Glascock and Neff 2004-Libre

INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY

Meas. Sci. Technol. 14 (2003) 15161526 PII: S0957-0233(03)56714-5

Neutron activation analysis andprovenance research in archaeologyMichael D Glascock1,3 and Hector Neff2

1 Research Reactor Center, University of Missouri, Columbia, MO 65211, USA2 Department of Anthropology, California State University, Long Beach, CA 90840, USA

E-mail: [email protected] and [email protected]

Received 27 November 2002, accepted for publication 7 April 2003Published 29 July 2003Online at stacks.iop.org/MST/14/1516

AbstractNeutron activation analysis is a powerful quantitative analytical techniquewith application in a broad range of disciplines such as agriculture,archaeology, geochemistry, health and human nutrition, environmentalmonitoring and semiconductor technology. Due to its excellent sensitivity,great accuracy and precision, and versatility, the technique is a suitablemethod for analysing many different types of samples. Archaeologists, inparticular, have made extensive use of neutron activation analysis for thepurpose of characterizing archaeological materials and determining theirprovenance. This paper presents a brief history of the technique and itsapplication to archaeology, describes the physics behind the analyticalmethod, and explains how the method is generally employed to determinethe sources of archaeological materials.

Keywords: neutron activation analysis, nuclear reactions, cross-sections,thermal neutrons, gamma-ray spectra, provenance, ceramics, clays,obsidian, chert, multivariate statistics

1. Introduction

The application of chemical analytical methods to archaeo-logical materials in support of provenance research has grownrapidly over the past few decades. Provenance research en-tails the use of compositional profiles of artefacts and sourcematerials to trace individual artefacts from their find spot totheir place of origin. The information obtained is used byarchaeologists to investigate questions regarding the locationof prehistoric production areas, the identification of routes oftrade and exchange of raw materials and artefacts, and the mo-bility patterns of prehistoric peoples. Although a number oftechniques have been employed to characterize archaeologi-cal materials, the analytical method with one of the longestand most successful histories of application for provenanceresearch has been neutron activation analysis (NAA).

Neutron activation analysis is a sensitive technique usefulfor qualitative and quantitative multi-element analysis ofmajor, minor, and trace elements present in many samplematrices. With the exception of inductively coupled plasma-3 http://www.missouri.edu/glascock/archlab.htm

mass spectrometry (ICP-MS) on liquid samples, NAA offerssensitivities that are superior to those possible by all otheranalytical methods. Moreover, the accuracy and precisionof the technique are such that NAA is still one of theprimary methods employed by the National Institute ofStandards and Technology to certify the concentrations ofelements in standard reference materials. Applications ofNAA are by no means limited to archaeology, but include abroad range of disciplines such as agriculture, geochemistry,health and human nutrition, environmental monitoring andsemiconductors.

The NAA technique involves the irradiation of a sampleby neutrons to make the sample radioactive. After irradiation,the gamma rays emitted from the radioactive sample aremeasured to determine the amounts of different elementspresent in the sample. As a result, NAA has a numberof advantages over most other analytical methods wheninvestigating archaeological specimens. First, it is nearly freeof any matrix interference effects because the vast majorityof archaeological samples are transparent to the probe, theneutron, and the emitted analytical signal, the gamma ray.Second, because NAA can be applied instrumentally (without

0957-0233/03/091516+11$30.00 2003 IOP Publishing Ltd Printed in the UK 1516

Neutron activation analysis and provenance research in archaeology

sample digestion or dissolution), there is little opportunity forreagent or laboratory contamination. Third, the preparationof samples from most matrices (especially geological sampletypes) for analysis by NAA is extremely easyin mostinstances a portion of the sample need only be weighed andplace in an appropriate container. In contrast, the difficultyof achieving complete digestion of geological samples foranalysis by ICP-MS can be challenging and the labour costs aremuch greater. Finally, although nuclear reactors are becomingless available while ICP-MS instruments are becomingmore widely available, many reactors offer competitive low-cost analyses on projects involving collaborative academicresearch.

This paper presents a brief history of NAA and itsapplication to archaeology, describes the physics behind theNAA technique, and explains how the method is generallyemployed to determine the provenance of archaeologicalmaterials. The final section presents a few examples of NAAapplied to recent archaeological studies.

2. A brief history

The notion that nuclear reactions might be used for quantitativeanalysis first occurred to Georg Hevesy and Hilde Levy in1936 when they exposed rare-earth salts to a naturally emittingRa(Be) neutron source (Ehmann and Vance 1991). They foundthat many of the rare-earth elements became highly radioactiveupon bombardment with neutrons, and the radiation emittedfrom the different elements decreased according to differenttime constants. From this discovery, they recognized thepotential for identifying elements present in mixtures ofsamples through measurement of different radiations and half-lives of the radioactive elements.

The 1950s and 1960s saw the construction of nuclearreactors with neutron fluxes sufficient to allow sensitivities forNAA at levels of interest to solving real analytical problems.In addition, there were improvements in the sophisticationand sensitivity of instrumentation used to make nuclearmeasurements, and hundreds of experiments were performedto measure the basic nuclear parameters (i.e. reaction cross-sections, half-lives, gamma-ray abundances and branchingratios) associated with nuclear reactions.

The potential of NAA as an archaeological tool was firstrecognized by Robert Oppenheimer in the autumn of 1954,when he suggested its use to Dodson and Sayre of BrookhavenNational Laboratory (BNL) as a possible way to establish theprovenance of archaeological ceramics (Harbottle 1976). Theexperimental work was undertaken by Sayre and reported toarchaeologists and chemists at Princeton in 1956 (Sayre andDodson 1957). At around the same time, a group at Oxfordbegan experimenting with the use of NAA on pottery andcoins (Emeleus 1958, Emeleus and Simpson 1960). The initialapplications were hampered by the poor resolution of availabledetection systems (e.g. Bennyhoff and Heizer 1965), but theadvent of lithium-drifted germanium Ge[Li] detectors in theearly 1960s offered significant improvements in resolution andprompted a flurry of archaeological applications (Harbottle1976). It is interesting to note that a paper by Sayre (1965)on the analysis of ancient glass was the first to report the useand advantages of the Ge[Li] detector in NAA.

Perlman and Asaro (1969) provided a description of thestandard-comparator method of NAA as applied to provenancedetermination at the Lawrence Berkeley Laboratory (LBL).Archaeologists turned more frequently to NAA during the1970s and 1980s to determine the sources of pottery, obsidian,chert and other materials (Hughes et al 1991, Kuleff andDjingova 1990, Neff and Glascock 1995). The NAAlaboratories at BNL and LBL were joined by laboratories atthe University of Michigan, University of Toronto, HebrewUniversity, National Institute of Standards and Technology,University of Missouri, and a number of smaller universityresearch reactors. By the early 1990s, NAA was regarded asthe technique of choice for provenance research (Bishop et al1990, Gilmore 1991).

Although the late 1980s and 1990s, saw reactordecommissioning and retirements of key personnel whichconcluded a number of the major programmes (i.e. BNL,LBL, the University of Toronto and Hebrew University), thedemand for NAA has not decreased. Fortunately, althoughthere are fewer places to perform NAA today, the remainingprogrammes have been able to increase their capacity such thataccess to NAA is still readily available.

3. Theory

3.1. Nuclear reactions

Nuclear reactions occupy a central role in all methods ofactivation analysis. In a nuclear reaction, an incident particle(e.g. neutron, proton or alpha particle) interacts with a targetnucleus either by scattering or by absorption. The diagramshown in figure 1 illustrates a typical nuclear reaction involvingabsorption of the incident particle followed by the emissionof both particles and prompt gamma rays and by productionof a radioactive nucleus. If the incident particle is a thermalneutron, a prompt particle is rarely emitted. If the reactioninvolves an incident fast neutron or a charged particle, a promptparticle is always emitted. In either case, prompt gamma rayswill always occur. The reaction can also be described by theexpression

a + A [X] b + B + Q (1)or in shorthand notation A(a, b)B. Where the symbol arepresents the incident particle, A is the target nuclide, [X] isthe compound nucleus in a state of excitation, B is the productnuclide (often radioactive), b is the exiting particle or radiation,and Q accounts for the amount of energy released or absorbedduring the reaction. If Q is positive, the reaction is calledexoergic. If Q is negative, the reaction is called endoergic.

Nuclear reactions caused by neutrons are typicallyexoergic, and the required threshold energy is zero. Thus,the reaction can take place when the incident neutron has akinetic energy of nearly zero. This is the situation for thermalneutron capture or (n, ) reactions. When the incident neutronenergy exceeds the threshold energy for a reaction involvingparticle emission, reactions such as (n, p), (n, ), (n, n), and(n, 2n) are possible. In most applications involving neutronactivation analysis, the product nuclide B is radioactive and isfollowed by emission of one or more delayed gamma rays.

Techniques based on measurement of the prompt anddelayed radiation are referred to as prompt gamma neutron

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M D Glascock and H Neff

Figure 1. Diagram illustrating of the nuclear processes occurringduring interaction of an incident neutron, proton or other nuclearprojectile with a target nucleus.

activation analysis (PGNAA) and delayed gamma neutronactivation analysis (DGNAA), respectively. The lattertechnique is frequently referred to as instrumental neutronactivation analysis (INAA) when the procedures employed donot involve extra pre- or post-irradiation steps such as chemicalseparations.

3.2. Reactor neutron spectrum and reaction cross-sections

Reactors based on the fission of 235U offer the most intenseneutron sources currently available for NAA. The spectrum ofneutrons in a reactor consists of three parts as illustrated infigure 2. In the high-energy region, neutrons still have mostof their original energy from fission (e.g. roughly 26 MeV)and are frequently called the primary fission neutrons or fastneutrons. Fast neutrons lose energy rapidly through elasticscattering with moderating materials in the reactor, such aswater and graphite. Neutrons in the energy range from 0.5 to1 MeV are commonly referred to as epithermal neutrons andhave been partially slowed down. The distribution of neutronsin the epithermal region approximates a 1/E slope. Belowenergies of 0.5 eV, the neutrons are usually referred to asthermal neutrons. Thermal neutrons have approximately thesame velocity (v) distribution as the molecules and atoms oftheir surroundings (i.e. a MaxwellBoltzmann distribution) ofthe form

dndv

= 4nv30piv2e(v/v0)

2. (2)

In a typical light moderated reactor, the fluxes of epithermaland fast neutrons are on the order of 23% and 710%respectively of the thermal neutron flux. Neutron fluxes aregenerally expressed in units of neutrons cm2 s1.

Tabulations of cross-sections for thermal neutron reactionsassume a velocity of 2200 m s1 which is the most probableneutron velocity for neutrons at 20 C and corresponds to amost probable energy of 0.0253 eV. Reaction cross-sectionsare usually expressed in barns (b) where 1 b = 1024 cm2.

For most nuclides at low neutron energies the cross-sectionfor the (n, ) reaction obeys a 1/v law as shown in figure 3.Although there are small deviations from the 1/v shape in thecross-section curves for some nuclides, the average thermalneutron cross-section th is assumed to be approximately thesame as the cross-section at exactly 2200 m s1.

As neutron energies increase above 0.5 eV, the cross-section curves for most target nuclides are characterized by anumber of resonance peaks added on top of the 1/v curve. Theenergies of the resonance peaks coincide with the excited states

Figure 2. A typical neutron energy spectrum from a nuclear fissionreactor.

Figure 3. Cross-section versus energy for a common neutroncapture (n, ) reaction involving thermal and epithermal neutrons.

of the compound nucleus. To facilitate calculation of reactionrates in the 1/E-flux region an epithermal cross-section I(also called the effective resonance integral) is defined by theexpression

I =

0.5 eV

(E)E

dE . (3)

Because both thermal and epithermal neutrons can induce(n, ) reactions, a non-rigorous but commonly used expressionfor the total reaction rate for a particular nuclide assuming ntarget atoms in the sample is given by

R = n[thth + epi I ] (4)

where th and epi are the thermal and epithermal neutronfluxes respectively. In most cases, the thermal and resonancecross-sections are similar in magnitude, but the number ofthermal neutrons is much greater. Therefore, thermal neutronactivation generally accounts for a majority of the inducedactivity in most elements. Examples of nuclides illustratingthe range of variability of thermal neutron (n, ) reactioncross-sections are 27Al (0.226 b), 45Sc (26.3 b), 58Fe (1.31 b),138Ba (0.405 b) and 164Dy (2725 b).

At higher neutron energies, the cross-sections for (n, )reactions are very small, and nuclear reactions that result in the

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ejection of one or more particles(n, p), (n, ), (n, n), and(n, 2n) reactionsdominate. These transmutation reactionsoccur only when the neutron energy is above the minimumthreshold energy ET required for the particular reaction tooccur. Because the neutron energy distribution is complexat high energies, the average cross-section for a fast neutronreaction f is defined by the expression

f =

ET (E)(E) dEET (E) dE

. (5)

Using this average cross-section, the total reaction rate for afast neutron reaction is given by

R = n f f (6)

where f is defined the average fast neutron flux. There areonly a few instances in which fast neutrons are important inNAA. Among these are the measurement of nickel using the58Ni(n, ) 58Co reaction and corrections to (n, ) reactions forseveral light-mass elements (e.g. Na, Mg, Al) from interferencedue to fast neutrons.

3.3. Radioactive decay

Radioactive decay is the spontaneous transformation of atomsby emission of particles or gamma rays from the nucleus,or of x-rays after capture of shell electrons by the nucleus.Radioactive decay is a statistical process. For a samplecontaining a large number of radioactive atoms, there is noway to predict which atom will be next to decay, but thedecay characteristics of the entire sample can be described.The number of atoms that decay per unit of time is definedas the activity A and is defined by the fundamental law ofradioactivity

A = dNdt

= N (7)where N is the number of radioactive atoms and is the decayconstant.

The value of is different for each species of radionuclide.An equation describing the time dependence of the number ofatoms of the radionuclide is

N(t) = N0et (8)

where N0 is the number of radioactive atoms at time t = 0.Therefore, the process of radioactive decay is an exponentiallaw, and the activity of the radionuclide is controlled by acharacteristic property known at the half-life (i.e. the periodof time during which half of the original atoms of that nuclidehave decayed). The half-life is related to the decay constantaccording to

t1/2 =ln 2= 0.693

. (9)

The half-lives of different radionuclides range frommilliseconds to several times the age of the universe.

For NAA using delayed gamma rays, the number of atomsdecaying during the post-irradiation measurement period ismeasured. The number of radioactive atoms present at any timedepends on the total number of radioactive atoms producedduring irradiation less the number that decayed both during the

irradiation and in the interval between the end of irradiation andthe beginning of measurement. Thus, the rate of production,half-life, length of irradiation (Ti), length of decay (Td), andlength of measurement (Tc) are important factors for NAA.

Mathematically, the rate of change in the number ofradioactive atoms during irradiation is the difference betweenthe rate of production and the rate of decay, i.e.

dNdt

= R N . (10)

Assuming there were no radioactive atoms present at t = 0, thenumber of radioactive atoms present at the end of irradiation(EOI) is

NEOI =R(1 eTi ). (11)

In general, measurement of radiation emitted from a samplemade radioactive does not begin immediately after irradiation,but after a period of decay. Under normal conditions, shortdecay times are used for radionuclides with short half-lives andlong decay times are used when the half-life is long. The longdecay time allows possible short-lived nuclides with initiallyhigh activities time to become insignificant. The equationsdescribing the number of radioactive atoms present at thestart of the counting period (SOC) and end of counting period(EOC), respectively, are

NSOC = NEOI eTd =R(1 eTi )eTd (12)

and

NEOC = NEOI eTd (1 eTc) =R(1 eTi )

eTd (1 eTc). (13)

3.4. Decay schemes and gamma-ray spectroscopy

In NAA, the radioactive nuclei produced usually decay intodaughter nuclei by emitting beta particles. The daughter nucleicreated are often in excited states, and undergo emission ofone or more gamma rays before arriving at a ground state.Measurement of these gamma rays yields the informationnecessary to determine the abundances of elements in theirradiated sample.

The decay schemes of nuclei range from simple tocomplex. A simple decay scheme is exemplified by the decayof 28Al (t1/2 = 2.24 min), which is produced by the irradiationof 27Al (e.g. Parry (1991), figure 4.2). The 28Al nucleus decaysvia emission into the 1779 keV excited state of the daughternucleus 28Si. In this case, the transition from excited state toground state always leads to emission of a gamma ray with anenergy of 1779 keV and branching ratio of 100%. Other decayschemes are more complex.

Gamma rays interact with matter in several ways, oneof which is an absorption process in which the energy ofthe gamma ray is transferred to photoelectrons inside asemiconductor detector. In general, the energies of gammarays from a neutron-irradiated sample will range up toabout 3200 keV, creating a spectrum of gamma rays whosecharacteristics are representative of the sample. The spectrumof gamma rays measured from a sample of pottery is shown infigure 4.

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Figure 4. Gamma-ray spectrum for a pottery sample made radioactive by NAA and counted with a high-purity germanium detector.

The actual number of gamma rays collected by the high-purity germanium (HPGe) semiconductor detector used tomeasure them is smaller than the total number of decays dueto several factors:

(1) The intensities (gamma-ray branching ratios) of emittedgamma rays are in many cases less than 100%.

(2) Some of the emitted gamma rays do not reach the detector.Due to the isotropic nature of gamma-ray emission, onlythose headed in the direction of the detector can bemeasured.

(3) A portion of the gamma rays will pass through the detectorwithout interacting, especially high-energy gammas. Inother cases, some of the gamma rays lose part of theirenergy by Compton scattering and pair production effects,thus contributing to the gamma continuum beneath thephotopeaks of primary interest.

The second and third factors comprise a characteristic of thedetector called the geometric efficiency . At energies above200 keV, the log of efficiency approximates a linear functionof the log of energy

log = b log E + log a (14)

where constants a and b are dependent on the sample-to-detector distance and dimensions of the detector crystal.

Various techniques are used to extract qualitative andquantitative information from gamma-ray spectra. Given agamma-ray spectrum, the first task is to identify the nuclidesresponsible for the various peaks and the second task isto determine the peak areas. Peak identification can beaccomplished by consulting a number of compilations of decayschemes and tables listing the associated gamma-ray energiesand branching ratios (Erdtmann and Soyka 1979, Firestoneet al 1996, Glascock 1998). For most peaks, the peak area(sometimes called the signal) can be determined by summingthe total number of counts under the peak and subtracting anestimated background as follows

S = T B. (15)

However, for overlapping multiplets, peak fitting routinesrelying on the Gaussian shapes of peaks are commonly used todetermine the areas of individual peaks. The measured activityis then calculated by dividing the peak area by count time.

The uncertainty in peak area is reported by calculatingthe relative standard deviation in per cent. One of themore common measures of standard deviation is given by theexpression

%s.d. = (100

S + 2B)/S. (16)The limit of detection for a peak depends on how well the

background is known. The usual definition for the detectionlimit is based on the two-sigma (95%) probability that a peakshould be observed above the background.

3.5. Calculating concentrations

In order to convert measured activities into concentrationsfor the sample one can use an absolute method by whichknowledge of all nuclear and experimental parameters isnecessary such that the following equation expressing theactivity present at any time can be used

A =(

m

MNA

)(thth + epi I)P S DC (17)

where m = mass of sample (g), M = atomicweight (g mol1), NA = Avogadros number (6.02 1023 molecules mol1), = isotopic abundance, P =intensity of the measured gamma ray, = efficiency of thedetector at the energy of the measured gamma ray, S =irradiation factor (1 eTi ), D = decay factor (eTd ) andC = count factor (1 eTc).

However, the absolute activation analysis procedure israrely used in archaeology where comparator methods arenormally preferred. The equation used to calculate the massof an element present in the unknown relative to a comparatorstandard of known concentration is

AsamAstd

= msam(eTd )sam

mstd(eTd )std(18)

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where A = activity of the sample (sam) and standard(std), m = mass of the element and Td = decay time.When performing short irradiations, the irradiation, decayand counting times are normally identical for all samples andstandards (i.e. the steps are performed on individual samplesand standards sequentially and all counting is performed ina reproducible geometry) such that all time-dependent andgeometric factors will cancel. Thus, the previous equationsimplifies to

csam = cstdWstdWsam

AsamAstd

(19)

where c = concentration of the element in sample and standardand W = weight of sample and standard.

The majority of laboratories involved in NAA utilizeone or more multi-element calibration standards. Thebasic procedure is to collect gamma-ray spectra for bothunknowns and standards under conditions that are as similaras possible, then to use one of the equations above to calculateconcentrations of the various elements whose peaks appearin the gamma spectra. Quality control or check standardsare generally included in each irradiation in order to providean independent check on the quality of the data and inorder to identify mistakes, such as weighing errors in thestandards. Certified reference standards can be purchased fromthe National Institute for Standards and Technology. Non-certified standards can also be obtained from the United StatesGeological Survey and other sources.

4. Methodology

4.1. The provenance postulate

The basic proposition underlying chemistry-based provenancedetermination was understood by the early 1970s (e.g. Bieberet al 1976, Harbottle 1976, Perlman and Asaro 1969, Sayreet al 1971). But, it was Weigand et al (1977) who firststated explicitly that the effort to link artefacts to sourcesthrough compositional analysis depends on the postulatethat there exist differences in chemical composition betweendifferent natural sources that exceed, in some recognizableway, the differences observed within a given source. Today,this statement is known as the provenance postulate byarchaeologists. It is interpreted to mean that the raw materialsource for responsible for an artefact can be successfullydetermined through chemical analysis as long as between-source chemical differences exceed within-source differences.

Source determination efforts based on the provenancepostulate can follow one of two separate paths as explainedby Neff (2000) and illustrated in figure 5. If the sourcesare localized and relatively easy to identify, as in the case ofvolcanic obsidian flows, raw materials from the known sourcesare usually characterized and then artefacts of unknownprovenance can be compared to the range of variation of theknown source groups. On the other hand, if sources arewidespread, as is especially true in the case of ceramic rawmaterials, the prospects of sampling and characterizing most orall of the possible sources are impractical. As a result, ceramicprovenance research generally involves an alternative approachby which reference groups are created from the unknownceramic samples. In this more common approach to ceramic

Figure 5. Two approaches to provenance determination.

sourcing, individual raw material samples are compared to therange of variation between ceramic reference groups.

4.2. Suitability of different archaeological materialsAs mentioned previously, obsidian artefacts are relatively easyto source by chemical analysis. In addition to the fact that mostobsidian sources are extremely homogeneous, the volcanicsources are limited geographically to certain regions. Obsidianis high in silica, but the trace and minor element constituentssometimes differ by orders of magnitude between sources.If all possible sources have been sufficiently characterized,the reliability of matching an obsidian artefact to its propersource is excellent and the number of elements required toidentify the source may be very small. However, the reliabilityof obsidian sourcing is sometimes challenged by processessuch as weathering and erosion which may distribute obsidiancobbles far from their source vent or by obsidian sources withmultiple flows, between which the differences may be subtle.For the latter, the determination of larger numbers of elementsby a high-precision multi-element technique such as NAA canbe essential.

Chert and flint are sedimentary rocks high in quartzthat were commonly used in tool making and for whichsource determination by chemical characterization is oftenchallenging (Luedtke 1992). Hoard et al (1992, 1993)successfully differentiated several archaeologically importantOligocene-age chert outcrops in the Great Plains, and Malyk-Selivanova et al (1998) were successful in separating chertbearing formations from Alaska. On the other hand, efforts todifferentiate between different chert outcrops in Belize havefailed to produce reliable source distinctions, the whole areabeing essentially a single chert source (Cackler et al 1999).Clearly the geographic extent and geological context of chertsources are crucial to determining whether chert provenanceanalysis will yield answers to archaeological questions.

Clays are so ubiquitous and their geological historiesare so varied that the reliability of distinguishing betweennatural sources varies widely. In general, if the parent rockcontributions and weathering histories of two argillaceous soilsor sediments are sufficiently distinct, then the provenancepostulate will apply. Unfortunately, geological processesof clay formation often do not create discrete, chemicallyhomogeneous sources but instead produce extensive depositsthat vary in composition both vertically and horizontally.

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More generally, in sedimentary clay deposits, the proportionsof material from different source rocks may vary graduallyacross horizontal space, while textural variation and chemicalweathering may create vertical differentiation within asingle stratigraphic column. Such conditions highlight theimportance of explicitly identifying the geographic scale atwhich the source is conceived (Neff 2000). After manufacture,the use of an artefact and post-depositional processes maymodify its chemistry. Lithic materials (i.e. rocks) are rarelyaffected by this problem, but for ceramic compositional studiesdiagenetic alteration is always a potential concern.

Steatite, pipestone, turquoise, limestone, marble, basalt,ancient glass, native copper, coins and other archaeologicalmaterials have been analysed by NAA with various degreesof success for archaeological interpretation (Harbottle 1976,Mead 1999, Truncer et al 1998).

4.3. Analytical procedures

In our laboratory, preparation of archaeological specimensfor instrumental NAA begins by removal of soil and otherforeign materials adhering to the surface. For lithic samples,we usually obtain the analytical sample from clean interiorfragments after breaking or crushing the specimen. Forceramics, the procedure involves burring away the surface witha tungsten carbide tool to remove glazes or slip material thatmay be contaminated by weathering or other post-depositionalprocesses. Lithic samples need only be fragmented into smallchips 2550 mg in size, while the interior paste from a ceramicsherd must be ground to a fine powder and homogenized.Individual samples are prepared for short and long irradiationsby weighing into clean polyethylene and high-purity quartzvials (i.e. low blanks) respectively. All sample weights arerecorded to the nearest 0.01 mg. Reference standards aresimilarly prepared.

A series of two irradiations and three gamma counts areperformed. The short irradiation is carried out on the samplesand standards in polyethylene vials using the pneumatic tubeirradiation system at the Missouri University Research Reactor(MURR) (flux of 8 1013 neutrons cm2 s1) in whichthe samples are sequentially irradiated for 5 s, decayed for25 min and counted for 12 min. The nine short-lived elementsmeasured are Al, Ba, Ca, Dy, K, Mn, Na, Ti and V. The samplesand standards in quartz vials used for long irradiation arebundled together in batches of 3550 samples, four unknownsand three quality control standards and irradiated in the reactorpool (flux of 51013 neutrons cm2 s1) using 24 h for potteryor 70 h for lithic artefacts. After a 7-day decay, the samplesare counted for 2000 s (the middle count) to measure sevenmedium-lived elements, including As, La, Lu, Nd, Sm, U andYb. Following an additional 3- or 4-week decay, the samplesare counted again for 10 000 s. This last measurement yieldsthe following 17 long-lived elements, including: Ce, Co, Cr,Cs, Eu, Fe, Hf, Ni, Rb, Sb, Sc, Sr, Ta, Tb, Th, Zn and Zr.

Standards and quality controls made from SRM-1633aCoal Flyash, SRM-278 Obsidian Rock, SRM-688 Basalt Rock,and Ohio Red Clay have been irradiated and counted with eachbatch of samples. These reference materials have been usedcontinually since the laboratory began in 1988. If necessary,corrections or adjustments to batches of samples in the 50 000

specimen database can be made to account for any observeddrift in the analytical data.

4.4. Evaluation of dataThe volume of compositional data generated in most NAAstudies of archaeological materials is substantial (rangingup to 35 elements). As a result, multivariate statisticalmethods are often required to quantify the similarities anddifferences between specimens and groups of specimens.Compositional groups can be viewed as centres of mass in thecompositional hyperspace described by the data. An individualgroup is characterized by the location of its centroid and theunique correlations of element concentrations to one another.Pattern recognition methods such as cluster analysis, plots ofthe original data in two or three dimensions, and principalcomponents analysis (PCA) are customary approaches to datahandling. These methods are described extensively elsewhere(Baxter 1994, Davis 1986, Glascock 1992, Neff 2002) and willbe described only briefly here.

Cluster analysis is a general term that applies to a varietyof specific techniques but the essential components are ameasure of the similaritydissimilarity between specimens(i.e. distance) and an algorithm that groups specimens on thebasis of the defined measure. The results of cluster analysis aregenerally presented in the form of dendrograms that show theorder and level of specimen clustering. Because interpretationof dendrograms is highly subjective, it is normally only usedto identify possible groups after which other techniques areemployed for group refinement and classification.

Bivariate and trivariate plots are used to examine thecorrelations between variables, identify obvious groups anddetect outlier specimens. Confidence ellipses (e.g. probabilityintervals) are usually drawn around groups to emphasizethe differences between groups or to show the associationsbetween individual specimens and known groups.

PCA involves a transformation of the dataset on thebasis of eigenvector methods to determine the magnitude anddirection of maximum variance in the dataset distribution inhyperspace. The PCA transformation provides a new basisfor viewing the entire data distribution to reveal structure notreadily observed when plotting the original variables.

Cluster analysis and many other multivariate approachesto data handling are dependent on the use of Euclideandistances to measure the dissimilarity between specimens.However, Euclidean distances are not always the best approachwhen working with geochemical data because they do notaccount for the correlations between variables. Instead, adistance measure known as the Mahalanobis distance (MD)is very useful. The MD is defined as the squared Euclideandistance between the specimen and group centroid, divided bythe group variance in the direction of the specimen. The MDfrom a specimen k to the centroid of a group of specimens Ais written as follows:

D2k A =n

i=1

nj=1

[Cik Ai]Ii j [C jk A j ] (20)

where Ai and A j are the mean concentrations of elements iand j in the group and Ii j is the i j th element of the inverse ofthe variancecovariance matrix. The MD statistic incorporates

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Figure 6. Map of the Mesoamerican region showing the locationsof major obsidian sources. The sources in Guatemala are: (1) SanLorenzo, (2) San Martin Jilotepeque, (3) San Bartolome MilpasAltas, (4) Laguna de Ayarza, (5) El Chayal, (6) Sansare, (7) Jalapa,and (8) Ixtepeque. The sources in Mexico are: (9) Pico de Orizaba,(1) Guadalupe Victoria, (11) Zaragoza, (12) Paredon, (13) SantaElena, (14) Tulancingo, (15) Tepalzingo, (16) Otumba,(17) Malpais, (18) Pachuca, (19) Zacualtipan, (20) El Pariaso,(21) Fuentezuelas, (22) Ucareo, (23) Zinapecuaro, (24) Tequila,(25) Magdalena, and (26) Teuchitlan.

information about the correlations between pairs of elementsas derived by the off-diagonal terms of a variancecovariancematrix, which simple Euclidean distance does not. Thus, itpermits calculation of the probability that a particular specimenbelongs to a group based not only on its proximity to the groupcentroid but also on the rate at which the density of data pointsdecreases away from the centroid in that direction.

5. Examples

5.1. Sourcing obsidian artefacts from Chichen ItzaThe Maya civilization was famous for its knowledge ofastronomy and for developing a writing system. The Mayaof the Classic period (AD 300900) built cities throughout

Figure 7. Bivariate plot of Na versus Mn showing 421 obsidian artefacts from the site of Chichen Itza projected against the 95%confidence ellipses for sources in Mexico and Guatemala.

the lowlands of northern Guatemala and southern Mexico,including the Yucatan Peninsula. Chichen Itza, in northernYucatan, was occupied during the Classic and subsequentEarly Postclassic period, when central Mexicoan people arethought to have intruded into the Maya area. Since ChichenItza is located approximately 700 km from the nearest obsidiansources in Guatemala and more a 1000 km from the sourcesin central Mexico (figure 6), changes in relative frequencies ofobsidian provide evidence about changing interaction patternsof the sites inhabitants.

A collection of 421 artefacts from Chichen Itza andnearby sites was submitted to the Archaeometry Lab forNAA by a collaborator (Geoffrey Braswell). The sampleswere analysed using a short-irradiation NAA procedure earlierproven successful for this region (Glascock et al 1994) andwere compared to a database of previously analysed obsidiansources. Figure 7 shows a bivariate plot of Mn versus Na for theChichen Itza artefacts compared to 95% probability confidenceellipses for nine sources located in Guatemala and Mexico.The comparison was highly successful with sources for nearlyall of the artefacts securely established. Nineteen (i.e. 4.5%)of the artefacts with the lowest probabilities of membership onthe Mn versus Na plot were submitted to the long-irradiationprocedure. Examination of the additional data found that 17of the artefacts agreed with the most likely sources suggestedby the short-irradiation procedure. The two remaining sampleswere found to be tektite (i.e. a type of glass thought to be causedby the impact of meteorites) instead of obsidian.

The Chichen Itza example illustrates that obsidianprovenance studies can be very valuable to archaeologistsinterested in studying long-distance interactions betweenprehistoric humans in the form of trade and exchange. Manyinteresting questions about the inhabitants of Chichen Itza andtheir contacts with peoples living near the obsidian sources canbe examined with the data from obsidian provenance studies.In this case, the importance of interactions with central Mexicowas established conclusively. Other objectives of obsidian

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Figure 8. Map of the Ica and Rio Grande river drainages insouthern Peru where the Nasca civilization prospered.

research are to say something about the people who usedobsidian and why their exploitation or trade patterns changed inantiquity. A comprehensive database of obsidian sources suchas that we have established at MURR is essential to answeringquestions such as these.

5.2. A pilot study on pottery from southern PeruThe Nasca culture developed along the coast of southernPeru during the Early Intermediate Period (about AD 1750).The Nasca ceramic tradition is distinguished by a finewarepolychrome pottery, found throughout the southern coastalregion and renowned for its elaborate iconography, artisticstyle and technical quality. The primary centres of Nasca

Figure 9. Biplot showing both the pottery samples and the element vectors on principal components 1 and 2 for the three Nasca potterysubgroups identified by INAA. The magnitude and direction of the vectors represent the contribution of individual elements to the principalcomponents. Projections of the vectors on to the axes are equal to the coefficients calculated by PCA. Confidence ellipses shown on the plothave been drawn at the 90% probability level for each group.

cultural development were located along the Ica and Grandedrainages (figure 8).

Recently, a MURR collaborator (Kevin Vaughn)conducted excavations at the Early Nasca (AD 1450)domestic site of Marcaya. Ceramic data and radiocarbon datesfrom the site indicate a relatively short span of occupation(Vaughn 2000). Marcayas ceramic assemblage consists of ahigh percentage of fineware pottery, especially when comparedto other sites in the central Andes. Visual examination of thefineware pastes under low-power magnification identified threedifferent paste types designated paste type A, B and C. To date,no evidence of pottery production has been found at Marcaya.

A sample of 100 excavated pottery sherds from Marcayawas submitted to MURR for NAA to determine if the potteryassemblage exhibited compositional variation. A total of 32of the 33 elements normally sought by NAA were measured.The sole exception was the element nickel, which we foundbelow our limit of detection by NAA in all 100 specimens.

The data were transformed to base-10 logarithmsand submitted to PCA. The transformation to logarithmsbefore PCA serves to make the data more normallydistributed and compensates for the different weightingeffects caused by using high concentration (e.g., Al and Fe)and low concentration (e.g. rare-earth elements) elementssimultaneously. Examination of biplots of the samplesand element vectors against the first and second principalcomponents (see figure 9) and the first and third principalcomponents showed that the majority of specimens fellinto a single homogeneous compositional group, designatedgroup 1, with a relatively small number of specimensclustering separately. The main group was evaluated andrefined using methods described in greater detail elsewhere(see Glascock 1992, Neff 2000). Specimens with probabilitiesof membership in group 1 of less than 1% were excluded.Some of the specimens not assigned to group 1 were clearlyassociated with two other distinct clusters of specimens

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Figure 10. Bivariate plot of samarium versus lanthanum for the three Nasca pottery subgroups with confidence ellipses drawn at the 90%probability level.

designated group 2 and group 3. Small sample sizes preventedtesting the latter groups as rigorously as group 1. Figure 10shows a bivariate plot of the data for the elements lanthanumand samarium with the different pottery groups surroundedby 90% confidence ellipses. Fourteen of the 100 specimenswere not assigned to any of the groups. Unassigned sherdsfrom paste types A and B (not shown) were found to have lessthan 0.000 0005% probabilities of membership in group 1.

The lack of analyses of clay sources precludes makinga strong conclusion that the pottery was not locally made.However, the data from this investigation serve as aninitial database against which future pottery analyses can becompared. The Nasca study demonstrates the strong need forsurveys of raw material sources followed by compositionalanalysis.

6. Summary

After more than three decades of successful application in thefield of archaeology, the reliability of NAA-based provenancedetermination has been firmly established. In addition to itssensitivity, accuracy and precision, the success of NAA is dueto the versatility of the method and the ease of preparingarchaeological materials for analysis. Archaeologists haverelied on NAA studies of artefacts to investigate humanactivities such as trade and exchange, population mobility andsettlement patterns. Although the number of NAA labs hasdecreased in recent years, the capacities of the remaining NAAlabs have been increased to keep pace with the still growingdemand.

Acknowledgments

The authors acknowledge their collaborators GeoffreyBraswell and Kevin Vaughn who supplied the samples ofobsidian and pottery used as examples in this paper. TheNational Science Foundation has supported the ArchaeometryLaboratory at MURR on a continuous basis since 1988.

The current grant number is BCS-0102325. We are veryappreciative of this support.

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