California Association of Chemistry Teachers
H. R. Lukens
General Dynamics General Atomic Division Son Diego, California 921 12
Activation analysis is a method for quantitatively determining the amounts or concentrations of selected elements in materials. The method utilizes nuclear reactions to produce radioactive analytical indicator isotopes from stable isotopes of the elements in a sample. This phase of the method is termed "activation." Identification and measurement of the radioisotopes gives quantitative information regarding the sample's elemental composition. Activation of a sample is generally carried out by bombarding the sample with neutrons, although highenergy photons or elementary charged particles have a useful, hut more limited, role as agents of activation. Neutrons in sufficient quantities for laboratory course work are available from isotopic neutron sources and small accelerators (1, 2 ) , and an excellent group of experiments with such sources has been described (3). However, the intense neutron environment in a nuclear reactor of even modest power rating provides the best average analytical sensitivity for a majority of elements, when compared to any other means of activation. For this reason, and because the ever increasing number of nuclear reactors extends the availability of this analytical technique to all sections of t,he country, this discussion is primarily concerned with neutron activation analysis (NAA) as carried out with the use of a nuclear reactor. Reactor Neutrons and Neutron Reoctions
There are five types of neutron reactions of interest in NAA with the nuclear reactor. Written in the usual form for describing nuclear reactions, target nuclide (bombarding particle, product particle) product nuclide, these are:
The first type of reaction, the (n,?) or neutron addition reaction, is exoergic; that is, the reaction liberates energy, most of which is carried off immediately by one or more "prompt" gamma rays. The other reactions are usually or always endoergic; that is, they require an euergy input before they can take place. The 668
/
journal of Chemical Education
input energy must be supplied by the kinetic energy of the "fast" bombarding neutrons; hence, these reactions are spoken of as fast-neutron reactions. Neutrons having several Mev (million electron volts) energy are required for most fast-neutron reactions. On the other band, the (n,y) reactions may be induced by very low energy neutrons. I n fact, these reactions are usually much more probable with neutrons of ambient kinetic energy ( 4 . 0 2 5 ev) than with fast neutrons, and therefore are called thermal-neutron reactions. Thermal-neutron reactions are, in general, about 1000-fold more probable than are fast-neutron reactions, all other things being equal. The nuclear reactor provides neutrons ranging from thermal energies up to about 20-25 Mev. The ueutrons born in fission have an average energy of about 1.5 Mev, but the energy spectrum, or "fission spectrum," of fission neutrons ranges from a few ev to about 25 Mev. The reactor includes a moderating material, such as materials rich in hydrogen or carbon, which degrades the energy of neutrons through elastic collisions. Thus, although the low-energy end of the fission spectrum itself is not highly populated, the number of thermalized neutrons in an operating- research reactor is quite high. A typical research reactor is the TRIGA Mark I reactor a t General Atomic. This reactor onerates a t a steady-state power level of up to 250 kilowatts (kw). At 250 kw the neutron flux a t sample positions in the outermost part of the core are 4.3 X 1012thermal neutrons/cm2-sec, and 3.5 X 1012fast neutrons/cm2-sec. The fast flux drops off by a factor of about 10 for each 3 Mev increment of neutron energy. Thus, the flux of neutrons 2 3 Mev is about 10'' n/cmRsec, and the flux 2 6 Mev is -10'0n/cm2-sec. It can be seen that the reactor is capable of causing all the five kinds of neutron reactions listed above. Of course, not every stable nuclide is subject to five useful reactions, since the isotopic product of some reactions are stable and some reactions give a relatively poor yield of radioisotopic product. However, there is at least one analytically useful reaction for almost every element. Reaction Yields
For each specific nuclear reaction that is caused in a sample by neutrons during a reactor irradiation, the
amount of its product activity, Ao, expressed in disintegrations per second, existing a t the end of the irradiationis given by the expression A* = Nflr(l- e+.'*'tiiT 1 (1) where N = the number of isotopic nuclei in the sample of a particular type-the type that can undergo a particular kind of reaction; f = the flux of neutrons to which the sample is exposed, expressed in neutrons/ cm2-sec; a = the reaction probability, or cross section, expressed in cm2/nucleus; T = the half life of the product radioisotope; tt = the duration of the irradiation. Often, the expression is simplified to A.
=
NjmS
8
=
(1 -
(2)
where e-9.BPU2'T)
It can be seen from eqn. (1) that Aa depends directly upon N, and that iff, o, T, and tt are known, N can be calculated after measuring Ao. Also, provided the natural distribution of stable isotopes of an element have not been artificially altered, measurement of N leads directly to the weight of the element in the sample. For example, if the product of the Cl37(n,r)Cl38reaction under defined conditions of irradiation is measured, Cla' and, thus, total chlorine can be calculated, since stable chlorine is known to consist of 75.529% CP5 and 24.471% Cla7. Since the cross sections for the (n,y) reactions are generally much greater for thermal neutrons than for fission-spectrum neutrons, and since the flux of thermal neutrons is usually about the same as or greater than that of fission-spectrum neutrons, the thermal-neutron value for o is usually used in eqn. (1) for (n,y) reactions. Significant exceptions to this rule are rare. Thermalneutron cross sections for the (n,y) reactions are given by Hughes and Schwartz (4). The cross sections for the (n,a), (n,p), and (n,2n) reactions for fission-spectrum neutrons are given by Roy and Hawton (6). These cross section values take into account the reaction threshold energies, and enable one to use the total fission-spectrumflux in eqn. (1). To exemplify the use of eqn. (I), we can calculate the MnS6 activity induced in 1 fig of manganese via the MnS6(n,y)Mn5'reaction, in a one-hour irradiation a t a thermal-neutron flux of 1013n/cm2-sec. N = 1.10 X 10" nuclei of MnS5,c = 13.3 X cm2per nucleus, T = 2.56 hr. Thus, AO = (1.10 X 10'6)(10La)(13.3 X X (1 -
e-0.693
X U2SB)
=
3.43 X 101 dpS
Radioisotope Identification
Since the irradiation of a sample will result in significant amounts of radioactivity from most of its elemental constituents, measures must be taken to discern unambiguously the particular radioisotope or radioisotopes of analytical interest. In the past, it was necessary to separate radiochemically and purify each of the desired elements, since no purely-instrumental means were available to untangle a complicated and unknown mixture of radioisotopes. Within the last decade, however, means have become widely available for measuring the energies and intensities of the various gamma rays (which are monoenergetic) given off by a radioactive sample.
Since each gamma-emitting radioisotope has a unique combination of half life and gamma-ray energy, gammaray spectrometry has made it possible to eliminate radiochemicalprocessing in many instances. The most common detector used for gamma-ray measurement is the thallium-activated sodium iodide scintillation crystal. Absorption of a gamma ray in NaI(T1) results in very short-lived fluorescence, and the intensity of the burst of fluorescent light photons is directly proportional to the gamma-ray photon energy absorbed by the crystal in an interaction event. The light signal is converted to an electric pulse and multiplied by a photomultiplier tube coupled to the crystal, and this pulse is amplified further in a linear amplifier. The amplitude.of each pulse is measured by a multichannel pulse-height analyzer. With this apparatus one obtains pulse-height spectra with peaks (photopeaks) that permit one to determine the energies of the various gamma rays emitted by a radioactive sample. The integrated peak area is a quantitative measure of the activity of the gamma emitter. A typical gamma-ray spectrum, obtained from 3.76min VS2,is shown in the figure. The broad region
I
100
< H n N n l l NUMBER
A simple pulre-height spectrum.
covering the lower-energy part of the spectrum, up to the Compton edge (C.E.), is called the Compton region, because of the fact that many of the gamma-ray photons undergo Compton scattering in the NaI(T1) crystal, and then leave the crystal. In such cases, only part of the gammsrray photon's energy is deposited in the crystal, and the fluorescence burst is less than for full absorption of the gamma-ray photon. The signal delivered to the analyzer will in such cases not be stored in a channel representing the gammsrray photon's primary energy, but will he stored in a channel representing the lower energy signal. The chief process responsible for total absorption of a gamma-ray photon is the photoelectric interaction, wherein the total energy is transferred to a single electron. Hence the peaks in the pulse-height spectra are often called photopeaks. The 0.217 Mev peak in the figure noted as B.S. is due to 180' backscattering of some of the 1.43 Mev VS2 gamma-ray photons off of the walls of the lead cave that is used to shield the detector from background radiation. The 0.511 Mev peak in the figure is from the annihilation of positrons produced by pair production interactions of some of the 1.43 Mev gamma-ray photons in the lead shield. Volume 44, Number 1 7 , November 1967
/
669
A single pulse-height spectrum may suffice to completely identify the indicator radioisotopes of interest. However, it is often necessary to have supplemental information. For example, several successive spectra will give half-life information that will enable one to calculate the contributions of Mgn (half life of 9.45 min) and Mnse (half life of 2.58 hr), both of which emit gamma rays of about 0.845 Mev. Some knowledge of a sample's characteristics or history can he helpful. For example, the 0.845-Mev gamma-ray photopeak from an activated sample of nichrome will be due to Mn55 since the alloy contains about 2% Mn and very much less Mg-and manganese is much more sensitively determined by thermal-neutron activation than is magnesium (about 10,000-fold more sensitively). Sometimes gamma-ray spectra do not completely suffice for an analysis. One or two elements may dominate the spectra by virtue of a combination of concentration in the sample and high specific radioisotopic yield. In such cases, some radiochemical processing may be required. Radioisotope Measurements and the Analytical Result
It is usual in NAA work to keep the sample and detector separate. This is necessary, of course, in gamma-ray spectrometry. As a result, some of the sample's emitted radiation will not strike the detector. Furthermore, in gamma-ray spectrometry only a fraction of the gamma-ray photons intercepted by the detector will appear as counts in the photopeak. Thus, there is an overall counting efficiency factor, CE, that relates the observed photopeak count rate to the sample's rate of gamma emission of a particular energy. In addition, not all of a sample's disintegrations necessarily give rise to the radiation being measured. For example, Crsl emits 0.323 Rlev gamma-ray photons in only 9% of its disintegrations. I t is thus said to have a yield factor, Y, of 0.09 for these gamma rays. Inclusion of Cb and Y in eqn. (2) gives the count rate, R, of the measured radiation: Equation (3) provides a practical basis for determining N, the basic desired analytical result. I t is especially useful where an unknown sample is to be surveyed for many elements. However, in many cases the values of f, a, and even T may not be known very precisely, which urill thus reflect on the precision of results computed with equation (3). Improved precision can be obtained by using the comparator method of analysis. If a known amount, w,, of an element to he determined is activated and counted under exactly the same conditions as the unknown sample, the relative intensitities of the indicator radioisotope in the comparator and sample will give the amount of the element, w,, in the sample:
51-here R, is the indicator count rate in the sample, and
R,is the indicator count rate in the comparator standard. In practice, it is possible to irradiate the sample and standard simultaneously under equal conditions. In 670
/
Journol of Chemical Education
the TRIGA reactor, a rotary specimen rack will rotate a large number of samples around the core at 1 rpm, which insures that simultaneously-irradiated samples receive exactly the same integrated irradiation, wen though the reactor may not have, for various reaions, exactly the same neutron flux in all directions. at a fixed distance from the center of the reactor core. However, samples will usually be counted on a particular counter in serial order. Thus, their comparison must be adjusted to a common time. It is usual to adjust sample count rates to the time at 11-hich the standard is counted, using, where R. is the indicator count rate adjusted to the standard reference time; Rois the observed indieator count rate in the sample; T is the half life of the indicator radioisotope; td is the time difference between the times at which the sample and standard 11-ere counted, assuming that the standard is counted first. Combining equations (4) and (5), ZU" =
(ROe*.~$J'dl=)(t&) R'
(6)
Analyses carried out with the use of eqn. (6) are more precise than those carried out with the use of eqn. (31, simply . . because the former involves fell-er variables. I t is accepted practice to use only the integrated nhoto~ealccounts of the indicator radioisotone. d e r e gamma-ray spectrometry data are available, eren where the sample's spectrum appears to have only one radioisotopic component. In a complex spectrum, all peaks except the most energetic peak will rest on a baseline, thus the necessity for using only integrated net peak counts for the determination of each radioisotope is evident. The integrated net counts of a peak are obtained by subtracting the baseline counts (counts below a line drawn between the inflection points a t which the peak begins and ends) from the gross counts in the peak (since the counts in the base are due to Compton interactions from higher-energy gamma rays, rather than from the gamma ray being measured). &
,
Analytical Sensitivity
Criteria for analytical sensitivity (i.e., limits of detection) for NAA are somewhat arbitrary. It is fairly realistic to require indicator activities that are roughly inversely proportional to half life. Thus, we may arbitrarily, but realistically, assume that 1000 cprn (counts per minute) are needed where T is less than one minute, 100 cpm where T is between one minute and one hour, and 10 cpm where T is greater than one hour. In general, these criteria allow for detection in a practical analytical situation, so long as interferences are negligible. Obviously, where the half life is very long, as in the case of Cow (T-5.24 years)- or Se7"T-121 days), it is possible, if one wishes, to use very long counting periods, in order to obtain sensitivities superior to those indicated by these criteria. However, demands for instrument time may render such long counting periods impractical, Sensitivities for the various elements, based on the above criteria, are given in the table. This table is based on gamma-ray emitting indicator radioisotopes
NAA Limits of Detection for 76 Elements (Conditions specified in text)
Sensitivity Range (ei
Elements
10-'0-10-" 10-9-10-"
Mn, In, I, Eu, Dy, Au Ar, Y, Br, Kr, Cs, Sm, Ho, Er, Lu, Hf, Re,
10'-10-0
N ~ , > ASe, I , Co, Cu, Ga, As, Sr, Rh, Ag, Cd, Sn, Sb, Xe, Ba, La, Nd, Gd, Yb, It' C1, K, Ti, Zn, Ge, Se, Rb, Zr, Mo Ru Pd, Te, Ce, Pr, Tb, Ta, Os, Pt, H g , ' d F,Mg, Si, Cr, Fe, Ni, Y, Nb, Tm, Th9'? Ne, P, Ca, Pb
TI
1O"lO" 1 - 1 lW-lO-' 10-~-10-~ 10-~10-4
3,
ST1
only, and gives those sensitivities attainable by using the integrated, most prominent, photopeak of each indicator's gamma-ray pulse-height spectrum. Accurate values have been accurately determined experimentally, in the author's laboratory, at a fluxof 4.3 X lo1?thermal n/em2-see, where the indicator activity is produeed by the ( n , ~reaetion, ) or at a fluxof 3.5 X 1012 fission-spectrum n/cm2-see, where the indicator activity is produeed by a fast-neutron reaetion. A 3-in. diam by 3-in. high solid NaI(T1) detector with a '/*-in. plastic cover at one end (to absorb beta partieles) was used, and 1-ce samples were centered on the cover. Irradiation times of 1hr (or less, if saturation is reaehed sooner) were used. The values presented in the tahle were rounded off to conserve space. They are sensitivities that can be reaehed under the specified eonditions in the absence of interferences. I t is seen from the table, that the limits of deteetion range from as low as 10-'I g (10-"g), for a few very sensitive elements, to as high as g (100 ~ g )for , a few rather insensitive elements. The median limit of detection for the 76 elements listed is about 10-=g (0.01fig). Again, where the indicator activity is long-lived, an improved sensitivity can he obtained by increasing the irradiation time. Special Techniques
The conditions of irradiation and counting given in the previous section satisfy the requirements for most analyses. However, a number of special procedures and types of equipment are available to further extend the method's capability, where needed, regarding praetical analytical sensitivit,y. These include coincidence eounting, anticoincidenee eount,ing, counting with semiconductor detectears, Cerenkov eounting, mnltichannel sealing, pulsed activation, activation ~ r i t h neutrons of selected energies, and reduction of data by computer. Coincidenee and anticoincidence eounting in the enhancement and suppression of relative eount rate, respectively, of positron emitters are examples of twodetector-system applications. A positron (@+) is annihilated when i t interacts with an electron to produce two 0.511 Mev gamma-ray photons, traveling in opposite directions. Thus, if a positron emitter is placed between two NaI(T1) detectors, there is a good chance that one 0.511 Mev photon, from a @+ annihilation event, will strike each detector. If the system requires simultaneous detection of a gamma-ray photon by each detector before a eount is registered, the counting of annihilation gamma rays will be favored relative
to events that give rise to single gamma-ray photons or randomly distributed sequential gammas-this is a form of coincidence counting. If the system is arranged to reject coincidences, then the counting of positron emitters will be suppressed, whieh is a form of anticoincidencecounting. A special form of coincidence counting utilizes a large NaI(T1) "well-counter," where the sample is placed in the well so that simultaneous deteetion of more than one gamma-ray photon will result in summation of the absorbed energy. Thus, the 1.17 and 1.33 cascade gamma-ray photons of Coeocan be summed to give a 2.50 Mev peak, whieh can serve to discern Co60from a relatively large amount of FeSg (whieh emits either a 1.10 or a 1.30 Mev gamma-ray photon, but not both, per disintegration). In recent years, lithium-drifted germanium semiconductor detectors have been developed for the measurement of X-rays and gamma rays. These devices, although not as sensitive to higher-energy gamma rays as NaI(Tl), have comparatively great resolving power. The usual NaI(T1) detector has a resolution (full width at half-height of the peak) of about 7-8% at the usual gammeray reference energy (the 0.622 Nev of Cs13'). This is not good enough, for example, to resolve the 0.633 Mev gamma rays of Ag'08 from the 0.618 Mev gamma rays of Br". However, Li-drifted Ge detectors have been made with resolutions of a few kev (1 kev = 0.001 Mev)-more than sufficient to resolve these two gamma rays. The improved resolntion often eliminates the need for radiochemical separations. It is relatively seldom that beta-particle @-) emissions are measured in NAA studies, because they lack the characteristic of being monoenergetic. An exception is the utilization of P3?,a pure beta emitter, for the determination of phosphorus-after, however, radiochemical separation. Other exceptions apply to radioisotopes that also emit high-energy @- partielesbetas that give rise to Cerenkov radiation in water, lueite, or other transparent media. The intensity of each Cerenlcov light pulse is proportional to the energy of the beta partiele. Thus, it is possible to use a photomultiplier tube and pulse-height analyzer to selectively measure the Cerenlcov radiation caused by high-energy beta partieles in the presence of other radiation. For example, the 10.4 Mev. (E.,) beta particles of N16 can be discerned with ease in the presence of many orders of magnitude more gamma or low-energy @- radiation from other radioisotopes. The Cerenkov detector is almost completely insensitive to gamma rays and to beta partieles below about 0.25 Mev. Many multichannel pulse-height analyzers may be operated as multichannel sealers. That is, all of the initial input counts are stored in the first channel for a preselected interval of time, after whieh they are stored in the second channel for a like interval, and then in the third channel, and so on. The result is a set of data that indicates the rate of deeay of the sample, and the deeay curve can be resolved into its component half lives to separate and identify the various contributing radioisotopes. The multichannel-sealing mode of operation is particularly useful in the measurement of shortlived radioisotopes. For example, the 0.841-see betapartiele emitter, Lia (8- Em..of 13.1 Mev) can be reVolume 44, Number 1 I, November
1967 / 671
solved in the presence of N" (10.4 Mev E,, (3, 7.35-sec half life) by Cerenkov counting in multichannel-scaling mode. The TRIGA reactor, mentioned earlier, incorporates a significant amount of moderator (hydrogen) in the fuel element, where it is instantly sensitive to the fuelelement temperature. Thus, when the fuel element becomes hot, so does this moderator, and promptly. When the moderator becomes hot, it cannot function so efficiently to slow neutrons to the low energies required for an efficient reactor operation. This feature allows one to pulse the reactor to very high power and flux levels, by allowing it to rapidly escalate to a very high power level, a t which point the fuel elements become hot, and the reactor automatically (intrinsically) shuts itself down-all within the period of about 20 milliseconds. The TRIGA Mark I reactor can be pulsed to a power level of about one billion watts, safely, and a t intewals of about 6-8 min between pulses. Very high neutron fluxes are available in such a reactor pulse-well over n/cm2-see. The pulse favors the formation of short-lived radioisotopes, and the amount of a particular activity, A,, produced in a pulse, relative to the amount of activity produced in the usual steady-state operation of the same reactor (to saturation activity), A,, is approximately: A J A , = 70/T (with T i n sec). Thus, for example, a sensitivity gain of 28-fold is obtained relative to steady-state operation in the determination of erbium via the pulsed activation of Erlam (2.5-sec half life). If a sample is wrapped with cadmium during an irradiation, thermal neutrons are largely prevented from reaching the sample, and ( n , ~ )reaction in the various elements present is largely suppressed. However, the fast-neutron reactions are unaffected. Thus, it is possible to emphasize fast-neutron reactions for NAA, if desired. The measurement of silicon via the SiZ8(n,p)AI28reaction, while suppressing the Aln (n,y)AIz8reaction, is a case in point. Computer programs have been devised for the interpretation of gamma-ray pulse-height spectra and decay curves obtained in NAA studies. There are programs for locating photopealts and defining their energies, programs for integrating peak areas and relating these to peak areas of comparator standards, programs for determining upper limits for elements not evidenced by the data (in other words, determining how much of such an element would be required for observation), and so forth. Furthermore, devices have become available for transferring the data stored in a multichannel analyzer directly to tape or cards that may be fed directly to a computer. Thus, NAA systems have been automated to a great extent. Applications
NAA has been utilized in virtually every field re-
672
/
Journol of Chemical Educafion
quiring elemental analysis. Example determinations are: (1) biomedical-trace elements (Mn, Cu, Zn, Se, F, etc.) in tissues, (2) metallurgy-trace impurities in metals, as well as checking the levels of main alloy constituents, (3) electronics-dopants and impurities in semiconductors, (4) petroleum-trace catalyst poisons in catalytic-cracker feed stocks, (5) agriculture-pesticide residues in crops, (6) geology-determination of composition of rocks, soils, and ores, (7) chemical industry-polymerization catalyst residues in plastic products, (8) forestry-trace elements in trees, (9) inorganic chenustry-composition of new inorganic compounds, (10) environmental pollution-trace elements in streams and stack effluents, and (11) crime investigation-detection of gunshot residues and characterization of physical evidence specimens. Summary
We have seen that reactor NAA has the virtues of great sensitivity and simultaneous multielement analysis. I n many cases it is a purely instrumental, nondestructive, highly-automated technique, wherein a weighed sample may be sealed in a polyethylene vial (carbon and hydrogen are among the few insensitive elements), activated, counted by multichannel gammaray spectrometry, and the results obtained by computer. Since it is a nuclear technique, NAA depends on very penetrating radiations, which sewe to minimize sample matrix effects, and permit a great flexibility in choice of sample size. Equation (2) shows us that, when carried out properly, we can expect a linear relationship between activity and concentration over the entire concentration range of the method. Furthermore, the n~ethod'sutility is constantly expanding, as new devices and techniques permit greater selectivity and speed of analysis. Literature Cited (1) WISE, E. N., THIS JOURNAL, 39, A771 (1962). R. S., AND MEINKE,W. W.,THIS (2) Nass, H. W., MADD~CK, JOURNAL, 41, 156 (1964). (3) VORRES, K. S., THIS JOURNAL 37, 391 (1960). (4) HUGHES,D. J., and SCHWARTZ, R. B., "Neutron Cross Sections," BNW2.5, July 1, 1958. Second edition. Bvailable from Superintendent of Documents, U.S. Government Printing Office, Washington, D. C. (5) ROY,J. C., AND HAWTON, J. J., "Table of Estimated Cross Sections for (n,p), (n,a), and (n,2n) Reactions in a Fission Neutron Spectrum," AECL-1181, December, 1960. Available from Atomic Energy of Canada Limited, Chalk River, Ontario. General References (6) LYON,W. S., JR., Editor, "Guide to Activation Analysis," Van Nostrand, Princeton, N . J., 1964. (7) BOWEN,H. J. M., AND GIBBONS,D., 'iRadi~acti~ation Analysis," Oxford University Press, London, 1963. J. AT. A,, AND THOMSON, S. J., "Activation And(8) LENIHAN, ysis," Academic Press, London and New York, 1965.
