Activation Analysis, Volume I

Analysis Volume I

Editor

Zeev B. Alfassi, Ph.D. Professor

Department of Nuclear Engineering Ben Gurion University of the Negev Beer Sheva

Israel

NIC

LIBRARY

CRC Press, Inc. Boca Raton, Florida

Library of Congress Cataloging-in-PublicationData Activation analyis / editor Zeev B. Alfassi. p. cm. Includes bibliographical references. ISBN 0-8493-4583-9 (v. 1). -- ISBN 0-8493-4584-7 (v. 2) 1. Nuclear activation analysis. I. Alfassi, Zeev B. QD606.A252 1990 543' ,0882--dc20

89-24021

CIP This book represents information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Every reasonable effort has been made to give reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. All rights reserved. This book, or any parts thereof, may not be reproduced in any form without written consent from the publisher. Direct all inquiries to CRC Press, Inc., 2000 Corporate Blvd., N.W., Boca Raton, Florida 33431.

" 1990 by CRC Press, Inc. International Standard Book Number 0-8493-4583-9 (Volume I) International Standard Book Number 0-8493-4584-7 (Volume 11) Library of Congress Card Number 89-24021 Printed in the United States

PREFACE Elemental analysis is done best by nuclear methods since these are determined only by the nuclei and are not affected (in most cases) by the surrounding electrons, i.e., the chemical environment. Activation analysis is a method of quantitative chemical analysis of the elemental composition of the samples based on the nuclear activation of the atoms of the chemical elements present in the analyzed sample. Activation analysis usually has the following advantages: (1) simultaneous multielement analysis, (2) very high sensitivities (detection of limit in the range of ppm and ppb or less), (3) nondestructive analysis, and (4) easy and fast analysis which in many cases can be automated. The book describes both prompt measurements (both y and particles) and delayed activities (mainly y-ray spectrum). The book treats the various methods of activation, i.e., activation by neutrons, accelerated charged particles, and high-energy photons. Special chapters are devoted to the application of these methods in the fields of life sciences, biological materials, coal and its effluents, environmental samples, archeology, material science, and forensic studies.

THE EDITOR Z. B. Alfassi, Ph.D., is a professor and the chairman of the Nuclear Engineering Department in the Ben Gurion University, Beer Sheva, Israel. Professor Zeev B. Alfassi received his B .Sc. and M.Sc. degrees from the Hebrew University in Jerusalem in 1964 and 1965, respectively, in the fields of chemistry and biochemistry. He received his Ph.D. from the Weizmann Institute of Science and the Soreq Nuclear Research Center in 1970. Professor Alfassi is a member of the council of the Israel Nuclear Society. He has published more than 100 scientific papers and edited the CRC book Chemical Kinetics of Small Organic Radicals. His current research interests include chemical analysis by nuclear methods, radioisotope production and uses, radiation chemistry and chemical kinetics of radicals in solution, and solubility of electrolytes in water-miscible organic-solvents mixture.

CONTRIBUTORS Volume I D. D. Burgess, Ph.D. Manager Chemex Labs Ltd. Mississauga, Ontario, Canada

Mariana Mantel, Ph.D. Senior Radiochemist Soreq Nuclear Research Center Yavne. Israel

William D. Ehmann, Ph.D. Professor Department of Chemistry University of Kentucky Lexington, Kentucky

S. Iraj Najafi, Dr. Ing. Senior Research Scientist Department of Engineering Physics Ecole Polytechnique Montreal, Quebec, Canada

John J. Fardy, M.S. Leader Radiochemistry Group Centre for Advanced Analytical Chemistry CSIRO Division of Fuel Technology Meani, New South Wales, Australia

Nobuo Suzuki, Dr. Sci. Professor Department of Chemistry Tohoku University Sendai, Japan

Vincent P. Guinn, Ph.D. Professor Department of Chemistry University of California Irvine, California

Masuo Yagi, Dr. Professor Institute for Materials Research Tohoku University Sendai, Japan

To my parents Arieh and Lea the lion and the lioness

TABLE OF CONTENTS Volume I I. GENERAL Chapter 1 Introduction - Principles of Activation Analysis ........................................3 Z. B. Alfassi Chapter 2 Computerized Analysis of y-Ray Spectra.. ...............................................9 , S. I. Najafi Chapter 3 Optimization of Instrumental Activation Analysis .......................................39. D. D. Burgess Chapter 4 Limits of Detection in Instrumental Neutron Activation Analysis .......................55 V. P. Guinn Chapter 5 Radiochemical Separations in Activation Analysis J. J. Fardy

......................................61

Chapter 6 Use of Delayed Neutrons in Activation Analysis.. ...................................... 9 7 Z. B. Alfassi Chapter 7 Use of X-Ray Emitters in Activation Analysis .........................................1 1 1 M. Mantel Chapter 8 .I31 Stable Isotope Dilution Activation Analysis ........................................... M. Yagi Chapter 9 Substoichiometric Radioactivation Analysis N. Suzuki

............................................145

Chapter 10 Utilization of Chemical Derivatives in Activation Analysis.. ...........................165 W. D. Ehmann Index ................................................................................... I 7 3

VOLUME OUTLINE Volume I1 ACTIVATION METHODS Activation with Nuclear Reactors 14 MeV Neutrons Activation Analysis Prompt Activation Analysis with Charged Particles Photon Activation Analysis Activation Analysis with Isotopic Sources Activation Analysis with Small Mobile Reactors APPLICATION OF ACTIVATION ANALYSIS Activation Analysis of Biological Materials Activation Analysis of Coal and Coal Effluents Activation Analysis of Water Samples In Vivo Activation Analysis Activation Analysis in Archaeology Activation Analysis in Forensic Studies Activation Analysis in Atmospheric Environmental Samples Activation Analysis in Agriculture and Botany Activation Analysis of Semiconductor Materials Depth Profiling of Silicon by Nuclear Activation Methods INDEX

General

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3

Chapter 1

PRINCIPLES OF ACTIVATION ANALYSIS Zeev B. Alfassi

TABLE OF CONTENTS I.

Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

11.

Basic Nuclear Chemistry.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4

Activation Analysis

I. INTRODUCTION Activation analysis is a method of quantitative chemical analysis based on the nuclear activation of the chemical elements present in the analyzed samples. The method is one of the most sensitive methods of chemical analysis. The discovery of nuclear activation, i.e., the reaction of elements with other nuclei or subnuclei particles to give radioactive substances, was made in 1934 by Irene Joliot Curie and Frederic Joliot who bombarded aluminum, boron, and magnesium with naturally occurring alpha particles. The suggestion to use the activation method for elemental analysis was done in 1936 by Hevesy and Levi who used neutrons as the bombarding projectiles to activate dysprosium and europium. The method could be used either if newly produced nuclei were radioactive with appropriate half-lives and emitted radiation (by measurement of this delayed radiation) or even if the newly produced nuclide was stable or had undesired radiation or half-life by the measurement of the radiation (photons or small particles) emitted in the time of activation - a prompt radiation measurement. The use of delayed measurement is the more common one. The use of prompt method is not limited to cases where the formed nuclide has undesired nuclear properties but also in some other cases where its advantages (e.g., less activation or smaller sources) overcome the disadvantages, (e.g., less sensitivity or selectivity), e.g., on line measurement of bulk elements in coal by isotopic source neutron irradiation or in vivo measurements. Activation analysis relies on the nuclear reaction between projectiles and target nuclei. In delayed measurement, the nuclear reaction leads to production of radioactive nuclides in the samples and the amount of the radioactive atoms of each element are measured subsequently by nuclear radiation detectors. In prompt measurements, nuclear radiation (photons or particles) emitted simultaneously with the nuclear reaction are measured, independent if the product of the nuclear reaction is radioactive or not. Activation analysis can be used to determine either trace elements or bulk elements. The trace elements are determined usually by delayed radiation since the prompt measurements are less sensitive. The analyzed samples can be activated by bombardment with thermal neutrons, fast neutrons, energetic charged particles, or high energy photons. The activation with thermal neutrons is the most widely used form of activation analysis due to larger flux and large cross-sections. The amount of emitted radiation, either prompt or delayed, depends on the number of atoms which have been activated. The number of activated atoms is proportional to the number of atoms in the target sample, and consequently, the activation method can be used to analyze quantitatively the elemental contents of the sample. The rate of nuclear reaction in a given irradiation system is proportional to the flux of the incident radiation and the number of the target nuclei. The proportionality constant depends on the probability that an incident particle will react with a target nucleus. This probability expressed in terms of area is called the cross-section s of a particular reaction. cmZ.Besides these factors (flux of projectiles, The unit used for s is the barn 1 b = number of target nuclei, and activation cross-section), the induced activity depends on the duration of the irradiation and the half-life of the formed radionuclide. The nuclear activation of the analyzed samples is followed by the quantitative detection (counting of radioactive emission) and identification of the induced activity as to the type of radiation emitted, its energy, and its half-life. The most common and sensitive method of activation analysis is by activation with thermal neutrons in the high flux of a research reactor and measuring the radioactivity induced in the newly formed radionuclides from the stable isotopes present in the sample. For example, the amount of bromine in a sample is measured by the 616 keV gamma emission of 'OBr formed from 79Br(n,y)80Br(abundance of 79Br = 50.7%, cross-section = 8.5 b, half-life of 80Br(t,,2) = 17.6 min, intensity of y

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5

rays = 6.7%) or by 82Br777 keV gamma line from 81Br(n,y)82Brand 81Br(n,y)82mBr+82Br 0.26)b, half-life of 82Br = 35.3 (abundance of 81Br = 49.3%, cross-section = (2.43 h, intensity of y rays = 83%). When all the parameters determining the induced activity (the flux of the projectile and its energy spectrum, the cross-sections and their energy dependence, the time of irradiation, half-lives, and detector efficiencies) are known, the quantity of the elements can be calculated from the measured radioactivity. However, in most analytical cases, a use of a comparator, which is irradiated under the same conditions as the sample, is preferred. The comparator consists usually of a mixture of elements in which the concentration of each element is known quite accurately. The quantity of an element X to be determined is given by the equation

+

quantity of X in sample

=

quantity of X in comparator .

radiation of X in a sample radiation of X in comparator

(1)

The use of multielement standards cancels the errors due to unknown energy spectrum and excitation functions (energy dependence of cross-sections), although other errors, e.g., self-shielding and interfering peaks are not removed. These errors depend not only on the contents of the determined elements, but also on the concentration of the main elements in the matrix, and unless the two matrices are quite similar, they are not removed. A great deal of effort is done to increase the accuracy of the measurements using a monostandard and to prepare reliable multielement standards. The irradiated samples usually contain more than one element which becomes radioactive and hence the accuracy and the sensitivity of the analysis are often dependent on the ability to distinguish between the radiation of the different radioisotopes or to separate the different elements in the irradiated mixture. If a complete separation of the elements is done, their radioactive emission can be measured very accurately with simple instrumentation. However, this method requires a lot of chemical work and this method is almost neglected in most cases and a purely instrumental activation analysis (IAA) is used or at least the separation of the mixtures to small number of fractions (see Chapter 5) in which several elements are measured simultaneously. The purely IAA has the advantages of (1) multielement determination in one measurement, (2) lower costs of analysis although it requires more expensive equipment for measurement, (3) ease in automation, (4) ability to use short-lived radioisotopes which for some elements are the only ones available, (5) being nondestructive and being able to be used for precious samples or those which do not dissolve easily, (6) no question of efficiency of the separation process and the errors due to this process are involved. Activation analyses are done mainly with the measurement of gamma rays due to their high penetration (in contrast to charged particles and X-ray photons), the large number of elements which produce gamma-emitting nuclides, and the existence of high resolution gamma-ray spectrometers which allow the determination of the energy of the gamma rays. The different radionuclides produced in activation analysis are distinguished by their different gamma-ray energies (see Chapter 2 for computerized analysis of gamma-ray spectra) and sometimes also by their half-lives. There are two kinds of interferences in IAA by gammaray analysis besides the interference from highly radioactive products due to major constituents which can mask the gamma-ray spectra. The first kind of interference is when the same radionuclide is produced from two different elements, e.g., 28A1which is produced from 27Al(n,y)28A1, 28Si(n,p)28A1,or 31P(n,a)28A1.This interference can be solved if one of the elements also produce another radionuclide, e.g., natural silicon also produces 29Alvia constant, ~ S i the amount of the contribution the reaction 29Si(n,p)29A1.Since the r a t i ~ ~ ~ S iisl ~ of silicon to '*A1 can be calculated from the activity of 29Al which is formed only from

6

Activation Analysis

silicon. Another way is in the case where the cross-sections of the interfering reactions depend differently on the energy of the activating particles. In that case, the irradiation with projectiles at different energies allows the measurement of both elements. For example, in the case of 28A1,the (n,y) reaction is done mainly by the thermal neutrons, while for the (n,p) and (n,a) reaction, fast neutrons are required. Thus the use of thermal neutron absorbers (cadmium or boron) enable the determination of both elements (see Volume 11, Chapter 1). Another example is the determination of lithium and boron by proton activation analysis via 7Be formed by the reaction 7Li(p,n)7Beand l'B(~,a)~Be. It was found that, with 1.%-MeV protons, only the second reaction occurs, while at 7.4-MeV protons, the first reaction has higher cross-section than the second one. Thus by the use of proton irradiation at both 1.55 MeV and 7.4 MeV, both Li and B can be determined. In most cases, the radiation measured is gamma radiation. However, in several cases, use of other radiation, such as beta particles, X-rays, and neutrons, are used. If it is impossible to separate the activities due to the undesired elements from the overall spectra; radiochemical separation of the irradiated sample is required in order to get rid of the interferences. The separation of the desired elements from the interfering ones is preferably performed after the irradiation and not before irradiation to eliminate the possible contamination of the sample by the chemicals used (see Chapter 5). Some techniques were devised to facilitate activation analysis where it is not possible or not sensitive enough, e.g., the use of derivative techniques or substoichiometric activation.

11. BASIC NUCLEAR CHEMISTRY In this chapter, only the basic ideas of nuclear reactions are dealt with. The notation for nuclear reaction is similar to chemical reaction notation, however, in a more concise form. For example, the first nuclear reaction which was studied was the reaction of radioactive nuclides of alpha particles with aluminum to give 30Pand neutron which the chemists write as 4He "Ab3OP In, while the nuclear chemist writes it in the concise form 27Al(4He,1n)30P or 27Al(a,n)30P.In this notation, the bombarding particle and the light product are written in parentheses between the initial and final nuclei. The atomic numbers are usually omitted and neutron, proton, deutron, triton, and alpha particles are represented by the symbols n, p, d, t, and a , respectively. In nuclear reactions, there is conservation of the number of protons and the number of neutrons (i.e., both the sum of atomic numbers and mass numbers are conserved). energy are conserved in nuclear reaction and the energies of the reaction The mass can be calculated from the differences between the masses of the products and the masses of the reactants. When a positively charged particle reacts with a target nuclei, the bombarding particle must have a sufficient energy to overcome the Coulombic repulsion energy - the Coulombic barrier:

+

+

+

E,,

= 1.109

A, + A2 Z,Z, (MeV) AF3 Al Akt3

+

where A is the mass, Z the charge, and 1 and 2 are the particles and target, respectively. The probability for a nuclear reaction is expressed in terms of the reaction cross-section -a. This term is derived from the elastic scattering geometric cross-section mz,which a target nucleus of radius r presents to an incident particle. Consider the irradiation of a target of area A, thickness X, and which contains n atoms per cm3 by a homogenous perpendicular beam of particle. The sum of cross-sections of all particles in the target is A X n a where a is the geometric cross-section. Assuming that the probability of an incident particle to react within the target is the ratio of the geometric cross-reactions of all target nuclei to

. .

Volume I

7

- -

the area of the target, the probability equals X n a. This use of u in the term of the probability is used for all reactions even if u is not always given by m 2 . The rate of a specified nuclear process, R, (events per unit time), induced by a beam of particle impinging on a thin target in which the beam is very little attenuated, is given by the equation

where ui is the cross-section for the specified process in units of cm2. The usual unit for cross-section is the barn where 1 b = lOPz4cm2.I, the fluence, is the number of bombarding particles per unit time. When the sample is situated in a uniform flux of particles bombarding it from all directions, as for example in a nuclear reactor, I is replaced by the flux 4, being the number of bombarding particles per unit time per unit area, (+ = VA). nXA gives the total number of nuclei in target, N,, and Equation 2 is transformed into the equation

+

+

the flux is given in units of number of impinging particles per unit area per unit time. When several reactions can occur between the incident particle and the target nuclei, each process has its own partial cross-section which gives the rate of formation of the specified product. The cross-section for disappearance of the target nuclei is the sum of the partial cross-sections. -

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Chapter 2

COMPUTERIZED ANALYSIS OF GAMMA-RAY SPECTRA

.

S Iraj Najafi

TABLE OF CONTENTS I.

Introduction ...................................................................... 10

I1.

Analytic Approximation of Gamma-Ray Spectra .................................10 A. Physical Aspect .......................................................... 11 B. Analytical Representation ................................................ 11 C. Fitting Method ...........................................................14 D. Calculation and Comparison ..............................................16 1. Distortion Is a Symmetrical Gaussian .............................17 Exponential Distortion ............................................17 2. 3. Asymmetrical Distortion Function ................................17 4. Deformed Gaussian ...............................................17

111.

Analysis of Gamma-Ray Spectra by Nonlinear Least-Squares Fit ................ 18 A. Analysis by the Program Developed by Najafi ...........................20 1. Smoothing of the Experimental Data ..............................20 Peak Searching ...................................................21 2. Selection of Fitting Intervals ......................................24 3. 4. Peak Energy Calculation ..........................................24 B. Analysis by SAMPO Program ............................................24 Analysis by SPAN .......................................................25 C. Calculation and Comparison .............................................. 25 D.

IV .

Analysis of the Spectra Using a Summation Method .............................27 A. Peak Search .............................................................. 27 B. Peak Integration .......................................................... 28 Application ............................................................... 28 C. 1. Single-Element Analysis ..........................................28 2. Multielement Analysis ............................................28

V.

Gamma-Spectra Analysis by an Empirical Method ...............................31 Parameters of a Photopeak ...............................................31 A. B. Experimental Study of Variation of Parameters ..........................31 C. Translation of Standard Peak .............................................33 D. Fitting Method ........................................................... 34 Application of the Method ...............................................34 E.

References ...............................................................................38

10

Activation Analysis

I. INTRODUCTION With the use of high-resolution semiconductor detectors and multichannel analyzers, gamma spectrometry has become an important tool for numerous applications: detection of natural and artificial radioactivity and activation analysis. The energy resolution of these systems allows the selective detection of radiosotopes and the determination of their activity. To benefit from the high resolution of these detectors, the gamma spectra should be digitized using a large number of channels. These spectra, especially those of fission products and those from samples activated by irradiation, can be very complex. It is not practical to analyze these spectra by manual numerical techniques. Use of computers is essential. Automatic analysis of the gamma-ray spectra has been studied by several investigators. The reported analysis approaches are based on different principles depending on the type of available computer and the complexity of the gamma spectrum. Many algorithms and computer programs will be mentioned in this chapter and quantitative comparison of several methods will be performed when different phases of numerical analysis are considered. A gamma spectrum consists of a series of rays which are characteristic of the radioisotopes present in the sample, and a continuous background. The two principal roles of the numerical analysis are the automatic peak search and the measurement of gamma-ray energies and intensities. In the literature, a number of methods for gamma-ray spectra processing have been reported. The methods of peak search are based on second derivative operation,' resolution enhancement using Fourier Tran~formation,'.~resolution enhancement transformation by convolution operati~n,~.' statistical comparison of channel inten~ities,~.~ and the first derivative method.8-" A few of these techniques will be examined and compared in this chapter. For energy and intensity calculation, many codes are based on the principle of leastsquare fitting of a portion of the spectrum using an analytical f ~ n c t i o n . ~ , ~ -The " ~ 'form ~-~~ of the peak depends on the physical process taking place in the detection of the gamma ray and varies from one detector to the other. One has to select an analytical function and then determine its parameters. This is generally performed by nonlinear least-square fitting. These methods involve the use of large and fast computers. In this chapter, we will discuss these techniques. Another class of codes uses more simple in which the peak area is simply calculated by a sum of channel contents with subtraction of an estimated background. These codes give the possibility of using small size and low cost computers. However, they cannot analyze the overlapped peaks. The performance of this kind of technique will also be studied and will be compared to the methods which use nonlinear least-square fit. Finally, we will discuss a technique36 which conciliates the advantages of the abovementioned methods: resolution of overlapped peaks, but using small computers. In this approach, several parameters defining the gamma ray can be fixed experimentally. The remaining parameters can be determined by linear least-square fit which can be done by a small computer. The performance of this technique will be examined and compared to the nonlinear least-square method using examples of activation analysis.

11. ANALYTIC APPROXIMATION OF GAMMA-RAY SPECTRA In analysis of the gamma-ray spectra by a germanium detector, the precise determination of the energy and the intensity is based on fitting of the photopeak by an analytical function. This fitting is performed by nonlinear least-square method. In order to achieve a fast and high-precision analysis, a minimum number of parameters should be utilized to define the peak. In this section, several analytical representations for the line shape of photopeak will will be used. be studied. In the calculations, a test spectrum, that of 177mL~,

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11

A. PHYSICAL ASPECT The exact calculation of the response of the detector to the photons is very difficult because of the complex physical and statistical phenomena involved in the process. This calculation requires a precise knowledge of the property and the structure of the detector which are not well understood in most cases. For this reason and because the shape of the peaks can be sensitive to small variations in the experimental parameters, such as counting rate and degree of collimation, one has to determine directly an analytical representation for the photopeak. However. to define an analytical representation, one has to take into account the physical mechanism involved in the detection of gamma rays. The first contribution to the photopeak in a semiconductor detector is due to the statistical fluctuations in sharing the absorbed energy between ionization and heating the crystal network. This gives rise to a Gaussian distribution with a small width. The average energy to create a pair of electron-hole in cooled germanium is E = 2.98 eV. The variance, crZ,of the produced electron-holes is given by

where E is the incident energy and F is Fano factor." F is about 0.13 for germanium. The contribution from statistics to the full width at half maximum is

The difference between the calculated value given by Equation 2 and the measurement depends on factors such as the quality of the detector and the associated electronics. The physical properties of the material and the impurities in the detector affect the charge collection and the electronic background. Incomplete compensation of the impurities and partial collection of the charges deteriorate the energy resolution and cause a distortion in low energy side of the peak. In low energies, the contribution of the preamplifier to the background is high. At higher energies, the instability of the amplificator and the analyzer affects the width of the photopeak. The continuum under the peak is due to Compton effect from the gamma rays of higher energies and the background.

B. ANALYTICAL REPRESENTATION Following the considerations mentioned in the preceding section, the analytical representation of the photopeak should have a principal Gaussian form. However, a deviation from this Gaussian form should be included in the analytical description. Moreover, the approximately linear region in two sides of the peak have different heights. The contribution to the low energy side of the peak can be taken into account using a step function. The second part of the distortion is usually eliminated; if included, it has to be described by a function which joins smoothly the background situated in each side of the peak. The functions proposed by different authors fall into two categories: (1) supplementary terms are simply added to a dominant Gaussian form, and (2) the principal Gaussian function is deformed by convolution, by multiplication by another function, or by joining it to another function. In general, the photopeak can be represented by

where n = channel number, D = tail distortion, G = Gaussian function, B = linear or polynomial background, and S = step. The symbol * indicates that the distortion should be added, multiplied by, or convoluted

12

Activation Analysis

FIGURE 1 . Analytical components of an isolated photopeak (see Equation 3). In (a) the tail D is incorporated in the main Gaussian G by multiplication or convolution; in (b) D is simply added.

with the Gaussian. These four components are shown in Figure 1. In most cases, the tail component is represented by an exponential or a second Gaussian in the low energy side. Routti and Prussinl have used a Gaussian form for the central part of the photopeak. Both left and right tails are approximated by exponential functions. These exponentials are joined to the central Gaussian so that the line shape and its first derivative are continuous. The function has the following form,

where n = channel number, PI = constant parameter in continuous background approximation, P, = slope of background approximation, P, = height of Gaussian, P4 = abscissa of Gaussian, P, = width of Gaussian (full width at half maximum = 2.354 P,), P,2 = distance to the lower junction point, and P,Z = distance to the higher junction point. Robinson15 has studied the gamma-ray peaks using an analytical form which consists of two Gaussians of the same width and an arctangent function. The adapted expression is fn

=

Aexp [-(n2i21b)2]

+ ~ [ +f

Volume 1

+

ex,[

- (n - no

2u2

+ Pu)

13

I

P a is the distance from the abscissa, n, of the main Gaussian to the abscissa of the secondary Gaussian of lower energy. A and u are the height and standard deviation of the main Gaussian. The second term in the equation is an arctangent function with the center at channel n, bu and with height B. The last term is the second Gaussian having the same width as the first one but with a height D and the maximum at n, - P a . An error function has been used to generate the continuum in the work of D o j ~The . ~ ~ photopeak is represented by a Gaussian with an exponential for low energy tail joined such that the function is continuous. The line shape is approximated by,

A,%, and u are, respectively, the height, the peak position, and the standard deviation of the Gaussian; the distance from the center of Gaussian to the junction point is t. The error function is defined by its height, h, and its width a,,

Sasarnoto et aL8 have utilized a similar functional form replacing the error function by another function. The analytical form is given by 2

f, = Aexp

, n,anan, -t

f,, = Aexp

fn = Aexp

t(2n - 2%

+ t) ] + : { 2 - e x P [ $ ( n - n o ) ] ) ,

n 30 h) were measured.

.

115

Volume 1

TABLE 2 Radioisotopes with High Detection Limit Advantage Factors5 (DLAF > 100 for Biological Matrices)

Radionuclide

Note:

X-ray measured

DLAF

y ray keV

B

G

AW5

X-ray sensitivityS c s-' p g - I

X-ray limits of detection5(ppm)

B

G

DLAF, detection limit advantage factor - gamma ray detection IimiVX-ray detection limit; B, biological matrix; G, geological matrix; AF, advantage factor - X-ray sensitivitylgamma-ray sensitivity.5

TABLE 3 Limits of Detection of Trace Elements in Biological Matrices Determined by INA using Ray Spectrometry and Magnetic Deflection of Beta Rays

Element Ir Co Br Se Nb Ge Sc Cu

u

Radionuclide LYZrnIr T o 82Br 7y"Se 94"Nb 75"Ge -sc 6"Cu 239U

Cr Th 0s Rb

51Cr 233Th 191"0s -Rb

Pt

198mpf

Hg

197Hg I-Y @Zn 8'mSr

Y Zn Sr a

X-ray measured

Average shown is of the results (range

IrL1 CoK, BrK, SeK, NbK, GeK, ScK, NiK, NPLI VK, Pal-,, 0&1

RbK, PtLd

YK, ZnK, SrK, %

X-ray energy (keV) 9.2 6.9 11.9 11.2 16.6 9.9 4.1 7.5 13.9 5.0 13.3 8.9 13.4 9.4 9.7 14.9 8.6 14.2

X-

Limit of detection (ppm) Average 6.0 7.0 1.4 1.5 2.0

Orchard leaves

Animal muscle

x lo-' x lo-)

x x x 10-2

2.8 x 5.0 x 7.0 x

1.8

1.1 x l o - '

3.4 x 10-1

3.0 x 10-I

7.0 x 10-I

X

lo-'

1.0 x lo-' 3.0 x lo-' 1.o 2.0 2.8

4.2

5.0

12.6

8.1 1.3

X

102

40%) obtained from all seven matrices.

Modified from Mantel, M., Analyst, 108, 1190, 1983. With permission.

116

Activation Analysis

The limits of determination obtained for the X-ray-emitting radioisotopes studied (Tb, Yb, Ta, U, and Th) are in the range of 10-lo to lo-" g.

B. FAST (14 MeV) NEUTRON ACTIVATION The most frequently occurring nuclear reactions by activation with 14 MeV neutrons are the (n, n') (n, 2 4 , (n, p) and (n, a)reactions. A number of radioisotopes produced by these reactions decay by internal conversion or electron capture emitting characteristic Xrays during their decay. The possibility of using these X-rays for analytical purposes has been investigated.I 0 ~ ' l Janczyszyn and Kwiecinski10 studied 68 elements, from Z = 24 (Cr) to Z = 92(U), and found that 50 of them emit X-rays after 14-MeV neutron activation. For these elements, the factor k defined as:

where a = abundance of the target isotope, 6 = reaction cross-section, X = number of characteristic X-rays per decay, X = decay constant, and f, t,, t, = irradiation, counting, and decay times was calculated. This factor directly influences the sensitivity of a nuclear reaction if the other parameters (neutron flux, counting efficiency, sample weight, etc.) remain constant. Of the elements for which a high k factor was found, 24 were studied experimentally. The "best" nuclear reactions, i.e., those reactions which could theoretically lead to high sensitivities, were chosen. Samples of thicknesses close to the "infinite layer" were irradiated in a 14-MeV neutron s-I. Table 4 shows the results generator with an average neutron flux of 2 X lo8 n obtained for the elements considered as most promising by the authors.I0 A determination limit of 0.1% may be obtained for the elements listed in Table 4. The same may be expected from selenium, rubidium, rhodium, hafnium, and iridium, judging from the values of their k factors. However, these elements have not been studied experimentally. It may be concluded that the technique of X-ray spectrometry following 14-MeV neutron activation may be applied to the determination of main and minor constituents but is not suitable for trace element analysis."

111. ERRORS AND LIMITATIONS A. ABSORPTION One of the most important sources of error in X-ray spectrometry is the absorption of X-rays by the matrix. This phenomenon may represent a serious limitation due to the low energy of X-rays. The mass absorption coefficient of an element, p,, expressed as cm2 g-I, defines the absorption process quantitatively. The mass absorption coefficient is dependent on energy; it decreases continuously with increasing photon energy, and for the same energy, it increases with the atomic number of the absorbing element. At a given energy, the mass absorption coefficient of a compound is the weighted sum of the absorption coefficients of the constituent elements.

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TABLE 4 Elements for which High Sensitivities were Obtained by 14-MeV Neutron Activation followed by X-Ray Spectrometry'' Element

Nuclear reaction'

X-ray measured

k

t,,,

mb.h

Target material

Thickness (mglcm~

Countsb

Si(Li) detector - 30 mm2 Co Ni In Sb Sn Ho Dy

10.5 min 9.7 min 10.9 min 4.2 min 15.9 min 37.0min 29.0 min

1.6 x 10-I 9.7 x 3.7 x 10-I 6.6 4.7

Metal

7.1

Ho@,

In,O, Sb20,

1.2

Ge(Li) detector - 80 cm3

Hg a

2wHg(n.2n)Iw"Hg

Hg

42.6 min

9.3

X

10-I

Hg(C,H,O,),

620

It is presumed that the measurements are based on the nuclear reaction with the highest k factor. Integrated K X-ray peaks, expressed as counts per 1000 s, after 600-s irradiation and 60-s delay time

where C, and p,(E) are, respectively, the concentrations (%) and the mass absorption coefficients (cm2 g-') at the energy (E) of the individual elements. Since tables of mass absorption coefficients for the elements are available,12those for compounds can easily be calculated. An example for the calculation of the mass absorption coefficient of a compound from the absorption coefficients of the constituent elements is given in Table 5 for an igneous rock at 16.0 keV. It follows that in a given matrix, the absorption of X-rays depends on their energy and on the composition of the matrix, which means that, for the same element, the absorption in a matrix composed of light elements (for instance organic materials) will be much lower than in a heavy-element matrix. For monochromatic X-rays, the degree of absorption (attenuation factor, A) in a given matrix may be estimated, provided the sample-to-detector distance is greater than the detector diameter,14 according to:

where, I and I, are, respectively, the attenuated and unattenuated X-ray intensity expressed as counts per unit time, p, = mass absorption coefficient of the matrix (cm2 g-I), p = density (g ~ m - ~and ) , d = sample thickness (cm). Thus, if p and d are known, the attenuation factor (A) may be evaluated for any matrix since the absorption coefficient may be calculated. Holzbecher and Ryan15 evaluated the attenuation of low energy photons in different materials by comparing their attenuation in the material studied (Am) to that in water (Aw). The ratio AmIAw was measured experimentally and calculated according to Equation 3. Very good agreement was obtained, in most cases, between the calculated and measured values. The nearly linear decrease of the absorption coefficient with increasing energy is interrupted by the absorption edges, i.e., abrupt increases of the absorption coefficient at energies

.

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Activation Analysis

TABLE 5 Calculation of the Mass Absorption Coefficient of an Igneous Rock at 16.0 keV (Equation 2) Composition (oxides)

"

Weight (9%)" Ci

~ ~ ( 1 6 keV)b .0

p,Ci

According to data on the composition of rocks.13 Absorption coefficients of the oxides calculated according to their elemental composition and to the absorption coefficient of the elements.I2

equal to the bond energy of an electron in the K- or L-shells of the elements. The absorption edges occur at strictly defined energies for each element and their energy increases with increasing atomic number. The elements, with absorption edges in the vicinity of the energy of the X-rays to be analyzed, have to be considered in the evaluation of the possible absorption during the measurement. The quantity of these elements which in a specific material will produce an preventing increase of maximum 1% in the overall error of the method, may be ~alculated,~ in this way unexpected high errors. At the absorption edges, the increase in absorption with energy is sharp and the decrease is mild. It follows that the highest absorption will be obtained from elements whose absorption edges are at energies just below those of the X-rays to be measured. For example, in the determination of Cu in geological materialsI6 by measuring the NiK,-X-rays (7.47 keV), the presence of iron (K, = 7. l l keV) presents a serious problem and reduces the sensitivity of the method due to the absorption of the Ni-K, photons by iron. Different techniques are used to overcome the errors due to absorption of X-rays by the matrix. The preparation of very thin samples reduces the absorption to a negligible value. Weaver1' prepared such samples by introducing a very thin layer of VaselineB into the bottom of the flat plastic containers used for the counting of irradiated coal samples. A similar approach was proposed by Mantel and ArnieP who used very small plastic containers (I.D. = 12 mrn) as irradiation and counting vessels and 10- to 30-mg samples evenly distributed on the bottom of the container by a few drops of hot paraffin added to the sample. Very thin liquid samples were prepared by Rapaport et al.I9 by dropping a few microliters of the liquid between two ultrathin mylar foils. Another approach, used by most worker^^^^^^ is the preparation of standards with similar composition to that of the samples.

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TABLE 6 Absorption Coefficients of Different Organic Matrices at 4.95 keV Matrix

Absorption coefficient [p, (cm2 g-I)]

Kidney

Liver

Heart

Cellulose

36.8

34.6

36.4

31.2

TABLE 7 Relative Quantities of CaCO, and MgCO, Necessary to Obtain Standards with Different Absorption Coefficients at Different Energies Standard Pm

cm2. g-'

energy (keV)

CaCO,

MgCO,

(%)

(%)

The absorption coefficient of the matrix as a whole is only slightly influenced by the small variations in the relative abundance of its major constituents. Thus, it will be possible to use, as standard, matrices with a composition similar to that of the sample without it being imperative that standard and sample match perfectly; the same type of rock for geological samples or the same type of tissue, drug, or food for organic materials (see Table 6). The presence of trace elements, even of those with high atomic numbers will influence only slightly the absorption coefficient of the matrix. However, as mentioned before, great attention must be given to the presence of elements, sometimes trace elements, with absorption edges near the energy of the X-rays to be determined. If standards similar to the sample are not available and the composition of the matrix is known, it is possible to prepare standards with absorption coefficients similar to that of the sample. The mass absorption coefficient of the sample, at the energy of the X-rays to be measured, is calculated according to Equation 2 and another matrix with a similar absorption coefficient at the desired wavelength, chosen as standard. As an example, such a standard may be obtained by vacuum drying a mixture of CaCO, and MgC0,22 in the necessary proportion, in a solution of the element to be determined. Table 7 shows the relative quantities of CaCO, and MgCO, necessary to obtain various absorption coefficients at different energies. ~ the In order to be sure to prevent all errors due to abdrption, some ~ o r k e r p !prefer k particular use of "infinite thick samples", i.e., samples which ptre infinitely thick for t energy of X-rays being measured. The maximum thickness of sample through which a

120

Activation Analysis

particular X-ray could pass may be calculated with the help of the absorption coefficients of the major elements in the sample. If standards and samples are similar in composition, then the X-rays counted come from equal volumes, so that the actual weight can be neglected in the calculation of the concentration. However, it has to be taken into account that only X-rays which originate from a portion of the sample nearest to the detector will be measured. Finally Bode et a1.I4describe a method for the correction of absorption losses in a matrix, using only information from the sample spectra. The attenuation coefficients can be determined as a function of photon energy from sets of intensity ratios between related peaks in the spectrum. The unattenuated intensities are calculated based on these absorption coefficients which were found sufficiently reliable to obtain correct results.

B. INTERFERENCE The possible interference with the measurement of X-rays obtained following neutron activation may be due to discrete X-rays and low-energy gamma rays, secondary X-rays, and beta rays. 1. Discrete X-Rays Due to the direct relationship between the atomic number of an element and the energy of its characteristic X-rays, the interference with the measurement of these X-rays will result chiefly from X-rays emitted by neighboring elements in the periodic table. Another possible source of interference are L X-rays emitted by elements with high atomic numbers in the same energy range as the K X-rays of an element with a low atomic number, or vice versa. Finally low-energy gamma rays, which may be emitted from the irradiated sample, must also be taken into account. Obviously, the possibility of determining in the same spectrum two elements with close X-ray energies will depend on the resolution of the detector. In other words, for two neighboring elements in the periodic table, the difference between the energy of the K,, Xrays of one element and that of K,, X-rays of its immediate predecessor should be greater than the resolution of the detector. This difference increases with the atomic number but at the same time the intensity of the K,, X-rays also increases and may interfere with the measurements. The resolution of the Si(Li) detectors generally used for energies up to 50 keVZ3decreases sharply with increasing energy (from 160 eV at 6.4 keV to about 450 to 500 eV at 50 keV) and the resolution of the LEPD detectors used for higher X-ray energies lies between 450 to 500 eV (for 60 and 122 keV, re~pectively).~ As an example, for elements with atomic numbers Z = 60 to 70, a problem arises in the simultaneous determination of element Z and (Z + 4); the Kp, X-rays of element Z 4) since their energies are too cannot be separated from the Ka, X-rays of element (Z close to be separated by the detector. However, since we are dealing with X-rays obtained after neutron activation, several other factors may facilitate the simultaneous determination of two elements whose characteristic X-rays have very close energies. These factors are the type of decay process responsible for the emission of X-rays (electron capture, internal conversion, p-), the halflife of the X-rays involved, and the relative sensitivities of measurement based on the respective fluorescent yield of the emitted X-rays. In the case of fast (14 MeV) neutron activation, another important factor is the nuclear reaction which is responsible for the production of X-rays, since different isotopes, or the same isotope, of an element may emit various X-rays according to the nuclear reaction (n, 2n), (n, n'), (n, a) or (n, p) which took place. A very good example of X-rays obtained after the (n, y) reaction are the elements silver (Z = 47), cadmium (Z = 48), and palladium (Z = 46) which all produce radioactive isotopes which decay by X-ray emission. All three elements may be determined in the same sample considering differences in decay processes, half-lives, and sensitivities.'*

+

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Another example is the determination of niobium in steels by instrumental neutron activation (INAA) based on the measurement of the 16.6-keV niobium K, X-rays.'' The elements in the periodic table which could interfere are yttrium (Z = 39), zirconium (Z = 40), molybdenum (Z = 42), and technetium (Z = 43), by the emission of K X-rays and uranium and thorium by the emission of L X-rays. From all these elements, only zirconium and molybdenum could be present in steels. Since zirconium does not emit X-rays following neutron activation, Mo remains the only possible interference. However, due to the difference in sensitivities5 and half-lives, the amount of molybdenum in the steel sample would have to be lo4 times that of niobium to produce any interference. An interesting approach to overcome interferences was used by Zaitsev." He applied differential filters to select a part of the X-ray spectrum specific to the element to be determined. For the separation of a radiation with a defined energy, a pair of filters is used. One of the filters consists of an element with a K-absorption edge just below the energy of the line to be separated, while the other consists of an element with a K-absorption edge above that energy. The width of the transmission band is generally 0.3 to 0.4 keV for light elements and 2 to 2.5 keV for heavy elements. Recent compilations of X-ray-emitting radioisotopes include the possible interferences with the measurement of X-rays emitted after neutron activation. Habib and M i n ~ k i in ,~ their comprehensive compilation of X-ray sensitivities from isotopes produced by the (n,y) reaction, identify for each isotope the interfering X-rays obtained from neighboring elements. The percentage of interference for the optimum irradiation, decay, and counting conditions of the isotope of interest, are calculated assuming an equal mass of 1 g for both the interfering and the measured element. Baedecker et al. ," during a study on the utility of low-energy measurements in epithermal neutron activation analysis of geological materials, indicate the most probable interfering radiation for each line, estimated on the basis of common elemental abundances in silicate rocks and resonance activation integrals. Finally, Hertogen and Gijbels3 studied the spectral interferences in the gamma spectra obtained from two U.S. Geological Survey standard rocks and a series of volcanic rock samples from the Canary Islands, measured with a LEPD detector. Though the emphasis of the study was on gamma rays, a few X-ray-emitting radioisotopes (especially rare-earth elements) are also included. 2. Escape Peaks The contribution of escape peaks was studied by Keith and LoomisZ3and Reed and Warez5for Si(Li) detectors. They found that the silicon escape peak is geometrically similar to the main peak. The ratio E = height of escape peak/height of main peak (both heights having been corrected for background) is of the order of at 3.5 keV and decreases with increasing photon energy to a negligible value at 25 keV. For higher energies, in spectra recorded with a LEPD detector, intense lines are accompanied by small peaks about 10 keV lower, due to the Ge-K X-ray escape efect (K, = 9.9 keV, Kp = 11.0 keV). The escape peak ratio has been measured by Hertogen and Gijbels3 (from 24 to 121 keV) and Ungrin and Johnsz6 (from 40 to 41 1 heV), for different LEPD detectors. The results showed that the ratio escape peak areatphotopeak area is of the order for 121.9 keV.3 for 24 keV and decreases to 1.5 X of 5.27 x

3. Secondary X-Rays Strong beta or gamma rays from the radioactive samples may interact with major elements present in the samples or materials in the vicinity of the detector and induce secondary fluorescent X-rays. Thus Au-K X-rays were reported by Hertogen and Gijbels3 in all spectra obtained with a small LEPD detector as a result of the excitation of the gold-electrode atoms by intense

122

Activation Analysis

beta emitters or by gamma rays with energies near the K-absorption edge. The same authors3 report intense Ba-K X-ray fluorescent radiation when glass counting vials are used. Generally the intensities of the X-rays and gamma rays obtained by neutron activation are too low to produce fluorescent X-rays in sufficient yield to interfere with the measurements. The possibility of secondary fluorescent X-rays must be taken into account only when very long irradiations are carried out or if one of the main components of the matrix is known to produce especially strong gamma or beta radiation following neutron activation.

4. Beta Particles The beta particles emitted from an irradiated sample are another serious source of interference in X-ray spectrometry. These beta particles produce a high background which completely obscures the X-ray peaks obtained from trace amounts of low and medium Z elements making their quantitative determination practically impossible. In addition, beta particles may increase the dead time of the Si(Li) detector which results in inaccurate integration of the X-ray peaks. The elimination of this interference becomes of critical importance for the determination of trace elements in matrices, such as biological materials or seawater whose major components, sodium, potassium, chlorine, and phosphorous, are themselves strong beta emitters. The interference of beta particles may be overcome by the use of plastic absorbers or by the deflection of the beta particles by magnetic fields. The latter technique has been extensively studied in our laboratory at the Soreq Nuclear Research Centre8p27.28 and its possible applicatim to neutron activation analysis, investigated. Theoretical calculations were carried out to determine the fraction of beta particles in a beta-particle beam moving perpendicular to the detector, which will be deflected by a given magnetic field. The results showeds that the intensity of the magnetic field necessary to deflect beta particles, depends on their energy and the source detector distance. For example, at a distance of 27 mm (the source-detector distance used in our experiments), a 0.2-T magnet is necessary to remove 91% of the beta particles emitted by "P (1.7 MeV) an3 a 0.5-T magnet is needed for a similar reduction of those emitted by 35C1(4.92 MeV). The influence of the magnetic fields on the performance of Si(Li) detectors and on the background obtained from irradiated samples was studied experimentally. A 100 mm2 Si(Li) detector was used throughout the experiments. Figure 1 is a picture of the experimental set-up used. The magnet shown in the picture is a 0.35 T magnet (manufactured by AEI for a Minimass mass spectrometer). This magnet was replaced in part of the experiments by a 1.3 T electromagnet (18-mm gap between poles). The influence of magnetic fields on the disturbance produced by beta particles in the performance of the Si(Li) detector was studied by measuring the 6.4-keV Fe K, X-rays and the 14-keV gamma rays emitted from a 1 0 - ( ~ C i ~ ~source C o in the presence of 50-(LC~ 32P (E max = 1.7 Mev) with and without a magnetic field. The results showed that a 0.4 T magnet corrects the peak to background ratio to 10.7 as compared to 16 obtained for the 57 Co source alone and the resolution of the detector approaches its experimental value of 500 eVZ3 The background obtained from 24Na, 38Cl, and 32P, the principal beta-emitting radioisotopes which may be present in an irradiated sample, was measured over an energy range up to 20 keV, both with and without a magnet. The results showed that the decrease in background is not the same for all the nuclides and varies with energy for the samc nuclide. Table 8 shows the reduction in background obtained for each of the four nuclides with a 1.3 T electromagnet. The greatest reduction in background is seen to be obtained for 32P.

the magnet. For th'e other nuclides which are beta and gamma emitters, the Compton peaks of the gamma rays will also contribute to the background.

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FIGURE 1 . Experimental set-up used for X-ray spectrometry and magnetic deflection of beta rays (0.35 T magnet and 100 mm2 Si(Li) detector).

Recently Garmann9 published a study on the influence of magnetic fields on the measurement of X-rays and low-energy gamma rays obtained from geological materials after epithermal neutron activation. A 200-mm2planar hyperpure germanium detector and an electromagnet, as deflector, were used throughout the experiments. The sample to detector distance was adjusted to 50 to 80 rnm; X-rays and low-energy gamma rays with energies higher than 45 keV were measured. The results showed that the reduction in background is smaller than that obtained for Si(Li) detectors,' however, a substantial improvement in the peak to background ratio, better resolution of the detector, and improvement in the shape of the peaks, were observed. Table 9 shows the improvement in the peak to background ratio obtained by Garmann9 by measuring different photopeaks in the presence of magnetic fields. Furthermore, better limits of detection (see "sensitivity and limits of detection") and higher precision and accuracy of the results, were obtained by the use of magnetic fields as deflectors. Table 10 shows the improvement in the detection and determination limits for the X-ray emitting-radioisotopes ~ t u d i e d . ~

124

Activation Analysis

TABLE 8 Reduction in Background Obtained with a 1.3 T Electromagnet

P-

Radionuclide

"

Remaining background (I)'

(Mev)

Average of values obtained for different energies (up to 20 keV) expressed as percentage of the background obtained without the magnet.

Modified from Mantel, M., Analyst, 108, 1190, 1983. With permission.

TABLE 9 Improvement in Peak to Background Ratios Energy Radionuclide

a

t,,

Gamma (keV)

p-max (MeV)

Peak background ratioa Without magnetic field

Measured with a 200-mm2 planar germanium detector-approximate

With magnetic field

Improvement

(%I

values.

From Garmann, L. B., J . Radioanal. Nucl. Chem., 99, 75, 1986. With permission.

As mentioned before, the interference of beta particles may also be overcome by the use of plastic absorbers. However, the latter absorb not only beta particles but also X-rays k of magnetic fields at a rate which decreases with increasing X-ray energy. ~ h advantage is the fact that they have no influence on X-rays and thus do not produce any reduction in the X-ray activity. However, due to the physical size of the magnet, the source-to-detector distance is increased which causes a reduction in sensitivity. For choosing between a magnet and a perspex absorber, all these factors have to be taken into account. For low-energy Xrays, a magnet is generally preferable especially for high activity samples where the emitted X-rays may be easily detected in spite of the reduction in sensitivity due to the geometric factor. For samples of low activity, the following equation may be used as a guideline to decide whether to use a magnet or a perspex ab~orber.~

where p, and p,@ are the linear absorption coefficients in perspex for X- and beta rays, respectively, a is the decrease in X-ray activity due to the geometric factor (size of magnet), and b the reduction in the background obtained from a given sample, by the same magnet. For X-ray energies where F, > pB(In alln ab), a magnet is preferable; in the opposite case, a perspex absorber is a better choice.

Energy (keV)

Calculated values. Without magnetic deflection. With magnetic deflection.

Type

Valueb

Valuec

Detection limit' (%)

Improvement

From Garmann, L. B., J. Radioanal. Nucl. Chem., 99, 75, 1987. With permission.

a

Element

X-rays Valueb

Valuec

(%)

Improvement

Determination limit'

TABLE 10 Improvement in the Detection and Determination Limits for Epithermal Neutron Activation Analysis (EINAA); Measured With and Without Magnetic Deflection on a Planar Detector

126

Activation Analysis

For a 1.3 T electromagnet and a sample to detector distance of 27 mm (the experimental set-up used at the Soreq Nuclear Research Centre), the use of a magnet was found to be preferable, up to 16 keV, for the analysis of trace elements in biological matrices. It is obvious that for different matrices and for every magnet and absorber pair, another borderline energy will be found.

IV. APPLICATIONS The present chapter is not intended to be an exhaustive bibliography of all the works published on the use of X-rays in activation analysis. Only a 'few examples are given to illustrate the possible analytical applications of X-ray spectrometry.

A. THERMAL NEUTRON ACTIVATION Most workers studied the analytical applications of X-rays obtained by the (n,y) reaction following thermal neutron activation. Single elements were determined in complex matrices and multielement nondestructive analyses were carried out. Allen and BrookhartI6 determined copper in biological materials and in several United States Geological Survey (U.S.G.S.) standard rocks by measuring the Ni K, X-rays which result from the 43% electron capture decay of TU (tlIz = 12.8 h). Standards similar to the sample and infinitely thick samples (see Section 1II.A.) were used to overcome errors due to absorption. Sensitivities of tenths of ppm were obtained for plant material (National Bureau of Standards [NBS] orchard leaves) and in the ppm level for more complex biological materials (NBS bovine liver). The analysis of geological materials was found to be problematic due to the absorption by iron of the Ni K, photons. Weaver17 used a LEPD detector for the determination of mercury and selenium in coal. The method is based on the measurement of the Au X-rays emitted by '97Hg (tlI2 = 65 h) and two low-energy gamma rays emitted from 75Se(t,,, = 120 d). The sensitivities obtained with a 10 to 14 h irradiation at a lOI3 ncm-2 s-' neutron flux are 50 ng of mercury and 150 ng of selenium per gram of coal. The possibility of determining thallium and bismuth by X-ray spectrometry following neutron activation was studied by Holzbecher and Ryan.29Detection limits of 50 pg/g and 250pg/g, respectively, in biological materials, were obtained by measuring the Pb X-rays obtained from 206Tl (tlI2 = 4 min) and the Bi and Po X-rays obtained from 'I0Bi (tlI2= 5.0 d). The interference of lead and bismuth with the measurement of thallium, and of mercury with that of bismuth, was studied and the maximum quantity of these elements which could be present in the sample without being a serious interference, calculated. Allen and Steines30 determined niobium in geological samples by solvent extraction in the presence of carrier-free 95Nbtracer prior to neutron irradiation. After reextraction into 1.5% H202, the aqueous samples were irradiated for 5 min and counted twice for 1 min, with and without a plexiglass absorber. The Nb K, + K, X-rays (16.6 and 18.7 KeV) were measured with a planar intrinsic germanium detector. A total of 15 U.S. geological survey standard rocks with considerably different compositions were analyzed. A limit of detection g was obtained. Due to the preirradiation separation, the contamination limit of 5 x was generally inferior to the detection limit of the method. Magnetic deflection of beta rays was applied by the group at the Nahal Soreq Nuclear Research Centre to the determination by INAA and X-ray spectrometry of bromine in blood serum,lg niobium in steels,,' and trace elements in active charcoal3' and in the Dead Sea.32 All the irradiations were carried out at la neutron flux of loL3ncm-' S - ' and a Si(Li) spectrometer was used for the measurement of X-rays. The determination of bromine in synthetic blood serum samples has been carried out for the first time by INAA and X-ray spectrometry by Peisach et However, the reduction

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in background due to the deflection of beta rays by magnetic fields made possible the determination of bromine in real blood serum sample^.'^ An average value of 7.38 r 0.44 mg Br per liter was obtained. This result is in the range of values considered as normal for bromine in blood serum. The 16.6-keV Nb-K X-rays were used for the determination of Nb by INAA in steel samples.20An error of + 20% was obtained by using Nb,O, in cellulose as standard. This error may be reduced to f 10% by the use of a National Bureau of Standards SRM steel standard of similar composition to the steel to be analyzed. A different approach was applied to the determination of trace elements in the Dead Sea.32Due to the very high salinity of the Dead Sea (340 gll), a concentration step was necessary. The trace elements of interest, cobalt, copper, and mercury, were first co-precipitated with lead-APDC, separated from the bulk of the dissolved salts, and then determined by X-ray spectrometry in the neutron-activated APDC precipitate. Results of 1.3 ppb for Co, 2.0 ppb for Cu, and 1.2 ppb for Hg were obtained in Dead Sea surface water, sampled after the complete overturn of the sea a few years ago which resulted in the homogenization of the seawater in the Dead Sea. A number of papers3.2',34-36 deal with the determination of rare earth in geological samples by X-ray spectrometry, since the lanthanide elements (except for La and Pr) produce radioactive isotopes on neutron capture which decay with emission of X-rays. The technique is especially attractive since the simultaneous determination of these elements by other analytical methods, including gamma spectrometry, presents a very difficult problem. V ~ l d e determined t~~ ten rare-earth elements (REE) in basic rocks (45 to 52% SiO,) with very low REE concentrations. A preirradiation chemical separation was used, consisting in a separation of the REE by ion-exchange chromatography followed by purification and concentration as REE oxalates. The latter are submitted to reactor neutron activation. Two irradiation and counting sequences were used: 1-h irradiation at a thermal-neutron flux of lo9 ncmp2s-' and 600-s counting time (after 7-min cooling time) for short-lived isotopes (Eu, Dy) and l-h irradiation at 1.6 X 1013 n cm-'sp' and 600-s counting time, after 2 to 5-d cooling time, for the other REE. The proposed technique presents several advantages: the chemical separation of the REE group before irradiation considerably reduces the cooling time required before measurement of the activities; a convenient choice of the cooling time eliminates the interferences between the REE themselves. A precision of 5 to 10% was obtained for REE concentrations in the range 0.1 to 50 ppm by using standards similar in composition to the rocks analyzed. Hertogen and Gijbels3 investigated whether X-rays could be useful in the INAA of silicate rocks. Special attention was given to 170Tm.'66Ho, 175Hf,and 169Ybwhose characteristic X-rays were well resolved by the LEPD detector, permitting their quantitative measurement. B. EPITHERMAL NEUTRON ACTIVATION (ENAA) Baedecker et al." applied ENAA to the instrumental neutron activation analysis of silicate rocks using planar intrinsic Ge detectors. A total of 8 U.S. Geological Survey standard rocks (7 rock samples and a marine sediment) ranging from granitic to basaltic composition, were analyzed for 15 trace elements. The irradiations were carried out for 2 d at a neutron ' a cadmium ratio of about 3.0 for '97Au. The samples flux of 1.5 x lOI3n ~ m - ~ s -and were counted for l-h, 1 week, and 3 weeks after irradiation, and the spectra processed on an IBM 370 computer using the program "SPECTRA". The results were compared with those previously obtained by the usual INAA procedure using the whole reactor neutron energy spectrum and a coaxial Ge(Li) detector. The measurement of X-rays gave very satisfactory results for Ba, Sm, Tb, and Ta (KX-rays) and for Th and U (L X-rays). Holzbecher and Ryan15 attempted to determine niobium in rocks, iodine in table salt, and uranium and thorium in Canadian certified reference material, uranium-thorium ore, by

128

Activation Analysis

irradiating the samples in a cadmium-shielded site, taking advantage of the low Cd ratios of the elements of interest. They arrived at the conclusion that for low energies (Nb-X-rays, 16.6 keV), the determination is not reproducible due to problems associated with absorption. With increasing energies, the method becomes more accurate. A standard addition method was necessary to obtain correct results for iodine (Te X-rays 27.5 keV) whereas for U and Th (74.6 and 86.5, low-energy gamma rays) the use of standards of similar matrix composition to the sample could adequately compensate all the errors. Garmann9 determined trace elements in geological materials by ENAA. Magnetic deflection of beta rays was used to reduce the bremstrahlung interference due to the high Na and Fe content of the samples (see Section III.B.4). A total of 18 elements were analyzed in alkalisyenite and meteoritic material (Grefsheim meteorite from Norway and Allende meteorite from New Mexico). Tb, Yb, Ta, U, and Th were determined by X-ray spectrometry using a planar hyperpure Ge detector and the U.S. Geological Survey basalt BSR-1 as standard.

C. 14-MeV NEUTRON ACTIVATION The possible analytical applications of X-ray spectrometry following 14-MeV neutron activation, have been in~estigated.'~,",~' AS mentioned before, this technique is not suitable for the determination of trace elements. However, it may be applied to the analysis of main and minor constituents of different matrices. Janczynszyn et al.1° successfully used this technique for the determination of tantalum in niobium and other industrial materials, with a detection limit of 0.1%. The same authorslo experimentally studied 24 elements and found that Sb, In, Cu, Ho, Ta, and Hg could be determined by this method with the same detection limit of O.1%, after optimizing the sample thickness to obtain optimum counting conditions. El Barouni et al." also studied the possible analytical applications of characteristic Xrays induced by 14 MeV neutrons and arrived at the conclusion that Se, Br, Ag, Cd, Sb, and Pr could be quantitatively determined by this technique.

REFERENCES 1. Shenberg, C., Gilat, J., and Finston, H. L., Use of X-ray spectrometry in activation analysis, Anal. Chem., 39, 780, 1967. 2. Pillay, K. K. S., Characteristic X-rays from (n, y) products and their utilization in activation analysis, J . Radioanal. Chem., 2 , 97, 1969. 3. Hertogen, J. and Gibels, R., Instrumental neutron activation analysis of rocks with a low-energy photon detector, Anal. Chim. Acta, 56, 61, 1971. 4. Mantel, M. and Amiel, S., X-ray spectrometry, in Nondestructive Activation Analysis, Amiel, S., Ed., Elsevier, Amsterdam, 1980, chap. 3. section 2. 5. Habib, S. and Minski, M. J., A compilation of X- and gamma-ray sensitivities from isotopes produced by the (n,y) reaction for utilization in instrumental neutron activation analysis, J . Radioanal. Chem., 62, 307, 1981. 6. Negi, B. S. and Sadasivan, S., X-ray emission intensities of radioisotopes produced by neutron activation, X-Ray Spectrom., 9, 159, 1980. 7. Mantel, M., Limits of detection of trace elements in biological materials analysed by instrumental neutron activation analysis using x-ray spectrometry and magnetic deflection of beta-rays, Analyst, 108, 1190, 1983. 8. Alfassi, Z. B., Biran-Izak, T., and Mantel, M., The removal of beta particles in the measurement of Xrays with a Si(Li) detector, Nucl. Instrum. Methods. 151, 227, 1978. 9. Garmann, L. B., Reduction of beta-interference in gamma-spectrometic measurements of neutron irradiated geological material, J . Radioanal. Nucl. Chem., 99, 75, 1986. 10. Janczynszyn, J. and Kwiecinskl, S., Utilization of characteristic X-rays in 14 MeV neutron activation analysis, J . Radiqanal. Chem., 56, 153, 1980.

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11. El Barouni, A. M., Bokos, L., and Zemplen-Dapp, E., Preliminary study on the analytical application of characteristic X-rays induced by 14 MeV neutrons, J . Radioanal. Nucl. Chem. Lett., 126, 407, 1988. 12. Strom, E. and Israel, H. Y., Photon cross sections from 1 keV to 100 MeV for elements 1 through 100, Nucl. Data Tables, 7, 565, 1970. 13. Weast, R. C., Ed., Chemical composition of rocks, F-151, Handbook of Chemistry and Physics, 64th ed., CRC Press, Boca Raton, FL. 1983-44. 14. Bode, P., De Bruin, M., and Korthoven, J. M., A method for the correction of self-absorption of low energy photons for use in routine INAA, J. Radioanal. Chem., 64, 153, 1981. 15. Holzbecher, J. and Ryan, D. E., Evaluation of same X-rays and low energy gamma-rays in instrumental neutron activation analysis, I . Radioanal. Nucl. Chem., 102, 507, 1986. 16. Allen, D. R. and Brookhart, W., Determination of copper in complex matrices by neutron activation analysis using X-ray detection, Anal. Chem., 46, 1297, 1974. 17. Weaver, N. Y., Determination of mercury and selenium in coal by neutron activation analysis, Anal. Chem., 45, 1950, 1973. 18. Mantel, M. and Amiel, S., Application of high resolution X-ray spectrometry to activation analysis, Anal. Chem., 44, 548, 1972. 19. Rapaport, M. S., Mantel, M., and Nuthman, R., Determination of bromine in blood serum by neutron activation analysis and X-ray spectrometry, Anal Chem.., 51, 1356, 1979. 20. Mantel, M., Shenberg, C., and Rapaport, M. S., Non-destructive determination of niobium in steel by neutron activation followed by X-ray spectrometry, J. Radioanal. Chem., 75, 145, 1982. 21. Baedecker, P. A., Rowe, J. J., and Steinnes, E., Application of epithermal neutron activation in multielement analysis of silicate rocks employing both coaxial Ge(Li) and low energy photon detector systems, J. Radioanal. Chem., 40, 115, 1977. 22. Mantel, M., Sung-Tung, P., and Amiel, S., Neutron activation analysis of thorium in rocks and ores by multiple y-ray peak ratio determination, Anal. Chem., 42, 267, 1970. 23. Keith, H. D. and Loomis, T. C., Calibration and use of a lithium-drifted silicon detector for accurate analysis of X-ray spectra, X-Ray Spectrom., 5, 93, 1976. 24. Zaitsev, I. E., Activation analysis based on characteristic and soft gamma radiation using differential filters, J . Radioanal. Chem., 11, 241, 1972. 25. Reed, S. J. B., and Ware, N. G., Escape peaks and internal fluorescence in X-ray spectra recorded with lithium drifted silicon detectors, J. Phys. E., 5 , 582, 1972. 26. Ungrin, A. and Johns, M. W., Germanium X-Ray escape peaks in the 40 to 41 1 keV range produced by small "windoless" Ge(Li) detectors, Nucl. Instrum. Methods, 70, 112, 1969. 27. Mantel, M., Alfassi, Z. B., and Amiel, S., Magnetic fields to eliminate beta-ray interference in measurement of X-rays following neutron activation, Anal. Chem., 50, 441, 1978. 28. Amiel, S., Mantel, M., and Alfassi, 2. B., Development of a new approach to trace element analysis using neutron activation followed by high resolution X-ray spectrometry, J. Radioanal. Chem., 37, 189, 1977. 29. Holzbecher, J. and Ryan, D. E., Study of thallium and bismuth characteristic X-rays, after neutron activation, for their determination, J . Radioanal Nucl. Chem., 81, 153, 1984. 30. Allen, 0. R. and Steinnes, E., Determination of niobium in geological materials by activation analysis with pre-irradiation separation, Anal. Chem., 50, 903, 1978. 31. Mantel, M. and Stiller, M., The determination of trace elements in active charcoal by INAA, J . Radioanal. Nucl. Chem. Lett., 105, 185, 1986. 32. Stiller, M., Mantel, M., and Rapaport, M. S., The determination of trace elements (Co, Cu, and Hg) in the Dead Sea by neutron activation followed by X-ray spectrometry and magnetic deflection of beta ray interference, J. Radioanal. Nucl. Chem.. 83, 345, 1984. 33. Peisach, M., Maziere, B., Loc'h, C., Comar, D., and Kellersohn, C., Rapid neutron activation of bromine using 6.1 minute bromine-82m: Application to the determination of bromine in blood plasma, J . Radioanal. Chem., 19, 269, 1974. 34. Voldet, P., Determination of the rare earths elements in basic rocks by neutron activation and high-resolution X-ray or gamma-ray spectrometry, Trends Anal. Chem., I , 262, 1982. 35. Muminov, V. A., Kheiderov, R. A., and Khamrakulov, T., Determination of rare earths using an Xray spectrometer, Zh. Anal. Khim., 34, 703, 1979. 36. Mantel, M. and Amiel, S., Determination of rare earths by high-resolution X-ray spectrometry following neutron activation, J. Radioanal. Chem.. 16, 127, 1973. 37. Navilikhin, L. V., in Metody Kontroloya Poluprovodn. Mater. Met., Khabibullaev, P . K., Ed., Tashkent, U.S.S.R., 1984, 37; Chem. Abstr., 102, 55229, 1985.

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Chapter 8

STABLE ISOTOPE DILUTION ACTIVATION ANALYSIS Masuo Yagi

TABLE OF CONTENTS I.

Introduction .....................................................................132

I1.

Description of the Method ......................................................132 A. Method for General Cases ...............................................132 B. Method for Special Cases ...............................................133

I11.

Discussion of the Method ....................................................... 134 A. Classification of the Method ............................................. 134 B. The Range of Elements which can be Determined ......................134 C. Obtaining the Enriched Stable Isotope ...................................135 D. Some Comments on the Chemical Processing ...........................136 E. Sensitivity of the Method ................................................ 137 F. Accuracy of the Method ................................................. 138 1. Amount of y ..................................................... 138 2. Interference Effects and Instrumental Errors .....................138

IV .

Applications ....................................................................139

References .............................................................................. 143

132

Activation Analysis

I. INTRODUCTION Many problems of activation analysis relate to accurate and precise determination of a particular element, often in very low concentrations. To solve the above problems, activation analysis itself requires a new method which has excellent precision and accuracy as well as sensitivity. Stable isotope dilution activation analysis' is the most suitable method and it is the purpose of this chapter to review the method, its advantages and limitations, and to indicate some research in which it has proved to be valuable.

11. DESCRIPTION OF THE METHOD A. METHOD FOR GENERAL CASES1 If it is assumed that an element of atomic mass M to be determined consists of at least two stable isotopes, MI and M, (abundance: 0, and 0,), which are converted easily to the radionuclides through particular nuclear reactions, the radioactivity ratio between two radionuclides produced in the sample containing x g of the element, R = a,/+, is expressed as

+

where F = flux of bombarding particles given by JOE- 4 (E) dE, where (E) is the flux of particles in the energy interval between E and E dE; a , , a, = cross-sections for the particular reactions of MI and M,, defined as So& ui (E) 4 (E) dE/F, where a (E) is the cross-section as a function of the particle energy; A,, A, = decay constants of radionuclides produced from MI and M,; t = time of irradiation, and A, = Avogadro's number. On the other hand, the reaction due to M, can be emphasized by adding y g of the isotopically enriched M, to the above duplicated sample. When the comparator as an isotopic mixture is prepared by using an isotopically enriched M, (atomic mass: M*), having the isotopic compositions of 0; for MI and 0; for M, (0; > 0,), and irradiated for the same time as above by particles with flux F*, and with the same energy distribution as that used for the sample, the radioactivity ratio between two radionuclides produced in this comparator, R* = a;/&, can also be written as

+

In this case, R* is given in a smaller value than that of R. Dividing Equation 2 by Equation 1, the R*/R ratio is given in a simple form as

Finally, the following equation is obtained for x

In Equation 3, it should be noted that several important terms for activation, such as flux, cross-section, Avogadro's number, and saturation factor are eliminated completely. The conditions for Equation 4 are x > 0,y > 0, and 1 > R*/R > 0~0210,0;. In the case of x

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= 0, the present method is unnecessary. In Equation 4, only the value of R*/R is unknown, but all the others are known. In order to evaluate x, therefore, the R*/R ratio should be measured cautiously. The radioactivity ratios of R and R* due to two radionuclides produced in the sample and comparator can be determined by measuring their detectable nuclear radiations. Gammaor X-ray spectrometry using germanium or silicon semiconductor detectors is the standard method of measurement and has become almost synonymous with instrumental activation analysis. If the above two radionuclides are measured by such a detector under the same conditions, R can be obtained as the ratio of the count rate in the net photopeak area under the selected gamma or X-line of a, at the end of irradiation to that of a, in the sample. Similarly R* can be obtained as the ratio of a; to a; in the comparator. Thus, Equation 4 makes it possible to determine the quantity of element A initially present in the sample even through the sample and comparator are irradiated separately by particles with different flux. On the other hand, when a highly enriched stable isotope is used as a spike to prepare the comparator, the value of 0;/0, ratio in Equation 4 is negligibly small as compared with the value of (R*/R) (0;/0,). In such a case, Equation 4 can be simplified to

B. METHOD FOR SPECIAL CASESZ The special method in which the self-shielding effect is negligible can also be introduced in a similar manner as above. Supposing that an element of atomic mass M to be determined also consists of at least two stable isotopes, MI and M, (abundance: 0, and O,), if an isotopically enriched M, (atomic mass: M*), having the isotopic compositions of 0; for M, and 01 for M, (0; > O , ) , is spiked to a sample containing x g of the above element, the nuclear reactions due to M, will be more emphasized than that in the natural element. When the sample is spiked with y g of the above enriched M,, and irradiated by particles with flux F*, the radioactivity ratio between two radionuclides produced in the sample, R* = a;/a;, is given by Equation 2. On the other hand, when an arbitrary amount of the element to be determined, z g, is irradiated as a comparator for the same time by particles with flux F f , but with the same energy distribution as that used for the above spiked samples, the radioactivity ratio between two radionuclides produced in this comparator, R' = a;/&, is also given by

In this case, R' is always given as a larger value than that of R*. Dividing Equation 2 by Equation 6, the following equation is finally obtained for x

It should be noted that the self-shielding effect of the comparator clearly differs from that of the sample spiked with the enriched isotope. Accordingly, Equation 7 should be applied only when the self-shielding effect of the sample is negligible, as in the case of photon activation. The conditions for Equation 7 are also x > 0, y > 0, and 1 > R*IRr > O;O,/ 0, 0;. In this case, the quantity x of element to be determined in the sample can also be evaluated by measuring only the value of R*/Rf ratio.

134

Activation Analysis

On the other hand, when the isotopically enriched M, of low quality is used as a spike, it is permitted to irradiate an arbitrary amount of it as a comparator instead of the natural element under investigation. If an arbitrary amount of the isotopically enriched M, of low quality, w g, is irradiated as a comparator for the same time as that of the spiked sample by particles with flux F', but with the same energy distribution, the radioactivity ratio between two radionuclides produced in this comparator, R" = a';/$, is also given by

In this case, R" always has a smaller value than that of R*. Dividing Equation 2 by Equation 8 also yields the following equation

The conditions for Equation 9 are x > 0, y

> 0, and 0, 0;/0;0, > R*/RV> 1.

111. DISCUSSION OF THE METHOD Discussion of the method may be divided into the following sections: 1.

2. 3. 4.

5. 6.

Classification of the method The range of elements which can be determined Obtaining of the enriched stable isotope Some comments on the chemical processing Sensitivity of the method Accuracy of the method

A. CLASSIFICATION OF THE METHOD This stable isotope dilution activation analysis is placed under the category of the internal standard m e t h ~ d Although .~ the method imposes a necessary condition that an element to be determined in the sample consists of at least two stable isotopes, one of the stable isotopes, MI, assumes an important role as an internal standard. Accordingly, this method makes it possible to evaluate accurately and precisely the amount of trace element to be determined in the sample, even though the sample and comparator are irradiated separately by particles with different flux.

B. THE RANGE OF ELEMENTS WHICH CAN BE DETERMINED As a result of mass-spectrographic investigations, it is well known that the elements with atomic numbers between 1 and 83 have on the average more than three stable isotopes each. All of 61 elements possess naturally occurring plural isotopes, and a further 20 elements are monoisotopic. Among the elements below bismuth, only two, technetium and promethium, do not have any stable species. The relative abundances of these isotopes in most cases are independent of the source of the material, and the stable isotopes of a given element occur together in constant proportions. Accordingly, the atomic weight determinations of a given element in widely different sources agree within experimental errors, although there are a few notable exceptions, such as abundances of lead isotopes, especially in ores containing uranium and thorium, and the abundance of 87Srin rocks containing rubidium.

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d B

* **

C N 0 FNe

9 Ir * * LaCePrNdhSmEuGdTbDyHoErTm)lbLu h

4

1

R

Ac Th Pa U N p P u AmCmBk C f Es FmMdNoLr

FIGURE 1. Elements which are likely to be determined by means of neutron activation.

Based on the above rule of the constant isotopic composition, the present method is established as well as the isotope dilution method in mass spectrometry. The method is characterized by that it can be applied only to elements which have more than two stable isotopes, and that it can also be applied to multielement determination in a wide variety of materials by various activation methods without any standard reference material. As a matter of course, however, the above applications would be limited to the elements having the following characteristics: two nuclides produced by particular nuclear reactions are radioactive, and formed in reasonable amounts. Both also have suitable half-lives, and decay by emission of detectable nuclear radiations. Such characteristic elements which are likely to be determined by activations using reactor neutrons and high energy photons' are shown in Figures 1 and 2, respectively. Though clear advantages of charged-particle activation are a variety of particles and a wide range of bombarding energies, as an example, elements applicable by proton activation are also shown in Figure 3. On the other hand, it has been proved that most of the elements containing the other inapplicable elements and monoisotopic can be determined effectively by applying another method,3-" i.e., the internal standard method coupled with the standard addition method developed recently by the present author.

C. OBTAINING THE ENRICHED STABLE ISOTOPE When one isotope is enriched, the others are depleted. This fact permits production of a radioactive nuclide in higher yield than with the natural element. Many enriched stable isotopes andlor isotopic mixtures sufficiently enriched in some isotopes are now available, and widely used to study nuclear chemistry, to produce specially designed radioisotopes, and to prepare useful labeled compounds. Such an enriched stable isotope is used as an effective spike to prepare the comparator containing the isotopic mixture which is different from the natural isotopic abundance. The enriched stable isotopes of most elements are available in milligram to gram quantities from the Isotopes Division of the United States Atomic Energy Commission at Oak Ridge, TN, and from the Atomic Energy Research Establishment in Harwell, England. Usually, the certification of isotopic analysis by mass spectrometry is served to such an enriched stable isotope together with the data of chemical impurities. The above isotopic

136

Activation Analysis

* **

t

r

r

L a c e PrNdRnSrnEu A c T h P a U NpPuAmCmBk C f E s F m M d N o L r

FIGURE 2. Elements which are likely to be determined by means of photon activation. (From Masumoto, K. and Yagi, M., J. Radioanal. Chem., 79(1), 68, 1983. With permission.)

* LaCeP r N d R n S m E u G d T b D y H o E r T m Y b Lu ** AclThPa U N p P u AmCmBkCf E s F m M d N o L r I

7

I\

f

r

r

\

-

-

F'IGURE 3. Elements which are likely to be determined by means of proton activation.

analysis can easily be checked by a suitable activation method, comparing with the natural element.

D. SOME COMMENTS ON THE CHEMICAL PROCESSING In preparation of the comparator, the chemical processing must ensure that the sample and the enriched stable isotope are mixed thoroughly in physical meaning. The comparator spiked with the enriched stable isotope in a known concentration may be prepared by either of the following two ways.

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In the first way, an exactly known amount of the enriched stable isotope or a material containing the same amount of that is mixed mechanically with a known quantity of the sample. In the second way, an aliquot of solution containing the enriched stable isotope is added to a known amount of the sample which was dissolved in a suitable diluent. The former is often very difficult to achieve adequate mixing of the sample and the enriched stable isotope in order to ensure homogeneity, and this difficulty is highly increased when more than two enriched stable isotopes are spiked. In the latter way, the chemical processing involves decomposition or dissolving of the sample and also necessarily requires a step where the final mixture is converted to a suitable physical form for irradiation. By this way, even the comparator spiked with several enriched stable isotopes can be easily prepared in such a manner that the solution containing a known amount of the sample is mixed with an aliquot of solution containing all of the enriched stable isotopes related to the elements to be determined. In the case of charged-particle activation, the self-shielding effects, which are often observed in the case of reactor neutron activation, can essentially be considered to be negligible. It is noteworthy, however, that the charged particles lose their energy within the target by excitation and ionization of the target atoms, and consequently, the nuclear reaction cross-section is varied markedly in the target. The rate of such energy loss per unit length inside the target, dE/dx, is well known as the stopping power of material, and it is closely related to the chemical compositions of the sample and comparator. Because of this stopping power, the sample and comparator should be prepared in the same chemical and physical form, and irradiated under the same conditions. The sample in this case, therefore, should also be processed chemically in the same manner as that of the above comparator. The above processings of the sample and comparator prior to irradiation produce the possibility of contamination. This is particularly dangerous in the cases of trace analysis for common elements. In the cases of minor constituent analysis or trace analysis for rare elements, this aspect becomes less important. In either case, however, it is preferred that the chemical processing is as simple as possible in order to minimize such contaminations, and that blank determinations would be included. On the other hand, when the relatively few predominant radionuclides in the gammaray spectrum of the sample obscure the contributions from less abundant indicator radionuclides, or when the half-lives and the radiation characteristics are very similar to each other, it may not be possible to resolve them simply by a purely instrumental method. This means that some elements at low concentrations are not detected, even though their actual sensitivities are sufficiently high. In such cases, it becomes necessary to resort to chemical separation. The decided advantage of activation analysis in comparison with the other analytical methods is the absence of blank values from reagents added after the end of irradiation. This opens the possibility of intentionally adding known amounts of the elements to be determined, which may serve as a chemical carrier. In the present method, moreover, it makes it possible to determine the interesting element without quantitative separation as well as that of the isotope dilution method in tracer chemistry.

E. SENSITIVITY OF THE METHOD In the present method, two radionuclides produced by particular nuclear reactions are proportional to amounts of two stable isotopes selected. These proportionality constants can be determined by parameters, such as activation cross-sections, flux density of activating particles, duration of irradiation, and half-lives of radionuclides produced. When these parameters are known, the sensitivity of the method may be calculated. Since the quantity of interesting elements in the present method is determined by measuring the ratios between two radioactivities produced in the sample and comparator, the above sensitivity is influenced by one of the selected stable isotopes, having a small value in the proportionality constant.

138

Activation Analysis

1

FIGURE 4. The relationships between x/y and R*/R or R*/R1 ratios in the case of Zn. (From Yagi, M. and Masumoto, K . , J . Radioanal. Nucl. Chem., 99(13), 293, 1986. With permission.)

On the other hand, the above sensitivity may also be affected by the following relevant facts. (1) The real detection limit of the element to be determined may well be dictated by the contamination introduced during the chemical processing of the sample or comparator prior to irradiation. This problem seriously affects the sensitivity of the method, so that special care should be taken to minimize blank corrections. (2) The activation by particles is not very specific, because the radioactivity is produced not only in the element to be determined, but also in many other elements contained in the sample. For this reason, measurement of the radioactivities must be made with the highest selectivity, most often in combination with radiochemical separation.

F. ACCURACY OF THE METHOD The main sources of errors in activation analysis are generally due to the facts that sample and comparator are not exposed to the same flux of bombarding particles, and that self-shielding effects are not always possible to eliminate, particularly when the matrix has a high absorption cross-section. In the present method, however, the nonuniformity of flux and differences of the self-shielding effects between the sample and comparator are compensated completely. Therefore, other sources of errors must be taken into account. A discussion of errors in the present method may be divided into the following two sections: (1) amount of y to be added, and (2) interference effects caused by other elements and instrumental errors.

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TABLE 1 Some Investigations by Stable Isotope Dilution Activation Analysis Investigation

Pair of isotopes

Ref.

Determination of Ca, Zn, and Ce by photon activation

Determination of Sr in biological materials by photon activation Determination of Sr in biological materials by proton activation Simultaneous determination of Ca, Rb, Sr, and Ce in environmental materials by photon activation

Determination of Sb in environmental materials by neutron activation

1. Amount of y When the present method is applied in practice, the quantity of y to be added to the sample is of importance. For example consider zinc. This element has five stable isotopes, 64Zn, 66Zn, 67Zn, 68Zn, and 70Zn, and in the natural element @Zn predominates - its abundance is 48.6%. An enriched 68Zn may be obtained with a @Zn/68Znratio of 0.00384. The relationship between x/y and R*/R in Equation 4 is shown in Figure 4 together with that between the x/y and R*/Rf ratio in Equation 7, because both relationships are identical. If the x/y ratio is small, the value of R*/R or R*/Rf ratio results in a small one which presents in the sensitive region to variation of y , so that the value of x to be determined will be subjected to large errors. If, on the other hand, the x/y ratio is large, the value of R*/R or R*/Rr ratio is obtained in a large one which also exists in the too sensitive region to variation of y. Consequently, determination of x is forced to serious errors. In this case, the optimum x/y ratio would be given when the value of R*/R or R*/R1 ratio is in the range from 0.3 to 0.7. Furthermore, much attention must also be paid to the following terms when the optimum x/y ratio is determined, that is, the count rate of gamma events in the net photopeak area of the selected gamma ray, the branching ratio of the selected gamma ray, the solid angle of the detector, and the detection efficiency of the detector for the selected gamma ray. Under normal conditions, the optimum x/y ratio may be given at R*/R or R*/ R' = 0.5, and this is found to be 4.5 for zinc. From this, the optimum quantity of the enriched stable isotope to be spiked to the sample can be determined easily.

2. Interference Effects and Instrumental Errors The interference effects caused by the other isotopes in the same element or the other elements may be subdivided into production of the same radionuclide by different nuclear reactions and overlapping of photopeaks in the same gamma-ray spectrum. Similarly, the instrumental errors may also be classified into random and systematic errors. However, these interference effects and instrumental errors would be given similar treatments to those in ordinary activation analysis.

IV. APPLICATIONS Some examples of the present method are listed in Table 1. The method using Equation 4 was carried out by proton activationI2 to determine strontium in tomato leaves [NBS] (National Bureau of Standards SRM-1572) and citrus leaves (NBS SRM-1573) using isotopically enriched 86Sr as a spike, and by neutron activationI4 to determine antimony in

140

Activation Analysis

TABLE 2 Isotopic Compositions of Enriched "Ca, 87Rb, %r, and '"Ce, and the Natural Abundances of the Respective Elements

Isotope

Enriched isotope composition (%)'

Element abundance (%)

"Ca 42Ca 43Ca "Ca T a "Ca Atomic mass 8SRb 87Rb Atomic mass "Sr 87Sr 88Sr Atomic mass 13Te W e '"Ce 14Te Atomic mass

"

As reported by Oak Ridge National Laboratories, Oak Ridge,

TN . From Yagi, M. and Masumoto, K., . I . Radioanal. Nucl. Chem., 99(13), 289, 1986. With permission.

environmental materials using isotopically enriched lZ1Sb.The method applying Equation 7 was also performed by photon activationZto determine strontium in the same biological materials as above using isotopically enriched 86Sr,and by photon activationI3to determine calcium, rubidium, strontium, and cerium in coal fly ash (NBS SRM-1633a), estualine sediment (NBS SRM-1646), and lake sediment (IAEA SL-1) using a mixture of isotopically enriched 48Ca,87Rb, and 142Ce. Although determinations of strontium in the above biological materials were carried out by proton and photon activations using a different pair of isotopes, the strontium fractions in the sample and comparator were isolated chemically together with most of the calcium before irradiation to avoid thermal decomposition of the sample and comparator during irradiation, and to eliminate interfering nuclear reactions due to matrix elements. As a matter of course, the above strontium fractions were isolated without quantitative separation. In order to prepare the most suitable physical and chemical form for irradiation, the above isolated fractions and/or the sample and comparator in the other cases were all processed finally as silica gel pellets, according to the procedure reported by Mitchell et al.I5 As a representative example of the method, the following describes the case of the simultaneous determination of four elements in the environmental materials.13 In Table 2, the isotopic compositions of the enriched 48Ca,87Rb,86Sr,and I4Te, and the natural isotopic abundances16 of the respective elements are listed together with their atomic masses. On the other hand, the principal photonuclear reactions leading to radionuclides on the four elements

1

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141

TABLE 3 Principal Photonuclear Reactions on Ca, Rb, Sr, and Ce Target nuclide (abundance, Half-life

%)

12.36 h 22.3 h 4.536 d 20.5 min 32.9 d 18.8 d 32.4 h 68 min 64.8 d 2.80 h 17.8 h 34.4 h 9.0 h 137.2 d 32.5 d

43Ca(0.135) MCa (2.09) " T a (0.187) 85Rb(72.17) 85Rb(72.17) 87Rb(27.83) @Sr(0.56) (9.8) 86Sr(9.8) (82.6) I3Te (0.190) (0.254) (0.254) I4"Ce (88.5) 14ZCe( 1 1.1)

Decay mode

Principal y-ray energy (MeV)

PPPIT

WP+ PECP'

IT ,EC EC IT EC,P+

IT,EC

WP+ EC

P

From Yagi, M. and Masumoto, K., J . Radioanal. Nucl. Chem., 99(13), 291, 1986. With permission

TABLE 4 Determination of Ca, Rb, Sr, and Ce in Environmental Materials Concentration of element (ppm) Sample

Ca

Rb

Sr

Ce

Coal fly ash

Average Certified value Estuarine sediment

Average Certified value Lake sediment

Average Certified value From Yagi, M. and Masumoto, K., J . Radioanal. Nucl. Chem., 99(13), 295, 1986. With permission.

to be determined are summarized in Table 3 together with their nuclear characteristics. Among them, the produced radionuclides and their gamma rays used for determination are underlined. The relationships between the x/y and R*/R or R*/R1 ratios for the interesting elements obtained by Equation 4 or Equation 7 are shown in Figure 5. From this, if the optimum x/y ratio would be given at R*/R = 0.5, it is found to be about 350 for calcium, about 3 for rubidium, 10 for strontium, and 7 for cerium, respectively. On the basis of the above ratios, the optimum quantities of four enriched isotopes to be spiked to each sample can easily be determined. As results, the concentrations of four elements on triplicate runs in three environmental materials are obtained as shown in Table 4. Although the sample

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Activation Analysis

FIGURE 5. The relationships between x/y and R*/R or R*IR1 ratios in the cases of Ca, Rb, Sr, and Ce.

and comparator in this case were irradiated separately under different beam intensities, all the results obtained are to be reproducible within the statistical limits. Moreover, the mean values are also in good agreement with either the certified or noncertified value within the usual limit of elemental analysis. The homogeneities of the sample and comparator processed chemically before irradiation can be checked by evaluating the reproducibility of data obtained on triplicate runs. As indicated by the values given in Table 4, the standard deviations from the means based on four elements are within 6% even in the case of maximum. From the above facts, it is concluded that the present stable isotope dilution activation analysis was demonstrated to be sensitive, highly specific, and reasonably accurate.

REFERENCES 1. Masumoto, K. and Yagi, M., Stable-isotope dilution activation analysis, and determination of Ca, Zn and Ce by means of photon activation, J . Radioanal. Chem., 79, 57, 1983.

2. Yagi, M. and Masumoto, K., Stable-isotope dilution activation analysis for special samples in which the self-shielding effect is negligible, J . Radioanal. Nucl. Chem., 90, 91, 1985.

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3. Yagi, M. and Masumoto, K., A new internal standard method for activation analysis and its application. Determination of Co, Ni, Rb and Sr in pepperbush by means of photon activation, J . Radioanal. Nucl. Chem., 83, 319, 1984. 4. Yagi, M. and Masumoto, K., A new internal reference method for activation analysis and its application. Determination of Ti, Cr, Ni and Zr in aluminium alloys by means of photon activation, J . Radioanal. Nucl. Chem., 84, 369, 1984. 5. Yagi, M. and Masumoto, K., Simultaneous determination of Ti, Cr, Fe, Cu, Ga and Zr in aluminium alloys by charged-particle activation analysis using the internal standard method, J. Radioanal. Nucl. Chem., 91, 379, 1985. 6. Masumoto, K. and Yagi, M., Highly accurate and precise multielement determination of environmental samples by means of photon activation using the internal standard method, J . Radioanal. Nucl. Chem., 100, 287, 1986. 7. Yagi, M. and Masumoto, K., Instrumental photon activation analysis of environmental materials using the internal standard method, J. Radioaml. Nucl. Chem., 109, 237, 1987. 8. Masumoto, K. and Yagi, M., Simultaneous determination of P, C1, K and Ca in several control serums by alpha-particle activation analysis using the internal standard method, J. Radioanal. Nucl. Chem., 109, 449, 1987. 9. Yagi, M. and Masumoto, K., Instrumental charged-particle activation analysis of several selected elements in biological materials using the internal standard method, J. Radioanal. Nucl. Chem., 111, 359, 1987. 10. Masumoto, K. and Yagi, M., Instrumental photon activation analysis of soil samples using the internal standard method coupled with the standard addition method, J . Radioanal. Nucl. Chem., 116, 375, 1987. 11. Masumoto, K. and Yagi, M., Revaluation of the internal standard method coupled with the standard addition method applied to soil samples by means of photon activation, J. Radioanal. Nucl. Chem., 121, 131, 1988. 12. Masumoto, K. and Yagi, M., Determination of strontium in biological materials by charged-particle activation analysis using the stable isotope dilution method, J . Radioanal. Nucl. Chem.. 91, 369, 1985. 13. Yagi, M. and Masumoto, K., Simultaneous determination of Ca, Rb, Sr and Ce in environmental materials by photon activation analysis using the stable isotope dilution method, J . Radioanal. Nucl. Chem., 99, 287, 1986. 14. Masumoto, K. and Yagi, M., Unpublished data, 1988. 15. Mitchell, J. W., Blitzer, L. D., Kometani, T. Y., Gills, J., and Clark, L., Jr., Homogeneously doped silica materials for trace element standards in neutron activation analysis, J. Radioanal. Chem., 39, 335, 1977. 16. Lederer, C. M. and Shirley, V. S., Eds., Table of Isotopes, 7th ed., John Wiley & Sons, New York, 1978.

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Chapter 9

SUBSTOICHIOMETRIC RADIOACTIVATION ANALYSIS Nobuo Suzuki

TABLE OF CONTENTS I.

Introduction ..................................................................... 146

I1.

Principle ........................................................................146

I11.

Substoichiometric Separation ...................................................147 A. Adsorption .............................................................. 147 B. Precipitation .............................................................148 C. Solvent Extraction .......................................................149

IV .

Application ..................................................................... 155 Determination of Oxygen using Substoichiometric Adsorption A. and Precipitation ........................................................155 Determination of Silicon using Substoichiometric Precipitation..........156 B. C. Determination of Chromium using Chelate Extraction ................... 156 Determination of Lanthanum using EDTA and 8D. Hydroxyquinoline .......................................................157 Determination of Uranium using Substoichiometric Separation E. of Barium or Lanthanum ................................................158 F. Determination of Antimony using Redox Substoichiometry ............. 160

References..............................................................................163

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Activation Analysis

I. INTRODUCTION Radioactivation analysis is one of the powerful techniques for the determination of many elements in a variety of matrices with different compositions such as geological, biological, and environmental samples. Especially neutron activation analysis (NAA) is particularly suited for this purpose. In particular, with the advent of sophisticated and computerized high resolution y-ray spectroscopy, NAA is adequate for instrumental determination of many elements. However, for example, the presence of predominant radionuclides, such as 24Na and 32Pfor biological samples masks the y-ray spectrum of the less abundant radionuclides. In this case, selective radiochemical separations must be introduced before the measurement of the neutron-activated samples. Various radiochemical separation procedures for NAA have been proposed, but usually the chemical separation is tedious to yield the complete recovery of the element of interest. Substoichiometric radioactivation analysis involves a chemical separation, but this does not require the complete recovery of the element of interest, hence the separation technique can be simplified. The substoichiometric radioactivation analysis has several advantages which can not be expected in instrumental radioactivation analysis and also in ordinary radiochemical radioactivation analysis.

11. PRINCIPLE The principle and the practical examples of the substoichiometric analysis are described in several review articles and monographs.'-6 The substoichiometric analysis is a definitive analytical method and has many excellent features compared with ordinary analytical methods including the radioactivation analysis. One of the characteristics of this method is summarized below: the element of interest can be determined by only the radioactivity measurement without any comparison with a standard sample. The present concept can easily be combined with the radioactivation analysis. The substoichiometric radioactivation analysis can be classified into the following three methods: 1. Direct method - The specific activity of a radioisotope induced by irradiation is NM,. If a known amount of the element m is separated, where m might be less than the total amount of the element M, (hence the term "substoichiometry"), the amount of the element of interest M, is easily determined by the measurement of radioactivity a

2. Method of carrier amount variation - The irradiated sample is divided into two equal parts; each contains the element of interest by the amount, M,. The specific activity, therefore, is AIM, = S. When a known amount of carrier (M) is added to one part, the specific activity becomes

From each part, the same amount of the element of interest is separated substoichiometrically and the radioactivities, a and a', are measured. The amount of the element is determined by Equation 3. This is based on the reverse isotope dilution principle, but by applying the stubstoichiometry, an unknown amount of the element of interest can be simply determined without any comparison with a standard sample. M, = Mal/(a - a')

(3)

3. Comparison method -After the samples to be analyzed have been irradiated together

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with the standard containing M,, a greater but equal amount of carrier M(M >> M,, M,) is added to both of them. The same quantity m(m > M) is separated from each and the radioactivities a, and a, are measured.

where A denotes produced radioactivity, accordingly the amount of the element of interest M, is determined by the following equation

In this method also, it is not necessary to pay any attention to the absolute amount of the separated portion m. The chemical procedure for the separation is much simpler than that of any ordinary destructive radioactivation analysis. Among these three, the first and the second methods do not require comparison with any standard, which means the errors to be involved in the radioactivation, such as fluctuation of neutron flux and self shielding can be avoided. Any interfering nuclear reaction produced the same nuclide to be measured does not introduce any error in contrast with conventional radioactivation analysis. It follows that for the successful determination of the element of interest by these methods, it is necessary to fulfill the following conditions: (1) the isotopic equilibrium between radionuclide and carrier must be achieved perfectly, (2) the exactly equal portion of the element must be constantly isolated from solutions. As clearly seen from Equations 3 and 4, the second and the third methods do not require any attention be paid to the chemical yield in the preliminary separation of the element of interest from an unknown sample with complex matrix composition. The second method is best among these three methods, however, in practice, the third method is widely used mainly due to simple substoichiometric separation in the presence of greater amount of carrier.

111. SUBSTOICHIOMETRIC SEPARATION Substoichiometric separation is performed by ordinary chemical separation methods, such as solvent extraction, ion exchange, precipitation, and electrochemical methods. In recent years, however, ion-exchange and electrochemical methods have not been used so much in substoichiometric separation. The precipitation technique is often used due to its simplicity, but the solvent extraction is most widely employed. This is because the procedure of solvent extraction is very simple and an appropriate extraction system can be selected from the great numbers of research papers dealing with solvent extraction of many different elements. A. ADSORPTION Adsorption of a fixed portion of the element of interest onto a constant amount of an adsorbent can be used for a simple substoichiometric separation. In general, adsorption mechanism is not so simple and can not be explained quantitatively, but the experimental procedure is simple and rapid, hence, if the substoichiometric separation is achieved, apparently this technique can be also used for the present purpose. Adsorption of a reproducible portion of fluorine onto various inorganic ion exchangers was examined.' A high adsorption

148

Activation Analysis

yield was observed in hydrated tin oxide, activated alumina, and commercial tin oxide. Similar substoichiometric adsorption of fluorosilicate onto hydrated tin dioxide was again clear.

B. PRECIPITATION The precipitation reaction of fluoride with a substoichiometric amount of lanthanum was used for the substoichiometric separation of fluoride, and this separation was also applied for the determination of oxygen in silicon crystals. Condition of the substoichiometric precipitation is theoretically di~cussed.~ If 50% of fluoride added (C,,) reacts with lanthanum in the substoichiometric precipitation, the following relation is obtained [HF]

1 2

= - CHF

where C, is the concentration of lanthanum added initially. If 99.9% added lanthanum reacts with fluoride, that is (La3+) = 0.001 C,, and by using the solubility product of lanthanum fluoride and the dissociation constant of hydrogen fluoride, the threshold pH can be given by Equation 6.

On the other hand, it can not be expected at pH higher than 8 that 99.9% of added lanthanum reacts with fluoride because lanthanum hydroxide is also precipitated at that pH. By substituting the solubility product of lanthanum hydroxide, the following expression is obtained for the value of the threshold pH:

When the concentration of fluoride added initially is 0.12 M, the pH range at which fluoride can be precipitated substoichiometrically with lanthanum is given by Equation 8:

Experimental results showed that fluoride can be precipitated substoichiometrically in the range between pH 2 and 8. The experimental results are little different from the theoretical one in lower threshold pH, but is in good agreement with that in higher threshold pH. It seems that this difference of lower threshold pH is caused by the kinetic effect in the precipitation of fluoride. A high reproducibility of the substoichiometric precipitation of fluoride with La was observed. The effect of coexistent elements for the precipitation of substoichiometric precipitation of fluoride, but sodium, copper, and manganese do not. A high reproducibility of the substoichiometric precipitation of fluorosilicate (SiF,Z-) with lanthanum was again clear, and in this case, the precipitation reaction was assumed as NhSiF, 2 La(NO,), + 3 H,0+2 LaF, + 2 NaNO, H,SiO, + 4 HNO,. The substoichiometric precipitation of fluorosilicate anion with barium as a counter cation was reproducible and used for the substoichiometric determination of ~ i l i c o nFigure .~

+

+

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t

FIGURE 1. Reproducibility of substoichiometric precipitation of fluorosilicic acid with barium (0.5 mmol barium added). (From Shikano et al., J. Radioanal. Nucl. Chem., 92, 309, 1985. With permission.)

1 shows the reproducibility of the substoichiometric precipitation of silicon as barium fluorosilicate using 3'Si tracer. The high reproducibility of the substoichiometric separation is only the essential point and the reaction ratio of the precipitate is out of concern in the substoichiometry, but the reaction ratio between fluorosilicate and barium was calculated simply from the inflection point in Figure 1 as 1:1 . The substoichiometric precipitation of the cation of interest with a substoichiometric amount of anion was examined. The example is a system of barium and sulfate ions.I0 The optimum conditions for the substoichiometric precipitation with an inorganic reagent can be derived from the solubility product, when 50% of barium initially added is used to form BaSO, in the substoichiometric separation without breaking down more than 0.1% of BaSO,, the threshold pH can be calculated from Equation 9.

where K,, is the solubility product of BaSO,, K, is the dissociation constant of HSO;, Cua2+and C,,: are the initial concentrations of Baz+ and SO:-, respectively. Assuming M, the threshold pH for the substoCBa2+= 4.5 X lo-' M, and C,,: = 2.25 x ichiometric precipitation is more than - 1.71. Figure 2 shows the dependence of the precipitated fraction of barium on the concentration of SO:-. The slopes of these curves indicate that the substoichiometric precipitation of barium can be performed with good accuracy and precision. From the equivalent points, the reaction ratio between barium and SO:- is found to be 1:l. The flat plateaus of these curves mean that SO:- is in excess of the barium content, and the unreacted barium is absent.

C. SOLVENT EXTRACTION Two extraction systems are commonly used: the chelate extraction system of metal ions with chelating agents, and the ion-association extraction system of metal ions with simple negative or positive ions. The ion-association extraction of ammonium phosphomolybdate (APM) has been frequently used for phosphorus separation. The ternary compounds of phosphomolybdate with organic agents, such as a-picoline, quinoline, oxine, and tetraphenylarsonium (TPA), have also been reported." All these extraction systems were used for the substoichiometric separation of phosphorus. Solvent extraction of 32P-labeledphosphorus as an ion associate with a substoichiometric amount of organic reagents, TPA and tri-n-octylamine (TNOA) is shown in Figure 3 where the dependence of phosphorus extraction

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Activation Analysis

A

"

0

0,2

0.4

0.6 SO:-,

0,8

1,0 1,2 1,4

mmo 1

FIGURE 2. Effect of the amount of SO:- on the substoichiometric separation of barium. Ba2+ (mmol): (1) 0.223; (2) 0.447; (3) 0.893. (From Katoh, M. and Kudo, K., J. Radioanal. Nucl. Chem., 84, 283, 1984. With permission.)

x10-~ phosphorus concentration, M FIGURE 3. Extraction of phosphorus with a substoichiometric amount of organic reagent. C,, = 9.29 x lo-) M, C,,, = 1.13 x 10-'M, and q , = 3.76 x M. (1) TPA and (2) TNOA. (From Shigematsu, T. and Kudo, K., J. Radioanal. Chem., 67, 33, 1981. With permission.)

on the quantity of phosphorus carrier was examined in the presence of excess molybdenum. It is clear that phosphorus can be separated substoichiometrically with a substoichiometric amount of TPACl or TNOA. The phosphorus concentrations at the equivalence points, for M and 1.30 x M, respectively, then the added TPA and TNOA are 3.60 x ratio of phosphorus to organic reagent is 1:3 for both TPA and TNOA. The substoichiometric extraction of phosphomolybdate with TPA in dichloroethane was applied to niobium sample. For a 100-mg sample, and irradiation time of 12 h with a thermal neutron flux of 8 x 10"

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FIGURE 4. Effect of pH on the substoichiometric extraction of chromium: (a) TPACI, (b) TNOA, ( c ) DDDC, (d) APDC, (e) NaDDC. (From Shigematsu, T. and Kudo, K . , J. Radioanal. Chem., 59, 66, 1980. With permission.)

n cmp3s-I, the detection limit of the substoichiometric activation analysis is estimated as low as 2 ng g-I. The substoichiometric extraction of chromium with a chelating reagent, such as sodium diethyldithiocarbamate (NaDDC), or with an ion-association reagent, such as TPA, was s t ~ d i e d . ' ~The - ' ~ substoichiometric extraction of chromium with TPA, TNOA, NaDDC, diethylammonium diethyldithiocarbarnate (DDDC), and ammonium pyrrolidinedithiocarbamate (APDC) was examined in detail.15 The effect of pH on the substoichiometric extraction of Cr(V1) with these reagents is shown in Figure 4, where the Cr(V1) concentration M for is 1.96 x lo-' M for extraction with ion-association reagents and 3.84 X chelating reagents, and substoichiometric amounts arbitrarily chosen are used in each extraction system. The optimum pH ranges for ion-association systems differ from those for chelate-extraction systems. The good reproducibility of substoichiometric extraction with these reagents was observed by extraction using a constant but substoichiometric amount of reagent from a series of Wr(V1) solutions containing different amounts of Cr(V1) carrier. Substoichiometry by using two complexing agents, a complexan and an extracting agent, is the method based on the formation of water-soluble complex with a substoichiometric amount of complexan followed by the separation of the unmasked element of interest by chelate-solvent extraction. This method is based on the differences of the reactivity of the competitive complexing agents used. The use of complexans as masking reagents for the substoichiometric separation is expected to extend the number of systems which can be applied for the substoichiometric determination of trace elements, and to increase the selectivity in the substoichiometric determination by nobel combination of two complexing agents with different formation constants for the element of interest and the coexisting elements. Possibility and applicability of this type of substoichiometry have been studied. 16-16 Equations have been derived to calculate the optimum conditions for the substoichiometric separation of elements and these theoretical results were examined experimentally. The substoichiometric separation of lanthanum by using EDTA and 8-hydroxyquinoline was examined and applied to the determination of lanthanum by activation analysis.19 The optimum conditions for the substoichiometric separation of the element by using two complexing agents were calculated from the following equations.

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Activation Analysis

where D and D' are the distribution ratios of the element of interest, M, between the aqueous and the organic phases in the absence and in the presence of a complexan in aqueous phase, respectively. HiY is complexan and i is its basicity. MY is the water-soluble complex of M with HiY. HA is the extracting reagent. K,, is the thermodynamic stability constant of MY. K,, is the extraction constant of M, ai is a factor which determined the quantitative distribution of any species of the complexan H,Y as a function of the pH of medium, and a, is a factor expressed as 1 + UP,, + KJ(PHA[H])where P,, and K, are the partition coefficient and the dissociation constant, respectively. In the extraction system of M with HA in the presence of H,Y, the extracting agent for the substoichiometric separation of the element of interest can be chosen from the relationship between the distribution ratios D' and D by using Equation 10. The condition for the substoichiometric separation is given as the constant region of D, and this constant region is dependent on the substoichiometric fraction shown as C,/CHlY. Equation 11 represents the concentration region of the extracting agent which can extract the unmasked element from a solution at the condition of C,/CHiy = 2. This condition is 50% stoichiometry without breaking down more than 0.1% of the complex with the complexan. EDTA was chosen as a complexan for the substoichiometric separation of lanthanum. Log Dr-log D plots of the lanthanum-EDTA system are shown in Figure 5. Three regions in Figure 5 can be observed on the log D' curves. In the region of log D' = 0, lanthanum can be extracted substoichiometrically since equilibrium exists between the competitive complexan and the extracting agent. The log D' < 0 region corresponds to the region where lanthanum unreacted with EDTA can not be extracted completely, while the log D' > 0 region corresponds to the region where the substitution of EDTA from the lanthanum-EDTA complex by the extracting agent takes place. 8-Hydroxyquinolinewas chosen as an extraction agent for uncomplexed lanthanum. From Figure 5 8-hydroxyquinoline was expected to be suitable for the extraction of unreacted lanthanum. Figure 6 shows the effect of pH on the substoichiometric separation of lanthanum under the condition of 50% stoichiometry; in other words, half of the lanthanum is complexed with EDTA. The flat plateau indicates that the substoichiometric separation of lanthanum can be performed in this region. The pH region corresponding to this plateau is 7.3 to 8.5, and this is in good agreement with the optimum pH region calculated theoretically. It is well known that a synergic extraction system involving an acidic chelating agent and a neutral basic ligand provide better extraction efficiency of the element of interest. In contrast to the number of research papers on the synergic extraction with various combinations of different types of reagents, very few papers on substoichiometry using synergic extraction have appeared. Applications of synergic extraction to substoichiometry are very interesting and sugggest further possibilities of substoichiometric separation. The application of the synergic extraction system to substoichiometric determinaton of calcium, uranium, manganese, and vanadium has been In the substoichiometric extraction of synergic extraction system using two reagents, two substoichiometric combinations are possible: the system with a substoichiometric amount of chelating agent and an excess of neutral ligand, and vice versa. Both systems for the substoichiometric extraction of uranium were theoretically disc~ssed.~' When 100x% of the chelating agent HA initially added is used to form the extractable adduct complex MA,L, in the presence of an excess of the neutral ligand L, pH of the aqueous phase can be readily calculated from the synergic extraction constant K,,.,

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b

6

10

8

log

D

FIGURE 5. Log Dl-log D plot of lanthanum in the presence of a constant substoichiometric amount (C,,,/C, = 0.5) of EDTA in the aqueous phase and \arious pH values. C,,, = M; pH: 7.0 for Curve 1 , 8.0 for Curve 2 , and 9 . 0 for Curve 3. (From Katoh, M. and Kudo, K., J. Radioanal. Chem., 79, 28, 1983. With permission.)

where C, V, P, and K,,,, are initial concentration, phase volume, partition coefficient, and synergic extraction constant, respectively, and subscript o denotes organic phase. For the substoichiometric determination of uranium, the extraction system involving a substoichiometric amount of 2-thenoyltrifluoroacetone (TTA) and an excess of tributylphosphate (TBP) was compared with a system involving a substoichiometric amount of trioctylphosphine oxide (TOPO) and an excess of TTA." In both systems, a high reproducibility of the substoichiometric extraction under 1% relative standard deviation (RSD) is possible. Another modified synergic extraction system was examined for the substoichiometric extraction of lower amounts of uranium in complicated matrix samples as phosphate rock. Hexafluoroacetylacetone (HFA) is one of P-diketones but stronger acid than TTA and can scarcely extract uranium into nonpolar solvent, furthermore, it is expected to have a larger synergic effect for U(V1) in the presence of a neutral ligand than the synergic system containing TTA. Effect of pH on the substoichiometric extraction of U(V1) with a substoichiometric amount of HFA in the presence of a large excess of TOPO was examined as shown in Figure 7.24A constant amount of U(V1) is extracted at pH over 4, and the extracted

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Activation Analysis A

I

FIGURE 6. Effect of pH on the substoichiometric separation of lanthanum. (From Katoh, M. and Kudo, K., J . Radioanal. Chem., 79, 33, 1983. With permission.)

FIGURE 7. Effect of pH on substoichiometric extraction. [U(VI)] = 3.0 x lo-' M; @[HFA] = 6.4 X 10-'M, [TOPO] = 1.8 X M, O[HFA] = 1.3 X l o - * M,[TOPO] = 1.0 X M. (From Suzuki et al., J . Radioanal. Nucl. Chem.. 97, 83, 1986. With permission.)

amount of U(V1) is in good agreement with the amount expected from the substoichiometric reaction of TOPO by considering the extracted species of UO,(HFA),TOPO. The extraction of U(V1) with an excess of HFA alone was negligible. A substoichiometric extraction was made to aqueous solutions containing various amounts of U(V1). Table 1 indicates the high reproducibility of the present substoichiometric extraction.

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TABLE 1 Reproducibility of

Substoichiometric Extraction Amount of U ( ~ g m

Activity of organic phase ( C P ~

Average: 7338 + 69 R.S.D.: 0.94% Note: [HFA] = 1.3 X lo-' M ,[TOPO] = 1.1 x lo-' M, pH 4.1 to 4.6.

From Suzuki et al., J . Radioanal. Nucl. Chem., 97, 85, 1986. With permission.

IV. APPLICATION A. DETERMINATION OF OXYGEN USING SUBSTOICHIOMETRIC

ADSORPTION AND PRECIPITATION The substoichiometric adsorption of fluoride onto hydrated tin dioxide was applied for the determination of oxygen in silicon crystals by neutron activation analysis via the nuclear reaction of 6Li ( n p ) t+160(t,n) 18F.' After irradiation of test and standard samples in a nuclear reactor, the test sample was dissolved in concentrated sodium hydroxide solution containing 12 mmol fluorine carrier by gentle heating and pH of the solution was adjusted to 8 to 9 with nitric acid. The hydrated silicon dioxide precipitated was filtered. The filtrate was adjusted with 1 M nitric acid and passed through the column packed with hydrated tin dioxide (2 g). The radioactivity of the column was measured by a coincidence counting system connected with two 3 in. X 3 in. NaI(T1) detectors. After appropriate dissolution of the standard sample, the solution obtained was treated exactly in the same way as the test sample. The oxygen content was calculated simply from both activities (Equation 4). The oxygen content of 28 ppm determined by the present method agreed with that determined by a nondestructive method 26 ppm. In the activation analysis of oxygen, "F produced by charged-particle activation as 160('He,p) 18F has frequently been employed for the determination of trace amounts of oxygen. The radiochemical separation of "F is required for the accurate determination of oxygen at ppb level in various materials inducing high radioactivity by irradiation. In the charged-particle activation analysis of oxygen in gallium arsenide, 76Br produced by the nuclear reaction of 75As('He, 2n) 76Brinterferes with the measurement of 'F activity. It is tedious to separate I8Fwith high purity and to correct the chemical yield in its radiochemical separation. Substoichiometric precipitation of fluoride with lanthanum was effectively introduced. *' Gallium arsenide sample wafer with the size of 20 mm x 20 mm X 0.5 to 1.0 rnm was set on a target holder and irradiated in a cyclotron with 3He at 15 MeV for 20 rnin. As a standard sample, fused quartz with the size of 20 rnm x 20 mm x 0.5 m m was irradiated. The irradiated sample wafer was etched to remove the surface contamination and dissolved

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Activation Analysis

TABLE 2 Analytical Result for Oxygen in Gallium Arsenide Sample no.

Location in crystal

Oxygen (ppb)

1 2 3 4 5 6 7

Front Front Middle Middle Tail Tail Tail

13 10 19 18 24 26 36

From Shikano, et al., J . Radioanal. Nucl. Chem., 91, 89, 1985. With permission.

in a solution of nitric and hydrochloric acids containing 12 mmol sodium fluoride. After two fractional distillations, a substoichiometric amount of lanthanum solution (1 mmol) was added to the filtrate and fluoride was precipitated as lanthanum fluoride at pH 5 to 6. The standard sample was washed and fused with sodium carbonate containing sodium fluoride. The melt was dissolved in hot water and the pH of the solution was adjusted to 8 to 9 with nitric acid. Hydrated silicon dioxide was centrifuged and the filtrate was treated in the same way as the test sample. Analytical results of oxygen are summarized in Table 2. It is found from the table that the concentration of oxygen is 10 to 36 ppb and increases a little along the position such as fron,t, middle, and tail in gallium arsenide crystal. The time required for the separation was 2 h, the detection limit was 10 ppb, and the decontamination factor of 76Brwas approximately lo6.

B. DETERMINATION OF SILICON USING SUBSTOICHIOMETRIC PRECIPITATION Silicon-doped gallium arsenide was used as test sample and a small piece of silicon wafer was used as standard sample. The test and standard samples were irradiated in a nuclear reactor for 5 min. After irradiation, the test sample was etched in the mixture of sulfuric acid, hydrogen peroxide, and redistilled water. Test sample was dissolved in a mixture of nitric and hydrochloric acids containing a silicate solution of 2 mmol as a camer. After addition of sulfuric acid and hydrofluoric acid, silicon was distilled as silicon tetrafluoride. The distillate was collected in a mixture of boric acid and hydrochloric acid. A small portion of hydrofluoric acid and a substoichiometric amount of barium chloride (0.5 mmol) were added to the distillate and silicon was precipitated as barium fluorosilicate. Standard silicon wafer was dissolved in a mixture of nitric and hydrofluoric acids. The solution was added to a mixture of boric acid and hydrochloric acid and treated in the same way as the test sample. The concentration of silicon in the test sample was determined by comparing the radioactivities of 31Sifrom the test and standard samples. The results are summarized in Table 3.9

C. DETERMINATION OF CHROMIUM USING CHELATE EXTRACTION The substoichiometric extraction of chromium with DDDC and APDC was applied for the determination of chromium in high purity calcium carbonate.'* Sample and standard were irradiated in a nuclear reactor at a thermal flux of 3 X lOI3 n s-' for 260 h. After an addition of 2 mg Cr(V1) carrier to the irradiated samples, these samples were dissolved by appropriate treatment. Cr(V1) was extracted from acidic media with methyl isobutyl ketone and was back-extracted with distilled water into aqueous solution. Chromium

.

.

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TABLE 3 Analytical Result for Silicon in Gallium Arsenide

Sample no.

Sample weight (mg)

Content in test sample (MA (14

Concentration (PP~)

0.303 0.274 0.364 0.280 0.320 0.321 0.253 0.254 Mean value Sequential substoichiometric precipitation from the same final solution of sample no. 1-1 or 4-1. From Shikano et al., J. Radioanal. Nucl. Chem., 92, 313, 1985. With permission.

TABLE 4 Analytical Results for Chromium in Calcium Carbonate Extracting agent

DDDC APDC

NaDDC

Weight of test sample (9)

Content (I%)

Concentration ( P P ~

0.2035 0.2035 0.2038 0.2085

0.045 0.044 0.043 0.045

0.22 0.22 0.21 0.22 0.22

From Shigematsu, T. and Kudo, K., J . Radioanal. Chem., 59, 70, 1980. With permission.

was extracted with a substoichiometricamount of DDDC or APDC from the aqueous solution of pH 5.6. The radioactivity of the organic extract was measured by a Ge(Li) detector. Analytical results of chromium in high purity calcium carbonate are summarized in Table 4.

D. DETERMINATION OF LANTHANUM USING EDTA AND 8HYDROXYQUINOLINE The substoichiometric separation of lanthanum by the solvent extraction with oxine in the presence of a substoichiometric amount of EDTA was applied to the lanthanum determination in some material^.'^ Orchard leaves and spinach of National Bureau of Standards (NBS) standard reference materials were dried in an air oven at 85°C for more than 4 h. About 0.5-g sample of NBS standard reference materials was irradiated together with a lanthanum standard in a nuclear reactor for 10 min at a thermal neutron flux of 8 X 10-13 n cm-2 s ~ ' After . irradiation, lanthanum carrier was added to the sample and standard. NBS standard reference materials were dissolved in a perchloric acid and nitric acid mixture by adding hydrogen peroxide, and evaporated nearly to dryness. The evaporated residue

158

Activation Analysis

was dissolved in water and hydrofluoric acid and was added to the solution. The precipitated lanthanum fluoride was centrifuged and dissolved in a boric acid and nitric acid mixture. To the solution, aqueous ammonia was added and lanthanum hydroxide was separated by centrifugation. After dissolution of lanthanum hydroxide, pH of the solution was adjusted above 5.5. Lanthanum was extracted with 0.5 M ?TA in methyl isobutyl ketone. To the organic phase, a diluted perchloric acid was added and lanthanum was back-extracted. Rock crystal sample was dissolved in a hydrofluoric acid and perchloric acid mixture. The solution was evaporated nearly to dryness. The residue was dissolved in hydrochloric acid and lanthanum was extracted with di(2-ethylhexy1)phosphoric acid (HDEHP) in toluene. Lanthanum was back-extracted with diluted hydrochloric acid. The pH of the lanthanum solutions obtained here was adjusted to greater than 9.5. A 10-ml portion of 0.25 M 8-hydroxyquinoline in chloroform was added and lanthanum was extracted. The organic phase was shaken with 10 rnl of 3.0 x M EDTA solution and lanthanum was separated substoichiometrically into the aqueous phase followed by the radioactivity measurement. The analytical results of lanthanum in orchard leaves, spinach of NBS standard reference materials, and rock crystal were 1.4 ppm, 315 ppb, and 52 ppb, respectively. The substoichiometric method using EDTA and 8-hydroxyquinoline is suitable for the determination of trace amount of lanthanum.

E. DETERMINATION OF URANIUM USING SUBSTOICHIOMETRIC SEPARATION OF BARIUM OR LANTHANUM Substoichiometric isotope dilution analysis for U in a synergic extraction system has been r e p ~ r t e d . ~Substoichiometry '.~~ was applied to the determination of trace amounts of uranium via nuclear fission of 235Uas 235U(n,f)'40Ba+140La. This is based on the substoichiometric separation of a fission product lmBa or its daughter product lWLaafter neutron irradiation of samples.'O Three methods were examined for the determination of uranium using the substoichiometric separation of 140Baor ""'La. In Method 1, I4OBa is separated substoichiometricallyas barium sulfate, and left to reach radioactive equilibrium between 140Baand ''"'La. Uranium is determined by measuring the activity of I4"La. In Method 2, a fission product of 14Ba is separated, and left to reach radioactive equilibrium. I4OLa is separated substoichiometrically, and uranium is determined by measuring the activity of lNLa. The substoichiometric separation of lanthanum was made by extraction technique using two complexing agents, DTPA (diethylenetriarninepenta-acetic acid) and TTA. In this method, it is necessary to correct the chemical yield of lmBa, because barium is separated by an ordinary method prior to the final substoichiometric separation. Therefore, a known quantity of 13'Ba tracer is added to the test sample for the chemical yield correction. Method 3 is based on the substoichiometric separation of lanthanum. When the radioactive equilibrium between IWBa-lWLais established, the substoichiometric separation of lanthanum is carried out using two complexing agents described above and uranium is determined by measuring the activity of '@La. In this method, lWLaproduced independently by (n,y) reaction of lanthanum in sample interferes in the determination of uranium. Thus, it is necessary to apply the substoichiometric separation for '40La produced by fission of "W after decay out of laLa produced by (n,y) reaction of lanthanum, or to correct the contribution of '@La produced by (n,y) reaction. Uranium is determined by Equation 4 in Methods 1 and 3, and Equation 13 in Method 2.

Volume I

159

I

Ba ,La carries HNOj -HCI mixture NH40H,Na2C03 solution

dil.HCI ~ e carrier ~ '

P Ba solution

Fe(OHh ,La(OHI3

[+, Method-1

Method - 2

Method-3

FIGURE 8. Analytical procedure for the determination of uranium using substoichiometric separation of barium or lanthanum. (From Katoh, M. and Kudo, K . , J. Radioanal. Nucl. Chem.. 84, 281, 1984. With permission.)

where M and a are the amount of uranium and the activity of I4OLa, y is the chemical yield of barium (100 y %). Analytical procedure for uranium in molybdenum sample as an example is shown in Figure 8. After irradiation of standard and molybdenum samples, barium and lanthanum carriers were added. In Method 2, barium carrier labeled with '33Ba was added for the chemical yield correction of 140Ba. Molybdenum was dissolved in nitric and hydrochloric acid mixture, other samples of rock crystal and glass were dissolved in perchloric and hydrofluoric acid mixture, and silicon wafer sample was dissolved in nitric and hydrofluoric acid mixture. Barium and lanthanum were finally precipitated as barium carbonate and lanthanum hydroxide, respectively. In Method 1, barium carbonate was dissolved in dilute hydrochloric acid. By adding a diethyl ether-hydrochloric acid mixture to the solution, barium was separated as barium chloride precipitate. The precipitate was dissolved in diluted hydrochloric acid and barium was precipitated substoichiometricallyas barium sulfate by adding a substoichiometric amount of sodium sulfate solution. In Method 2, after reaching radioactive equilibrium between I4OBa and I4'La, lanthanum and ferric carriers were added and barium carbonate was dissolved in dilute hydrochloric acid. Lanthanum and ferric hydroxydes were precipitated by aqueous ammonia. These hydroxides were dissolved in hydrochloric acid, and the ferric carrier was extracted with isopropyl ether. Lanthanum was extracted with HDEHP in toluene solution, and then back-extracted with hydrochloric acid. Lanthanum was separated substoichiometrically by extraction with TTA in the presence of a substoichiometric amount of DTPA. In Method 3, lanthanum was separated by the same treatment as in Method 2 and the substoichiometric separation of lanthanum was carried out successively.

160

Activation Analysis

TABLE 5 Analytical results for uranium (ppb) Samples Mo-1 Mo-2

Rock crystal Glass Silicon wafer

Method 1

Method 2

Method 3

80 k 5

84 2 5 60?5

81 +. 5

194

?