nuclei is directly proportionalto the number of stable nuclei of the isotope that underwent a nuclearreaction.

The number of stable nuclei of the isotope is directly proportionalto the total number of nuclei of the corresponding element and,assuming given abundances of the stable isotopes, to the total mass ofthat element in the irradiated test portion.

Measurement equation and metrological traceability

The metrological traceability of the values of the masses obtainedby an NAA procedure, can be derived from the measurement equation[Eq. (1-16)]. The dimensional units of the physical constants in thisequation are:

λ decay constant (= ln 2/t1/2) s−1

σeff spectrum averaged cross section, m2

Γ fraction of decays producing γ-ray of Eγ, dimensionlessNAv Avogadro's number, mol−1

θ isotopic abundance of the target isotope, dimensionlessMa atomic mass, g mol−1

of the experimental parameters are:ϕeff neutron fluence rate during irradiation, s−1 m−2

ε detection efficiency for γ-ray of Eγ, dimensionlessand of the measured quantities

C net counts in the γ-ray peak of Eγ, dimensionlessti irradiation duration, std decay time to start of count, stm duration of the measurement, smx mass of the irradiated element, g

Hence, the values of all constants, parameters and measuredquantities in the measurement equation have the potential of beingmetrologically traceable to the S.I.

Calibration

Calibration is based on the determination of the proportionalityfactors F that relate the net peak areas in the gamma-ray spectrum tothe amounts of the elements present in the sample under givenexperimental conditions:

F =Cm

: ð1� 17Þ

Both absolute and relative methods of calibration exist.

Absolute calibration

The values of the physical parameters determining the propor-tionality factor θ, NAv, M, σeff Γ, λ, are taken from literature. Theparameters σeff respectively Γ, λ are not precisely known for many(n,γ) reactions and radionuclides, and in some cases θ is also notaccurately known. Since the various parameters were often achievedvia independentmethods, their individual uncertainties will add up inthe combined uncertainty of measurement of the elemental amounts,leading to a relatively large combined standard uncertainty. More-

over, the metrological traceability of the values of the physicalconstants is not known for all radionuclides. The other parameters C,mx, Φ, ε, ti, td, tm are determined, calculated or measured for the givencircumstances and uncertainties can be established.

Relative calibration

Direct comparator method

The unknown sample is irradiated together with a calibrator8

containing a known amount of the element(s) of interest. The calibratoris measured under the same conditions as the sample (sample-to-detector distance, equivalent sample size and if possible equivalent incomposition). From comparison of the net peak areas in the twomeasured spectra themass of the element of interest can be calculated:

mx unkð Þ = mx calð Þ·

Ctm:e

−λtd· 1−e−λtm� �

!unk

Ctm:e

−λtd· 1−e−λtm� �

!cal

ð1� 18Þ

in which

mx(unk), mx(cal) mass of the element of interest, in unknown sampleand calibrator, respectively; in g

In this procedure many of the experimental parameters — such asneutron fluence rate, cross section and photopeak efficiency cancelout at the calculation of the mass and the remaining parameters areall known. This calibration procedure is used if the highest degree ofaccuracy is required.

The relative calibration on basis of element calibrators is notimmediately suitable for laboratories aiming at the full multi-elementpowers of INAA. It takes considerable effort to prepare multi-elementcalibrators for all 70 elements measurable via NAA with adequatedegree of accuracy in a volume closely matching the size and theshape of the samples.

Single comparator method

Multi-element INAA on basis of the relative calibration method isfeasible when performed according to the principles of the single-comparator method. Assuming stability in time of all relevantexperimental conditions, calibrators for all elements are co-irradiatedeach in turn with the chosen single comparator element. Once thesensitivity for all elements relative to the comparator element hasbeen determined (expressed as the so-called k-factor, see below),only the comparator element has to be used in routine measurementsinstead of individual calibrators for each element.

The single comparator method for multi-element INAA was basedon the ratio of proportionality factors of the element of interest andof the comparator element after correction for saturation, decay,counting and sample weights. Girardi et al. [38] defined the k-factorfor each element i as

ki =Mað Þi;calγcompεcompθcompσeff ;comp

Ma;compγi;calεi;calθi;calðσeff Þi;cal: ð1� 19Þ


Masses for each element i then can be calculated from these ki-factors; for an element determined via a directly produced radionu-clide the mass mx(unk) follows from

mx unkð Þ = mx compð Þ⋅

C1−e−λti� �

⋅tm⋅e−λtd ⋅ 1−e−λtm� �

!unk



!comp

⋅ki ð1� 20Þ

with

mx(comp) mass of element x in comparator, in g.

These experimentally determined k-factors are often moreaccurate than when calculated on basis of literature data as in theabsolute calibration method. However, the k-factors are only valid fora specific detector, a specific counting geometry and irradiationfacility, and remain valid only as long as the neutron fluence rateparameters of the irradiation facility remain stable.

The single comparator method requires laborious calibrations inadvance, and finally yield relatively (compared to the directcomparator method) higher uncertainties of the measured values.Moreover, it requires experimental determination of the photopeakefficiencies of the detector. Metrological traceability of the measuredvalues to the S.I. may be demonstrated.

The k0-comparator method

At the Institute for Nuclear Sciences in Ghent, Belgium, an attempthas been made to define k-factors which should be independent ofneutron fluence rate parameters as well as of spectrometer char-acteristics. In this approach, the irradiation parameter (1+Q0(α)/f)(Eq. (1-11)) and the detection efficiency ε are separated in theexpression (1-19) of the k-factor, which resulted at the definition ofthe k0-factor [39]

k0 =1ki

1 + Q0;comp αð Þf

1 + Q0;cal αð Þf

εcomp

εcal=

Mcompθcalσ0;calγcal

Mcalθcompσ0;compγcompð1� 21Þ

and themass, again for an element determined via a directly producedradionuclide, is found from

mx unkð Þ = mx compð Þ

1 +Q0;comp αð Þ

f

1 +Q0;unk αð Þ

f

εcomp

εunk



⋅m

!unk



⋅m

!comp

⋅1k0

:

ð1� 22Þ

All in the above is based on the assumption that the cross section inthe thermal energy region varies with the inverse of the neutronenergy. For a small group of nuclear reactions (151Eu(n, γ) 152,152mEu,168Yb(n, γ)169Yb, 176Lu(n, γ)177Lu) this assumption results insignificant deviations, requiring the use of the Westcott formalisminstead of the Høgdahl convention for describing the relation betweenactivation cross section and neutron energy, thereby introducing theneutron temperature as a parameter. The impact of the equations iswell documented [40].

The k0-factor thus has become a purely nuclear parameter forthe thermal neutron spectrum. In the k0-convention, Au is oftenproposed as comparator element. The k0 values and associatedparameters such as Q0 are tabulated [e.g., 41] and based on

elsewhere measured ratio(s) of the activation rate(s) of element(s)and the standard element, Au. Some of these values and parametersare still regularly updated. The neutron fluence rate parameters f(ratio of thermal to epithermal neutron fluence rate) and α no longercancel out in mass calculations and must be measured in eachirradiation facility, preferably even for each irradiation and sample[42]. At least three isotopes must be activated and measuredto determine these parameters. A composed fluence rate monitorcontaining adequate quantities of Au and Zr is suitable for thispurpose; in a single measurement the induced activities of198Au, 95Zr and 97Zr can be assessed; recently an alternative set ofMo, Cr and Au was suggested for monitoring of well-thermalizedfacilities [43]. As such, the k0-method is not a single comparatorbut e.g. a triple comparator method. The photopeak efficiencies of thedetector must also be (experimentally) determined in this approach.

The k0-method requires tedious characterizations of the irradia-tion and measurement conditions and results, like the singlecomparator method, in relatively high uncertainties of the measuredvalues of the masses. Moreover, metrological traceability of thecurrently existing k0 values and associated parameters to the S.I. is notyet transparent and most probably not possible.

Summarizing, relative calibration by the direct comparatormethod renders the lowest uncertainties of the measured valueswhereas metrological traceability of these values to the S.I. can easilybe demonstrated. As such, this approach is often preferred from ametrological viewpoint. The measurement equation can be furthersimplified, substituting

A0 =λCeλtd

1−e�λtm� �

⋅ 1−e�λti� � ð1� 23Þ

to

munk = mcal

A0 unkð ÞA0 calð Þ

RθRΦRσRε ð1� 24Þ

in which

Rθ ratio of isotopic abundances for unknown sample andcalibrator.

Rϕ ratio of neutron fluence rates (including fluence gradient,neutron self shielding, and scattering) for unknown sampleand calibrator.

Rσ ratio of effective cross sections if neutron spectrum shapediffers from unknown sample to calibrator.

Rε ratio of counting efficiencies (differences due to geometryand γ-ray self shielding) for unknown sample and calibrator.

1.6. Analytical characteristics

Total sample analysis

Neutron activation analysis provides information on the total massof elements in the sample processed. Since INAA, originally denoted as‘non-destructive NAA’ does not require dissolution of the sample,there are in principle no losses by incomplete digestion, precipitationor wall adsorption effects nor does the technique suffer fromcontaminations that might be introduced by the solvents used. It iswell known that special measures have to be taken to prevent lossesby volatilization of some elements during irradiation (e.g. Hg and Br);in such cases often sealed quartz ampoules are preferred abovepolyethylene vials. The degree of volatilization depends whether theelement is bound to an inorganic or organic ligand, and the irradiationconditions (neutron and gamma-ray fluences and temperature).


In an INAA procedure the elementmass in the entire (bulk) sampleis determined, which distinguishes the technique from X-rayfluorescence analysis, which provides information only on the surfacecomposition of a sample.

In an RNAA procedure the dissolution takes place after theirradiation. The chemical yield determination can be done with highdegree of accuracy by either addition of a non-radioactive spike ofthe same element(s) to be separated, and or by quantitation of therecovery of a radiotracer (same element(s), produced separately)added after irradiation.

No effects from the chemical state and physical form of the element to bedetermined

All phenomena (nuclear reaction, decay, and emission of radia-tion) are related to the properties of the atomic nucleus. The valenceelectrons are with some exceptions (see footnote 7) not involved inthese processes. Hence, the determination of an element viameasurement of its induced radioactivity is in principle independentof its chemical state or physical form; there is no difference whetheran element is bound to an inorganic compound or an organiccompound, or if it is present as a pure metal, provided the degreesof gamma-ray self-attenuation in sample and calibrator are equivalentand can be quantified (cf. parameter Rε in Eq. (1-24)). Chemicalmatrix effects, known to be significant sources of error in some othertypes of instrumental chemical analysis, are insignificant in NAA orcan be quantified and corrected for.

This characteristic implies that the calibrators (standards) in NAAdo not have to be identical in composition than the measurands. Itallows for use of single element comparators of the highest purity andknown stoichiometry (e.g. metal foils) with relatively small contri-bution to the combined standard uncertainty of measurement. Thedifferences in neutron and gamma-ray self-shielding, and in irradi-ation and counting geometry between calibrator and sampleare described by physical parameters, and can be calculated and/orexperimentally determined.

Self-validating characteristics

The nuclear physical principles of NAA also provide many self-validating opportunities of the measurement results, contributingfavorably to the degree of accuracy.

Most of these result from the fact that many elements havemultiple stable isotopes from which more than one radionuclide canbe produced upon neutron irradiation (e.g. 122Sb and 124Sb).Moreover, these multiple radionuclides from one element havedifferent half-lives (e.g. 122Sb: 64 h and 124Sb: 60 days), and emitseveral gamma-rays with different energies with accurately knownemission probabilities (intensity ratios) e.g. 122Sb: 564 keV (63%emission probability) and 693 keV (3.3%), and 124Sb: 602.7 keV (98%),723 keV (11%) and 1691 keV (52%).

The combination of half-life and gamma-ray energy makesconfirmation of identity of the radionuclide 100% and confirmationof identity of the element (on basis of known nuclear reactions) inmost cases also 100%. In addition, quantitative results derived fromthe different peak areas of one radionuclide, as well as from differentradionuclides of the same element should be in agreement. Equally so,results from the same radionuclide, registered after different decayintervals, should agree with each other.

Interferences during irradiation may occur. As an example,the radionuclide 28Al may result from the nuclear reactions 27Al(n,γ)28Al, 28Si(n,p)28Al or 31P(n,α)28Al. Such interferences can beidentified, quantified and corrected for. Similarly, interferencesduring measurement may occur (e.g., the gamma-ray line at320 keV may result from either the decay of 51Ti or 51Cr to levels in51V) but identification and correction is possible taking advantage

of the differences in half lives of the radionuclides (e.g., 51Ti: 5.8 m,51Cr: 27.7 days) and/or the information obtained from other radio-nuclides formed from the element of interest and intensity ratiosfromdifferent gamma-ray lines (e.g., in the decay of 51Ti also gamma-rays of 605 keV and 928 keV is emitted, which does not occur in thedecay of 51Cr).

The impact of some of these interferences is mass dependentbut such interferences can easily be identified and quantified bymeasurements after different decay intervals. Multiple measure-ments after different decay intervals also serve for assessing pile-up effects and interference corrections, and to test all counting-related nonlinearities. The degree of gamma-ray self-attenuationcan be derived from the intensity ratios of peaks in the spectrumor calculated after experimental determination of the measuredtransmission through the sample of an external beam of gamma-rays.

The peak areas can be determined in several ways – e.g., withfitting routines or via channel-by channel counting and backgroundsubtraction – thus providing an additional validation of this step.

Finally, as will be demonstrated in detail in Chapter 2 (Evaluationof Uncertainties for NAA Measurements Using the ComparatorMethod of Standardization) of this paper, the type A evaluations ofcontribution to uncertainty of measurement are mass dependentand can be measured. Most of the type B evaluations of contributionto uncertainty of measurement are not mass dependent, and affectall elements in the same irradiation or measurement to the sameextent.

Many adjustable experimental parameters for optimization ofexperimental design

A NAA procedure has many adjustable experimental para-meters, which is reflected by the measurement (Eq. (1-16)).These can be used for optimizing the design of the NAA proceduretowards e.g. minimization of uncertainty of measurement, mini-mization of interfering effects during irradiation and/or measure-ment, minimization of the limit of detection or reduction of thetotal analysis (turnaround) time. Sample and calibrator mass maybe optimized for e.g. reduction of geometric effects duringirradiation and measurement, for reduction of self attenuationeffects or for increasing the signal-to-noise ratio. Irradiation timeand neutron fluence rate have an effect to the amount of inducedradioactivity of the radionuclide of interest but irradiation timemay also be varied for changing the ratio of induced radioactivity ofthis radionuclide and interfering ones. Cadmium or boron filters inthe irradiation facility remove the thermal neutrons and thuschange the neutron energy spectrum. This is a well-establishedapproach for selective activation of elements with epithermal andfast reactor neutrons.

It was illustrated already by Fig. 1.3 that complementaryinformation can be obtained from measurements after differentdecay periods. This is also an approach for reduction of spectralinterferences such as closely spaced gamma-ray peaks, or forimprovement of the detection limit of small amounts of inducedradioactivity of radionuclides with long half lives in the presence ofhigh amounts of radionuclides with shorter half lives. Moreover, suchmultiple measurements are often preferred for taking full advantageof the self-validating opportunities of the various radionuclidesproduced from activation of a given element.

Elements such as H, C, N, O, and Si do not affect the determination ofother elements

The neutron activation of a number of low Z elements (H, He, Be, Li,B, C, N, and O — which belong often to the most abundant in manymaterials-) and of a few high Z elements (Bi, Tl, and Pb) is

Table 1.2Detection limits for elements inmg kg−1 as observed in a NAA procedure of a plantmaterialand a soil material [33]. Experimental conditions: plant: ti=4 h at 5⁎1016m−2 s−1,td=5 days, tm=0.5 h at coaxial detector, followed at td=3 weeks and tm=2 h atwell-typedetector; sample size=200 mg; soil: ti=1.5 h at 5⁎1016m−2 s−1, td=5 days, tm=1 h atcoaxial detector, followed at td=3weeks and tm=1 h at well-type detector; samplesize=200mg.

Plant Soil Plant Soil

Na 2 10 K 200 1500Ca 700 4000 Sc 0.001 0.02Cr 1 1 Fe 8 100Co 0.02 0.3 Ni 2 30Zn 0.4 6 Ga 2 10As 0.2 0.8 Se 0.1 1Br 0.3 0.8 Rb 0.4 6Sr 5 60 Zr 5 80Mo 4 10 Ag 0.2 2Cd 3 8 Sn 10 20Sb 0.02 0.2 Te 0.3 3Cs 0.02 0.3 Ba 10 40La 0.1 0.3 Ce 0.2 1Nd 0.7 8 Sm 0.01 0.03Eu 0.006 0.05 Tb 0.008 0.1Yb 0.03 0.2 Lu 0.004 0.02Hf 0.01 0.1 Ta 0.01 0.2W 0.3 1 Re 0.08 0.2Os 0.1 0.6 Ir 0.0006 0.004Au 0.003 0.01 Hg 0.05 0.4Th 0.01 0.1 U 0.2 2


characterized by either one, or a combination of (i) very lowactivation cross sections, (ii) activation products with very shorthalf-lives (in the order of seconds) and (iii) the emission of radiationwhich is not recorded in the gamma-ray spectrum and therefore doesnot interfere with the measurement of the gamma radiation emittedby the other activation products. As such, these elements are virtuallyabsent in gamma-ray spectrometry in NAA, making the sample‘transparent’ for the signals from the radionuclides.

Suitable for measurement of total element mass in the order of 10−6

to 10−9 g, or less

The detection limit in NAA is based on the signal-to-noise ratio, theselectivity of determining, with a certain degree of confidence, a peak inthe gamma-ray spectrum. The photopeak in the spectrum of thegamma-ray emission by the radionuclide of interest is the ‘signal’. The‘noise’ results from the detection of photons from the ambientbackground, from the Compton continuum due to the interaction ofhigher energyγ-rays, aswell as fromγ-ray spectrum interferences frome.g. the blank from pre-irradiation treatment, from packing materialsand from(partly) overlappingpeaks. Thedetection limit depends on theirradiation, the decay and the counting conditions. It is quite common toestimate the detection limit using Currie's formula [44]:

DL = 2:71 + 4:65ffiffiffiB

pð1� 25Þ

where DL is the detection limit and B is the background under a γ-raypeak. This approach is valid only when the γ-ray background(counting statistical error) is the major interference.

The detection limits depends in the practice of INAA on:

– The amount of material to be irradiated and to be counted: oftenset by availability, sample encapsulation aspects and safety limitsboth related to irradiation andmeasurement, and possibly becauseof neutron self-shielding and gamma-ray self-absorption effects.For these reasons in the practice of INAA the sample mass is oftenlimited to approximately 250 mg.

– The neutron fluence rates: set by available irradiation facilities.– The duration of the irradiation time: set by practical aspects, such

as the limitations in total irradiation dose of the plastic containersbecause of radiation damage, or by reactor operation cycles.

– The total induced radioactivity that can be measured is set by thestate-of-the-art of counting and signal processing equipment, withadditional radiation dose and shielding considerations.

– The detector size, measurement geometry and backgroundshielding.

It all illustrates that the detection limit for a given element by INAAmay be different for each individual type of material, and analysisconditions. In Table 1.2 [45] are given, as an indication, typical detectionlimits as derived from the analysis of a plant and a soil material.

1.7. Applicability of NAA

Neutron activation analysis, like any other trace element analysistechnique, is not a panacea for any trace element determination in anytype of material. The selection of NAA as a method of choice may bebased on the fact that element of interest and sample material(matrix) should have specific chemical properties, physical forms andphysical characteristics for analysis by NAA.

Preferred conditions for selection of NAA

The nuclear properties of the element of interest are ofimportance: the activation rate and the decay characteristics of the

radionuclides produces such as half life and energies of the gamma-ray emission. As was mentioned in the above, the very low Z elements(like H, He, B, Be, C, N, and O) are therefore not suitable for detectionby NAA, but also a few other elements cannot be determined too (e.g.,Tl and Bi) or at least not at a low level. The activation of lead (Pb), forinstance, results only at milligram quantities to measurable activitieswhich is for many applications an inadequate sensitivity.

The sample matrix should not have both high density (resulting instrong gamma-ray self-attenuation), high atomic number (alsoaffecting gamma-ray self attenuation) and extremely high neutronabsorbing properties. With respect to the latter, high mass fractions ofB, Cd, Gd, and Dy will cause neutron self-absorption of the thermalneutrons inside the sample, resulting in a neutron energy distributiondifferent from the distribution in the standard. Moreover, it may causea neutron fluence rate depression outside the sample, affecting theneutron fluence in the calibrators which surround the sample. Largeamounts of the elements with strong neutron absorbing propertiesare also unwanted in NAA if their neutron capture results in theemission of charged particles such as α-radiation (either prompt ordelayed). This occurs mainly with the elements B, Li and U and maycause excessive thermal heating during the irradiation.

Samples particularly suited for NAA

The analytical characteristics of neutron activation analysis areemployed at full advantage for the analysis of three major categoriesof materials:

• Solid materials that are difficult to bring completely into a solutionExamples are:– soils, rocks, minerals, ores, cosmic material, air particulate matter,

zeolites, and new composite materials– materials in with C, H, N, and O as major elements: plants and

similar biological material, plastics• Solid materials that are easy to contaminate during preparation ofthe test portion, if e.g. digestion would be needed for a differentanalytical techniqueExamples are:– ultra pure substances: Si semiconductor material and carbon fiber– ultra small quantities: air particulate matter and cosmic dust


– biological tissues and fluids (blood, serum, and urine)• Solid materials that are unique and should keep their integrityExamples are:– materials from forensic studies– archaeological, cultural and art objects

• Solid materials of which the bulk composition has to be determinedand for which surface techniques such as XRF and solid-statespectroscopic techniques (e.g. LIBS and laser ablation ICP) aretherefore inadequate.

Examples of such samples,within a selected groupof disciplines, are:

(1) Archaeology — amber, bone, ceramics, coins, glasses, jewelry,metal artifacts and sculptures, paintings, pigments, pottery,soils and clays, and stone artifacts.

(2) Biomedicine — animal and human tissues, blood and bloodcomponents, bone, drugs and medicines, gallstones, hair,implant corrosion, kidney and kidney stones, medical plantsand herbs, milk, nails, placenta, snake venom, teeth, dentalenamel and dental fillings, urine and urinary stones.

(3) Environmental science and related fields — aerosols, atmo-spheric particulates (size fractionated), fossil fuels and theirashes, animals, birds, insects, fish, aquatic and marine biota,seaweed, algae, lichens, mosses, plants, trees, household andmunicipal waste, soils, sediments, and sewage sludges.

(4) Forensics — bomb debris, bullet lead, explosives detection, glassfragments, paint, hair, gunshot residue swabs, and shotgun pellets.

(5) Geology and geochemistry — asbestos, bore hole samples, bulkcoals and coal products, coal and oil shale components, crudeoils, cosmo-chemical samples, cosmic dust, coral, diamonds,exploration and biogeochemistry, meteorites, ocean nodules,rocks, sediments, soils, glacial till, ores and separated minerals.

(6) Industrial products — alloys, catalysts, ceramics and refractorymaterials, coatings, electronic materials, fertilizers, fissilematerial detection and other safeguard materials, graphite,high purity and high-tech materials, integrated circuit packingmaterials, oil products, pharmaceutical products, plastics,semiconductors, pure silicon and silicon processing.

(7) Nutrition — composite diets, foods, honey, seeds, spices,vegetables, milk and milk formulae, and yeast.

Additional aspects of the use of NAA

Some additional operational aspects of NAA are worth mentioninghere for completeness. NAA is not available as a stand-alone push-button apparatus with a fully integrated software package to beoperated ‘on-the-spot’ at just any analytical laboratory. First, access toa nuclear research reactor is essential, obviously. Though most NAAlaboratories are found on-site of the reactor, there are quite a fewother cases in which the NAA laboratory is not on-site and samples(before and after irradiation) are transported over distances up tomore than 100 km.9 This implies limitations with respect to themeasurement of radionuclides with (very) short half lives. Thereactor's irradiation facilities define the available neutron fluencerates, neutron energy distributions and set technical constraints withrespect to sample encapsulation, maximum and minimum irradiationduration.

The required instrumentation for measurement of the inducedradioactivity, viz. the gamma-ray spectrometer with semiconductordetector, is build up with modular units that all are commerciallyavailable. Sample changers for NAA, versatile with respect to be used

9 The NAA laboratory of one of the authors of this paper (EADNF) is atapproximately 150 km from the research reactor in São Paulo.

with sample vials of specific dimensions and different detector types(e.g. well-type detectors) are limited commercially available. In mostcases a laboratory has to develop and build its own automation.Spectrum analysis and interpretation software is nowadays availablewith all major suppliers of gamma-ray spectrometers as well as theInternational Atomic EnergyAgency.However, getting startedwithNAAstill requires considerable effort, especially with respect to masteringsources of error in the conduct of the technique and with theinterferences in the spectrum analysis and interpretation. The mergeof a physical method and chemical analysis requires simultaneousexpertise from both disciplines for an effective operation.

The NAA laboratory has to meet the legal requirements forradiological safety. This may imply high investment costs if a non-radiological laboratory has to be adapted to such requirements. Aradiological health officer may be required (which could be a part-time function of an employee of the NAA laboratory) and provisionshave to exist for storage and disposal of radioactive waste. Employeeshave to be trained in the radiological safety and practical aspects ofhandling radioactivity. If the research reactor is not on-side of the NAAlaboratory, the safety in transportation of the radioactive samplesrequires attention too.

The fundamentals of NAA are further described in detail in e.g.reference [15].

1.8. References for Chapter 1

[1] H. Levi, Semicentennial Lecture, held on June 23, 1986 at the opening of the7th International Conference Modern Trends in Activation Analysis, Copenha-gen, Denmark.

[2] G. Hevesy, Hilde Levi, The Action of Neutrons on the Rare Earth Elements, Det.Kgl. Danske Videnskabernes Selskab, Mathematisk-fysiske Meddelelser XIV, 5(1936) 3–34.

[3] G. Hevesy, Hilde Levi, Artificial Activity of Hafnium and some other Elements,Det. Kgl. Danske Videnskabernes Selskab, Mathematisk-fysiske MeddelelserXV, (1938) 11–21.

[4] G.E. Boyd, Method of Activation Analysis, Anal. Chem. 21 (1949) 335–347.[5] H. Brown, E. Goldberg, The Neutron Pile as a Tool in Quantitative Analysis;

The Gallium and Palladium Content of Iron Meteorites, Science 109 (1949)347–353.

[6] T.P. Kohman, Measurement Techniques of Applied Radiochemistry, Anal.Chem. 21 (1949) 352–364.

[7] W. Wayne Meinke, Nucleonics, Anal. Chem. 28 (1956) 736–756.[8] W.B. Lewis, Isotope production, how to choose irradiation times, Nucleonics

12 (1954) 30–33.[9] W.B. Lewis, Flux perturbations by material under irradiation, Nucleonics 13

(1955) 82–88.[10] R.C. Plumb, J. E. Lewis, How to minimize errors in neutron activation analysis,

Nucleonics 13, (1955) 42–46.[11] L.H. Rietjens, G.J. Arkenbout, G.F. Wolters, J.C. Kluyver, Influence of distance

between source and crystal on detection efficiency of gamma-ray scintillationspectrometers, Physica 21 (1955) 110–116.

[12] G. Leliart, J. Hoste, J. Eeckhaut, Activation analysis of Vanadium in highalloy steels using Manganese as internal standard, Anal. Chim. Acta 19 (1958)100–107.

[13] G.B. Cook, Radioactivation analysis in a nuclear reactor, Pure and AppliedChemistry 1(1960) 15–30.

[14] H.J.M. Bowen, D. Gibbons, Radioactivation Analysis, Oxford University Press,Oxford, UK, 1963, 295 pp.

[15] D. De Soete, R. Gijbels, J. Hoste, Neutron Activation Analysis, Wiley-Interscience, London, 1972.

[16] Advisory Group of the International Atomic Energy Agency, Qualityassurance in biomedical neutron activation analysis, Anal. Chim. Acta165 (1984) 1–29.

[17] H. Kawamura, R.M. Parr, H.S. Dang, W. Tian, R.M. Barnes, G.V. Iyengar, Analyticalquality assurance procedures developed for the IAEA's Reference Asian ManProject (Phase 2), J. Radioanal. Nucl. Chem. 245, (2000) 123–126.

[18] P. Bode, J.P. van Dalen, Accreditation: a prerequisite, also for neutron activationanalysis laboratories, J. Radioanal. Nucl. Chem.179 (1994)141–148.

[19] M. Rossbach, J. Gerardo-Abaya, A. Fajgelj, P. Bode, P. Vermaercke, M. Bickel,Quality system implementation in Member States of the IAEA, Accred. Qualit.Assur. 10 (2006) 583–589.

[20] G.L. Molnar (Ed). Handbook of prompt gamma activation analysis withneutron beams. Kluwer Academic Publishers, Dordrecht, (2004) ISBN1402013043, 423 pages.


[21] E. Steinnes, D. Brune, Determination of uranium in rocks by instrumentalactivation analysis using epithermal neutrons, Talanta. 16 (1969) 1326–1329.

[22] R.R. Rao, A. Chatt, Microwave acid digestion and preconcentration neutronactivation analysis of biological and diet samples for iodine, Anal. Chem. 63(1991) 1298–1303.

[23] A. Egan, S.A. Kerr, M.J. Minski, Determination of selenium in biologicalmaterials using Se-77 m (T=17.5 s) and cyclic activation analysis, Radio-chem. Radioanal. Lett. 28 (1977) 369–378.

[24] P. Bode, R.M.W. Overwater, Trace element determinations in very largesamples — a new challenge for neutron activation analysis, J. Radioanal. Nucl.Chem. 167 (1993) 169–176.

[25] L.R. Opelanio, E.P. Rack, A.J. Blotcky, F.W. Crow, Determination of chlorinatedpesticides in urine by molecular neutron activation analysis, Anal. Chem. 55(1983) 677–681.

[26] Table of Isotopes, Eight Edition, R.B. Firestone, V.S. Shirley, Eds., J. Wiley, NewYork, 1996.

[27] D.D. Sood, A.V.R. Reddy, N. Ramamoorthy, ‘Fundamentals of Radiochemistry’,IANCAS, Mumbai, India, 2000.

[28] Gamma-Ray Spectrum Catalogue, CD-ROM 1999, Dr. R.G. Helmer. IdahoNational Energy & Environmental Laboratory, Idaho Falls, ID, USA.

[29] International Vocabulary of Metrology — Basic and General Concepts andAssociated Terms (VIM) 3rd edition, 2007.

[30] Adapted from: P. Bode, J.J.M. de Goeij, Activation Analysis, in; Encyclopedia ofEnvironmental Analysis and Remediation, R.A. Meyers, Ed., J. Wiley, New York(1998), ISBN 0-471-11708-0, pages 68-84.

[31] Adapted from: G. Erdtmann, H. Petri, Neutron Activation Analysis: Fundamentalsand Techniques, in: Treatise on Analytical Chemistry, Part 1, Theory and Practice,Volume 14, P.J. Elving, Ed., J. Wiley, New York (1986), ISBN0-471-80648-X, 795pages.

[32] Reference neutron Activation Library, IAEA Technical Document TECDOC-1285(2002) Vienna, Austria.

[33] O.T. Høgdahl, Neutron Absorption in Pile Neutron Activation Analysis,Michigan Memorial Phoenix Project, Univ. of Michigan, Ann Arbor, USA,Report MMPP-226-1 (1962).

[34] H. Daniel, Influence of Chemical Environment on Lifetimes in NuclearPhysics, in: The Use of selective Nuclear Techniques for the Elucidation ofChemical Bonding, Topical Issue of Atomic Energy Review 17 2 (1979),287–344.

[35] M. de Bruin, P.J.M. Korthoven, The Influence of the Chemical Form ofRadionuclides on the Shape of the Gamma-Ray Spectrum, Radiochem.Radioanal. Lett. 21, 5 (1975) 287–292.

[36] R.J. Gehrke, R.H. Helmer, R.C. Greenwood, Precise relative χ-ray intensitiesfor calibration of Ge-semiconductor detectors, Nucl. Instr. Meth. 147 (1977)405–423.

[37] International vocabulary of metrology — Basic and general concepts andassociated terms (VIM), JCGM200: 2008.

[38] F. Girardi, G. Guzzi, J. Pauly, Reactor Neutron Activation Analysis by the SingleComparator Method, Anal. Chem 37 (1965) 1085–1092.

[39] A. Simonits, F. de Corte, J. Hoste, Single Comparator Methods in Reactor NeutronActivation Analysis, J. Radioanal. Chem. 24 (1975) 31–46.

[40] F. de Corte, A. Simonits, F. Bellemans, M.C. Freitas, S. Jovanovic, B. Smodis,G. Erdtmann, H. Petri, A. de Wispelaere, Recent advances in the k0-standardization of neutron activation analysis: extensions, applications,prospects, J. Radioanal. Nucl. Chem. 169 (1993) 125–158.

[41] F. de Corte, A. Simonits, Recommended nuclear data for use in the k0-standardization of neutron activation analysis, Atomic Data Nuclear DataTables 85 (2003) 47–67.

[42] P. Bode, M. Blaauw, I. Obrusník, Variation of Neutron Flux and related Parameters inan Irradiation Container, in Use with k0-Based Neutron Activation Analysis,J. Radioanal. Nucl. Chem. 157 (1992) 301–312.

[43] M.J.J. Koster-Ammerlaan, M.A. Bacchi, P. Bode, E.A. De Nadai Fernandes, A newmonitor for routine thermal and epithermal neutron fluence rate monitoringin k0 INAA, Appl. Rad. Isotop. 66 (2008) 1964–1969.

[44] L.A. Currie, Limits for qualitative detection and quantitative determination —

application to radiochemistry, Anal. Chem., 40 (1968) 586–593.[45] P. Bode, Instrumental and organizational aspects of a neutron activation

analysis laboratory Ph.D. dissertation, Delft University of Technology, Delft.(1996).

1.9. List of symbols used in Chapter 1

A0 decay corrected count rateB background counts under a γ-ray peakC net peak countsa as subscript denoting element of interest in samplec as subscript denoting element of interest in comparatorDL detection limitDti disintegration rate (Bq) at the end of the irradiation time tid as subscript denoting decayEγ gamma-ray energyECd neutron energy at the cadmium cut-off point, 0.55 eVEmax maximum energy of epithermal neutronsEn neutron energyF C/mf Φth/Φepi

I0 resonance integralI0(α) resonance integral, taking into account the not perfect

inverse proportionality of Φepi to the neutron energyi as subscript denoting irradiationk Girardi's proportionality factor for calibration in NAAk0 proportionality factor for the k0-method of calibration in

NAAMa atomic massm massm as subscript denoting measurementN number of radioactive nuclei producedNAv Avogadro's numberN0 number of target nuclein neutron densityn(v)dv neutrondensity of neutronswith velocities between v and v+

dv, considered to be constant in timeQ0(α) I0(α)/σ0

R reaction rate per nucleus capturing a neutronRj ratio of parameter j (= θ, Φ, σ, ε) for unknown sample and

calibratort timet1/2 half-lifev neutron velocityv0 most probable neutron velocity at 20 °C: 2200 ms−1

vCd neutron velocity at the cadmium cut-off point, ECd=0.55 eVmx mass of the irradiated elementα epithermal fluence rate distribution parameterΓ fraction of decays producing γ-ray of energy Eγγ gamma-ray abundanceε photopeak efficiencyλ decay constantσ(v) neutron cross section, m2, for neutrons with velocity vσ0 thermal neutron activation cross section at 0.025 eVσeff effective neutron cross section during irradiationθ isotopic abundanceΦth ‘conventional’ thermal neutron fluence rate for energies up

to the Cd cut-off energy of 0.55 eVΦepi ‘conventional’ epithermal neutron fluence rate equivalent

to the epithermal neutron fluence rate density per unitenergy interval at 1 eV


Chapter 2. Evaluation of uncertainties for
neutron activation analysis measurementsusing the comparator method of standardization
Robert R. Greenberg *, Richard M. Lindstrom, Elizabeth A. Mackey, Rolf Zeisler

National Institute of Standards and Technology, Analytical Chemistry Division, 100 Bureau Drive, Gaithersburg, MD 20899-8395, USA

2.1. Introduction

This chapter describes the individual uncertainty componentsassociated with measurements made with neutron activation analysis(NAA) using the comparator method of standardization (calibration),as well as methods to evaluate each one of these uncertaintycomponents. This description assumes basic knowledge of the NAAmethod, and that experimental parameters including sample andstandardmasses, as well as activation, decay, and counting times havebeen optimized for each measurement. It also assumes that theneutron irradiation facilities and gamma-ray spectrometry systemshave been characterized and optimized appropriately, and that thechoice of irradiation facility and detection system is appropriate forthe measurement performed. Careful and thoughtful experimentaldesign is often the best means of reducing uncertainties.

The comparator method involves irradiating and counting a knownamount of each element under investigation using the same or verysimilar conditions as used for the unknown samples. The NAA processcan be described by the following measurement equation (Eq. (2-1)):

mx unkð Þ = mx stdð ÞA0 unkð Þ� �A0 stdð Þ� � RθRϕRσRε−blank ð2� 1Þ

where:

mx(unk) mass of element x in the unknown samplemx(std) mass of element x in the comparator standard (calibrator)A0(unk) decay corrected count rate in the unknown sampleA0(std) decay corrected count rate in the comparator standardRθ ratio of isotopic abundances for unknown and standardRϕ ratio of neutron fluences (including fluence drop off, self

shielding, and scattering)Rσ ratio of effective cross section differences (if neutron

spectrum shape changes)Rε ratio of counting efficiencies (differences due to geometry

and γ-ray self-shielding)blank mass of element x in the blank

and:

A0 =λCeλtd

1−e−λtL� �

1−e−λti� � fPfltc ð2� 2Þ

with:

A0 decay corrected count rate,C net counts in γ-ray peak,λ decay constant ln 2/t1/2td decay time to start of counttL live time of countti irradiation time

⁎ E-mail address: [email protected].

fP correction for pulse pileup (correction method dependsupon the actual hardware used)

fltc correction for inadequacy of live time extension (correctionmethod depends upon the actual hardware used)

Note that the “R” values are normally very close to unity, and allunits are either SI-based or dimensionless ratios. Thus an uncertaintybudget can be developed using only SI units and dimensionless ratiosfor an NAA measurement by evaluating the uncertainties for each ofthe terms in Eqs. (2-1) and (2-2), and for any additional correctionsrequired (e.g., interferences, dry mass conversion factors, etc.).Uncertainties for some of the terms in Eq. (2-1) have multiplecomponents. If we sub-divide the uncertainty for each term in theabove equations into individual components, add terms for potentialcorrections, and separate into the four stages of the measurementprocess, including: pre-irradiation (sample preparation); irradia-tion; post-irradiation (gamma-ray spectrometry), and radiochemis-try, we arrive at the complete list of individual uncertaintycomponents for NAA listed in Table 2.1. Only uncertainties from thefirst three stages should be considered for instrumental neutronactivation analysis (INAA) measurements, while all four stagesshould be considered for radiochemical neutron activation analysis(RNAA) measurements.

2.2. General irradiation and gamma-ray spectrometryfacility considerations

A brief discussion of the facility and equipment characterizationthat is necessary before complete uncertainty budgets can beevaluated is provided here as a precondition for the uncertaintyevaluation process addressed later in this chapter. This characteriza-tion addresses the general facility parameters that do not substantiallychange from one measurement to the next; the characterizationrequired to evaluate components of uncertainty specific to anindividual measurement is addressed point-by-point in subsequentsections.

Neutron field characterization: gradients and energy spectrum —

characterization of the neutron irradiation field is necessary to correctfor any potential differences in neutron exposure among samples andstandards, to correct for potential interferences causedby reactionswithhigh-energy (fast) neutrons, and to evaluate the uncertainties for suchcorrections. It is important to characterize both the neutron fluence rateand the neutron energy spectrum as functions of location and timewithin each irradiation facility. Although specific corrections may differfrom measurement to measurement, an initial characterization of eachirradiation facility allows the analyst to select the best facility to use for aparticular measurement, and to estimate the magnitudes of potentialirradiation interferences and other effects due to potential variations inthe neutron fluence rate and spectrum shape. The initial characteriza-tion allows the analyst to decide in advance for each analysis howbest toposition samples and standards within an irradiation container (e.g., a“rabbit”), and whether precise determinations of correction factors(with uncertainties) for fluence-rate variations and/or fast neutroninterferences will be necessary, or whether the likely effects areinsignificant and uncertainty estimates only are sufficient.

Table 2.1Complete list of individual uncertainty components for NAA measurements using thecomparator method of standardization; line numbers in this table reflect subsectionwhere the uncertainty component is discussed.

2.3 Pre-irradiation (sample and standard preparation) stage2.3.1 Elemental content of standards (comparators)2.3.2 Target isotope abundance ratio — unknown samples/standards2.3.3 Basis mass (or other sample basis) — including drying2.3.4 Sample and standard blanks

2.4 Irradiation stage2.4.1 Neutron fluence exposure differences (ratios) for unknown samples

compared to standards (comparators)2.4.1.1. Physical effects (fluence gradients within a single irradiation)2.4.1.2. Temporal effects (fluence variations with time)2.4.1.3. Neutron self shielding (absorption and scattering) effects within a

single sample or standard2.4.1.4. Neutron shielding effects from neighboring samples or standards

2.4.2 Irradiation interferences2.4.2.1. Fast (high energy) neutron interferences2.4.2.2. Fission interferences2.4.2.3. Multiple neutron capture interferences

2.4.3 Effective cross section differences between samples and standards2.4.4 Irradiation losses and gains2.4.4.1. Hot atom transfer (losses and gains by recoil, nanometer movement)2.4.4.2. Transfer of material through irradiation container2.4.4.3. Sample loss during transfer from irradiation container2.4.4.4. Target isotope burn up differences

2.4.5 Irradiation timing and decay corrections during irradiation (effects of halflife and timing uncertainties)

2.5 Gamma-ray spectrometry stage2.5.1 Measurement replication or counting statistics (depending on number of

replicates) for unknown samples2.5.2 Measurement replication or counting statistics (depending on number of

replicates) for comparator standards2.5.3 Corrections for radioactive decay (effects of half life and timing

uncertainties for each measurement)2.5.3.1. From end of irradiation to start of measurement2.5.3.2. Effects of clock time uncertainty2.5.3.3. Effects of live time uncertainty2.5.3.4. Count-rate effects for each measurement (either 2.5.2.3.1 and 2.5.2.3.2

or 2.5.2.3.3 but not all three)2.5.3.4.1. Corrections for losses due to pulse pileup for conventional analyzer

systems2.5.3.4.2. Effects due to inadequacy of live-time extension for conventional

analyzer systems2.5.3.4.3. Uncertainties due to hardware corrections for Loss-Free or Zero

Dead Time systems2.5.4 Corrections for gamma-ray interferences2.5.5 Corrections for counting efficiency differences (if necessary), or uncertainty

for potential differences2.5.5.1. Effects resulting from physical differences in size and shape of samples

versus standards2.5.5.2. Corrections for gamma-ray self absorption

2.5.6 Potential bias due to peak integration method2.5.7 Potential bias due to perturbed angular correlations (γ-ray directional

effects)2.6 Radiochemical stage (only if radiochemical separations are employed)

2.6.1 Losses during chemical separation2.6.2 Losses before equilibration with carrier or tracer


Neutron fluence-ratemonitoring (e.g., [1]), is typically used for theinitial characterization of the spatial neutron fluence rate gradient,and the temporal differences in neutron exposure for each irradiationfacility. Appropriate metal wires or foils are rigidly positioned atdifferent locations within an irradiation container or containers,irradiated, and counted under identical conditions. The decaycorrected count rate per unit mass for each piece of wire or foil isproportional to the monitor's neutron exposure; a comparison ofthese values can be used to establish a “map” of the relative neutronintensity as a function of position within each facility. Repeating thisprocess at different points in the reactor fuel cycle providesinformation on temporal variability. When such measurementsindicate that the fluence rate gradient is stable for a given irradiationfacility, it may be useful to fully characterize that gradient and usecorrection factors derived from those measurements for subsequent

analyses. The uncertainties associated with these corrections can beestimated based on the results of characterization measurements. Ifthis method is used, it is a good practice to include at least a fewfluence-rate monitors with each experiment to verify that the facilityis still stable. If the initial characterization indicates that the fluence-rate gradients are not stable, a sufficient number of fluence-ratemonitors (or some othermethod)must be used to provide correctionsfor each analysis (see Section 2.4.1).

Initial characterization of the neutron energy spectrum providesvaluable information regarding the general magnitude of effects suchas interferences from fast neutron reactions (see Section 2.4.2), thepotential for neutron energy spectrum changes from neutronscattering interactions within the sample, and resonance self-shielding (see Section 2.4.3). This initial characterization allows theanalyst to evaluate whether more precise measurements are needed(for a particular measurement) to fully evaluate a correction factor(with an uncertainty), or whether the likely contribution is insignif-icant and an uncertainty estimate alone is sufficient. For example, ifthe irradiation facility is very highly thermalized and the fast neutroncomponent is very small, a shift in the energy spectrum due toneutron scattering is not likely to occur and therefore not likely tosignificantly contribute to measurement uncertainty. Similarly, con-tributions from threshold reactions may be less important, dependingon the matrix and relative amounts of the elements of interest (seeSection 2.4.2). Activation foils are commonly used, e.g., [1], tocharacterize the neutron energy spectrum by determining theabsolute thermal, epithermal, and fast (fission spectrum) neutronfluence rates in reactor irradiation facilities and other neutron fields. Aknownmass of the appropriate monitor element is irradiated, and theinduced activity is measured with a detector of known efficiency. Thefluence rates are then calculated through use of the appropriate crosssection values (see e.g., [2]).

Gamma-ray spectrometry system characterization: stability overdynamic range — the uncertainty components associated withgamma-ray spectrometry cannot be evaluated in any meaningfulway without first assuring that the spectrometry systems are properlycalibrated and optimized for the energy and count-rates ranges to beused. Gamma-ray spectrometry system optimization and character-ization are performed to achieve the best resolution and mostsymmetric peak shapes, and to determine the dynamic range overwhich the system is stable. System stability is needed to assure theaccuracy of software pileup corrections (based on determinations ofthe pileup constant), or the accuracy of corrections provided byhardware to compensate for losses during system dead times, as wellas to assure that peak shapes and resolution are optimal over therange of count-rates and system dead-times used. After the system isoptimized and the dynamic range for a given system is established,the analyst should verify that the system is stable over this range atappropriate intervals (possibly at each use). These procedures help toreduce uncertainties associated with corrections for pileup, loss-freeor zero dead-time system corrections, and peak integration.

2.3. Uncertainty evaluation — pre-irradiation(sample preparation) stage

2.3.1 Elemental content of comparator standards

The method used to evaluate this uncertainty will depend upon thenature of each standard used [3,4]. For highest accuracy work, a high-purity material may be used directly, or more typically, a standardsolution prepared from a high-purity material is deposited onto filterpaper. In this case there will be uncertainties associated with:

• the purity and/or stoichiometry of the high-purity material used• potential losses during dissolution• gravimetric or volumetric standard solution preparation


• gravimetric or volumetric deposition onto individual filter papers and• contamination during the standard preparation process• losses of solvent during the standard preparation process• determination of the element content of the filter paper, acids and

water or other diluent used in preparation, or “blank” [5,6].

If a high-purity material CRM is used as the starting material, theuncertainty for the elemental content of the material is given on thecertificate supplied by the CRMprovider. If a high-purity CRM solutionis used, the uncertainty for dissolution losses is included in theuncertainty of the certified value. If multielemental standards areprepared, special caution must be taken to evaluate impuritycontributions of one element to another, since typically multi-elemental standards for NAA contain widely differing amounts ofthe different elements [3]. In some cases, matrix CRMs are used asstandards for lower-accuracy NAA measurements, however, caremust be taken to include the uncertainty of the certified value of thecontent of each element in the CRM, since these are often quite large.

Table 2.2Elements relevant in NAA with natural or man-made uncertainties in their isotopic composi[9]. Values of u(Rθ ) given in the last column were calculated assuming a triangular distribu

Atomic number Element Name Atomic weight

8 O Oxygen 15.9994(3)10 Ne Neon 20.1797(6)14 Si Silicon 28.0855(3)16 S Sulfur 32.065(5)17 Cl Chlorine 35.453(2)18 Ar Argon 39.948(1)19 K Potassium 39.0983(1)20 Ca Calcium 40.078(4)23 V Vanadium 50.9415(1)29 Cu Copper 63.546(3)

36 Kr Krypton 83.798(2)37 Rb Rubidium 85.4678(3)38 Sr Strontium 87.62(1)

40 Zr Zirconium 91.224(2)42 Mo Molybdenum 95.96(2)44 Ru Ruthenium 101.07(2)46 Pd Palladium 106.42(1)47 Ag Silver 107.8682(2)48 Cd Cadmium 112.411(8)50 Sn Tin 118.710(7)51 Sb Antimony 121.760(1)

52 Te Tellurium 127.60(3)54 Xe Xenon 131.293(6)57 La Lanthanum 138.90547(7)58 Ce Cerium 140.116(1)60 Nd Neodymium 144.242(3)62 Sm Samarium 150.36(2)63 Eu Europium 151.964(1)64 Gd Gadolinium 157.25(3)

66 Dy Dysprosium 162.500(1)68 Er Erbium 167.259(3)70 Yb Ytterbium 173.054(5)

71 Lu Lutetium 174.9668(1)72 Hf Hafnium 178.49(2)76 Os Osmium 190.23(3)

92 U Uranium 238.02891(3)

aGeological specimens are known in which the element has an isotopic composition outsidein such specimens and that given in the Table may exceed the stated uncertainty.bRange in isotopic composition of normal terrestrial material prevents a more precise valuecModified isotopic compositions may be found in commercially available material becausedeviations in atomic weight of the element from that given in the table can occur.dElement has no stable nuclides. However a characteristic terrestrial isotopic composition a

2.3.2. Target isotope abundance ratio — unknowns/standards

NAA is an isotopic technique and Eq. (2-1) considers differences inthe isotopic abundances of elements (Rθ=ratio of isotopic abun-dances for unknown and standard). While no corrections oruncertainties are needed for the determination of monoisotopicelements (Rθ=1 with absolutely no uncertainty), corrections anduncertainties may be necessary for elements with more than oneisotope and whose abundances vary in nature or are perturbed byman. Table 2.2 lists the elements relevant for NAA for which IUPAC [7]identified uncertainties in their atomic weights due to natural or man-made variations in their isotopic composition.

The isotopic abundance variability influences the NAA results inwidely varying degrees depending on the isotope used in themeasurement. In many instances the uncertainty of the abundanceratio is insignificant, in particular for determinations based on a highlyabundant isotope. However, if a minor isotope is used, the isotopicabundance ratio between unknown and standard may differ

tion; abundance values are expressed as a range or as a single value with an uncertaintytion for the ratio of isotopic abundances of unknowns and standards.

Note NAA target Abundance (%) u(Rθ)

a,b 18O 0.2217–0.1877 4.8%a,c 22Ne 9.96–9.20 2.3%b 30Si 3.102–3.082 0.19%a,b 36S 0.019–0.013 10.8%c 37Cl 24.356–24.077 0.33%a,b 40Ar 99.6003 (6) 0.0009%a 41K 6.73022 (292) 0.06%a 48Ca 0.188–0.186 0.31%a 51V 99.7513–99.7498 0.0004%b 63Cu

65Cu69.338–68.98331.017–30.662

0.15%0.33%

a,c 86Kr 17.29835(26) 0.002%a 85Rb 72.1654 (132) 0.03%a,b 84Sr 0.58–0.55 1.5%

88Sr 82.75–82.29 0.16%a 94Zr 17.380 (12) 0.98%a 98Mo 24.19 (26) 1.52%a 102Ru 31.55 (14) 0.63%a 110Pd 11.72 (9) 1.1%a 109Ag 48.161 (8) 0.02%a 114Cd 28.73 (42) 2.1%a 116Sn 14.54 (9) 0.88%a 121Sb

123Sb57.21 (5)42.79 (5)

0.12%0.17%

a 130Te 34.08 (64) 2.7%a,c 134Xe 10.4357 (21) 0.03%a 139La 99.910 (1) 0.001%a 140Ce 88.449–88.446 0.001%a 146Nd 17.35–17.06 0.49%a 152Sm 26.75 (16) 0.85%a 153Eu 52.19 (6) 0.16%a 152Gd

160Gd0.20 (1)21.86 (19)

7.1%1.2%

a 164Dy 28.260 (54) 0.27%a 170Er 14.910 (36) 0.34%a 168Yb

176Yb0.13 (1)12.76 (41)

11%4.5%

a 176Lu 2.59 (2) 1.1%a 180Hf 35.100–35.076 0.02%a 184Os

192Os0.02 (1)40.78 (19)

71%0.66%

a,c,d 235U238U

0.7207–0.719899.2752–99.2739

0.036%0.0004%

the limits for normal material. The difference between the atomic weight of the element

being given; the tabulated value should be applicable to any normal material.it has been subject to an undisclosed or inadvertent isotopic fractionation. Substantial

nd an atomic weight are tabulated.


significantly from unity. An extreme example in which the isotopicratio between unknown and standard can be significantly differentfrom unity is the determination of sulfur by NAA using the reaction 36S(n,γ)37S [8]. In this example, Rθ can range from 1.4 to 0.7 dependingwhether the sample or the standard, or both, exhibit an extremevariation in the abundance of 36S, resulting in a bias of up to 40% ifthese abundance differences are ignored. However, most isotopesused for NAA vary only slightly in nature.

Corrections and uncertainties associated with isotopic abundancedifferences between samples and standards may be directly includedin the uncertainty budget if they are known (or have been measured).However, this type of information is rarely available. When the actualabundances are not known, no corrections can be applied and Rθ mustbe assume to be unity. However, the uncertainty for Rθ=1 can beestimated from the degree of natural variability for samples andstandards that have not been isotopically manipulated using the datafrom Table 2.2.

For a simple case where accurate values for the isotopicabundances in samples and standards are not known, it is reasonableto assume that the abundance values for samples and standards liewithin the range given in Table 2.2. The relative range of potentialvalues for the isotope abundance for either sample or standard wouldbe:

range %ð Þ = θH−θL12 θH + θLð Þ

!� 100; ð2� 3Þ

where θH=highest abundance, and θL=lowest abundance inTable 2.2.

If we assume that the actual (“true”) value of sample and standardisotope abundances can lie anywhere between the two extremes ofthis range, but the actual (“true”) isotopic abundances of both sampleand standard most likely lie at the midpoint of the two extremes, ourbest estimate of Rθ is 1. The uncertainty for Rθ will be 1/2 the relativerange divided by√6 (for a triangular distribution) multiplied by √2 toaccount for the uncertainty of both the sample and standard. On theother hand, if we have no reason to believe that both sample andstandard abundances most likely lie at the midpoint of the twoextremes, or if we wish to be more conservative, our best estimate ofRθ is still 1, however, to evaluate the uncertainty for Rθ, we shoulddivide 1/2 the relative range by √3 (for a rectangular/uniformdistribution) instead of √6 and multiply by √2 to account for theuncertainty of both the sample and standard. If an abundanceuncertainty in Table 2.2 is given for the isotope abundance, insteadof an abundance range, the uncertainty in Rθ, can be estimated bydividing the abundance uncertainty by the isotope abundance, andmultiplying by √2 (to account for differences in samples andstandards).

In the case of the determination of S via the 36S(n,γ)37S reactiondiscussed above, if we wished to make the measurement (despite thelarge potential bias resulting from a potential Rθ range of 40%), andweassume that the actual (“true”) isotopic abundances of both sampleand standard most likely lie at the midpoint of the two extremes of0.019% and 0.013% (e.g. there are multiple sources of S composingboth samples and standards), our best estimate of Rθ would be 1, andwe would assume a triangular distribution. The relative standarduncertainty for Rθ would be 38%/2* √6*√2, or 10.8%. However, if wewish to be more conservative, or we have no reason to believe thatboth sample and standard abundances most likely lie at the midpointof the two extremes, our best estimate of Rθ would still be 1, however,we would assume a uniform/rectangular distribution, and evaluatethe relative standard uncertainty for Rθ as 38%/2*√3*√2, or 15.3%. Thechoice between these two possibilities should be based on chemicalknowledge of the samples and standards.

For practically all NAA applications the mid-point of the range orthe stated isotopic abundance is a valid assumption. The notes in

Table 2.2 are intended to draw attention to the possibility ofdeviations in rare cases of special geological materials, or samplesfrom industrial materials where elements with enriched or depletedabundances are used. Obtaining assurance of the true isotopicabundance of the unknown sample will be necessary for a reliableNAA determination based on isotopes with abundances exhibitingsignificant variability in the types of samples analyzed or standardsused.

2.3.3. Determination of the basis mass (or other sample basis)The uncertainty associated with determining the mass basis of the

sample may be simply the uncertainty associated with use of ananalytical balance. For the analysis of many biological or environ-mental samples such as tissues or sediments, the element massfractions of the sample are typically reported on the basis of dry mass.The sample used for NAA may have been dried in advance or may beanalyzed as received and the dry mass basis determined usingseparate portions. In either case the uncertainty associated with thedetermination of the correction factor will be that associated with themass determinations. Similarly, in the analysis of biological tissues,themass fraction valuesmay be reported on a fresh tissue basis, a lipidbasis, or protein basis but the material will be analyzed as a driedmaterial. The uncertainty is calculated from the determination of eachof the components of that correction factor, i.e., the wet mass to drymass, the lipid to wet mass, or protein to wet mass ratios. Changes inthe mass basis that occur as a result of irradiation are discussed in aseparate section below.

2.3.4. Sample blanksDue to time constraints in the determination of elements for which

the products of neutron irradiation are short-lived isotopes, or due tothe nature of the samples, it may not be practical or possible totransfer each sample from the irradiation container or packagingmaterial into a clean (unirradiated) container prior to performinggamma-ray spectrometry. In these cases, a complete characterizationof the element content of the packaging material (and its variabilitywithin a lot) may be required to account for its contribution to thetotal amount of element measured. Where possible, it is preferable totransfer the samples from the packaging material into non-irradiatedcontainers to eliminate the need for this type of correction. Wheretransfer is not practical or preferred, a statistically valid number ofblanks must be analyzed to determine the amount of element per unitmass of packaging material in order to derive appropriate correctionsfor those elements. Evaluation of the uncertainty will include thevariability of amount of element in the blank and the uncertaintyassociated with the analytical determination of amount content.Uncertainty associated with analyte losses (or gains) during irradi-ation is discussed in a separate section below.

2.4. Uncertainty evaluation: irradiation stage

2.4.1. Neutron fluence exposure differences (ratios) for samplescompared to comparator standards

As induced activity is directly proportional to the neutronexposure, the ratio of decay-corrected activities of unknown samplesand comparator standards is also directly proportional to the neutronexposure of the samples versus the standards. Assuming that they areirradiated at nominally the same neutron fluence rate in the samereactor facility, for the same amount of time, there are four factors thatresult in unequal neutron exposures: temporal and spatial neutronfluence-rate variations, and neutron absorption and scattering effects.Spatial neutron fluence rate variations or irradiation geometry effectsresult from differences in neutron fluence rate at the differentpositions of each sample and standard in the irradiation facility.Temporal neutron fluence rate changes are also commonwithinmany


facilities and must be evaluated when more than one irradiation isrequired. Neutron self-shielding can be significant when the outerportion of a sample or standard absorbs a significant fraction of theneutrons, and so the interior of that sample or standard gets a reducedneutron exposure. Neutron scattering effects, although very small forNAA, may perturb the neutron exposure of some samples in a mannersimilar to absorption effects. Although it is possible to evaluate theabsorption and scattering effects separately, it is most convenient toevaluate their combined effect as described below.

2.4.1.1. Differences in neutron exposures for unknown samples comparedto standards (comparators) due to physical effects (fluence gradientswithin a single irradiation)

In a typical irradiation facility, the reactor fuel is not symmetri-cally located around the irradiation position, and therefore theneutron fluence rate differs in different locations within the rabbitleading to potential differences in neutron exposures among andbetween standards and unknowns within one irradiation. In general,the neutron fluence rate decreases with distance from the reactorcore and if the rabbit's axis is perpendicular to the flux contours, thegradient is nearly linear. The analytical bias introduced by thisgradient can be compensated by inverting the rabbit midwaythrough the irradiation time (i.e., by removing the rabbit midwaythrough the irradiation, rotating (flipping) it 180°, and reinsertingthe rabbit for the second half of the irradiation). The results of usingthis procedure tominimize the linear gradient at the NBSR are shownin Fig. 2.1. This procedure greatly decreases but does not entirelyeliminate effects of the neutron gradient within the irradiationcontainer.

Other physical manipulations can be used to equalize the neutronexposure within the irradiation container. Many reactors have a“Lazy-Susan” facility for long irradiations where the samples arerotated throughout the irradiation. In either case, residual differ-ences can be corrected, and uncertainties evaluated, as describedunder the flux-monitoring approach, or if corrections are notnecessary, uncertainties can be evaluated as for the historical-dataapproach.

2.4.1.2 Differences in neutron exposures for unknown samples comparedto standards (comparators) due to temporal effects

Over the course of a reactor cycle, neutron fluence rates within asingle facility vary as a function of time so that differences in neutronexposures exist from one irradiation to the next. During the first hoursof reactor operation, the moderator temperature gradually reaches a

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 1 2 3 4 5 6 7 8

Rel

ativ

e flu

ence

rat

e

Axial position, cm

Flipped

Fig. 2.1. Neutron fluence exposure variations for samples irradiated in one irradiationfacility in the NBSR.

steady state and thus the neutron spectrum will change during thistime. As the fuel is consumed, regulating rods move in the lattice,changing the spatial distribution of the neutron field. It is essentialthat each irradiation facility be fully characterized for both spatialneutron gradients within a given irradiation, and temporal differencesin neutron fluence rates from one irradiation to the next for NAAexperiments that involve more than one irradiation.

Corrections for both physical and temporal differences inneutron exposure (described in Sections 2.4.1.1 and 2.4.1.2), andtheir associated uncertainties can be evaluated using historical dataand/or fluence monitoring measurements. Historical data is partic-ularly useful for facilities that are stable over time, especially whenno corrections are necessary. In this case, a large number of identicalsamples are irradiated and counted (preferably far from thedetector) with very good counting statistics for one or moregamma rays. The relative uncertainty due to irradiation geometryis the observed relative standard deviation (rsd), reduced inquadrature by the uncertainty due to counting statistics. As anexample, an irradiation container filled with identical samples isirradiated. The samples are individually counted, and the observedrsd of the decay corrected count rate per unit sample mass of aradionuclide is 0.5%. If the typical counting uncertainty for eachsample is 0.3%, and all other sources of variation are negligible, theuncertainty due to irradiation geometry effects would be the squareroot of [(0.5%)2–(0.3%)2], or 0.4% for each sample (or standard). Ifthere are additional significant sources of variation, such as countinggeometry differences, those uncertainties can also be subtracted (inquadrature) from the observed rsd. This uncertainty of 0.4% can beused to characterize each sample and standard irradiated in allfuture irradiations in this facility, as long as nothing is done tochange the flux distribution. If one sample and one standard areirradiated together in this facility, the combined irradiationgeometry uncertainty for sample and standard would be the squareroot of [(0.4%)2+(0.4%)2], or 0.57%. If multiple samples (of the samematerial) and/or standards are irradiated together, the samplecounting geometry uncertainty and the standard counting geometryuncertainty (for the mean value) would be reduced by the squareroot of the number of samples and/or standards irradiated.

Neutron fluence monitors (also known as flux monitors) are oftenused to determine the static spatial gradient, the temporal gradient,and neutron spectrum changes. Results from NAA experiments areoften normalized by irradiating fluence monitors of known mass anduniform composition along with the samples. A number of monitorshave been used: foil and wire of iron, copper, nickel, zinc, or othermetals, standard solutions pipetted onto filter paper, or speciallyfabricated alloys such as Au/Al (IRMM-530R) or Co/Al (NIST SRM953). For relative measurements it is not necessary to determine theabsolute activity of the monitors. After irradiation, the monitors areremoved and gamma rays counted to determine the relative neutronexposure for each sample, and corrections applied, if necessary.Uncertainties for these corrections can be determined from thecounting statistics observed for the monitors. As with the historicaldata case, if multiple samples (of the samematerial) and/or standardsare irradiated together, the sample counting geometry uncertaintyand the standard counting geometry uncertainty (for the mean value)would be reduced by the square root of the number of samples and/orstandards irradiated.

2.4.1.3. Neutron self-shielding: neutron absorption and scattering effectswithin a single sample or standard

When a sample or standard is immersed in a neutron field, itsinterior will be exposed to a smaller neutron fluence rate than theexterior due to neutron absorption and scattering by the sample. Thiseffect, neutron self-shielding, varies with the macroscopic scatteringand absorption cross-sections and the size and shape of the sample.The correction factor for neutron self-shielding, fϕ, is the ratio of the

image of Fig.�2.1

0.994

0.995

0.996

0.997

0.998

0.999

1.000

0.1 1 10

Sel

f-sh

ield

ing

fact

or f

Length/Diameter

Sphere

Fig. 2.2. Calculated self-shielding factor fϕ for 250-mg cylinders and a sphere of SRM1632c bituminous coal. For this material Σa=0.015 cm−1 and Σs=2.7 cm−1: themajor absorbers are hydrogen, boron, and nitrogen, and the major scattering elementshydrogen and carbon.

Table 2.3Calculated self-shielding factors for 200 mg spherical samples of representativematerials.

Material Self-shielding factor Principal absorbers

Quartz 0.999 SiSRM 2709a Soil 0.997 Si, FeSRM 1632c Coal 0.994 H, CSRM 1633b Fly Ash 0.998 B, FeCellulose 0.996 HSRM 1577c Bovine Liver 0.991 H, NIron 0.970 Fe


mean fluence rate over the entire sample volume, compared to thefluence rate incident on the sample. For an absorbing and scatteringsample surrounded by an isotropic neutron field, the value of fϕ isalways less than unity [10], unless the sample contains fissilematerials.

2.4.1.3.1. Monte Carlo methods and calculated valuesA rigorous calculation of self-shielding correction factors requires

knowledge of the neutron energy spectrum inside and outside thesample, and the absorption and scattering cross sections as a functionof energy. Monte Carlo methods may be used to determine valuesfor fϕ, but few calculations performed to date have included bothchanges in the neutron energy spectrum due to neutron scatteringand spectrum averaged cross-section values for the nuclides ofinterest.

Scattering affects the history of neutrons in the sample even ifthere is no change in neutron energy. Copley [10] studied the effectsof neutron scattering and absorption within spherical samplesimmersed in an isotropic neutron field and calculated the values offϕ using an iterative solution to the neutron transport equation andMonte Carlo methods. Results from both approaches were consis-tent and indicate that neutron scattering may decrease fϕ values,contributing to further self-shielding, for samples that both scatterand absorb neutrons within an isotropic neutron field. Similarresults are expected and have been demonstrated for other sampleshapes. Copley's results for spherical samples in an isotropicneutron field were approximated by Blaauw [11] using a modifica-tion of the Stewart and Zweifel [12] formulation. SubsequentlySalgado et al. [13] modified Blaauw's formulation with similaragreement.

Analytic expressions for fϕ as a function of the scalar cross sectionsand sample composition have been derived for a few specificgeometries. A frequently cited summary paper is that of Fleming,[14], who collected the equations for a sphere, an infinite slab, and aninfinite cylinder, irradiated in either an isotropic mono-energeticneutron field or a monoenergetic parallel neutron beam. By employ-ing a geometrical argument [15], these equations have been extendedto finite cylinders, a common configuration in many irradiationexperiments. In addition, Fleming tabulated macroscopic cross-section values for a large number of materials and mixtures. Formost materials, where the comparator standard and standard havesimilar scattering properties, an approximation based on calculationsfor absorption only using a slab geometry introduces little or no bias,e.g., when comparing biological samples with comparator standardsprepared using filter papermatrices. The approximation of fϕ for a slabof thickness T, taking into account only absorption is

fϕ =1= 2−E3 ∑aTð Þ

∑at; ð2� 4Þ

where ∑a is the macroscopic absorption cross section and E3 is theexponential integral of order 3. Corrections for neutron self-shieldingfor typical 200-mg biological or environmental samples are normallyon the order of several tenths of a percent, and are rarely greater thana percent or two. Strongly absorbing materials such as somemetals orsome ceramics may require more careful evaluation. The shape of thesample may be important. For a cylindrical sample fϕ as a function ofthe length/diameter ratio is shown in Fig. 2.2. The maximumabsorption occurs when the shape is most nearly spherical.

Self-shielding factors (including both absorption and scattering)have been calculated for 200-mg spherical samples of some represen-tative materials typically analyzed by NAA and are given in Table 2.3.

In practice, hydrogen is the most important scattering element,with a free-atom absorption cross-section of 20.5 b and a maximumbound atom cross-section of 82 b. Other important scatteringelements in typical samples are N, Cl, Fe, Ni, and Pb, with scattering

cross sections between 10 and 20 b. Based on Copley's results forspheres within a range of macroscopic absorption and scatteringcross-sections corresponding to the ranges expected of mostbiological and environmental samples, the bias introduced byignoring scattering is typically between ≤0.1% and 0.3%, dependingon the diameter of the sphere and the values for those cross-sections[10]. The bias introduced would be worse for very strong absorbers(∑a≥2 cm−1), though there are few examples of materials thisstrongly absorbing.

Spreadsheets for calculating fϕ for the Fleming geometries areavailable on request from one of the authors ([email protected]). An example for a 200-mg pellet (radius=0.65 cm) of BovineLiver (SRM 1577c) is given in Fig. 2.3. Note that the calculatedcorrection for scattering is significantly smaller for the pellet (0.995)compared to the sphere (0.991), which is listed in Table 2.3.

When these spreadsheets are used to calculate fϕ values forsamples and standards, an uncertainty estimate of about 10% of thecorrection is reasonable in cases where the mass fractions of allmajor absorbing and scattering components reasonably well-known.When the neutron spectrum contains epithermal neutrons thenresonance self-shielding must also be taken into account [16]. Aquasi-universal self-shielding expression has been formulated [17,18] and shown to be adequate for most work in a mixed neutronfield [19].

2.4.1.3.2. Experimental fϕ evaluationThe consequence of thermal scattering by hydrogen on induced

activity for NAA has been determined experimentally [20] byirradiating sandwiches of iron foils in the well-thermalized NISTreactor with and without polyethylene spacers. No significantdifference was detectable at a precision of order 0.1%. One may best



Fig. 2.3. Calculated self-shielding for a 200-mg pellet of SRM 1577c bovine liver.


estimate the value of fϕ for a given material experimentally byperforming NAA on a series of samples of varying thicknesses anddetermining the correction factors based on comparison with a thinsample for which the fϕ value is essentially 1. Indeed, for a material ofunknown composition this is the only possible method.

2.4.1.3.3. Uncertainty in fϕ estimatesCorrection factors may be determined by appropriate Monte Carlo

methods, calculated using one of the approximations, or determinedexperimentally. Where determined experimentally or by Monte Carlosimulation, the uncertainty associated with the correction factor maybe determined based on statistical considerations of the method used.Where formulaic approximations are used, the uncertainty of thecorrection factor may be estimated as 10% of the correction. Note thatfor either Monte Carlo simulations or calculated corrections based oneither∑a or∑a and∑s, additional uncertaintymay need to be addedwhen the sample composition is partially unknown.

2.4.1.4. Neutron shielding effects from neighboring samples or standardsWhen a set of multiple samples and standards are irradiated

together, neutron absorption and scattering effects on individualsamples/standards resulting from absorption and scattering by neigh-boring ones should be considered, especiallywhen they are of large size,closely packed, and/or are composed of highly absorbing constituents.Correction for fluence depression by neighboring samples/standardscan often be calculated if the sizes, shapes and compositions of allmaterials are known; however, corrections are oftenmost convenientlyaccomplishedbynormalizing to embeddedfluencemonitors, at least forsamples with sizes and compositions typically analyzed by NAA. Largesamples (i.e., much greater than 1 g), especially those with a highcontent of neutron absorbing materials, may require additionalcorrections. In addition to fluence monitoring corrections for effectsexternal to the samples/standards, neutron fluence monitors can beused to determine and correct for the effects of static spatial fluencegradient, the temporal gradient, and neutron spectrum changes (asdiscussed in Sections 2.4.1.1 and 2.4.1.2). However, the effects ofneutron self-shielding within each sample (or standard) need to beaddressed separately (as discussed in Section 2.4.1.3).

The number and placement of fluence monitors will depend uponthe number, mass, shape, composition, closeness (or packing density)of the samples and standards, as well as knowledge of the fluencegradients in the irradiation facility when no samples or standards arepresent. For example, in an irradiation facility with a linear drop-offperpendicular to the samples/standards, which are all relatively small,well-separated and not particularly absorbing, one fluence monitor ateach end of the irradiation container and one in the middle of thesample/standard pack may be sufficient. However, for relativelyabsorbing samples that are closely packed, a fluence monitor betweenevery sample and/or standard may be necessary. The average decaycorrected activity for the two surrounding fluence monitors providesthe correction factors for each sample and/or standard. Uncertaintiesfor the corrections will depend upon the counting statistics for each ofsurrounding monitors, combined in quadrature.

The NAA measurement with the perhaps the highest demonstrat-ed accuracy and smallest uncertainty to date was the measurement ofCr in stainless steel (SRM 1152a) by Zeisler et al. [21]. Iron fluencemonitors were used to correct for neutron exposure differences at thesurface of the samples and standards, and neutron self-shieldingcorrections were calculated as described in Section 2.4.1.3. Themeasured Cr value (for 300 mg samples) with an expanded relativeuncertainty of 0.2% agreed within 0.05% relative to the certified value,which also had an expanded relative uncertainty of 0.2%. Chromiumcalibration was accomplished with pure metal chips and slabs(approx. 1.5 mg and 80 mg each). The uncertainty from the neutronself-shielding corrections actually dominated all other uncertaintycomponents (approx. 90% of the combined uncertainty) due to thedifficulties in characterizing the actual dimensions and shapes of themetal pieces used. Most of the samples and standards each requiredrelative self-shielding corrections of several percent.

2.4.2. Irradiation interferences

During the irradiation step, three types of interferences arepossible for some of the elements frequently determined by NAA.Most nuclear reactions used for NAA are based on reactions withthermal or epithermal neutrons. However, high-energy neutrons can


knock out a proton or alpha particle from a nucleus, and interfere withthe determination of some elements. For example, Al is typicallydetermined via the reaction 27Al(n,γ)28Al. 28Al can also be producedby Si and P with high-energy neutrons via the reactions 28Si(n,p) 28Aland 31P(n,α) 28Al [22]. The relative size of the interference willdepend upon both the mass fraction of Al compared to that of eachinterfering element in the sample, as well as the fraction of fastneutrons in the irradiation facility relative to the amount of thermalneutrons. Fortunately, these (n,p) and (n,α) reactions cannot occurunless the incoming neutron carries enough energy to equal the massdifference between reactants and products, as well as the additionalenergy needed to overcome the Coulomb barrier for emission ofcharged particles. Only a few such reactions are typically encounteredin neutron activation analysis. In a similar manner, thermal fission of235U will produce (as fission fragments) some of the same nuclidesused to determine other elements by NAA, e.g., 99Mo is one of themost commonly produced fission products and is also used todetermine Mo via the reaction 98Mo(n,γ) 99Mo. Finally, in rare casesinterferences can be caused by double neutron capture.

2.4.2.1. Fast (high energy) neutron interferencesThe more significant fast neutron interferences for the RT-2

pneumatic tube facility of the NIST (NBSR) reactor are listed inTable 2.4, where the thermal and fission fluence rates are 3.4×1013

and 1.4×109 cm−2s−1, respectively. The interferences (X0) listedrepresent the apparent μg of the interference per gram of theinterfering element irradiated. Note that this facility is exceptionallywell thermalized, since the NBSR is a D2Omoderated reactor and RT-2is located far from the reactor core. Fast neutron interferences in mostlight water moderated reactors would typically be two to three orders

Table 2.4Fast neutron interferences for the RT-2 facility of the NBSR.

Analyteelement

Activationproduct

Half life Interferingnuclide

σ(fast), mb X0, μg/g

(n,p) interferenceNa 24Na 15 h 24Mg 1.53 4.0Mg 27Mg 9 m 27Al 4.0 1566Al 28Al 2 m 28Si 6.6 46Si 31S 3 h 31P 36 17,353P 32P 14 days 32S 69 626S 35S 88 days 35Cl 78 7811S 37S 5 m 37Cl 0.218 2657Sc 46Sc 80 days 46Ti 12.5 0.064Ti 51Ti 6 m 51V 0.87 157V 52V 4 m 52Cr 1.09 0.33Mn 56Mn 3 h 56Fe 1.07 0.13Fe 59Fe 40 days 59Co 1.42 653Co 60Co 5 y 60Ni 2.1 0.026Ni 65Ni 3 h 65Cu 0.48 15.8Cu 64Cu 13 h 64Zn 31 8.8Cu 66Cu 5 m 66Zn 0.62 0.4As 76As 26 h 76Se 0.17 0.007Rb 88Rb 18 m 88Sr 0.15 7.2Sr 89Sr 50 days 89Y 0.31 113.5

(n,α) interferenceNa 24Na 15 h 27Al 0.725 2.1Mg 27Mg 9 m 30Si 0.155 1.8Al 28Al 2 m 31P 1.9 13.0P 32P 14 days 35Cl 8.8 57.6V 52V 4 m 55Mn 0.11 0.038Cr 51Cr 30 days 54Fe 0.6 0.09Mn 56Mn 3 h 59Co 0.156 0.02Fe 59Fe 40 days 62Ni 0.09 1.49Co 60Co 5 y 63Cu 0.50 0.02Ni 65Ni 3 h 68Zn 0.05 1.02As 76As 26 h 79Br 0.02 0.004Sr 89Sr 50 days 92Zr 0.01 0.86

of magnitude greater. Even in RT-2, there are several significantinterferences that are routinely encountered: the (n,p) interference ofAl on the determination of Mg in geological and related materials, andthe (n,α) interference of 31P on the determination of Al in biologicalmaterials. Other interferences have been significant in a few selectedapplications, such as the (n,α) interference of 54Fe on the determi-nation of Cr in whole blood.

These interferences were calculated using published fission-spectrum cross sections [23] to calculate products that have not beenmeasured directly. Most values were normalized to the measured 28Si(n,p) 28Al interference. It should be noted that although theseinterferences were normalized to the (n,p) reaction on 28Si, themeasured 51Cr interference for the (n,α) reaction on 54Fe was within10% of the similarly calculated value in RT-4, which has a neutronspectrumvery similar to RT-2. Themeasured 28Si (n,p) 28Al) interferencein RT-4 was measured to be 43 μg-Al/g-Si versus 46 μg-Al/g-Si in RT-2.

As mentioned above, interferences in a light water reactor areconsiderably higher. To estimate the severity of interferences, the fast-neutron fluence rate in the irradiation facility can be determined [1] byirradiationof anyof thepurenuclides in thepreceding table and scaling tothe fast/thermal ratio in RT-2. It is relatively easy to determine the (n,p)interference of 28Si on 28Al, by irradiating somehigh purity Si (e.g., a pieceof semiconductor grade Si metal) with a small piece of Al foil, anddetermine the apparent Al content of the Si. The scaling factor for otherfast reactionswill be the ratio of themeasured Si interference (in μg/g) tothe value of interference (46 μg/g) determined for RT-2. However, thecalculated interferencevalues shouldonlybeusedasaguide todeterminewhich interferences may be significant. If interference is judged to besignificant, it should be measured and corrected. The uncertainty for thecorrected value is determined from the uncertainty of the interferenceratio measurement, the uncertainty of the content of the interferingelement in the sample of interest, and the uncertainty of thedetermination of the element of interest before the correction is applied.

2.4.2.2. Fission interferencesFission of 235U will produce (as fission fragments) some of the same

nuclides that are used to determine other elements byNAA. Some of themore important interferences are for molybdenum and barium. Theseand other potentially significant ones are listed in Table 2.5, with theapparent interference in μg of element per μg of natural uranium in thesample. Since the interferences are due to 235U fission, they will bedifferent for samples with non-natural isotope abundances of uranium.Twoof the interferences listedneed furtherdiscussion.Although 131Ba isnot produced by fission, the 496 keV gamma ray from 131Ba, frequentlyused for the determine barium by NAA, can be interfered with by the497 keV gamma ray of 103Ru, which is a fission product. This can be animportant interference, especially in geological type materials. Due tothe difference in half-lives of 131Ba (11.5 days) and 103Ru (39 days), theapparent interference increases with decay time. In addition, 140La(40.3 h) is not produced directly fromuraniumfission, but as a daughterof the 140Ba (11.7 days) fission product. Since most geological materialshave much higher mass fractions of lanthanum compared to uranium,this interference is rarely significant about aweek or so after irradiation,but becomes increasingly more important as the decay time increases.

In view of the potential for fission interferences, it is important toknow the approximate level of uranium in samples when determiningelements that have fission interferences. If the amount (or massfraction) of uranium is known, the potential interferences can beapproximated using the information in Table 2.5 (data from [24]),however, if the uranium content is not known, and if elements withpotential interferences are under investigation, it is important todetermine uranium in the samples under investigation, subtract anyrelevant interferences, and calculate uncertainties. This can beaccomplished by preparing single-element uranium standards,irradiating these standards with the samples under investigation,and counting them with the samples. The standards are first used to

Table 2.5Typical uranium fission interferences — apparent μg of element per μg uranium.

Element Isotope Thermal neutrons Epithermal neutrons

Molybdenum 99Mo 1.4–31 0.1Barium2 131Ba 3.4 e0.0402D

Barium 139Ba 0.6Cerium 141Ce 0.3Lanthanum 140La 0.02 (after 6 days decay)3

Neodymium 147Nd 0.2Ruthenium 103Ru 0.1Tellurium 131Te 0.8 0.5Zirconium 95Zr 10 3Zirconium 97Zr 20

1 Dependent on thermal to epithermal ratio due to high resonance integral for Moactivation.

2 Contribution to the 496.2 keV line from 103Ru. D signified decay time (td) in daysfrom end of irradiation to start of count. Greater decay intervals result in greaterapparent interferences.

3 140La daughter (40.3 h) fed by longer lived 140Ba (11.7 days). Interference can bevery significant after long decay.


determine the uranium mass fractions in the samples. The Ustandards are then are processed as samples themselves to determinethe interference ratios, i.e., the apparent amounts of the interferedelements per μg (or μg/g) of uranium (in the standard). Theuncertainty for each fission interference correction will include theuncertainty of the determination of the uranium content in eachsample (predominantly from the counting statistics of the sample andthe standard), as well as the uncertainty of the interference ratiodetermined from the counting uncertainty of the individual fissionproducts in the uranium standard. It should be noted that theinterferences listed in Table 2.5 are for bulk samples, i.e., a mg or moretotal mass. Samples consisting of thin films, surface deposits, orhaving very small total masses may appear to have lower levels ofinterferences due recoil losses of fission fragments from surfaces,especially if samples are transferred after irradiation.

2.4.2.3. Multiple neutron capture interferencesInterferences due to double neutron capture are very rare, since high

cross sections are usually necessary for both the target and daughterisotopes. The classic example is the determination of Pt via the 198Pt(n, γ) 199Pt, which decays to 199Au, and is used to quantify Pt. Goldinterferes with this determination via the double neutron capture of197Au [25]. This interference is highly significant, since both 197Au and198Au have very high (n,γ) cross sections, and Au and Pt are often foundat similarmass fractions inmanymaterials [26]. Double neutron captureby 45Sc can interfere with the determination of Ca via the reaction 46Ca(n,γ) 47Ca, which decays to 47Sc. This interference may be important ingeological type materials mainly due to the extremely low isotopeabundance and cross section of 46Ca and the high (8 b) cross section of46Sc. The measurement of 129I/127I ratios in nature by NAA via 130I islimited by triple neutron capture in stable 127I [27].

When double capture interferences are potentially significant, theymust be measured and corrected with the uncertainty propagated. Sincethe double-capture interference rate depends on (ϕ•ti)2, while theactivation rate of the element of interest will increase as (ϕ•ti), therelative interference will increase as a function of irradiation time. For the197Au interference on the determination of Pt via 199Au, the authors [25]determined the apparent Au interference as a function of irradiation timein each facility used, determined the Au content of each sample, and thensubtracted the interference. The uncertainty for the interference correc-tion included the uncertainty in the interference ratio combined inquadraturewith the uncertainty of the Au determination for each sample.

2.4.3. Effective cross section differences between samples and standards

A central tenet of activation analysis is that in dilute samples theprobability of neutron capture σ(E) per target atom is a constant for a

given neutron energy E. However, if an irradiation facility is not wellthermalized, neutron scattering within a sample may change theneutron energy spectrum within a sample, with quantitativeconsequences. With a harder neutron spectrum (a larger epithermalcomponent), scattering of high-energy neutrons within the sampleshifts the spectrum downward in energy. Because neutron crosssections typically are inversely proportional to neutron velocity (the“1/v law”), this leads to an increase in reaction rate, and results in anincrease in apparent element mass fraction in highly scatteringsamples when compared to a standard that scatters less. While thismay be significant in a poorly thermalized facility, there is no largechange in effective cross section for a well-thermalized irradiationfacility, since thermal neutrons dominate the reaction rate andscattering overall will not result in a net change in the averageenergy of the neutrons. Although most irradiation facilities in lightwater or heavy water reactors are well thermalized, the degree ofthermalization should be evaluated during the initial reactorcharacterization measurements. An example has been given by St.Pierre and Kennedy [28].

In a few very rare cases, a change in the neutron energy spectrummay be caused by resonance self-shielding. This effect refers toremoval of a significant portion of resonance energy neutrons by amaterial with a large resonance absorption cross-section, for instancegold, indium, samarium and gadolinium. Because activation isproportional to the product of the neutron fluence rate and theenergy-spectrum averaged absorption cross-section, any change inthe energy spectrum will affect the amount of activity produced. Themagnitude of the effect is greatest for facilities with poorlythermalized neutron spectra, and samples/standards with a largeamount of a strong neutron absorber with a sharp low resonanceenergy. Correction factors for epithermal neutron resonance self-shielding have been calculated using Monte Carlo methods [29].Where very highly absorbing samples with significant resonanceabsorption are analyzed, these effects should be determined exper-imentally through irradiation of successively diluted portions anddetermination of the correction factors needed to account fordifferences between the samples and comparator standards withrespect to effective neutron exposures.

2.4.4. Irradiation losses and gains

There are several mechanisms that have the potential to producelosses and or gains during the irradiation process. Although in the vastmajority of cases these effects are very small, it is important toconsider them since they can be significant in a few cases. Theseinclude: transfer of material to or from the sample through theirradiation container; hot atom transfer to or from the samplecontainer itself; target isotope burn up differences when samplesand standards are irradiated under different conditions, sample masschange during irradiation [30,31], and loss of sample material upontransfer of sample out of the irradiation container. Such gains andlosses are typically extremely small, and thus uncertainties aretypically negligible. However, in the rare cases where gains or lossesare significant, corrections should be applied and uncertaintiesevaluated.

2.4.4.1. Hot atom transfer to and from the surface of a sample duringirradiation as a result of recoil

Upon activation, nearly all nuclides emit gamma or other radiationand recoilwith enough energy to break the chemical bonds between theatoms within the molecules that comprise the sample or standard(Szilard–Chalmers effect). There is often enough recoil energy totransfer some of the activated nuclides from the surface of a sample tothewalls of thematerial used to encapsulate the sample. This will resultin losses of a portionof the activatedmaterial if the sample is transferredout of the irradiation container. However, since the maximum recoil


distance is typicallymuch less than about 10 nm, the amountofmateriallost through hot atom transfer is rarely significant for bulk samplesunless the element of interest is predominantly at or very near thesurface of the sample or the sample encapsulation material. For mostsamples, this effect is negligible. For example, if a 1 mm thickhomogeneous sample is irradiated, 0.0005% of a nuclide recoiling10 nmwill be lost. A similar loss would be expected from a 1 mm thickstandard. Although maximum recoil energy can be obtained for eachnuclear reaction, and the corresponding distance in various matricescalculated [32], this potential loss of material can be considerednegligible (with a negligible uncertainty) for bulk samples. However,if thin film samples are analyzed, potential losses should be calculated,or samples should not be transferred from the irradiation containerbefore counting, eliminating the possibility of losses.

Hot atom transfer can also result in unexpected transfers (gains)from the surface of the container (blank) to the sample or standard ifan element is concentrated at or near the surface of the encapsulationmaterial, resulting in a higher than expected blank if the sample istransferred. This has been frequently observed for the determinationof low-level Cr in biological samples encapsulated in polyethylenebags. Polyethylene films used to prepare bags are often left with asurface deposit of Cr during the manufacturing process that is difficultto remove by acid washes. Up to about 20% of the total (activated) Crin a polyethylene bag may be transferred to the sample duringirradiation. Of course this will depend on the distribution of Cr in thepolyethylene, as well as the amount of surface area of the bag that is indirect contact with the sample. It is thus important to assess theamount of each element to be determined in the encapsulationmaterial compared to the sample, and to assess the amount ofpotential transfer via recoil. Alternatively, acid-washed, high-purityquartz can be used to encapsulate samples with very low massfractions of Cr and other common elements, where recoil transfer ofsurface deposits is extremely unlikely.

One way to assess the amount surface transfer (blank) frompolyethylene or another plastic is to prepare samples of a test materialwith very low, but known,mass fractions of the element(s) of interest.These samples can then be encapsulated in the irradiation containersto be tested, irradiated, counted after sample transfer, and massfractions of the elements of interest determined. The transfer blank isjust the difference between the observed elemental content comparedto the known content. Uncertainties can be calculated by combiningthe uncertainty of the known value and the measurement uncertaintyfor the test material.

2.4.4.2. Transfer of material through irradiation containerUpon activation, volatile Hg species can be formed as a result of

recoil, and can pass through polyethylene under certain conditionsthat may occur during sample irradiation. This can result in a loss or again of activated mercury in each sample when only polyethyleneencapsulation is used for irradiation. It is thus a good practice toencapsulate samples in quartz when Hg is to be determined, thuseliminating the possibility of gains or losses. Smaller losses have beenobserved for selenium from standards prepared using seleniummetalin dilute nitric acid dried on filter paper, but the selenium is retainedby the polyethylene film packaging. When Se-containing standardsare transferred from the inner-most irradiation container, it is a goodpractice to count the empty container to check for Se loss. Correctionswith uncertainties should be applied if appropriate.

In a similar manner, activated forms of mercury and the halogensare sometimes found in the vapor phase of an encapsulated sample,and may be lost upon transfer. This is a rare occurrence, and to thebest of our knowledge, has only been observed when reducing liquids(e.g., urine, oil, etc.) have been irradiated. If reducing liquids areanalyzed for Hg or halogens, it is probably best to leave the sample inthe original encapsulation, if possible, and count the samples inseveral different orientations to check for non-homogeneous spatial

distribution of these elements within the container [33]. If samplesmust be transferred, e.g., to perform a radiochemical separation forHg, extreme care must be taken to prevent losses. Freezing in liquidnitrogen prior to opening the sample, followed by a very rapidtransfer, has been effectively used for this purpose.

Mass loss may also be observed due to radiolysis or exposure toheat in the irradiation position generated by gamma rays from thereactor and the sample itself. This is often the case for materials thathave appreciable moisture content providing an added complicationto the determination of the mass basis. Iyengar [30] and Kiem et al.[31] have studied weight losses in blood samples during irradiation asa function of irradiation and other experimental conditions anddiscussed the effects of weight loss on analytical uncertainty.Corrections for this type of mass loss may be determined experimen-tally by determination of the differences between individual orcombined masses of the containers and samples before and afterirradiation. The standard uncertainty is then calculated frommeasurement replication, i.e., s/√n.

2.4.4.3. Sample loss during transfer from irradiation containerThis loss mechanism corresponds to the bulk material left behind

when a sample is transferred out of an irradiation container such as apolyethylene bag. Powders, even when pressed into pellets, oftenleave a small surface film behind upon transfer. This is rarelysignificant for bulk samples when no visible residue is left in thesample container, however, it is important to visually inspect eachcontainer for residue if the samples are transferred. If residue isvisible, it is important to assess whether a significant amount hasbeen left behind. The simplest way to do this is to record the massof the irradiated sample in the container before and after transferand to record the mass of each empty container prior to irradiationand reweigh after sample transfer post irradiation. Note that althoughthe mass of the irradiation container is not likely to change duringirradiation, one must record the mass of the sample in the irra-diation container after irradiation because the mass of the samplemay change during the irradiation. This procedure is necessary todetermine the proportion of mass loss that is attributable toincomplete transfer in addition to that attributable to loss duringirradiation.

2.4.4.4. Target isotope burn up differences (when samples and standardsare irradiated under different conditions)

Unlike many analytical methods, consumption of the analyteduring the INAA process is entirely negligible, although for the mostexacting work it should be considered when standards and samplesare irradiated for different times or in different facilities [34]. Theextreme case is the determination of gadolinium, which has thelargest neutron capture cross section σ of any element, 47,700 b; thenext, samarium, is nearly an order of magnitude less. If a sample isirradiated for ti=12 h in a neutron fluence ϕ=1013cm−2s−1, thefraction of Gd transmuted is σϕti=2.1%. However, Gd is determinedthrough 153Gd, produced from 152Gd with a cross section of 811 b, sothe error in INAA even under these extreme irradiation conditions is0.03%. The uncertainty of this correction may be estimated as asignificant fraction of the correction, such as 10%. However, whenstandards and samples are irradiated for the same time in samefacility, the fraction of each isotope lost in the standard(s) will beidentical to that for the sample(s), and so the activity ratio will be notbe affected.

2.4.5. Irradiation timing and decay corrections

When samples and standards are irradiated separately, the actualstart times of irradiation will have uncertainties, as will the lengths ofirradiation. Although these are rarely significant, they should beconsidered for the irradiation systems are used.


2.5. Uncertainty evaluation: gamma-ray spectrometry

2.5.1. Measurement replication or counting statistics (depending onnumber of replicates) for unknown samples

Uncertainties for measurement replication are common to allanalytical measurement methods. Typically uncertainties need to beconsidered separately for samples and standards. The most commonway to evaluate the standard uncertainty for measurement replica-tion of the unknown samples is to divide the observed standarddeviation by the square root of the number of independent samplesmeasured. However, such an evaluation is not possible if only onesample is analyzed. In addition, if only a few samples are analyzed,the observed standard deviation is not very meaningful (i.e., there isa high degree of uncertainty for the standard deviation). In thesecases, it is often more appropriate to compute the uncertainty formeasurement replication using the uncertainties from countingstatistics, since radioactive decay follows a Poisson distribution. Thusthe replication uncertainty of a single measurement would just bethe square root of the net peak area combined with twice thebackground area under the peak if equal numbers of peak andbackground channels are used [35].

2.5.2. Measurement replication or counting statistics (depending onnumber of replicates) for standards

Discussion for the standards is essentially the same as for theunknown samples in the preceding section (2.5.1). The uncertaintyfor measurement replication of the standards may be evaluated eitheras the observed standard deviation of the mean A0 value for thestandards (typically A0 per µg of each element) when multiplestandards for are used each element, or as the propagated uncertaintyfrom counting. If only a limited number of standards are measured, itis often more appropriate to use the observed uncertainty duecounting statistics. If only a limited number of standards aremeasured, it is often more appropriate to use the propagateduncertainty due to counting statistics. Note that when countingstatistics uncertainties are used for the measurement replicationuncertainty for the standards, it is extremely important to make surethat all other standard preparation, irradiation, and countinguncertainties are considered and fully evaluated.

2.5.3. – Corrections for radioactive decay (effects of timing and half-lifeuncertainties)

Radioactive decay strictly follows A=A0e−λt, where λ=ln(2)/t1/2.

If the error in the decay time td is δ, then the error in the decaycorrection fd is

δ fdð Þ = e−λtd−e−λ td + δð Þ: ð2� 5Þ

For example, a 1% error in either td or λ corresponds to a relativeerror of 0.01λt.

Since quantification of NAA measurements depends uponcomparing the decay corrected count rates of unknown samples tocomparator standards, uncertainties due to the corrections forradioactive decay of samples and standards during irradiation,prior to gamma spectrometry and during the gamma spectrometryprocess itself must be considered. Uncertainties due to the half-livesof each radionuclide, as well as uncertainties in establishing thevarious decay times and counting intervals (live time, clock time) allcontribute to the overall uncertainty of the measurement. Fortu-nately, half-lives of the radionuclides used in NAA are generally sowell known that the decay corrections are rarely significant for thetotal uncertainty budget. Some exceptions have been noted,however. In a high-precision analysis of arsenic via 76As, the use of

a recently published and compiled half-life gave a serious andreadily detected bias in the analytical results. Re-determination ofthat half-life [36] and of three other nuclides [37] that had beenmeasured by the same author gave values compatible with theconsensus of the earlier literature. More recently, a determination ofGe in Ge–Si alloy via 77Ge was hampered by a poor half-life in theliterature, and again a new determination was necessary to achievesatisfactory results [38].

2.5.3.1. Decay corrections from end of irradiation to start of eachmeasurement

Since timing information for irradiation and counting is usuallydetermined from different instruments, timing errors resulting fromimproperly synchronized clocks are possible. However, in mostcases, the potential biases, and uncertainties for corrections due toradioactive decay from the end of irradiation to start of measure-ment are typically extremely small (and insignificant). If samplesand standards are irradiated together, any effects resulting fromtiming errors will cancel when ratios of A0s are calculated. If half-lives of the nuclides under investigation are relatively longcompared to possible timing errors of the different clocks, biaseswill also be insignificant. Only when the half-life of the nuclideunder investigation is very short and the samples and standards areirradiated separately is there any possibility of significant bias oruncertainty. In such cases, the bias can be evaluated (and correctedif necessary) by comparing the times of the different clocks. If nodifference is observed, the maximum possible difference can beestimated, and an uncertainty calculated by calculating the effect ofthe maximum possible difference on A0 (when samples andstandards are irradiated separately). A standard uncertainty canthen be assessed by assuming a uniform distribution and dividing bythe square root of 3.

2.5.3.2. Clock time uncertaintyEarly multichannel analyzer systems (MCAs) often had timing

resolutions of one second. When measurements were performed toa preset live time, the clock time could be off by nearly a full second.This could result in minor biases in decay corrections for nuclideswith very short half-lives. However, current MCAs typically havetime resolutions of 0.01 s or better, making any potential biasinsignificant for nuclides with half-lives more than about onesecond. The potential bias can be evaluated by calculating the effecton A0 by adding an additional increment of analyzer time (i.e., anadditional 0.01 s) to the clock time of a count. That would representthe maximum possible bias. A standard uncertainty can be evaluatedby assuming a uniform distribution and dividing by the square rootof 3.

2.5.3.3. Live time uncertaintyIn a manner similar to that described above for clock time

uncertainty, live time measurements could be in error by up to onesecond for early MCAs whenmeasurements were performed to presetclock times. However, most measurements are made using preset livetimes rather than preset clock times, eliminating this error. As above,biases are typically insignificant with current MCAs, but can still beevaluated by calculating the effect of adding an extra unit of timeresolution.

2.5.3.4. Count-rate effects for each measurementDepending upon the type of analyzer system used the corrections

and uncertainties described in Sections 2.5.3.4.1 and 2.5.3.4.2, or thosedescribed in Section 2.5.3.4.3 should be considered, but not all three.

2.5.3.4.1. Correction for pulse pileup lossesPulse pileup is the result of two or more gamma rays arriving at

the detector during a time period too short to be resolved by the

Table 2.6Differences in corrections for inadequacy of live time extension.

28Al (t1/2=2.24 min)

Live time(s)

Clock time(s)

Dead time(%)

Correction (Cs)for singleradionuclide

Correction (Cc)for constantdead time

Ratioof Cs/Cc

300 360 20 1.172 1.119 1.047600 720 20 1.385 1.174 1.179

Table 2.7Corrections for 28Al in multiple counts of one sample of SRM 1633b (fly ash) following ashort irradiation.

Decay(min)

Livetime(s)

Clocktime(s)

Deadtime(%)

Correction (Cs)for singleradionuclide

Correction (Cc)for constantdead time

Ratioof Cs/Cc

19 60 72 17 1.0316 1.0297 1.001921 120 134 10 1.0370 1.0327 1.004124 300 319 6 1.0506 1.0371 1.013031 900 937 4 1.1018 1.0394 1.0601


amplifier, and results in lost counts. Hardware corrections for theselosses can be made using: pileup rejection/live-time correctioncircuitry in the amplifier; a high-accuracy pulser where the pulserloss rate equals the loss rate of all counts in the spectrum; or loss-free or zero dead time hardware to assess count losses as they occurand correct the spectra by adding a number of counts for the timethat the counting system is unavailable to record gamma rays orcalculating a correction factor for each channel. Uncertainties for thehardware corrections depend on the actual hardware used. Uncer-tainties for corrections using a high-accuracy pulser can bedetermined by combining in quadrature the relative countingstatistics uncertainty for the number of counts in the pulser peakwith the relative uncertainty of the pulser count rate whenradioactive source is being counted. Uncertainties for the loss-freeor zero-dead-time systems depend on the linearity of these systems,which can be evaluated by collecting multiple counts of a decayingsource over the appropriate range of system count-rates; the effectsof the corrections on the counting statistical uncertainty are furtherdiscussed in Section 2.5.3.4.3.

Software solutions are also possible. For example, corrections forpileup losses (FP) can be made via Eq. (2-6):

FP = eP tc−tLð Þ

tL ð2� 6Þ

where: FP=Pileup Correction, tc=Clock (or Real) Time, tL=LiveTime, and P is an experimentally determined pileup constant [39,40].The constant P is usually evaluated by a least squares regression ofcount rates of a single (fixed) source at varying dead times (oftenthrough the use of a second radioactive source at varying distances tothe detector). Using the uncertainty of P from the least squaresregression, the standard uncertainty for the count rate is calculated bycomparing the ratios of FP's for a sample/standard pair calculatedusing P, versus the ratios of FP's calculated using P+uP, where uP is theuncertainty in determining the pileup constant P.

2.5.3.4.2. Inadequacy of live-time extension (for conventional countingsystems)

Conventional gamma-ray spectrometry systems extend thecounting time to make up for time that the analogue to digitalconverter (ADC) of the MCA was unavailable (system dead time).This does not fully correct for lost events due to radioactive decaybecause the probability of observing an event after the originalcounting period is lower during the extended counting period.This loss can be corrected either with hardware (loss-free or zerodead time systems), or through software. If hardware corrections areused, no additional uncertainty is necessary since there is noextension of counting time. Any residual uncertainty will be includedin the uncertainty evaluated as described in Section 2.5.3.4.3.

However, if software corrections are used, information about howthe dead time varies with time may be necessary for an accuratecorrection and uncertainty evaluation. Since this information (variationof dead time as a function of time) is typically not recorded by mostgamma spectrometry systems, an exact solution is not often possible. Acomplete discussion of these effects using conventional gammaspectrometry systems can be found in De Soete et al. [41]. Normally,Eqs. (2-7) and (2-8) for the corrections of two boundary cases areconsidered: the case of a single radioisotope and the case where deadtime is constant over the duration of the count. The correction for asingle radioisotope is the maximum correction necessary for nearly allNAA measurements. The correction for constant dead time is theminimum correction necessary, and rapidly goes to unity as the half-lifeof the isotope under investigation greatly exceeds the counting interval.However, when the counting interval approaches or exceeds the half-life of the nuclide under investigation, the constant dead time correctionmay significantly underestimate the losses.

Equations [41] for the correction of live-time extension lossesusing conventional counting for single radioisotope and for constantdead time are given below:

Fltc sð Þ =eλðtc−tLÞ−1λ tc−tLð Þ Single radioisotope ð2� 7Þ

Fltc cð Þ =1−e−λtL� �

tcð Þ1−e−λtc Þ tLð Þ Constant dead time ð2� 8Þ

where: Fltc=the correction factor of the inadequacy of live timecorrection (the ratio of “true” count rate compared to the observedcount rate; tc=clock or real time; tL=live time and λ=the decayconstant for the nuclide under investigation. Table 2.6 shows thedifferences for the two correction factors for caseswhere the dead timeis 20% and the count time is nominally two and four times the halflife of the radionuclide under investigation, 28Al (t1/2=2.24 min)in this case. There is almost a 5% difference in the correction factorsfor a live time of 300 s, and an 18% difference for a live time of 600 s.Unless the analyst has recorded separately the dead time at the startand/or end of the count, it can be difficult to determine whichcorrection to apply. However, if shorter counting intervals are used,the difference between the two corrections becomes smaller, andtherefore it is less important which one is used. As a general rule ofthumb, when the clock (real) time of a count is less than half of thehalf-life of the radionuclide of interest, the difference between the twocorrections becomes insignificant in all but the highest accuracyapplications. Although shorter counts will result in poorer countingstatistics, multiple short counts can provide nearly the same countingstatistics uncertainty as a longer count without the problem ofchoosing which correction factor to use. Table 2.7 shows actualmeasurement data for multiple counts of the same sample and thevalues of the two different correction factors for 28Al. The first countwas started when the 28Al activity was approximately the same as thenextmost intense peak, and the samplewas counted for a clock time of72 s, just over 50% of the 28Al half-life. As shown in Table 2.7, thedifference for the two correction factors was only 0.2%. In addition,since the 28Al activity did not dominate, and all other significantsources of activity had longer half lives, the midpoint of the twocorrection factors was the most appropriate to use. The relativestandard uncertainty for this correction would be 0.1% (the differencebetween the correction used and the two boundary conditions)divided by the square root of 6 (triangular distribution), or 0.4%.Although the difference between the two correction factors became

Table 2.8Validation of pulse pileup and live — time extension corrections. Data for multiplecounts of one sample of SRM 1633b (fly ash) following a short irradiation.

Count Deadtime(%)

Livetime(s)

Al (%)t1/2=2.24 min

V (μg/g)t1/2=3.75 min

Mn (μg/g)t1/2=2.58 h

Na (μg/g)t1/2=14.9 h

#1 17 60 14.90±0.101 305±7 130.7±2.1 2033±157#2 10 120 15.03±0.11 294±5 134.2±1.4 1930±77#3 6 300 14.97±0.13 291±5 132.8±0.8 1979±39#4 4 900 14.48±0.46 313±9 133.9±0.5 1994±23#5 3 600 – – 133.6±0.7 1991±27Red. Chi. Sq. 0.615 2.089 0.858 0.196Probability ofexceeding

60.5% 9.9% 48.8% 94.1%

1 Uncertainties represent 1 sigma counting statistics.


significantly greater for subsequent counts, since the 28Al activityconstituted aminor contribution to the total activity, the correction forconstant dead time was appropriate, and uncertainties for thiscorrection were insignificant.

Another advantage to the use of multiple shorter counts(instead of one longer one) is that multiple counts provide theopportunity for quality assurance checks of the pileup andinadequacy of live time extension corrections. Table 2.8 showsthe mass fraction results for Al, V, Mn and Na based on the countsdescribed in Table 2.7. Additional data for Mn and Na are also listedfor a fifth count of the same sample. Both Mn and Na have half-lives that are many times longer than any of the counting intervals,so the choice of correction factor for live time extension isinsignificant. Therefore, any trend in the data for Mn and Na as afunction of dead time would be due to bias in the pileup correction.Looking at the data for these two elements in Table 2.8, it is apparentthat there is no increasing or decreasing trend. It is often instructive tocalculate the probability that a random sample of n points taken from anormal distribution of mean xw and standard deviation sx=

ffiffiffin

pwill

exceed the observed value of reduced chi-squared [42,43]. The reducedchi squared values for Mn and Na in Table 2.8 indicate that all variationcan be explained by counting statistics alone. Because the half-lives ofthe isotopes used for both Al and V are relatively short, corrections forboth pileup and live time extension can be both significant and difficultto separate. However, since pileup affects all peaks in a spectrum to thesamedegree, and has been shownnot to be a significant problem forMnand Na in these data, it is not a significant problem for the Al and Vdeterminations listed in Table 2.8. Thus the lack of any trend in the datafor Al and V, combined with reduced chi squared values indicating thatall observed variations can be explained solely by counting statistics(95% confidence), provide a great deal of confidence in the correctionsapplied.

2.5.3.4.3. Uncertainties due to hardware corrections for Loss-Free10 orZero Dead Time10 (ZDT) systems

Commercially available systems for loss-free data acquisition [44]may overcome the inadequacies of live-time extension and pulsepileup calibrations. The uncertainty associated with the use of thesereal-time correction modes is experimentally evaluated by compar-ison of corrected and uncorrected spectral data.

The statistical uncertainty of the channel content M of a spectrummeasured with real-time correction of counting losses essentiallydepends on the number N of analog-to-digital conversions into thatchannel and has been described by Westphal [45] as:

dM=Mð Þ2 = dN=Nð Þ2 + 1=Nð Þ dW =Wð Þ2; ð2� 9Þ

10 Certain commercial equipment and materials are identified in this work for thepurpose of adequately describing experimental procedures. Such mention does notimply endorsement by the National Institute of Standards and Technology.

where dW/W is the relative statistical uncertainty of the weightingfactors. Under the reasonable assumption of Poisson statistics for thenumber N of analog-to-digital conversions into a channel the totalrelative uncertainty dM/M may be rewritten as:

dM =M = N–1=2 1 + dW =Wð Þ2h i1=2

; ð2� 10Þ

illustrating the increase over the basic relative uncertainty which iscaused by the correction procedure.

The relative uncertainty dW/W of weighting factors is determinedfor every peak in the spectrum by direct comparison of simulta-neously measured loss-corrected and non-corrected spectra in therespective regions of interest, according to the formula for thevariance of grouped data:

σ2W =

1n−1ð Þ∑n Ni

Mi

Ni−W

2� �

; ð2� 11Þ

W =∑n

Mi

∑n

Ni; and ð2� 12Þ

dWW

=σW

W; ð2� 13Þ

whereMi and Ni are the contents of corresponding loss-corrected andnon-corrected channels. The weighting factors for each channel arecalculated and the average weighting factor W is determined. Thestandard uncertainty σW of W over each peak region is calculatedand Eq. (2-9) is applied to the calculation of the standard uncertaintyof each peak area.

An alternate method to determine the uncertainty is implementedin the DSPECPLUS ™ digital spectrometer where a variance spectrumrepresents the statistical uncertainty of the loss correction process. Inthe interpretation of Pommé [46], the variance spectrum ∑n2 isformed by multiplication of the loss corrected channel content withits weighting factor (Eq. (2-14), using the same symbols as above):

∑n2 = wM: ð2� 14Þ

Integration of the variance spectrum in the regions of interest (peakareas) provides the uncertainty of the peak area in the usual manner.

Table 2.9 gives an example for the uncertainties encountered withloss-free data acquisition. A 152Eu source was counted together with a137Cs source placed at different distances. Peak areas N and M arecalculated from the channel contents in the spectrum, the number ofchannels for the background is set equal to the number of channels inthe peak. Columns in the table show data according to Eq. (2-9). Thenext to last column of Table 2.9 shows the relative increase over thecounting statistics uncertainty due to the ZDT process, and the lastcolumn gives an estimate of the total uncertainty using themodel of thevariance spectrum,whichwas artificially created from the example datausing Eq. (2-14) for each channel. The estimates are slightly differentbecause of the experimental uncertainty in W. The increases are nearlyinsignificant in peaks with excellent counting statistics. Here theuncertainty in the correction factor W is small as well. For peaks withlarger uncertainties the additional uncertainty may gain significance.For practical purposes, an upper limit can be estimated by determiningthe variance of the correction factorW in the high-energy region of thespectrum and using the applicable part of Eq. (2-9). If dW/W were ashighas10% relative, the additional uncertaintywouldnot exceed0.5% ofthe uncertainty of the uncorrected peak counts. Thus if dW/W is≤10%,

Table 2.9Example data for loss-free counting of a 152Eu source with a 137Cs source placed at different distances to create different count rates.

Energy (keV) N dN/N (%) M W dW/W (%) dM/M Relative increase (%) uZDT (%)

Count rate 76 kHz121 142,134 0.72374 1,639,975 11.551 0.60 0.72376 0.0018 0.72482661 8,557,932 0.03520 98,827,818 11.511 2.50 0.03521 0.031 0.0352041408 14,134 0.92784 161,797 11.48 5.74 0.92937 0.16 0.93409

Count rate 15 kHz121 262,799 0.286775 399,800 1.523 0.57 0.286779 0.0016 0.28707661 1,982,894 0.071777 3,011,938 1.517 1.55 0.071786 0.012 0.0717841408 26,422 0.62465 40,199 1.521 7.57 0.62644 0.29 0.62452


the total uncertainty (including ZDT-related uncertainties) for a peakwith a counting statistics uncertainty of 1.000% would be ≤1.005%.

2.5.4. Corrections and uncertainties for gamma-ray interferences

Although there are many interference-free gamma lines, there aremore interferences than most NAA practitioners expect. Examples ofinterferences observed in three geological materials are listed inTable 2.10.

However, rarely (if ever) do interfering nuclides have half-livessimilar to that of the nuclide of interest. Therefore, agreement ofresults from replicatemeasurementsmade at different decay intervals(with no apparent trends) gives added confidence that there are nosignificant, unrecognized interferences, since the relative contributionfrom interfering nuclides would increase or decrease with decreasewith decay time depending upon the whether the half-life of theinterfering nuclide was greater or smaller than the nuclide of interest.Similarly, in cases where interference corrections are applied,agreement of results from replicate measurements made at differentdecay times gives added confidence that interferences have beenaccurately corrected. The authors have seen about 40 significantinterferences, listed in Table 2.11, however, none of these werefrom radioisotopes with half-lives similar to the isotope underinvestigation.

Correcting interferences can be relatively simple when they arerecognized since most potentially interfering nuclides typically haveadditional gamma rays that can be used for identification andcorrection. For example, in many geological/environmental samples,182Ta often interferes with the determination of Se when using the265 keV gamma ray from 75Se. The presence of 182Ta is indicated bythe presence of a 1221 keV gamma ray in the unknown spectrum. An

Table 2.10Typical errors that would be observed in three geological certified reference materials ifinterferences were not corrected.

Nuclide Energy(keV)

Interferingnuclide

Brick claySRM 279

Buffalo River Sed.SRM 2704

Fly ashSRM 1633

46Sc 1120.5 182Ta 0.5% 0.4% 0.4%51Cr 320.1 147Nd 1% 0.3% 0.1%51Cr 320.1 177m+gLu 0.5% 0.2% 0.05%65Zn 1115.6 160Tb 3% 1% 2%75Se 136.0 181Hf N100%1 500% 90%75Se 264.7 182Ta N100%1 150% 30%122Sb 564.2 76As 5% 2% 7%122Sb 564.2 134Cs 15% 4% 2%131Ba 496.3 103Ru – 50% 40%153Sm 103.1 239Np 1.5% 2% 3%153Sm 103.1 233Pa 0.5% 2% 0.3%153Gd 103.2 233Pa 60% 70% 40%177Lu 208.4 239Np 3% 2% 10%198Au 411.8 152Eu 100% 100% 100%

1 Within counting statistics, the 136 and 265 keV peaks observed for brick clay weredue entirely to 181Hf and 182Ta interferences to 75Se.

interference ratio for the 265/1221 keV lines is obtained by counting a182Ta source (with the same gamma attenuation characteristics) onthe counting system used for the unknown samples. The number ofcounts of the 1221 keV peak in each unknown sample is multiplied bythe 182Ta 265/1221 interference ratio to determine the contribution of182Ta to the 265 keV peak. This interference is then subtracted fromthe gross 265 keV peak to obtain the net 75Se peak area. The absoluteuncertainty (in counts) for the interference contribution is obtainedby multiplying the absolute uncertainty of the 1221 keV peak in eachunknown sample by the uncertainty of the interference ratio, which isdetermined by combining in quadrature the (relative) countingstatistics of the 265 keV and 1221 keV peaks used to determineinterference ratio. The absolute uncertainty of the corrected (net)265 keV peak of 75Se is determined by combining in quadrature theabsolute counting uncertainty of the 265 keV peak with the absoluteuncertainty of the interference contribution.

This method for interference correction and uncertainty evalua-tion depends upon the sample and 182Ta source having the samegamma-ray attenuation characteristics. This is especially importantwhen the energy of the gamma ray of interest (in this case 265 keV)and the gamma ray indicating the interference (in this case 1221 keV)is relatively far apart. Although a 182Ta source with matchingcharacteristics to the sample can be readily prepared by pipettingand mixing a liquid 182Ta spike onto unirradiated sample material (ofthe same size and shape as actual samples under investigation, it isoften more convenient to choose an interference indicator with anenergy closer to the gamma ray of interest. For example, 182Tahas a 222 keV gamma ray in addition to the 265 keV and1221 keV gammas, which is close enough to the 265 keV peakto minimize gamma attenuation differences for most materials.Although 82Br (t1/2=35 h) has a 222 keV gamma ray, most measure-ments of Se via 75Se are performed after a decay period of at least amonth (N20 half-lives of 82Br), at which time essentially all the 82Br222 keV gamma rays are gone.

In cases where an interference is possible (or expected), but theindicator gamma ray is not observed, an upper limit value (at 95%confidence level) for the indicator gamma ray in the spectrum ofinterest can be calculated [47], and an upper limit on the interferencecan be calculated via an interference ratio determined as above. Onepossible approach would be to make no correction and use a standarduncertainty equal to 1/2 of the upper limit value. An alternativeapproach would be to subtract 1/2 of the upper limit value from thepotentially interfered peak. Assuming a uniform distribution, thestandard uncertainty would then be 1/2 of the upper limit valuedivided by the square root of 3.

2.5.5. Corrections and uncertainties for counting efficiency differences

The NAA measurement equation (Eq. (2-1)) listed earlier in thissection includes a factor (Rε) to account for any differences incounting efficiency between samples and standards. Although thisratio is usually very close to unity, two factors are may contribute tosignificant deviations. The first results from differences in the physical

Table 2.11Interferences observed in several common matrices.

Analyte nuclide γ-ray energy(keV)

Interferingnuclide

Interference energy(keV)

Indicator energy(keV)

Typical ratio of interferenceto indicator peak2

Range of relativeerrors if uncorrected3

Comment codes4

Geological materials46Sc 1120.5 182Ta 1121.3 1221.4 1.4 0–75%51Cr 320.1 147Nd 319.4 531.0 0.2 0.5–1000% M,S51Cr 320.1 177m+gLu 321.3 208.4 0.02 0.2–100% M51Cr 320.1 177mLu 319.0 208.1 0.001 0–2% M65Zn 1115.6 160Tb 1115.1 879.4 0.05 1–10%75Se 264.7 182Ta 264.1 222.1 0.4 10–200%75Se 136.0 181Hf 136.55 133.1 0.15 20–500% D110mAg 657.8 152Eu 656.5 1408.1 0.01 0–20%122Sb 564.2 76As 563.2 559.1 0.03 3–15%122Sb 564.2 134Cs 563.2 795.8 0.13 5–30% S131Ba 496.3 103Ru6 497.0 None – 2–100% X,S152Eu 964.0 152mEu 963.5 841.6 0.8 0–100% D153Sm 103.1 239Np 103.7 106.37 0.8 0.5–5%153Sm 103.1 233Pa 103.8 312.0 0.03 0.2–3% S153Sm 103.1 153Gd 103.2 None – 0.1–100% X,S153Gd 103.2 233Pa 103.8 312.0 0.03 50–500%177Lu 208.4 239Np 209.8 106.3 0.1 1–20%177Lu 208.4 183Ta 209.9 246.4 0.1 0–1%198Au 411.8 152Eu 411.0 1408.1 0.4 10–100% S

Botanical materials51Cr 320.1 147Nd 319.4 531.0 0.2 5–100% D75Se 136.0 181Hf 136.55 133.1 0.15 10–50% D75Se 264.7 182Ta 264.1 222.1 0.4 5–30%110mAg 657.8 152Eu 656.5 1408.1 0.01 10–1000%113Sn 391.7 160Tb 392.5 298.6 0.03 100–1000%122Sb 564.0 76As 562.8 559.1 0.01 1–10%122Sb 564.0 152Eu 564.0 1408.1 0.3 0–5% S153Sm 103.1 239Np 103.7 106.37 0.8 1–10%198Au 411.8 152Eu 411.0 1408.1 0.4 1–10% S203Hg 279.1 75Se 279.5 264.7 0.4 20–100% S

Biological tissues46Sc 1120.5 182Ta 1121.3 1221.4 1.4 0–75%64Cu 511 24Na 5118 1368 0.1 10–500%64Cu 511 65Zn 511 1115 0.1 0–5%122Sb 564.0 76As 562.8 559.1 0.01 1–10%122Sb 564.2 134Cs 563.2 795.8 0.13 0–20%124Sb 602.7 134Cs 604.6 795.8 1 0–300%203Hg 279.1 75Se 279.5 264.7 0.4 20–100%

Additional miscellaneous interferences observed60Co 1173.2 82Br9 1173.4 554.3 Varies60Co 1332.5 82Br9 1330.8 554.3 Varies64Cu 511.0 cosmic10 511.0 1460 564Cu 511.0 β+, PP11 511.0 Various Varies80Br all 80mBr all half-life Varies85Sr 513.9 β+, PP11 511.0 Various Varies116mIn 1293.3 41Ar 1293.6 None –140La 487.0 131Ba 486.5 496.3 0.04181Hf 133.1 131Ba 133.6 496.3 0.1197Hg 68.8, 80.2 198Au 69.0, 80.1 411.8 0.04, 0.02199Au 158.3 47Sc 159.4 None –199Au 208.2 177Lu 208.4 None –

1Nominally clean indicator peak used to identify interfering nuclide.2Typical ratio of interfering peak to interference indicator observed for the interfering nuclide.3Relative range of errors observed if interference is not corrected.4Comment codes:M – Multiple peaks often present – can be difficult to integrate accurately.D — Interfering nuclide has significantly shorter half-life than analyte nuclide. Better results obtained after additional decay.S — Interfering nuclide has significantly longer half-life than analyte nuclide. Shorter decay intervals often provide better results.X — Cannot be accurately subtracted by interference ratio technique; track half-life or use other correction method.5Includes equal intensity 181Hf peaks at 136.3 and 136.9 keV.6Fission product.7Includes equal intensity 239Np peaks at 106.1 and 106.5 keV.8Result of pair production events, which often occur in the detector shield. Other sources of high-energy gamma rays may similarly interfere.9Interferences from 82Br to 60Co are sum peaks; γ-ray ratios will vary with counting geometry.10Although the 1460 keV peak is from 40K, it can be used as an indicator for natural radiation.11Resulting from pair production (PP) events, normally in the Pb detector shield.


Table 2.12Calculated gamma-ray self-absorption correction factors for 2 mm thick pellets (withdensities of 1) for some typical matrices and energies.

Energy(keV)

Matrix

SiO2 Cellulose(CH2O)

Cellulose (99.9%)with 0.1% Pb

Al2O3 Na2SiO3

100 0.9844 0.9844 0.9839 0.9849 0.9849300 0.9895 0.9888 0.9887 0.9897 0.9896500 0.9914 0.9908 0.9908 0.9915 0.99151000 0.9937 0.9933 0.9933 0.9938 0.99381500 0.9948 0.9945 0.9945 0.9949 0.9949


size and shape of the samples, and can be highly significant sinceradiation decreases as distance squared. In fact, ignoring these effectsis frequently a common source of significant bias for NAA measure-ments. The second results from differences in the fraction of thegamma rays internally absorbed by the sample and standard duedifference in size, shape and composition.

2.5.5.1. Effects resulting from physical differences in size and shape ofsamples versus standards

Since radiation decreases as a function of distance squared, smalldifferences in sample size and shape relative to the standards can causesignificant differences in the fraction of radiation reaching the detector,and lead to biased results if ignored. Although it is possible to calculatethe solid angle differences for samples and standards to theactive regionof the detector, the bulk of this effect in most cases is largely due todifferences in sample/standard thickness. A simple model based uponaverage sample/standard distance to the detector works well for smalland thin samples and standards countedmore than several cm from thedetector, i.e., the samples and standards are smaller than about half thediameter of the detector, and are less than about 0.5 cm thick. Using thismodel, the average distance to the active region of the detector is thesum of half the thickness of the sample or standard, the distance fromthe sample/standard to the surface of the detector surface, and anestimate of the distance from the detector surface to the averagedistance below the surface that the interaction between gamma ray andthe crystal occurs. A value of 3 cmworkswell for the detector surface tointeraction distance for most modern coaxial Ge(HP) detectors withrelative efficiencies of about 25% to 100% of a 3 in.×3 in. Na(Tl)Idetector. A value of 2 cm may be more appropriate for detectors withrelative efficiencies less than 25%, and a value of 4 cm may be moreappropriate for detectors with relative efficiencies greater than 100%.However, at typical sample-to-detector counting distances for activatedsamples, the value chosen has only a small effect on the calculation forthe efficiency correction, which is obtained by squaring the ratio ofaverage distances to the detector for sample to standard. As an example,assume that samples are 0.3 cm thick, standards are 0.2 cm thick,gamma-ray spectrometry measurements are made 10 cm from thesurface of the detector, and the average interaction of the gamma rayoccurs 3 cm below the surface of the detector endcap. Then the averagedistance for the samples is 10+(0.3/2)+3 cm or 13.15 cm, and theaverage distance for the standards is 10+(0.2/2)+3 cm or 13.10 cm.The sample count rates need to be multiplied by (13.15/13.10)2, or1.00765 to account for the thickness differences. Estimating a standarduncertainty of 1 cm (33%) for the interaction depth, the correctionwould become (12.15/12.10)2 or 1.00828. The relative uncertainty forthe efficiency correction would be the difference between the twocorrections, or 0.06%.

2.5.5.2. Corrections for gamma ray self absorptionA major advantage of INAA is that both the probing (neutron) and

indicating (gamma) radiations are highly penetrating. Neutron self-shielding, generally the larger term, was discussed in Section 2.4.1.3.Most gamma rays employed in INAA have energies on the order of1 MeV. At this energy, the transmission through 1 mm of wood, bone,and steel is 99.6%, 99.3%, and 96%, respectively.

Gamma-ray absorption is strictly exponential with thickness. For apencil beam through a material of density ρ (g/cm3) and thickness T

(cm), the attenuation factor Iout = Iin = exp − μρ ⋅ρT

� �, where the mass

attenuation coefficient μ/ρ (dimensionally cm2/g) depends on thecomposition. Values of μ/ρ for many elements and compositematerials have been tabulated [48], but are most convenientlycalculated by the widely available XCOM program [49]. To calculatethe attenuation for a finite source, integration over the sample volumeis necessary. While in the general case a Monte Carlo calculation maybe necessary, many geometries of interest have been solved

analytically [35]. For the most common geometry in INAA, ahomogeneous plane source of thickness T (in cm), the self-absorptionfactor is:

Fγ =1−e−μT

μTð2� 15Þ

where the density ρ is incorporated into the linear attenuationcoefficient μ. The standard uncertainty may be difficult to assessquantitatively, since μ/ρ depends on the composition which, for thesample is not fully known. However, the major elements can usuallybe estimated within reasonable limits, and minor elements have arelatively small effect on self-absorption. In addition, varying thesample size will give empirical information about the importance ofthis effect. Since the physics of XCOM is so complete, and theprogram is so widely accepted, the uncertainty in compositionusually dominates. Therefore it is usually reasonable to estimate arelative standard uncertainty of 5% to 10% of the correctiondepending upon how well the major constituents of the sampleare known.

Because gamma radiation is highly penetrating, NAA practitionersoften do not consider the effects of gamma ray absorption. However,significant bias can be introduced in many cases by ignoring this effect,especially when samples and standards have significantly differentdensities, thicknesses, and/or contents of higher-Z elements (i.e., massfractions greater than about several g/kg). Thus it is important to befamiliar with methods to calculate gamma-ray self-shielding factors.One method is to use the NIST web resource for XCOM at http://www.nist.gov/physlab/data/xcom/index.cfm (updated November 2010, lastaccessed December 17, 2010). First, use the “Database Search Form” tocalculate the gamma-ray mass attenuation coefficients for each gammaray of interest for the material under investigation. Elements,compounds or mixtures can be specified in the search form. Totalmass attenuation coefficients without coherent scattering should beused for most matrices; however, total mass attenuation coefficientswith coherent scattering (that is, including diffraction) may be moreappropriate for single crystals.

The next step is to calculate the gamma-ray attenuation factor foreach energy of interest in the samples and standards using Eq. (2-15).The mass attenuation coefficients need to be multiplied by the sampleor standard density to determine each attenuation coefficient (μ).Examples of the calculated gamma-ray self-absorption correctionfactors for 2 mm thick pellets of the above matrices (assumingdensities of 1) are given in Table 2.12. Corrections are applied bydividing the observed gamma-ray intensity by the calculatedcorrection factor.

Note that there is very little difference among the correctionfactors for these common matrices as long as the thicknesses anddensities are the same; thus the ratio between samples and standardswould be very close to unity. A small admixture of heavy elements, forexample 0.1% Pb, makes little difference. However, when there aredifferences in either density or thickness, significant bias may occur.

http://www.nist.gov/physlab/data/xcom/index.cfm

http://www.nist.gov/physlab/data/xcom/index.cfm

Table 2.13Comparison of calculated self-absorption corrections for 2 mm thick pellets of CH2Owith density 1 compared to 2 mm thick pellets of SiO2 with density 2.

Energy(keV)

MatrixCH2ODensity=1

MatrixSiO2

Density=2

Correction ratio forCH2O w/density=1versus SiO2

w/density=2

Potential biasResulting fromdensity differences

100 0.9844 0.9691 1.0158 1.6%300 0.9888 0.9791 1.0099 1.0%500 0.9908 0.9828 1.0081 0.8%1000 0.9933 0.9874 1.0060 0.6%1500 0.9945 0.9897 1.0048 0.5%


For example, Table 2.13 shows the differences in self-absorptioncorrection factors and the potential biases for 2 mm thick samples ofSiO2 compared to dilute standard solutions pipetted onto cellulose(i.e., CH2O).

2.5.6. Potential bias and uncertainty due to peak integration method

Themethod used to integrate the areas of gamma ray peaks can leadto measurement bias if peak size, shape and background regions aresignificantly different for samples and standards. Although this bias istypically negligible for large, well-resolved peaks, it is important to lookfor potential integration biases for multiplets, small peaks, and peaksoverlying complex background regions. Often the peaks for thecomparator standard arewell defined,without complicated backgroundand without nearby interferences that may affect peak shape, whereasthe peaks for samples may be much more difficult to integrate.

Onemethod thatmay be used to estimate the uncertainty associatedwith the determination of the peak areas involves comparing differentpeak integration methods for singlets including: peak search withchannel-by-channel summation; standard peak fitting using automaticroutines; interactive peakfitting inwhichpeakboundaries andnumbersof channels used for background subtraction are selected manually. It isoften useful to vary the number of peak and background channels toobserve potential effects. If significant differences are observed for theratio of samples to standards, the most appropriate integration methodshould be selected for use, and a standard uncertainty estimated fromthe distance between sample/standard ratio of the selected method tothat of the other method(s). In cases where one method is obviouslymore appropriate than the others, it may be appropriate to assume atriangular distribution and divide this distance by √6 to determine thestandard uncertainty. In other cases, a rectangular/uniform distributionmay bemore appropriate, and the distance from the selectedmethod toother methods divided by √3.

Evaluating the uncertainty for peak integration methods formultiplets may be more difficult since fewer methods of integrationare available. However, comparison of two or more peak fittingroutines is essential, unless the estimated uncertainty can be obtainedby other methods, e.g., evaluation of residuals. Many commerciallyavailable routines display the residuals. Alternatively, other mathe-matical models can be used. The different parameters used for thefitting routines should be varied to observe the effects of smallchanges. An interactive peak fitting routine is particularly useful inthat the effects of small changes in peak and background channelselection demonstrate how the net peak area changes. Again it isimportant to compare the sample/standard ratios of the differentmethods to estimate the standard uncertainty.

2.5.7. Potential bias due to perturbed angular correlations (γ-raydirectional effects)

Although gamma rays from irradiated samples are emittedisotropically (in the absence of strongmagnetic fields), the directions

of two gamma rays emitted in rapid sequence in the decay of a singlenucleus may be correlated. This perturbed angular correlation isexploited in materials science to study the microscopic environmentof certain tracer nuclides, of which only a few are encountered inNAA [50]. Because angular correlation is measurable with goodefficiency only by gamma-gamma coincidence with two or moredetectors, this effect is not experienced in the usual one-detectorconfiguration used in INAA unless a cascade sum peak were to beused for analysis, or if loss of counts via summing is significant. Inpractice, this is the case only when the counting efficiency is veryhigh, for examplewithin awell detector. Furthermore, in comparatorNAA the effect cancels in the ratio of sample to standard if both arecounted using the same geometry, with the caveat that a subtledependence on chemical form has been observed in a few rare cases[51, 52].

2.6. Uncertainty evaluation: radiochemical stage(only if radiochemical procedures are used)

2.6.1. Losses during chemical separation

Loss of analyte can present a significant bias for RNAA measure-ments, especially if samples and standards are not processed in anidentical manner. To avoid such problems, carriers or radiotracers aretypically used to evaluate the chemical yield [41] for each elementdetermined in every sample, unless the separation is known to bequantitative, and both samples and standards are processed in anidentical manner (standards are dissolved with unirradiated samplematerial). Based on the yield determination, corrections can beapplied to all samples and standards. Uncertainties are derived fromthe determination of the chemical yield, and will depend on themethod used. For example, when radiotracers are used, uncertaintieswill be largely due to a combination of counting statistics (before andafter separation), and the pipetting precision. When gravimetricmeasurement of carrier is used for yield determination, theuncertainty of the chemical yield will depend largely on massdetermination of the carrier before and after separation, and purityof the separated carrier, i.e., moisture content, stoichiometry andimpurities.

2.6.2. Losses before equilibration with carrier or tracer

Losses prior to equilibration with carrier and/or tracer are oftennot detected by yield determinations and can lead to measurementbias. Similar problems are possible for IDMS measurements if lossesoccur prior to equilibration of sample and isotopic spikes. The mostcommon types of these losses include incomplete sample decompo-sition (leaving residual undissolvedmaterial), and volatility of specificchemical species found in the unknown samples. Losses due toundissolved material can be evaluated by filtering representativesample solutions and counting the filters. Volatility losses are oftenmore difficult to detect; however, a closed-vessel dissolution is usefulwhen analyzing new matrices, or determining analytes that havepotentially volatile species.

2.7. Methods to evaluate complete uncertainty budgets for NAA

2.7.1. Manual approach general considerations

Once the standard uncertainties for each uncertainty componenthave been evaluated, a combined uncertainty for the can bedetermined manually from the measurement equation (Eq. (2-1)).

mx unkð Þ = mx stdð ÞA0 unkð Þ� �A0 stdð Þ� � RθRϕRσRε−blank: ð2� 1Þ


Note that mx(unk) and mx(std) are the masses of the element ofinterest in sample and standard. If mass fractions are desired, thisequation becomes:

wx unkð Þ =wx stdð Þmstd

munk

A0 unkð ÞA0 stdð Þ

!RθRϕRσRε−

blankmunk

ð2� 16Þ

where wx,unk and wx,std are mass fractions of element x in the unknownandstandard,munkandmstd are the (total)massesof sampleand standard,and blank/munk is the relative blank.

Since A0 is determined from a complex equation, the uncertaintyof the A0 ratio of unknowns and standards should first be evaluatedfrom the standard uncertainties of each term in the A0 equation(Eq. (2-2)):

A0 =λCeλtd

1−eλtLð Þ 1−eλtið Þ fPfltc: ð2� 2Þ

Themost straightforwardmethod to combine the uncertainties forthe terms of the A0 equation (Eq. (2-2)) is to increase or decrease eachparameter (individually) by its standard uncertainty and evaluate therelative effect on the sample/standard A0 ratio. In many cases it isappropriate to use the average value of the samples compared to thestandards. These relative effects are then combined in quadrature toestablish the relative A0 ratio uncertainty.

The relative uncertainty for the A0 ratio is then combined inquadrature with the relative uncertainties for the other terms (exceptfor the blank) in the measurement equation (Eq. (2-1)), andconverted to an absolute uncertainty. This absolute uncertainty(calculated from the uncertainties of all terms except blank) is thencombined in quadrature with the absolute uncertainty of the blank toestablish the combined standard uncertainty.

Alternatively, a term of (1−blank/munk) can be substituted for therelative blank subtraction in the mass fraction equation (Eq. (2-16)),and a standard uncertainty evaluated for (1−blank/munk). Thismakesall operations multiplicative, allowing a combination in quadrature ofall the relative standard uncertainties in this form of themeasurementequation (Eq. (2-17)).

wx unkð Þ =wx stdð Þmstd

munk

A0 unkð ÞA0 stdð Þ

!RθRϕRσRε 1− blank

munk

� �ð2� 17Þ

2.7.2. Manual approach — example of a calculation of a completeuncertainty budget

2.7.2.1. Measurement descriptionArsenic in Silicon – Standard Reference Material (SRM) 2134

(Arsenic Implant in Silicon) was produced at the National Institute ofStandards and Technology (NIST) to serve as a calibrant for secondaryion mass spectrometry, and its arsenic content was certified usingINAA as a primary method of measurement [53]. Ten samples of SRM2134 and two blank chips of silicon were heat-sealed into envelopesof conventional polyethylene that had been cleaned in high-purityHNO3. A dilute solution standard was prepared by gravimetricallydiluting a 10-mg/g solution of As2O3 (stated purity 99.999%) in diluteammonia to about 2 mg/kg. Another solution was prepared similarlyfrom SRM 3103a Arsenic Spectrometric Solution. Aliquants of bothsolutions were weighed from a polyethylene pipette onto 1-cm disksof acid-leached filter paper and dried to produce standards with about200 ng As each. Two standards from each solution were irradiatedwith the samples. A blank filter paper was shown in a separateexperiment to contain no significant arsenic (≪0.01% of the amountin the standards).

Samples, standards, and blanks were stacked in the irradiationcontainer (rabbit) in a quasi-random sequence: standard, blank, fivesamples, two standards,five samples, blank, and standard. The stackwas

irradiated for four hours in the RT1 pneumatic tube of the NIST researchreactor (NBSR) at a thermal fluence rate of 7.7×1013 cm−2s−1,inverting the rabbit halfway through the irradiation to equalize to thefirst order for the linear axial fluence rate gradient along the rabbit.

After irradiation the gamma-ray activity was assayed at 10 cmfrom a Ge detector with a 1.71 keV resolution and 40% relativeefficiency at 1333 keV, with the ion-implanted surface toward thedetector. Pulse pileup rejection/live time correctionwas performed byhardware (in the amplifier). Spectra were acquired with a conversiongain of 0.4 keV/channel. The order of sample counting was random-ized for the first count, and the sequence reversed for the secondcount in order to equalize precision from counting statistics. Onaverage more than 200,000 counts were collected in the 76As peak ineach sample and standard spectra, with a mean Poisson relativestandard deviation of 0.25%. A few samples were re-counted as long assix days after irradiation to check the half-life and search for long-lived radioactive impurities. The combined 559+563 keV doublet of76As in each spectrum was integrated using a channel-by-channelsummation routine.

2.7.2.2. Pre-irradiation (sample preparation)

2.7.2.2.1. Elemental content of standards (comparators) [3]Two solution standards were used: SRM 3103a and one prepared

gravimetrically from As2O3 (stated purity 99.999%). The certified(expanded) uncertainty for SRM 3103a was 0.3%, which approx-imates a 95% confidence interval. Therefore a 1 s relative standarduncertainty was essentially 0.15%. An uncertainty for the secondstandard was difficult to evaluate directly. If an uncertainty werecalculated from the uncertainties in gravimetric preparation com-bined with the stated purity, the resulting value would be a fewhundredths of a percent. However, stated purities often do notconsider all contaminants, or non-stoichiometric behavior ofcompounds. Since no differences were observed (over the countingstatistics) between the decay-corrected count rates (per unit mass ofAs) for the standards prepared from the As2O3 solution, and thoseprepared from SRM 3103a, the relative standard uncertainty theAs2O3 solution was conservatively assumed to be equal to that ofSRM 3103a, or 0.15%. The combined relative standard uncertainty forconcentrations of the two standard solutions (1 s) was approximat-ed as 0.15%/√2, or 0.106%. The standard solutions were depositedgravimetrically onto filter papers. Since≈100 mg of solution wastransferred, and readings were made to 0.1 mg, the uncertainty perweighing is 0.1/√3 (rectangular distribution) or 0.058%. Two massdeterminations were required for each standard prepared (i.e.,before and after deposition), and four individual filters standardswere used in this analysis. Therefore the overall relative standarduncertainty for transfer of standard solutions is 0.058%·√2/√4 or0.041%. The uncertainty for the standards concentration wascombined in quadrature with that of the uncertainty for standardsdeposition to obtain standard uncertainty of the As content of thecomparator standards of 0.114%.2.7.2.2.2. Target isotope abundance ratio (unknowns/standards) — sinceAs is monoisotopic the standard uncertainty was 0%.

2.7.2.2.3. Basis mass (in this case sample area)All samples were cut with nearly identical sizes from the original

wafer. The micrometer used to measure the length and width of thesamples had a resolution of 0.001 mm. This micrometer was checkedwith a calibrated gauge, and found to be accurate to within 0.001 mm.Assuming a uniform (rectangular) distribution, the 0.001 mmabsolute accuracy was divided by √3 to obtain the standarduncertainty, or 0.00058 mm. Therefore the relative standard uncer-tainty for the accuracy basis for computing sample area (≈1 cm2) wasequal to [(1.000058 cm/1 cm)2−1]/100, or 0.012%. An additionaluncertainty resulted from the reproducibility of measuring the


dimensions of the wafers. Three replicate measurements were madeof the area of nine of the wafers, yielding an average relative standarddeviation of 0.046% for each measurement. Dividing by the squareroot of 27 yielded a measurement replication uncertainty of 0.009%,which was combined in quadrature with the micrometer accuracyuncertainty of 0.012% to obtain the total uncertainty for sample area of0.015%.

2.7.2.2.4. Sample blanksNo arsenic was seen in the blanks, with a detection limit of 50

counts. The samples each had approximately 200,000 counts in the559 keV peak of 76As, and so the blank detection limit (at 95%confidence) was 0.025% of the As content of the samples. The blankrelative standard uncertainty was estimated as half of the detectionlimit (2σ), or 0.013%.

2.7.2.3. Irradiation stage

2.7.2.3.1. Neutron fluence exposure differences (ratios) for unknownsamples compared to comparator standards (4 individual components)

2.7.2.3.1.1. Neutron fluence exposure differences (ratios) for unknownscompared to standards due to physical effects (fluence gradients)

This uncertainty was approximated from previous measurementsin the same irradiation facility from the previously observed relativestandard deviations (RSDs) observed for samples (of the samematerial) irradiated within a single irradiated rabbit. Since observedRSDs also include effects of other sources of variation, such ascounting statistics and material heterogeneity, the previous measure-ment with the smallest observed RSD among a relatively largenumber of samples (to minimize fortuitous agreement) was selectedfor evaluation. Previously, the smallest variation observed for samplesirradiated in RT-1 was 0.2% (1 s relative) for Br among 12 aliquants ofa coal SRM that entirely filled a rabbit. For the current (As)measurement, approximately one third of the length of the rabbitwas filled and so we divide the previously observed variation value by3. The overall uncertainty in the mean value due to geometrydifferences for the 10 samples for the As in silicon measurement wastherefore 0.2%/3/√10 or 0.021% relative. The overall uncertainty forthe mean of the 4 standards was 0.2%/3/√4 or 0.033%, and thecombined relative standard uncertainty (in quadrature) for samplesand standards was 0.039%.

2.7.2.3.1.2. Neutron fluence exposure differences (ratios) for unknownscompared to standards due to temporal effects (fluence variations withtime)

All unknown samples, standards and blanks were irradiatedtogether, so there are no temporal effects, and the uncertainty was 0%.

2.7.2.3.1.3. Neutron self shielding (absorption and scattering) effects –

the difference in the self shielding for each sample compared to eachstandard

The self-shielding for a finite cylinder [14] was calculated via:

ffinite cyl:≅R⋅fslab + L⋅f∞ cyl

R + L; with x≡ R⋅L

R + L∑ ð2� 18Þ

where R and L are the radius and the length of the cylinder, ∑ is themacroscopic cross section, and

fslab = 1− x2

ln 1= xð Þ− x2

32−γ

� �− x2

6ð2� 19Þ

f∞ cyl = 1−4x3

+x2

2ln 2 = xð Þ + x2

254−γ

� �ð2� 20Þ

and γ (Euler's constant) is 0.577216. Note that if using Eq. (2-19) tocalculate the self-shielding factor for a slab, the definition of x changesto T∑, where T is slab thickness. In a similar manner, if Eq. (2-20) isused to calculate the self-shielding factor for an infinite cylinder, xbecomes R∑ [14].

The resulting self-shielding factor (absorption) for each samplewas 0.9985, and for each standard was 0.9986. A correction factor of1.0001 (0.01% difference) was applied, and a standard uncertaintyequal to 10% of the correction, or 0.001% was approximated.Scattering effects contributing to self-shielding were not significantsince the cellulose standard used was only 0.2 mm thick, andscattering effects go to zero as thickness goes to zero. In addition,there are no significant scattering effects from the siliconmatrix of thesamples. Because this measurement employed nearly isotropicirradiation conditions, any potential changes in activation due toscattering within the sample stack were undetectable [20] 0.001%.

2.7.2.3.1.4. Neutron shielding (absorption and scattering) effects— effectson the average sample versus the average standard due to combinedeffects of neighboring samples and standards

The combined cumulative self-shielding effects for the multiplesamples and standards depended upon actual path length for eachneutron passing through samples or standards. Since the standardswere placed on the ends of the stack of samples as well as in the centerof the samples, we considered two boundary conditions: neutronspassing parallel and perpendicular to stack of samples and standards.The self-shielding for the two boundary conditions was calculatedusing a simple exponential function for neutron transmission. In onecase, the samples see 0.033% greater neutron exposure than do thestandards, and in the other case the samples see 0.05% less. Acorrection factor of 1.00009 (midpoint of two cases) applied, and theuncertainty calculated by dividing the range from the correction toeither limiting case (0.042%) by √3, or 0.024%.

2.7.2.3.2. Irradiation interferences (3 individual components)

2.7.2.3.2.1. Fast (high energy) neutron interferencesPossible interferences are from 76Se (n,p) or 79Br (n,α). No

activation products of Se or Br were observed; Se and Br detectionlimits were calculated (95% confidence level) with fast neutronfluence rates and appropriate fast neutron cross sections. Themaximum interference from Se=0.00069%, and the maximuminterference from Br=2×10−8%. Using half of maximum interfer-ences based on the 95% detection limits for the (1 s) standarduncertainties and combining in quadrature, the uncertainty for theinterference from fast neutron reactions was 0.0003%.

2.7.2.3.2.2. Fission neutron interferences76As cannot be made by fission reactions, therefore the standard

uncertainty was 0%.2.7.2.3.2.3. Double neutron capture interferences

76As cannot be made by a double neutron capture of a stablenuclide. Double neutron capture on 74Ge produces 76Ge, which isstable; therefore the standard uncertainty was 0%.

2.7.2.3.3. Effective cross section differences between samples andstandards

The uncertainty component and potential correction are due todifferences in the resonance integral due to removal of narrow, high-σresonance peaks. The largest resonance peak of 75As has a crosssection of 1000 b (10−21 cm2). Assuming that the entire resonancecross section for arsenic has a value of 10−21 cm2, which is a grossoverestimation, and that 14% of activation comes from resonanceneutrons, self-shielding calculation were performed in same manneras for normal neutron self-shielding (except for zero contributionfrom the matrix). In one case the samples see 0.0000013% greater


neutron fluence than standards, and in the other case the samples see0.000008% less. Since this is an overestimation no correction wasapplied, and the standard uncertainty was (estimated by dividing thelarger correction by √3 (uniform distribution between 0 and0.000008) or 0.000005%.

2.7.2.3.4. Irradiation losses and gains (4 individual components)

2.7.2.3.4.1. Hot atom transfer (losses and by recoil,nanometer movement)

Since the As was present as a near surface implant, evaluation ofthe potential transfer during irradiation via recoil was necessary. Anypotential gains were evaluated as part of the blank determination. Forpotential losses, the maximum possible recoil energy for theabsorption of a neutron by 75As is 380 eV. The maximum range ofAswith this energy in siliconwas calculated by the TRIM program [32]to be 2.2 nm+1.0 nm for straggling. Since the implant depth wasnominally 100 nm, both losses and uncertainty were considered to be0%.

2.7.2.3.4.2. Transfer of material through irradiation containerAs is not volatilized during neutron irradiation of a solid sample

under the irradiation conditions used, therefore the uncertainty was0%.

2.7.2.3.4.3. Sample loss during transfer from irradiation containerSince element of interest was below the surface, there is no

possibility of loss, and the uncertainty was 0%.

2.7.2.3.4.4. Target isotope burn up differencesSamples and standards were irradiated for the same time so there

is no burn up differences and the uncertainty was 0%.

2.7.2.3.5. Irradiation timing and decay correctionsSince the samples and standards were irradiated together no decay

correction was necessary. The standard uncertainty was 0%.

2.7.2.4. Gamma-ray spectrometry stage

2.7.2.4.1. Measurement replication or counting statistics) for unknownsamples

The standard uncertainty was just the observed relative standarddeviation of the mass fractions of the 10 samples divided by √10 or0.081%.

2.7.2.4.2. Measurement replication or counting statistics) for standardsSince only 4 individual standards were measured, the propagated

counting statistics uncertainty (1σ) for the 7 counts of the standardswas used, which was equal to 0.073%.

2.7.2.4.3. Corrections for radioactive decay for each measurement (effectsof timing and half-life uncertainties — 4 components)

2.7.2.4.3.1. Decay correction from end of irradiation to start of eachmeasurement

The half-life used for 76As was 1.097 day with a standarduncertainty (1 s) of 0.0011 day [54]. The unknown samples measuredin this study decayed from 0.81 day to 2.96 days prior to start ofcounting and no trend was observed for samples as function of decaytime during this interval. The standards decayed from 1.77 day to3.66 days prior to start of count. The difference between samples andstandards for the midpoints of these counts is 0.83 day. The decaycorrection for 0.83 day for a t1/2 of 1.097 day=1.6895, and the decaycorrection for 0.83 day for a t1/2 of (1.097+0.0011) day=1.6886which is equivalent to a relative difference of 0.053%. Thus themeasurement uncertainty due to the half-life uncertainty was 0.053%.

2.7.2.4.3.2. Clock time uncertaintySince all measurements were made to a preset clock time, the

effect of clock inaccuracy was 0%.

2.7.2.4.3.3. Live time uncertaintySince all measurements were made to a preset clock time,

uncertainties for live time may be significant for counts of shortduration. In this case, the multichannel analyzer system used recordsthe live time to the nearest centisecond. Thus each count has a live timeuncertainty of 0.005 s. Since live times for all counts were 7200 s (ormore in a few cases), the relative uncertainty for each count is 0.00007%.The combined live time uncertainty for samples (20 counts) andstandards (7 counts) was [(0.00007%/√20)2+(0.00007%/√7)2]1/2, or0.00003%.

2.7.2.4.3.4. Uncertainties due to count rate effects for conventionalcounting systems (2 individual components)

2.7.2.4.3.4.1. Inadequacy of live-time extensionThe dead time for this measurement was controlled entirely

by 76As after the 2.62 h 31Si decayed away. The samples decayedfrom 0.81 to 2.96 days prior to start of counts, corresponding to7.5 to 27 half lives of 31Si. The single nuclide decay correctionwas applied to samples and standards. This may provide a veryslight underestimation for the first few counts of unknowns, anda very slight overestimation for the last few counts of theunknowns. The corrections ranged from factors of 1.00025 to1.00285. Using a conservative estimate of 10% for eachcorrection, and an average correction of 0.067%, the standarduncertainty for the 20 counts of the samples was (.067%) (10%)/√20 or 0.001%.

2.7.2.4.3.4.2. Correction for pulse pileup lossesPileup rejection/live time correction was performed via hard-

ware, however, it became apparent through a comparison ofcounts of the same samples/standards at different dead times thata small degree of overcompensation was applied. This is notunexpected, since various types of electronic noise can beinterpreted by the rejection circuit as gamma rays arriving at theamplifier at the same time as real gamma rays. The overcompen-sation for the measurement was evaluated through subsequentcounts at different dead times using a high-accuracy pulser andcounting. The samples and standards for the As measurement wereboth counted over the same fractional dead time range of 0.5% to10%, and so no bias was introduced; however some additionalmeasurement uncertainty needed to be considered. The pulsercount rate was observed to increase by 0.52% over the dead-timerange of 0.5% to 10%. The midpoint of the overcompensation rangewas 0.26%. If we treat the overcompensation for each count ofsample or standard as a uniform (rectangular) distribution anddivide by √3 to obtain 1 s, we obtain a relative standarduncertainty of 0.150% per count. Thus the combined uncertaintyfor the mean of 20 counts of samples is 0.150%/√20 or 0.034%, andfor the mean of 7 counts of standards the uncertainty is 0.150%/√7or 0.057%. Combined in quadrature the total relative standarduncertainty was 0.066%.

2.7.2.4.4. Corrections for gamma-ray interferencesThe only possible significant interference for the 559 keV peak

of 76As in this measurement was from the 564 keV peak of 122Sb,which also has a 697 keV gamma ray. No 697 keV peak from122Sb was observed in the spectrum for the sample that wascounted for longest time. The detection limit at 95% confidencecorresponds to an interference of 0.000007% for the 76As peak.The uncertainty was estimated as half of this 2σ detection limit,or 0.000004%.

Table 2.14Uncertainty evaluation for the determination of arsenic in silicon, SRM 2134.

Uncertainty component ui (%)

Pre-irradiation stageElemental content of standards

Elemental content of standard solutions 0.106Amount of standard solutions used 0.041

Target isotope abundances 0Basis mass (or other basis unit) 0.015Blank (1 — relative blank) — see Eq. (2-16) to permitcombination in quadrature

0.013

Irradiation stageNeutron fluence exposure differences (ratios) betweensamples and standardsIrradiation geometry differences (ratios) between samplesand standards

0.039

Neutron fluence exposure differences due to temporaleffects

0

Neutron self shielding differences (for individual samplesand standards)

0.001

Neutron shielding differences (effects of neighboringsamples/standards)

0.024

Irradiation interferencesFast neutron 0.0003Fission neutron 0Double neutron capture 0

Effective neutron cross section differences between samplesand standards

0.000005

Irradiation losses and gainsHot atom transfer (losses and gains by recoil, nanometermovement)

0

Transfer of material through irradiation container 0Sample loss during transfer from irradiation container 0Target isotope burn up (for samples and stds. irradiatedunder diff. conditions)

0

Irradiation timing and decay corrections (if samples andstandards irradiated separately)

0

Post irradiationMeasurement replication (or counting statistics) of samples 0.081Measurement replication (or counting statistics) of standards 0.073Corrections for radioactive decay (due to timing and half-lifeuncertainties for each measurement)Decay correction to start of count 0.053Clock time uncertainty 0Live time uncertainty 0.00003Count-rate effects for each measurementInadequacy of live-time extension for very short lived nuclides 0.001Corrections for pulse pileup 0.066

Corrections for gamma-ray interferences 0.000004Corrections for counting efficiency differences

Physical differences in shape and thickness of samples andstandards

0.009

Gamma-ray self absorption differences between samplesand standards

0.004

Peak integration biases 0.019Perturbed angular correlation (almost never encountered) 0Losses during chemical decomposition and separation (for RNAA) 0Relative combined uncertainty (uc) 0.19%k-value 2.04Relative expanded uncertainty 0.38%


2.7.2.4.5. Corrections for counting efficiency differences (2 individualcomponents)

2.7.2.4.5.1. Effects resulting from physical differences in size and shape ofsamples versus standards

All counts were made at a distance of 10 cm from the detector. Thesample thickness was 0.00002 cm (surface implant) and the standardthickness was 0.02 cm with the As distributed uniformly. The averagegamma-ray interaction with the detector used was estimated to occur1 cm below the detector endcap. The correction for the (midpoint)counting geometry difference between samples and standards was(11.01/11.00001)2 or 1.00182, which was applied. This geometryestimate was tested by counting one sample in two orientations: withthe implanted face up and with the implanted face down. Theobserved ratio of corrected counting rates was 1.014, with a 1σuncertainty of 0.004 from counting statistics alone. The expected ratiofrom a 1/r2 model of counting efficiency, as described above, gives aratio 1.013, in good agreement with the observed value. If thestandard uncertainty on the interaction depth were estimated to be50%, or 0.5 cm, the correction factor would become (10.51/10.500001)2 or 1.00191, 0.009% different. Thus the uncertainty ongeometry correction was 0.009%.

2.7.2.4.5.2. Corrections for gamma-ray self-absorptionThe calculated self-absorption factor for the 559 keV gamma ray

within the 0.02 cm cellulose standard is 0.99962. The appliedcorrection was therefore 0.038%. If we estimate the relativeuncertainty as 10% of the correction it is equivalent to 0.004%. Theattenuation factor for the 559 keV gamma-ray through the0.00002 cm silicon layer on top of the As in the samples (surfaceimplant) is 0.9999985. The correction is therefore≈10−4%, and if weagain estimate the uncertainty for the correction as 10% of thecorrection it is equivalent to 10−5% relative. Combining these twouncertainties in quadrature, the relative standard uncertainty forgamma-ray self-absorption was 0.004%.

2.7.2.4.6. Potential bias due to peak integration methodThe spectra for samples and standards were nearly identical

(essentially only 76As). Peak integration was accomplished by achannel-by-channel summation using the same peak and baselineregions (background channels) for both the samples and thestandards. This summation method was essentially the same asused previously for high-accuracy gamma-spectrometry measure-ments of uranium isotopic compositions in bulk U3O8 standards [55].In that study, the mean relative difference between the gammaspectrometry measurements and the ultimately certified values for 5sets of materials (at different isotopic ratios) was 0.033% (0.012% to0.090%). We conservatively estimated the total peak integrationuncertainty for the current arsenic study as equivalent to entire(average) difference for the U isotopic study. The relative standarduncertainty was calculated assuming a rectangular distribution anddividing by √3 to obtain a value of 0.019%.

2.7.2.4.7. Potential bias due to perturbed angular correlations (γ-raydirectional effects)

76As is not subject to perturbed angular correlation effects, andboth samples and standardswere counted under identical geometries,therefore the uncertainty was 0%.

2.7.2.5. Potential losses during chemical decomposition and processingSince radiochemistry was not performed for this measurement,

the uncertainty was 0%.

2.7.2.6. Combined standard uncertainty and expanded uncertaintyThe combined standard uncertainty for this measurement was

calculated by combining each of the individual uncertainty compo-

nents in quadrature. Based on the effective degrees of freedom, ak value of 2.04 was chosen, and the expanded uncertainty was 0.38%.Results are summarized in Table 2.14.

2.7.3. Kragten spreadsheet approach (for one sample and one standard) –general considerations and example

When a measurement equation f(x1…xn) is at all complicated,calculating the propagation of uncertainties can require substantialskill in calculus to construct all the required derivatives. Kragten [56]has proposed a straightforward spreadsheet method in whichstandard uncertainties Δx replace derivatives dx. This numerical

Fig. 2.4. Example of uncertainty calculation for mass fraction using the Kragten procedure.

Fig. 2.5. Calculation of A0 uncertainty for the unknown sample in the example of the Kragten procedure.


procedure is especially useful in studying the sensitivity of individualsources of uncertainty to the final result [57].

As an example, in Fig. 2.4 the Kragten procedure has been applied tothe simplest form of the INAA equation, inwhich themass fractionwx iscalculated from the fundamental measurement equation.

Fig. 2.4 illustrates the uncertainty calculation for one sample ofarsenic implant in silicon, and one comparator of an evaporatedstandard arsenic solution taken from the example of the manualcalculation described in Section 2.7.2. The calculation ofwx is performedfive times, oncewith all four variables asmeasured and again with eachparameter incremented by one standard uncertainty u. Examination ofthe four variance contributions shows clearly that the countingprecision of the unknown sample is the dominant contributor to theoverall uncertainty, as it should in a well-designed measurement. Thecombined relative standard uncertainty (shown in Fig. 2.4) is 0.35%.

Calculations of uncertainties for both the A0 value of the sampleand the A0 value of the standard are approached in a similar manner,conveniently on separate pages of the spreadsheet. Fig. 2.5 shows theuncertainty calculation of A0 for the unknown sample.

In this version of the A0 equation there are seven parameters, so thecalculation is performed eight times. For this example, significantuncertainty in A0 once again comes from only counting statistics of the

sample.Note that theA0 equation above is just thegeneral equationgivenpreviously with FP and Fltc(s) replaced with an explicit pileup correction,andusing the live-timeextensioncorrection for a singledecayingnuclide.

For all its convenience in identifying themost important sources ofuncertainty in an analytical process, the Kragten method has severaldrawbacks. Compensating errors and other kinds of covariance areignored, and the experimental design that is implicitly modeled (onevariable changed at a time) is not themost efficient one for optimizinga multivariate experiment. When a large numbers of parameters areinvolved, or when multiple samples and standards are involved, thespreadsheets become unwieldy. The method is further discussed inthe Eurachem quality manual [58]. A detailed uncertainty budget fork0 NAA has been constructed by this procedure [59].

2.7.5 Partial derivatives approach (for one sample and one standard) –

general considerations

Calculation of uncertainty

The combined standard uncertainty of a quantity of interest, themeasurand y, is the effect of all variables' uncertainties on theuncertainty of the measurement function based on them. Thus the

image of Fig.�2.4

image of Fig.�2.5


combined standard uncertainty of y, uc(y), is calculated in terms ofcomponent uncertainties, u(xi):

ucðy x1;…xnð Þ =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑n

i=1

∂y∂xi

� �2

u xið Þð Þ2s

; ð2� 21Þ

where y(x1,x2,…xn) is a function of several parameters x1,x2,…xn.Each variable's contribution is just the square of the associateduncertainty expressed as the standard deviation multiplied by thesquare of the associated partial derivative.

The above Eq. (2-21) is valid only if the quantities xi areindependent (uncorrelated), the distribution of each xi is a Gaussiandistribution, and if u(xi)≪xi. In most cases Eq. (2-21) is used evenwhen the aforementioned restrictions are not met. (Deviations ofparameter distributions from the Gaussian distribution are not soimportant. According to the central limit theorem of statistics, thedistribution for the values of the derived quantity y approaches theGaussian distribution as the number of individual quantities xiincreases, independent of the details of the distribution.)

The expanded uncertainty u is obtained by multiplying thecombined standard uncertainty by a suitable coverage factor kα. Theunknown value of themeasurand is believed to lie in the interval y±uwith a confidence level of approximately α.

Applying this calculation to a slightly modified form of activationequation (Eq. (2-22))

wx unkð Þ = wx stdð Þ⋅A0 unkð ÞA0 stdð Þ

⋅Rθ⋅Rϕ⋅Rσ ⋅Rε−B

!⋅

mstd

αunk⋅munk; ð2� 22Þ

with B=blank, and α=appropriate corrections to mass leads tothe following expressions for the uncertainty. The combined uncer-

Table 2.15Partial-derivative equation evaluations of relative standard uncertainties, and an evaluationusing one unknown sample and one comparator standard.

Parameter Source Standard uncertainty Type A/B

Gravimetrywx(std) (%) Purity uwx stdð Þ =

up

2ffiffiffi3

p B

mu (kg) Balance um =ubalance

kffiffiffin

p A

ms (kg) Aα Between units um =

udry

kffiffiffin

p A

A0 calculationsCx,u Poisson statistics uN =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiN + 2B

pA

Cx,s Aλ (s−1) Literature values uλ =

δλ2ffiffiffi3

p 1 + λtd−tLftLð Þ B

td(unk) (s) Time tag utd =δutd

2ffiffiffi3

p λ B

td(std) (s) B

tL(unk) (s) Time tag utL =δutL

2ffiffiffi3

p ftL B

tL(std) (s) BIrradiation and counting

Rθ Literature values uRθ =δθ2ffiffiffi6

p B

Rϕ Absorption, flux gradient uRϕ =δϕ2ffiffiffi3

p B

Rσ Neutron spectrum uRσ =δσϕ

2ffiffiffi3

p B

Rε Geometry, density uRε =δσε

2ffiffiffi3

p B

Measurement blank

B Measured uB =

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑n

i=1yB;i−B� �2n−1ð Þ

vuuutB

tainty uc is a function of the uncertainties of the independentparameters M.

uc = f wx stdð Þ;A0 unkð Þ;A0 stdð Þ;Rθ;Rϕ;Rσ ;Rε ; B;mstd;munk;αunk

� �ð2� 23Þ

u2wx unkð Þ = ∑

M

i=1

∂f∂xi

� �2

u2xi

ð2� 24Þ

u2wx unkð Þ

=∂f

∂wx stdð Þ

!2

A0ðunkÞ;A0ðstdÞ;Rθ;Rϕ;Rσ ;Rε; B;mstd;munk;αunk u2wx stdð Þ

� �

+∂f

∂A0 stdð Þ

!2

wx stdð Þ;A0ðunkÞ;A0ðstdÞ;Rθ;Rϕ;Rσ ;Rε ;B;mstd;munk;αunk uA0ðunkÞ

� �2+ …

ð2� 25Þ

with A0 =C⋅λeλtd1−e−λtL

, and tL=live time of count with appropriate

corrections applied.

Let ftL =λe−λtL

1−e−λtL, then

uA0

A0

� �2

=uC

C

� �2+

uλ

λ

� �21 + λtd−tL⋅ftLð Þ2 + u2

tdλ2 + u2

tL f2tL : ð2� 26Þ

Quantification of uncertainty

Not all from the above-mentioned uncertainty components willcontribute significantly to the combined uncertainty. An initialevaluation should be made to identify the relevant uncertainties inaccordancewith the experiment that is to be evaluated, for example isit an individual measurement or a series of similar measurements that

of the relative combined standard uncertainty for the arsenic in silicon measurement

Description ui

Mass fraction in primary assay standard 0.033%

Mass of sample used 0.015%

Mass of primary assay standard used 0.121%Standard uncertainty of n dry mass determinations n/a

Number of counts in indicator gamma-ray peak for sample 0.251%Number of counts in indicator gamma-ray peak for standard 0.189%Decay constant 0.026%

Decay time until start of measurement for sample 0.00021%

Decay time until start of measurement for standard 0.00021%

Elapsed time of measurement for sample 0.0044%

Elapsed time of measurement for standard 0.0090%

Ratio of isotopic abundances for sample and standard n/a

Ratio of neutron fluences (including fluence gradient,self absorption and scattering)

0.033%

Ratio of effective cross section if neutron spectrum shapediffers between sample and standard

0.0004%

Ratio of counting efficiencies (including geometry, gamma-rayself shielding and counting effects)

0.069%

Amount of analyte in blank in g; most INAA procedures canbe carried out essentially blank free. An estimate from the limitof detection is included.

0.013%


are combined into one result. Table 2.15 assumes the calculation of acombined uncertainty from a single measurement of an unknownsample that is compared to a single measurement of a standard. Foreach component a standard uncertainty is calculated based on likelydistributions of the value.

2.7.6. Example of the partial derivatives approach

Data from a single unknown sample and a single standard from thearsenic in silicon experiment described in Section 2.7.2 wereevaluated using the partial derivative approach and the results arelisted in Table 2.15. The combined relative standard uncertainty wascalculated by combining, in quadrature, all ui values from the lastcolumn of Table 2.15, and was found to be 0.35%, the same as foundusing the Kragten spreadsheet approach described in Section 2.7.3.

2.7.7. — Monte Carlo approach

The use of a Monte Carlo method for estimating the uncertainty ofmeasurement is described in Supplement 1 [60] to the GUM [61]. Thisapproach is especially useful if, e.g., it is difficult or inconvenient toprovide the partial derivates of the model, or if the probability densityfunctions of the input quantities are asymmetric. These (and otherconditions, see [59]), are not applicable with the use of comparatorNAA; therefore this approach will not been discussed in detail here.However, the Monte Carlo method can be useful if the measurementequation is complicated, as for the k0-NAA method, since theuncertainty of the parameter α appears as an exponent.

2.8. References for Chapter 2

[1] ASTM, Standard Practice for Determining Neutron Fluence, Fluence Rate, andSpectra by Radioactivation Techniques (E261). ASTM International, WestConshohocken, PA, 1998.

[2] R.M. Lindstrom, R. Zeisler, E.A. Mackey, P.J. Liposky, R.S. Popelka-Filcoff, R.E.Williams, Neutron irradiation in activation analysis: a new rabbit for the NBSR,J. Radioanal. Nucl. Chem. 278 (2008) 665–669.

[3] R.R. Greenberg, Accuracy in standards preparation for neutron activationanalysis, J. Radioanal. Nucl. Chem. 179 (1994) 131–139.

[4] J.R. Moody, R.R. Greenberg, K.W. Pratt, T.C. Rains, Recommended inorganicchemicals for calibration, Anal. Chem. 60 (1988) 1203A–1218A.

[5] K. Heydorn, E. Damsgaard, Gains or losses of ultratrace elements inpolyethylene containers, Talanta 29 (1982) 1019–1024.

[6] C. Yonezawa, M. Hoshi, Blank analysis of quartz container for instrumentalneutron activation analysis, Bunseki Kagaku 39 (1990) 25–31.

[7] M.E. Wieser, Atomic weights of the elements 2005, Pure & Appl. Chem. 78(2006) 2051–2066.

[8] R.F. Fleming, R.M. Lindstrom, Limitations on the accuracy of sulfurdetermination by NAA, Trans. Am. Nucl. Soc. 41 (1982) 223.

[9] J.R. de Laeter, J.K. Böhlke, P. De Bièvre, H. Hidaka, H.S. Peiser, K.J.R. Rosman, P.D.P. Taylor, Atomic weights of the elements. Review 2000, Pure & Appl. Chem. 75(2003) 683–800.

[10] J.R.D. Copley, Scattering effects within an absorbing sphere immersed in a fieldof neutrons, Nucl. Instrum. Methods A307 (1991) 389–397.

[11]M. Blaauw, The derivation and proper use of Stewart's formula for thermal neutronself-shielding in scattering media, Nucl. Sci. Eng. 124 (1996) 431–435.

[12] J.C. Stewart, P.F. Zweifel, Self-shielding and Doppler effects in the absorption ofneutrons, Prog. Nucl. Energy, Ser. 1 3 (1959) 331–359.

[13] J. Salgado, I.F. Gonçalves, E. Martinho, Development of a unique curve forthermal neutron self-shielding factor in spherical scattering materials, Nucl.Sci. Eng. 148 (2004) 426–428.

[14] R.F. Fleming, Neutron self-shielding factors for simple geometries, Int. J. Appl.Rad. Isot. 33 (1982) 1263–1268; R.M. Lindstrom andR. F. Fleming, Neutron Self-Shielding Factors for Simple Geometries, Revisited, Chem. Anal. (Warsaw) 53(2008), 855-859.

[15] J. Gilat, Y. Gurfinkel, Self-shielding in activation analysis, Nucleonics 21 (8)(1963) 143–144.

[16] C. Chilian, J. St-Pierre, G. Kennedy, Dependence of thermal and epithermalneutron self-shielding on sample size and irradiation site, Nucl. Instrum.Methods A564 (2006) 629–635.

[17] E. Martinho, I.F. Gonçalves, J. Salgado, Universal curve of epithermal neutronresonance self-shielding factors in foils, wires and spheres, Appl. Radiat.Isotop. 58 (2003) 371–375.

[18] E. Martinho, J. Salgado, I.F. Gonçalves, Universal curve of the thermal neutronself-shielding factor in foils, wires, spheres and cylinders, J. Radioanal. Nucl.Chem. 261 (2004) 637–643.

[19] C. Chilian, J. St-Pierre, G. Kennedy, Complete thermal and epithermal neutronself-shielding corrections for NAA using a spreadsheet, J. Radioanal. Nucl.Chem. 278 (2008) 745–749.

[20] R.M. Lindstrom, R.R. Greenberg, D.F.R. Mildner, E.A. Mackey, R.L. Paul, Neutronscattering andneutron reaction rates. in: B. Smodis (Ed.), Second International k0Users Workshop, Jozef Stefan Institute, Ljubljana, Slovenia, 1997, pp. 50–53.

[21] R. Zeisler, R.M. Lindstrom, R.R. Greenberg, Instrumental neutron activationanalysis: a valuable link in chemical metrology, J. Radioanal. Nucl. Chem. 263(2005) 315–319.

[22] R. M. Lindstrom, R.F. Fleming, in: J.R. Vogt (Ed.), Proc. 3rd Int. Conf. Nucl.Methods in Envir. and Energy Res. (CONF-771072), U. S. Dept. of Energy,Washington, 1977, pp. 90–98.

[23] A. Calamand, Handbook on Nuclear Activation Cross-Sections, IAEA, Vienna,1974, pp. 273–324.

[24] S. Landsberger, Update of uranium fission interferences in neutron activationanalysis, Chem. Geol. 77 (1989) 65–70.

[25] R. Zeisler, R.R. Greenberg, Ultratrace determination of platinum in biologicalmaterials via neutron activation and radiochemical separation, J. Radioanal.Chem. 75 (1982) 27–37.

[26] R. Zeisler, R.R. Greenberg, in: P. Brätter, P. Schramel (Eds), Trace element analyticalchemistry in medicine and biology, de Gruyter, Berlin, 1988, pp. 297–303.

[27] R.M. Lindstrom, G.J. Lutz, B.R. Norman, High-sensitivity determination ofiodine isotopic ratios by thermal and fast neutron activation, J. TraceMicroprobe Tech. 9 (1991) 21–32.

[28] J. St-Pierre, G. Kennedy, Effects of reactor temperature and samplemass on theactivation of biological and geological materials with a SLOWPOKE reactor,Biol. Trace Elem. Res. 71–72 (1999) 481–487.

[29] I.F. Gonçalves, E. Martinho, J. Salgado, Monte Carlo calculation of epithermalneutron resonance self-shielding factors in foils of different materials, Appl.Radiat. Isotop. 56 (2002) 945–951.

[30] G.V. Iyengar, Loss of sample weight during long time reactor irradiation ofbiological materials, J. Radioanal. Chem. 84 (1984) 201–206.

[31] J. Kiem, G. Rumpf, K. Beyer, G. Koslowski, Weight loss as error source in neutronactivation analysis of biological samples, Fresen. J. Anal. Chem. 328 (1987) 221–225.

[32] J.F. Ziegler, J.P. Biersack, U. Littmark, The stopping and range of ions in solids,Pergamon, New York, 1985.

[33] R.R. Greenberg, R.F. Fleming, R. Zeisler, High sensitivity neutron activationanalysis of environmental and biological standard reference materials,Environ. Internat. 10 (1984) 129–136.

[34] S. Pommé, A. Simonits, R. Lindstrom, F. De Corte, P. Robouch, Determination ofburnup effects in 197Au(n,γ)198Au prior to reactor neutron field characterisa-tion, J. Radioanal. Nucl. Chem. 245 (2000) 223–227.

[35] K. Debertin, R.G. Helmer, Gamma- and X-ray spectrometry with semiconduc-tor detectors, North-Holland, Amsterdam, 1988.

[36] R.M. Lindstrom, M. Blaauw, R.F. Fleming, The half-life of 76As, J. Radioanal.Nucl. Chem. 257 (2003) 489–491.

[37] R.M. Lindstrom, M. Blaauw, M.P. Unterweger, The half-lives of 24Na, 43K, and198Au, J. Radioanal. Nucl. Chem. 263 (2005) 311–313.

[38] R.M. Lindstrom,R. Zeisler, R.R.Greenberg,Accuracyanduncertainty in radioactivitymeasurement for NAA, J. Radioanal. Nucl. Chem. 271 (2007) 311–315.

[39] A. Wyttenbach, Coincidence losses in activation analysis, J. Radioanal. Chem.8 (1971) 335–343.

[40] R.M. Lindstrom, R.F. Fleming, Dead time, pileup, and accurate gamma-rayspectrometry, Radioact. Radiochem. 6(2) (1995) 20–27.

[41] D. De Soete, R. Gijbels, J. Hoste, Neutron activation analysis, Wiley-Interscience, London, 1972.

[42] P.R. Bevington, Data reduction and error analysis for the physical sciences,McGraw-Hill, New York, 1969.

[43] R.M. Lindstrom, SUM and MEAN: standard programs for activation analysis,Biol. Trace Elem. Res. 43–45 (1994) 597–603.

[44] G.P. Westphal, Review of loss-free counting in nuclear spectroscopy,J. Radioanal. Nucl. Chem. 275 (2008) 677–685.

[45] G.P. Westphal, On the performance of loss-free counting — a method for real-time compensation of dead-time and pileup losses in nuclear pulsespectroscopy, Nucl. Instrum. Methods 163 (1979) 189–196.

[46] S. Pommé, A plausible mathematical interpretation of the ‘variance’ spectraobtained with the DSPECPLUS digital spectrometer, Nucl. Instrum. MethodsA482 (2002) 565–566.

[47] L.A. Currie, Limits for qualitative detection and quantitative determination:application to radiochemistry, Anal. Chem. 40 (1968) 586–593.

[48] J.H. Hubbell, S.M. Seltzer, Tables of X-ray mass attenuation coefficients andmass energy-absorption coefficients 1 keV to 20 MeV for elements Z=1 to 92and 48 additional substances of dosimetric interest, NISTIR 5632, Natl. Inst.Stds. & Tech., Gaithersburg, 1995, p. 111.

[49] M.J. Berger, J.H. Hubbell, S.M. Seltzer, J. Chang, J.S. Coursey, R. Sukumar, D.S.Zucker, XCOM: Photon cross section database. NIST, Gaithersburg, MD.,1998, available online at http://www.nist.gov/pml/data/xcom/index.cfm.


[50] M. de Bruin, P.Bode, Application of gamma–gamma directional correlationmeasurements in trace element research, Analusis 11 (1983) 49–54.

[51] M. de Bruin, P.J.M. Korthoven, The influence of the chemical form ofradionuclides on the shape of the gamma-ray spectrum, Radiochem. Radio-anal. Lett. 21 (1975) 287–292.

[52] K. Yoshihara, H. Kaji, T. Mitsugashira, S. Suzuki, Chemical and environ-mental effects on γ-ray sum peak intensity of 111In due to perturbedangular correlation of cascade γ-emission, Radiochem. Radioanal. Lett. 58(1983) 9–16.

[53] R.R. Greenberg, R.M. Lindstrom, D.S. Simons, Instrumental neutron activationanalysis for certification of ion-implanted arsenic in silicon, J. Radioanal. Nucl.Chem. 245 (2000) 57–63.

[54] J.F. Emery, S.A. Reynolds, E.I. Wyatt, G.I. Gleason, Half-lifes of radionuclides—IV, Nucl. Sci. Eng. 48 (1972) 319–323.

[55] R.R. Greenberg, B.S. Carpenter, High accuracy determination of 235U innondestructive assay standards by gamma-ray spectrometry, J. Radioanal.Nucl. Chem. 111 (1987) 177–197.

[56] J. Kragten, Calculating standard deviations and confidence intervals with auniversally applicable spreadsheet technique, Analyst 119 (1994) 2161–2166.

[57] C.E. Rees, Error propagation calculations, Geochim. Cosmochim. Acta 48 (1984).[58] S.L.R. Ellison, M. Rosslein, A. Williams (Eds.), Quantifying Uncertainty in

Analytical Measurements (2nd ed.; QUAM:2000.P1), Eurachem/CITAC, 2000.[59] P. Robouch, G. Arana, M. Eguskiza, S. Pommé, N. Etxebarria, Uncertainty

budget for k0-NAA, J. Radioanal. Nucl. Chem. 245 (2000) 195–197.[60] Joint Committee for Guides in Metrology, Evaluation of measurement data –

Supplement 1 to the “Guide to the expression of uncertainty inmeasurement” –Propagation of distributions using aMonte Carlomethod (2008) JCGM101:2008(ISO/IEC Guide 98-3-1).

[61] Joint Committee for Guides in Metrology, Evaluation of measurement data —

Guide to the expression of uncertainty in measurement (2008) JCGM 101:2008(ISO/IEC Guide 98-3.

2.9 List of Symbols used in Chapter 2

A count rateA0 decay corrected count rateC net counts in γ-ray peakfp correction for pulse pileup (general case)fltc correction for inadequacy of live time extension (general case)fϕ correction for neutron self shielding (general case)FP calculated correction factor for pulse pileupFltc calculated correction factor for inadequacy of live timeextensionFγ gamma-ray attenuation factorϕ neutron fluence rateλ decay constant (ln 2/t1/2)m total mass of the unknown sample standard (munk, mstd)mx mass of element x in the unknown sample or standard (mx(unk),

mx(std))μ gamma-ray attenuation coefficient

μ/ρ mass attenuation coefficientN0 Number of target atoms originally presentNtrans Number of target atoms transmutedP Pileup constant for software correctionRθ ratio of isotopic abundances for unknown and standardRϕ ratio of neutron fluences (including fluence drop off, self

shielding, and scattering)Rσ ratio of effective cross section differences (if neutron

spectrum shape changes)Rε ratio of counting efficiencies (differences due to geometry

and γ-ray self-shielding)ρ densityσ neutron cross sectionT thickness of sample or standardtc clock time of counttd decay time to start of countti irradiation time (duration)tL live time of countt1/2 half-lifeθ isotope abundanceui standard uncertainty for uncertainty component (i)wx mass fraction of element x in the unknown sample or

standard (wx(unk), wx(std))

Symbols used for evaluation of neutron self-shielding correctionsin the example of the determination of arsenic in silicon

L length of cylinderR radius of cylinder∑ macroscopic cross sectionT thickness of slabγ Euler's constant

Symbols used for discussion of hardware corrections for Loss-Freeor Zero Dead Time systems

B blankM channel contents of a multichannel analyzerN analog-to-digital conversions into that channel andW weighting factorsdM/M statistical uncertainty of the channel with content MdN/N statistical uncertainty for the number of analog-to-digital

conversions into channel with content MdW/W relative statistical (uncertainty) of the weighting

Chapter 3. Performance of neutron activation analysis laboratories in CCQM key


comparisons and pilot studies

Elisabete A. De Nadai Fernandes *, Márcio Arruda Bacchi

Centro de Energia Nuclear na Agricultura, Universidade de São Paulo
Avenida Centenário 303, 13416-000 Piracicaba, SP, Brazil
3.1. Introduction

Table 3.1Overview of all pilot studies and key comparisons (with reference to their organizer) inwhich NAA laboratories participated since the year 2001. The authors' laboratory(CENA/USP) participated in pilot studies and key comparisons listed in this table,except for P33, P62, K44, P74, and P86.

Year studybegan

CCQM key comparison (K) or pilot study (P) and organizing NMI

2001 –P11 arsenic in shellfish, NIST–P29 cadmium and zinc amount content in rice, IRMM–K24 cadmium amount content in rice, IRMM–P34 constituents in Al alloy, BAM

2002 –K31 arsenic in shellfish, NIST2003 –P39 As, Hg, Pb, Se and methylmercury in tuna fish, IRMM

–P33/P56 boron in Si, PTB–K33/P56 minor elements in steel, NMIJ/NIST/BAM

2004 –P34.1 constituents of an aluminum alloy, BAM–K42 constituents of an aluminum alloy, BAM–P39.1 As, Hg, Pb, Se and methylmercury in salmon, IRMM–K43 As, Hg, Pb, Se and methylmercury in salmon, IRMM–P62 trace analysis of high purity nickel, BAM–P65 chemical composition of clay, CENAM

2005 –P64 nonfat soybean powder, NRCCRM–P66 key metals in fertilizer, NIST–K44/P70 trace metals in sewage sludge, IRMM–P74 composition of fine ceramics, NMIJ

2006 –K49/P85 essential and toxic elements in bovine liver, NIST

The CCQM, after a PrimaryMethods Symposium in April 2000 at theBIPM in Sèvres, France, concluded that insufficient evidence wasavailable on the actual performance of NAA at the highest metrologicallevel (as reflected by key comparisons) to accept the claim that NAAmeets all the requirements in the definition of a primary ratio method.Both the CCQM and its Inorganic Analytical Working Group (IAWG)questioned whether multiple laboratories could make NAA measure-mentswith thehighestmetrological properties, and in particular submitresults in CCQM comparisons that demonstrated agreements anduncertainties similar to those demonstrated by IDMS; IDMS had beendesignated by the CCQM in 1997 as one of the potentially primary ratiomethods for determining amounts of substance. Shortly after thePrimary Methods Symposium, the Inorganic Analytical Working Groupbegan organizing pilot studies and key comparisons on matrices andmeasurands that were appropriate for NAA measurements, and anumber of NAA laboratories were encouraged to participate.

NAA is not available at most national metrology institutes (NMIs),which distinguishes it somewhat from other methods for determiningamount of substance (such as IDMS or AAS). This is largely due to lackof access to nuclear research reactors, radiological laboratories, andtrained personnel. It would be difficult drawing conclusions aboutNAA's performance from results of only the few NMIs with such NAAlaboratories in their facilities. However, the participation of selectedNAA laboratories in pilot studies, and in particular those pilot studiesorganized in parallel to many key comparisons, enabled a directcomparison of the results of NAA and IDMS laboratories. It should benoted that unless these laboratories were officially designated by anNMI, their results could not be included in the BIPM MRA Appendix Bnor used for establishing the key comparison reference value (KCRV).

In the period 2000–2006, 13 NAA laboratories have participated inpilot studies and key comparisons (Table 3.1). Except for a few cases,whichare identifiedbelow, the laboratoriesused the instrumental (non-destructive) variety of NAA (instrumental neutron activation analysis orINAA). These NAA results have been used to evaluate the method'spotential as a primary ratio method by comparing NAA's performancewith the performance of a previously-recognized primary ratiomethod,i.e. IDMS. The comparison is based on agreement with accepted values(i.e., the KCRV if available), magnitude and completeness of theestimated uncertainty budgets, and dispersion of the results amonglaboratories operating the same method.

3.2. NAA performance of various laboratories: mono-isotopicelements

The first opportunity for NAA laboratories to demonstrate theperformance of the method occurred in 2001, via the CCQM PilotStudy P11 (CCQM-P11) “Arsenic in Shellfish” [1] followed in 2002 bythe associated CCQM Key Comparison K31 (CCQM-K31) “Arsenic inShellfish” [2]. Selection of arsenic as a measurand was largely due toits importance as a common, toxic element, and the lack of a primarymethod available for its determination. It is not possible to determinearsenic by IDMS since the element is mono-isotopic.

⁎ Email address: [email protected].

In total eleven laboratories participated in CCQM-P11, six of themused NAA. In the CCQM-K31, a total of eight laboratories participated.Three laboratories used NAA including two NMIs, and one universityaffiliated laboratory (the authors’ laboratory, CENA/USP), as anunofficial participant. The results are presented in Figs. 3.1 and 3.2,respectively. Dashed lines in these and subsequent figures representthe best estimate of the central value uncertainty (k≈2) for eachstudy.

The results from the CCQM-P11 demonstrated good agreementamong the six NAA laboratories. The observed relative standarddeviation was 1.5%, compared to 5.9% for the five non-NAAlaboratories. The reported measurement uncertainties for the NAAlaboratories were in general similar to the uncertainties reported bylaboratories employing other methods (ICP-AES, HR-ICP-MS, GFAASand FI-HGAAS).

The observed relative standard deviation among the three NAAlaboratories participating in CCQM-K31 was 1.4%, and considerablysmaller than the observed relative standard deviation of 8.2% for theresults reported by laboratories employing other methods (GFAAS,ICPMS, and FI-HG-GFAAS). In addition, the three NAA values appeartowards the middle of all reported values. It can also be seen fromFig. 3.2 that the estimated measurement uncertainties of the threeNAA laboratories were similar to, and in some cases smaller than, theones reported by the non-NAA laboratories.

The results from thesefirst two studies demonstrated that a significantnumber of NAA laboratories, distributed among three continents, eachwith different levels of metrological expertise, different nuclear reactors,and different NAA instrumentation can provide results that are in good

–P86 total Se and Se–methionine in yeast, LGC/NRC

0.11

0.12

0.13

0.14

0.15

INAA

INAA INAA

INAA

INAA

INAA

mm

ol k

g-1

-20

-10

0

10

20As

Per

cent

age

diffe

renc

e (%

)

Fig. 3.1. Results from CCQM-P11 “Arsenic in shellfish”, adapted from [1].

KRISSNRC

CENANIST

IAEA-1IMGC

NMIJIAEA-2

0.09

0.10

0.11

0.12

0.13

INAA

INAA

INAAmm

ol k

g-1

-20

-10

0

10

20As

Per

cent

age

diffe

renc

e (%

)

Fig. 3.2. Results from CCQM-K31 “Arsenic in shellfish”, adapted from [2].


agreementwitheachother andwithotheranalyticalmethods. In addition,the observed relative standard deviations among the NAA laboratories, aswell as themagnitudesof their reporteduncertainty statements, appearedto be similar to those observed for IDMS measurements in other CCQMstudies of trace element content in complex matrices.

3.3. NAA performance compared to IDMS performance:initial studies of the determination of trace element content incomplex matrices

The next step was to directly compare the performance of NAA andIDMS in the same study. This first became possible via CCQM-K24/P29,

CENAMLN

E

VNIIM

KRISS

EMPA

LGC

NMIJ

PTBNARL

NIST-1

NMi

12

13

14

15

16

17

IDMS

Cd

nmol

g-1

Fig. 3.3. Cadmium amount content in rice, result

“Cadmium Amount Content in Rice” and “Cadmium and Zinc AmountContent in Rice”, respectively. In addition, CCQM-P39, “As, Hg, Pb, Se andMethylmercury in Tuna Fish” and CCQM-K43, “As, Hg, Pb, Se andMethylmercury in Salmon” allowed comparisons of Se mass fractionsreported by similar numbers of INAA and IDMS laboratories.

The NAA and IDMS results reported for CCQM-K24/P29 are shownin Figs. 3.3 and 3.4. These figures have been adapted from the originalreports to facilitate the comparison between performance of NAA andIDMS. It can be seen from these figures that the mean values of the Cdand Zn amount contents determined by NAA and IDMS, as well as thevariability among the NAA and IDMS laboratories and the estimates ofmeasurement uncertainty are similar for the two techniques. Note

BAMIR

MM

NRCCRMNRC

CSIR

NIST-2

CENA

NMi-T

UDelft

INAA

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

s from CCQM-K24/P29, adapted from [3, 4].

image of Fig.�3.1

CENAM

KRISS

NMIJ

VNIIM-1

BAMLG

CNARL

NIST-1

PTBNRC

LNE

CENA

NMi-T

UDelft

NIST-2

IRM

M0.30

0.32

0.34

0.36

0.38

0.40

0.42

INAAIDMS

Zn

µmol

g-1

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

Fig. 3.4. Zinc results of CCQM-P29 “Cadmium and zinc amount content in rice”, adapted from [4].


that, in general, results from pilot studies are not publically available.However, in a few cases agreement was obtained from all participantsto make the results public. When such agreement was reached, andthe data from the pilot studies are publically available, theparticipating laboratories will be identified here. When pilot studydata is not publically available laboratories will not be identified,except for the authors' own laboratory (CENA/USP).

The Se data from CCQM-P39, “As, Hg, Pb, Se and Methylmercury inTuna Fish” and CCQM-K43, “As, Hg, Pb, Se and Methylmercury inSalmon” are presented in Fig. 3.5 (CCQM-P39) and Fig. 3.6 (CCQM-

KRISS

NMIJ

BNM-L

NELG

C

65

70

75

80

85

90

95

IDMS

Se

µmol

kg-

1

Fig. 3.5. Selenium results from CCQM-P39 “As, Hg, Pb, Se

LGC

NMIJ

NMIA

LNE

6.0

6.5

7.0

7.5

8.0

8.5

IDMS

Se

µmol

kg-

1

Fig. 3.6. Selenium results from CCQM-K43 “As, Hg, Pb, Se and methylmercury in salmon”, ad

K43). A numerical comparison of the results for the two methods(NAA and IDMS) is given in Tables 3.2 and 3.3. Note that in Fig. 3.6, theSe result from the authors' laboratory (CENA/USP) is included sincethe laboratory participated as an invited expert laboratory inthe associated pilot study CCQM-P39.1 that was carried out in parallelto CCQM-K43, as well as CENA/USP's long history of successfulparticipation in CCQM studies. CCQM-P39.1 involved the determina-tion of the same measurands in the same salmon material as CCQM-K43. However, CENA/USP's results have not been included in thecalculation of the Key Comparison Reference Value since the

NIST

IMGC

CENA

IRM

M-S

CKBAM

INAA

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

and methylmercury in tuna fish”, adapted from [5].

IRMM

IMGC BA

MCENA

INMETRO

NIST

INAA

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

apted from [6]. Also includes results from CENA in the parallel Pilot Study CCQM-P39.1.

Table 3.2Comparison of results of Se determination in CCQM-P39 “Hg, Pb, Se, As andmethylmercury in tuna fish” by NAA and IDMS.

NAA IDMS

Mean1 79.7 80.1U (2 s/√n)1 1.7 0.94# of labs 5 41 s% 2.4 1.2Range (%) 6.0 2.7

1 Units are 10−6mol kg−1.

Table 3.3Comparison of results of Se determination in CCQM-K43 “As, Hg, Pb, Se andmethylmercury in salmon” by NAA and IDMS.

NAA IDMS

Mean1 7.36 7.33U (2 s/√n)1 0.17 0.43# of labs 5 41 s% 2.4 5.8Range (%) 5.4 13

1 Units are 10−6mol kg−1.


laboratory is not affiliated to an NMI or an NMI designated laboratory;hence CENA/USP's results were not included in the data of Table 3.3.

The mean Se content reported by the NAA laboratories in CCQM-P39 was very close to the mean Se content reported by the IDMSlaboratories (79.7 μmol kg−1 versus 80.1 μmol kg−1), andwell withinexpanded uncertainties calculated as 2 s/√n for each method(1.7 μmol kg−1 and 0.94 μmol kg−1). The relative standard deviation,and the range of results for the NAA laboratories in CCQM-P39 (2.4%and 6.0%) were about twice as large as the corresponding values forthe IDMS laboratories (1.2% and 2.7%). However, this may be partiallydue to the larger number of NAA laboratories (5 versus 4). In addition,the NAA RSD and range appear relatively typical for most CCQMcomparisons of trace elements in complex matrices, and are quitesmall for most non-CCQM comparisons.

The mean Se content reported by the NAA laboratories in CCQM-K43 was very close to the mean Se content reported by the IDMSlaboratories (7.36 μmol kg−1 versus 7.33 μmol kg−1), andwell withinexpanded uncertainties calculated as 2 s/√n for each method(0.17 μmol kg−1 and 0.43 μmol kg−1). The relative standard deviationand the range of results for the NAA laboratories in CCQM-K43 (2.4%and 5.4%) were quite similar to the NAA results for CCQM-P39 (2.4%and 6.0%); however, the corresponding values for the IDMSlaboratories in CCQM-K43 (5.8% and 13%) were significantly greaterthan those of CCQM-P39 (1.2% and 2.7%). In addition, the dispersionvalues were more than twice as large for the IDMS laboratories as

40

45

50

55

IDMS

Zn

µmol

kg-

1

Fig. 3.7. Zinc results from CCQM-P70 “Trace m

those of the NAA laboratories in the same study (CCQM-K43), despitea greater number of NAA labs reporting results (5 versus 4). Thedifference between the IDMS results for the two studies seems, atleast partially, to be due to the order of magnitude lower Se massfractions for the key comparison. In conclusion, the results of the twostudies of Se in fish indicate that for similar number of laboratories,the NAA results were similar, or perhaps a little better, than the IDMSresults.

3.4. NAA performance compared to IDMS performance: additionalcomplex matrices

Subsequent key comparisons and pilot studies provided additionalopportunities to compare the performance of IDMS and NAA for moremeasurands in other complex matrices. Additional CCQM compar-isons including CCQM-P70 “Trace Elements in Sewage Sludge”; CCQMP64 “Nonfat Soybean Powder”; CCQM-P65/K57 “Chemical Composi-tion of Clay”; and CCQM-K49/P85 “Essential and Toxic Elements inBovine Liver” will be discussed.

Sewage sludge offers analytical challenges since it can be quitedifficult to dissolve, and the high levels of many elements providemany opportunities for potential interferences. The results of fourNAA laboratories and four IDMS laboratories for Zn in sewagesludge pilot study (CCQM-P70) are compared in Fig. 3.7. Note thatalthough the mean of the NAA and IDMS appears to be relativelysimilar, there is a much greater interlaboratory dispersion amongthe IDMS values. Although two of the IDMS values have muchsmaller uncertainties than the NAA values, there is little overlap ofany of the IDMS values within reported uncertainties compared tostrong overlap of the uncertainties of all NAA values. Clearly thismeasurand/matrix combination provided unrecognized challengesto the IDMS method despite the relatively high amount content ofZn.

Results for three NAA laboratories for Fe and Zn in CCQM-P64“Nonfat Soybean Powder” are compared with those of six (Fe) orseven (Zn) IDMS laboratories in Figs. 3.8 and 3.9. Although all NAAvalues agree with all IDMS values within expanded uncertainties, oneNAA laboratory reported results with significantly larger uncertaintiesfor both Fe and Zn compared to the other two NAA laboratories, aswell as to all the IDMS laboratories. The large uncertainty appears tobe a result of lack of metrological experience, as this laboratory was arelative newcomer to the field of metrology, and had very limitedexperience participating in high-level intercomparisons.

Some clays can be quite difficult to totally dissolve, and thus provideanalytical challenges for methods requiring sample dissolution. CCQM-P65, “Chemical Composition of Clay” allowed the comparison of Ca, Feand K results from one NAA and one IDMS laboratory. Results from allmethods are included in Figs. 3.10, 3.11 and 3.12. The results of all three

INAA

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

etals in sewage sludge”, adapted from [7].

110

120

130

140

150

160

170

180

190

IDMS INAA

mg

kg-1

-30

-20

-10

0

10

20

30Fe

Per

cent

age

diffe

renc

e (%

)

Fig. 3.8. Iron results from CCQM-P64 “Nonfat soybean powder”, adapted from [8].

32

36

40

44

48

52

56

INAAIDMS

Zn

-30

-20

-10

0

10

20

30

Per

cent

age

diffe

renc

e (%

)

mg

kg-1

Fig. 3.9. Zinc results from CCQM-P64 “Nonfat soybean powder”, adapted from [8].


elements determined by the NAA laboratory (the authors' laboratory atCENA/USP) fall well within the range of results reported by laboratoriesusing other methods, as do the results from the IDMS laboratory. Theuncertainties of the NAA measurements appear to be similar to thosereported bymost other laboratories and smaller than those reported bythe IDMS laboratory. Theuncertainty reported forCaby IDMSappears tobe the largest uncertainty reported.

Quite a few laboratories participated in CCQM-K49/P85 “Essentialand Toxic Elements in Bovine Liver”, including some with limitedexperience in such high-level, metrological comparisons. In fact, somelaboratories were participating for the first time in a CCQMcomparison. In view of this lack of metrological experience, the

IDM

INAA

Ca

70

75

80

85

90

95

CaO

(m

g g-

1 )

Fig. 3.10. Calcium results from CCQM-P65 “Chem

results of only the key comparison will be compared in Figs. 3.13 to3.17. However, results from the authors' laboratory (CENA/USP) thatwere submitted to the CCQM-P85 pilot study have been included inthese figures in view of CENA/USP's long history of successfulparticipation in CCQM studies (since 2001).

CCQM-K49/P85 includedmeasurands of varyingdegrees of difficultyin thismatrix. Iron and zincwere considered to be relatively easy due totheir high levels, and the ease of matrix decomposition. The results forNAA and IDMS participants in the key comparison are compared inFigs. 3.13 and 3.14. Note that the dashed lines in these figures,representing the relative key comparison reference uncertainties, areboth about1%.Overall, the INAAand IDMSmeanvalues agree quitewell.

S

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

ical composition of clay”, adapted from [9].

45

48

51

54

57

60

63

IDMS

INAA

Fe 2

O3

(mg

g-1)

-20

-10

0

10

20

Fe

Per

cent

age

diffe

renc

e (%

)

Fig. 3.11. Iron results from CCQM-P65 “Chemical composition of clay”, adapted from [9].

22

24

26

28

30

IDMSINAA

K2O

(m

g g-1

)

-20

-10

0

10

20

K

Per

cent

age

diffe

renc

e (%

)

Fig. 3.12. Potassium results from CCQM-P65 “Chemical composition of clay”, adapted from [9].


The magnitudes of the expanded uncertainties of the NAA laboratoriesappear quite similar to those of the IDMS laboratories.

Selenium, Cd and Cr were considered to be more challenging dueto their lower content and the higher potential for matrix interfer-ences. The IDMS and NAA results from the key comparison arecompared in Figs. 3.15 (Se), 3.16 (Cd), and 3.17 (Cr). Results from thethree laboratories using INAA and two laboratories using IDMS todetermine Se in CCQM-K49 are compared in Fig. 3.15. All five results

NIMLN

ELG

C

KRISS

NMIA

NMIJ

HKGL

160

170

180

190

200

210

220

230

IDMS

Fe

mg

kg-1

Fig. 3.13. Iron results from CCQM-K49 “Essential and toxic elements in bovine liver”, adap

were within the uncertainties of the key comparison. The magnitudesof the reported expanded uncertainties for the two techniques aresimilar, with the uncertainty from one IDMS laboratory larger and onesmaller than those of the three NAA laboratories.

Six IDMS results and one RNAA result were reported for Cd inCCQM-K49. One laboratory reported both IDMS and RNAA results. Ascan be seen in Fig. 3.16, the reported Cdmass fraction and uncertaintydetermined by RNAA was indistinguishable from the IDMS values.

PTBNIS

T

CENA

INRIM

INAA

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

ted from [10]. Also includes results from CENA in the parallel Pilot Study CCQM-P85.

NIMLN

EHKGL

NIST

LGC

NMIA

KRISS

NMIJ

BAMCENA

NIST

INRIM

150

160

170

180

190

200

210

IDMS INAA

Zn

mg

kg-1

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

Fig. 3.14. Zinc results from CCQM-K49 “Essential and toxic elements in bovine liver”, adapted from [10]. Also includes results from CENA in the parallel Pilot Study CCQM-P85.

NIST

INRIM

NIMNM

IA

CENA

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

IDMS

IDMS

INAAINAA

INAA

Se

mg

kg-1

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

Fig. 3.15. Selenium results from CCQM-K49 “Essential and toxic elements in bovine liver”, adapted from [10]. Also includes results from CENA in the parallel Pilot Study CCQM-P85.


Three IDMS laboratories and one INAA laboratory reported results forCr in CCQM-K49. Note that this measurement is extremely challeng-ing with Cr present at approximately 50 μg/kg in a solid, complexmatrix. As can be seen from Fig. 3.17, both mean values and expandeduncertainties from the individual laboratories were similar.

3.5. Discussion

Neutron activation analysis differs from other methods of chemicalanalysis in that there is an absence of integral, commercially-availableinstruments and standardized software. Nuclear research reactors, as

LNE

NIST-1

NMIJ

NIS0.080

0.085

0.090

0.095

0.100

0.105

0.110

0.115

IDMIDMS

IDMS

RNAA

Cd

mg

kg-1

Fig. 3.16. Cadmium results from CCQM-K49 “Essential an

sources of neutrons, have different neutron intensities and energyspectra available for activation; the gamma-ray spectrometers arecomposed of individual detectors, amplifiers and multichannel analy-zers, and can therefore not be compared with e.g. a standard(catalogued) AAS or ICP instrument. In addition, software for gamma-ray spectrum analysis and interpretation is also often not standardized,but developed in-house. The very good agreement among the NAAlaboratories submitting results for the CCQM studies demonstrates therobustness of the method, and the typically good agreement (withinuncertainties) of the NAA values with the reference values of thecomparisons indicates that the metrological principles of NAA are well

T-2NIM

BAMNM

IA

IDMS

IDMS

IDMSS

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

d toxic elements in bovine liver”, adapted from [10].

Table 3.4Comparison of IDMS and NAA characteristics for trace element determination; the symbols mark the characteristics in which a technique differs favorably from the other.

IDMS NAA

Instrumentation availability ++Expanded uncertainties (U) — g/kg level ++Expanded uncertainties (U) — mg/kg level (+) (+)Blank ++Dissolution losses ++Elemental coverage Missing mono-isotopic elements Missing some key elements (Pb etc.)Metrological expertise required yes yesAgreement in comparisons Quite good, but dependent on level,

element, and matrixQuite good, but dependent on level,element, and matrix

PTBNM

IJNIS

TNIM0.042

0.045

0.048

0.051

0.054

0.057

0.060IDMS

IDMS

IDMS

INAA

Cr

mg

kg-1

-20

-10

0

10

20

Per

cent

age

diffe

renc

e (%

)

Fig. 3.17. Chromium results from CCQM-K49 “Essential and toxic elements in bovine liver”, adapted from [10].


understood and practiced in many NAA laboratories; even in ones thatare not affiliated with an NMI. However, metrological experience isextremely important, and laboratories with less experience are morelikely to provide less reliable results and have problems in developingcomplete uncertainty budgets.

It should be noted that the NAA laboratories participating in thestudies presented here applied the comparator method of standard-ization, in which a calibrator consisting of a known amount of eachelement to be determined in the sample of interest was used. The so-called k0 method for standardization, often applied in many fieldlaboratories for direct multi-element determinations, was not used inthese comparisons because of the relatively high uncertainties ofsome of the physical constants needed, and the still existing lack ofclarity on the traceability of the results obtained by this method ofstandardization.

The niches and limitations of neutron activation analysis for traceelement determinations have been described and discussed in Chapter1. During the last decade, NAA laboratories have participated in keycomparisons and pilot studies in which both the matrices and theelements of interest were suitable for this method. A number of thesestudies, beginning between 2001 and 2006, allowed for directcomparison of NAA and IDMS determinations of amount content,uncertainty budgets, anddispersionof reported results for eachmethod.As a result, it may be concluded that, in general, the metrologicalproperties of NAA and IDMS appear to be similar for the determinationof trace elements in complexmatrices. Dissolution aspects may explainthat in some cases the range in NAA results was smaller than in IDMSresults. Lack of metrological experiencemay explain some of the resultswith larger uncertainty budgets and deviations from the accepted studyvalues.

Although only a limited type of matrices and measurands wereinvolved in the key comparisons and pilot studies, a general

comparison of the characteristics and potential metrological perfor-mance of both methods could be made, and is given in Table 3.4.

3.6. Conclusion

It has beendemonstrated, viaparticipation inCCQMkey comparisonsand pilot studies starting between 2001 and 2006, that resultsdetermined by metrologically-experienced NAA laboratories haveproperties similar to those obtained by metrologically-experiencedIDMS laboratories for the determination of many trace elements incomplex matrices. INAA, because of the non-destructive nature, itsfreedom from blank, and its elemental coverage provides a goodcomplement to IDMSmethods. Neutron activation analysis, based on thecomparator method for calibration, can therefore meet all requirementsof a primary ratio method, and has been accepted as such by the CCQM.TheCCQM, in itsmeetingof April 19, 2007, decided subsequently “…thatNAA had claims to a similar status to that of the five methods listedoriginally by theCCQMand thatNAAwill be added to that list….” [11,12].

Acknowledgements

The authors wish to express their thanks to all laboratories thatparticipated between 2001 and 2006 in the CCQM key comparisonsand pilot studies discussed above.

3.7 References for Chapter 3

[1] R. R. Greenberg, E.A. Mackey, CCQM-P11 Pilot Study Arsenic in Shellfish, FinalReport November 28, (2001) NIST, Gaithersburg, USA.

[2] R.R. Greenberg, E.A. Mackey, CCQM-K31 Key Comparison: Arsenic in Shellfish,Metrologia 43, (2006) 08003.

[3] Y. Aregbe P. Taylor, CCQM-K24 Key Comparison. Cadmium Amount Content inRice, Metrologia 40, (2003) 08001.


[4] Y. Aregbe P. Taylor, CCQM-P29 pilot study. Cadmium and Zinc Amount Contentin Rice, Metrologia 40, (2003) 08002.

[5] Y. Aregbe, C. Quétel, P.D.P. Taylor, CCQM-P39: As, Hg, Pb, Se andMethylmercury in Tuna Fish, Metrologia 41, (2004) 08004.

[6] Y. Aregbe, P.D.P. Taylor, CCQM-K43: As, Hg, Pb, Se and Methylmercury inSalmon, Metrologia 43, (2006) 08005.

[7] Y. Aregbe, P.D.P. Taylor, presentation at CCQM-IAWG Meeting, Oct. (2005),CCQM-K44 and P70: Trace Metals in Sewage Sludge.

[8] M. Liandi et al., 2006, Report of the CCQM-P64 & APMP.QM-P07, Cu, Zn, Fe andCa in Nonfat Soybean Powder.

[9] J.A. Salas, E.M. Ramírez, (2006) Report of CCQM-P65 Study, ChemicalComposition of Clay.

[10] R.R. Greenberg, Final Report on Key Comparison CCQM-K49: Essential andToxic Elements in Bovine Liver, Metrologia 45, (2008) 08016.

[11] Report of the 13th meeting of the CCQM, 19–20 April (2007), http://www.bipm.org/utils/common/pdf/CCQM13.pdf (last accessed August 19, 2010).

[12] Report of the 14th meeting of the CCQM, 3–4 April (2008), http://www.bipm.org/utils/common/pdf/CCQM14.pdf (last accessed August 19, 2010).

3.8 Acronyms used in Chapter 3

AAS atomic absorption spectroscopyBAM Bundesanstalt für Materialforschung und -prüfung, GermanyBIPM Bureau International des Poids et MesuresBNM-LNE BureauNational deMétrologie– LaboratoireNational d’Essais,

FranceCCQM Consultative Committee for Amount of Substance–Metrology

in ChemistryCENAM Centro Nacional de Metrología, MéxicoCENA/USP Centro de Energia Nuclear na Agricultura – Universidade de

São Paulo, BrazilCSIR Council for Scientific and Industrial Research, South AfricaEMPA Swiss Federal Laboratories forMaterials Testing andResearch,

SwitzerlandFI-HGAAS flow injection hydride generation atomic absorption

spectroscopyFI-HG-GFAAS flow injection hydride generation graphite furnace

atomic absorption spectroscopyGFAAS graphite furnace atomic absorption spectroscopyHKGL Hong Kong Government Laboratory, Hong Kong

HR-ICP-MS high resolution inductively coupled plasma massspectrometry

ICP inductively coupled plasmaICP-AES inductively coupled plasma atomic emission spectrometryICPMS inductively coupled plasma mass spectrometryIDMS isotope dilution mass spectrometryIMGC Institute of Metrology Gustavo Colonnetti, ItalyINMETRO Instituto Nacional de Metrologia Normalização e Qualidade

Industrial, BrazilINRIM Instituto Nazionale di Metrologia delle Radiazioni

Ionizzanti, ItalyIRMM Institute for Reference Materials and Measurements,

European CommissionKRISS Korean Research Institute of Standards and Science,

Republic of KoreaLGC Laboratory of the Government Chemist, United KingdomLNE Laboratoire National de Métrologie et d'Essais, FranceMRA Mutual Recognition ArrangementNARL National Analytical Reference Laboratory, AustraliaNIM National Institute of Metrology, ChinaNIST National Institute of Standards and Technology, United

States of AmericaNMi Nederlands Meetinstituut, The NetherlandsNMI national metrology instituteNMIA National Measurement Institute, AustraliaNMIJ National Metrology Institute of Japan, JapanNMI-TUDELFT Nederlands Meetinstituut, Delft University of

Technology, The NetherlandsNRC National Research Council of Canada, CanadaNRCCRM National Research Centre for Certified Reference Materials,

ChinaPTB Physikalisch-TechnischeBundesanstalt, GermanySCK Belgian Nuclear Research Centre, BelgiumVNIIM D.I. Mendeleyev Scientific and Research Institute for

Metrology, Russia

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neutron activation analysis: a primary method of measurement

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