widely, no interelement effeds are detectable in the measured intensity ratios. The data shown in Table I1 on the complete set of reference ore samples provide further documentation that the analytical procedure described in this communication can determine uranium accurately in a wide variety of low grade uranium ores with a relative standard deviation a t 1 u of f3.3%. The limit of detection of the present technique is 5 ppm. Figure 7 shows a pair of recordings for a YP04.Bi phosphor blank and for a phosphor prepared from an ore containing 10 ppm U. It is clear that 5 ppm of U, or even less, should be visually detectable on the recordings. ACKNOWLEDGMENT We are grateful to M. Tschetter of the Ames Laboratory for help in the chemical processing of monazite samples. LITERATURE CITED (1) E. W. Grut, Jr., “The Search for Uranium-A Perspective”, CONF 700219-1, US. Energy Research and Development Administration, Denver, Colo., 1975. (2) R. D. Nininger, “Uranium Exploration Methods”,STi/PUB/334, international Atomic Energy Agency, Vienna, 1973, pp 3-17. (3) F. S. Grimaldi and M. H. Fletcher, U.S. Geol. Bull., 1006 (1954). (4) “Proceedings of a Symposium on the Analytical Chemistry of Uranium and Thorium”, T. M. Florence, Ed., AAEWTM 552, Sydney, Australia, 1970. (5) J. Korkish and H. Hubner, Talanta, 23, 283 (1976).
(6)R. H. Scott, A. Strasheim, and M. L. Kokot, Anal. Chim. Acta, 82, 67 (1976). (7) J. B. Zimmerman and V. Reynolds, Scl. Bull., CM 75-4, Canada Centre for Mineral and Energy Technology, 1975. (8) E. L. DeKalb, V. A. Fassel, T. Taniguchi and T.R. Saranathan, Anal. Chem., 40,2082 (1968). (9) A. P. D’Silva and V. A. Fassel, Anal. Chem., 44, 2115 (1972). (10) A. P. D’Siiva and V. A. Fassel, Anal. Chem., 45, 542 (1973). (11) V. A. Fassel, E. L. DeKalb, and A. P. D’Siiva. “Trace Level Rare Earth Determinations by X-ray Excited Optical Fluorescence(XEOF) Spectroscopy”, in “Analysis and Applications of Rare Earth Materials”, 0. B. Micheison, Ed., Universltetsforlaget,Osio, Norway, 1973. (121 . . S. A. Goidstein. A. P. D’Siiva. and V. A. Fassel, Radiat. Res., 59, 422 (1974). (13) G. H. Dieke and A. B. F. Duncan, “Spectroscopic Properties of Uranium Compounds“, McGraw Hill, New York, N.Y., 1949. (14) F. A. Kroger, “Some Aspects of the Luminescence of Solids”, Eisevier, New York, N.Y., 1948, Chap. IV. (15) G. Blasse, J. Electrochem. Soc., 115, 738 (1968). (16) P. P. Sorokin and M. J. Stevenson, IBM J. Res. Dev., 5, 56 (1961). (17) M. V. Hoffman, J. Electrochem. SOC., 117, 227 (1970). (18) “Fluorimetry Reviews-Uranium,’’ Acc. No. 9914, G. K. Turner Associates, Paio Alto, Calif., 1968. (19) G. Blasse and A. Bril, J. Chem. Phys., 47, 5139 (1967). (20) G. Blasse and A. Bril, J. Chem. Phys., 48, 217 (1968).
RECEIVEDfor review October 29,1976. Accepted January 21, 1977. Work performed for the US. Energy Research and Development Administration under Contract No. W-7405eng-82.
Matrix Corrections for Energy Dispersive X-ray Fluorescence Analysis of Environmental Samples with Coherent/lncoherent Scattered X-rays Kirk K. Nielson Battelle, Pacific Northwest laboratories, Richland, Wash. 99352
A numerical method is given for computing matrix effects In relatively thick (63 mg/cm2), pelletized homogeneous or particulate samples of biological and environmental origin. The method relies on estimating an approximate light element (Z 5 13) content of the sample from the coherent and incoherent scatter peaks after they have been corrected for absorption and for scattering from the heavy elements (Z 13). The total sample absorption due to both light and heavy elements Is computed by an iterative procedure which yields self absorption corrections with a relative precision of several percent. Enhancement and particle size effects are also computed in the iterative procedure on the same basis as the absorption corrections. Since the corrections are based on a thin sample x-ray calibration, repeated calibrations for specific sample types are avoided. The method yields matrix corrected quantities of 24 elements from 1024 channels of raw data In approximately 20-50 s (5-15 iterations) using a 24K, PDP-15 computer.
>
The advent of commercially available energy dispersive spectrometers for x-ray fluorescence measurements has provided an economical and powerful tool for environmental, clinical, and industrial analyses. Although x-ray fluorescence measurements are simple for qualitative work, accurate quantitative measurements often depend on matrix corrections which require large numbers of standards or multiple analyses. Matrix corrections become necessary when samples
are of sufficient thickness to absorb significant fractions of the fluorescent radiation, and when the sample matrix absorption characteristics differ significantly from those of the standard. Certain samples such as air particulates collected on thin filters are easily analyzed for many elements because they are sufficiently thin for matrix effects to be negligible. In such cases, peak areas are proportional to elemental masses, and are simply calibrated using thin film standards. However, a wide variety of materials such as ion-exchange resins, plant and animal tissue, and sediments are most conveniently prepared by simply pressing them into relatively thick (20-80 mg/cm2) homogeneous wafers. The matrix correction problem can often be eliminated for these latter sample types by utilizing standards of similar composition and geometry to the unknown. Excellent results can be obtained, for example, using an NBS standard orchard leaf or bovine liver wafer to calibrate for multielement analyses of many food, plant, or animal tissue samples. The risk in such a calibration is in the tendency to accept it for a wide variety of samples, some of which may have significant differences in their matrix absorption characteristics. A convenient check on such differences can often be made by monitoring the intensities of the coherent and incoherent scatter peaks. Samples not suited to the standard being used must then be analyzed using an alternate standard for calibration. Samples having high mineral contents tend to require more standards of varying major element composition than lighter matrices such as cellulose, because of the greater chance of ANALYTICAL CHEMISTRY, VOL. 49, NO. 4, APRIL 1977
641
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OBSERVED S P E C T R U M
Y///H,H E A V Y ELEMENT C O N T R I B U T I O N
COHERENT 3 1 INCOHERENT
w
s
5
CONTRIBUTION TO TOTAL SCATTE
0 w
WERCY
SCATTERED E X C I T I N G RADIATION
Figure 1. Schematicdiagram of the light element contributions to x-ray scattering, from which absorption corrections are computed
significant variations in absorption properties. Calibration methods for extremely high concentrations such as encountered in metal alloy analyses have been reviewed and proposed by Rasberry and Heinrich (1). Since most environmental samples being analyzed in this laboratory have been intermediate between the low and high mineral contents just mentioned and were not readily prepared as thin membranes, attention has been given to matrix corrections for these thick, intermediate-Z samples. A rapid method of determining matrix corrections for pelletized samples is required if sample preparation methods are to be sufficiently simple for a large volume of analytical work. Giauque et al. (2) have reported a simple method for measuring the matrix absorption of a thick, homogeneous sample pellet utilizing the transmission of x-rays through the sample. The method gives accurate results if the critical thickness is not reached for the x-ray energy of interest. However, if large numbers of samples are to be analyzed, the necessityof several analyses to properly analyze and determine absorption corrections for each sample becomes prohibitive. In a recent report, Reuter (3) proposed an alternative to the specific absorption measurements for each sample by numerically computing the absorption of each measured element in the sample, and attributing the remainder of the sample mass to cellulose, for which an additional absorption correction was computed. Since most sediment and tissue samples do not contain the relatively constant bulk matrix as with cellulose in plants, an alternative method has been developed to reliably estimate the light element composition of environmental samples. The method proposed here utilizes the coherent and incoherent x-ray scatter peaks to identify and estimate the quantities of two light elements representative of the bulk sample composition. Absorption by these light elements in addition to that of the measured heavy elements is computed for use in matrix corrections for the individual sample. By thus computing the matrix corrections, calibration for pelletized environmental samples becomes identical to that for thin samples. Self-absorption corrections are readily computed using the equations given by Giauque et al. (2).Enhancement effects can also be readily evaluated from the estimated and measured bulk and trace compositions using fundamental parameter methods such as were reported by Clark (41,and reviewed by Sparks ( 5 ) .Particle size corrections can also be applied to pelletized particulate samples utilizing the bulk and trace compositions if an estimate of particle size and density is available. Berry et al. (6) have reported equations for these corrections. This paper thus presents a matrix correction method which separately accounts for self-absorption, enhancement, and particle size effects to permit analysis of 642
0
Table I. Definitions of Symbols Used in Equations and in
I
ANALYTICAL CHEMISTRY, VOL. 49, NO. 4, APRIL 1977
Quantity of element i (pglcm2). Net peak area for element i (counts). Analysis livetime interval (s). Thin film spectrometer calibration for element i (counts.cm2/pg.s). Self absorption factor (Equation 2). Enhancement factor (Equation 5). Particle size correction factor (Equation 7 ) . Subscript referring to an interfering element. Subscript referring to the exciting radiation. Mass absorption coefficient of element j for xrays from element i. Mass absorption coefficient of element j for the exciting radiation. Mean angle formed by the fluorescent radiation with the specimen surface. Mean angle formed by the exciting radiation with the specimen surface. Subscripts referring to the two representative light elements. Subscripts referring to incoherent and coherent scatter. Scatter peak calibration factors. Incoherent and coherent scattering cross-sections for element i (cm2/pg). Fluorescent yield. Absorption function jump ratios. Average sample mass absorption coefficient (Equation 6). Reference particle thickness (pm). Mean sample particle thickness (pm). Volume fraction occupied by particulate matter [m = P A P h + P h 1 . Volume fraction occupied by cellulose binder [n = Ph/(Ph -k P1)1.
Densities of particulate matter and cellulose binder (pg/cm3). Linear absorption coefficients for particulate matter and cellulose (Equations 8,9) (cm-l). Uncorrected quantity of element i (pg/cm2) (Figure 3, Equation 10). Calibrated x-ray scatter (Figure 3, Equation 11). Total measured sample mass (pg/cm2)(Figure 3, Equation 14). Total measured heavy element mass (pg/cm2) (Figure 3, Equation 14). Sample heavy element attenuation (Figure 3, Equation 15). Sample light element attenuation (Figure 3, Equation 15). Peak overlap correction coefficient.
relatively thick sample pellets using thin calibration standards. The method has been applied to samples varying in average atomic number from about 5 to 13. Scattered x-ray intensities taken from varying wavelength dispersive spectral regions have previously been used to normalize x-ray fluorescent intensities, reducing both instrumental error and error arising from differences in absorption among samples and standards (7-1 1). This approach has been shown to work well for selected elements or in selected types of sample matrix. Scattered radiation has also been used to estimate both background and mass absorption coefficients for trace elements in selected spectral regions (12-16).Use has also been made of coherent/incoherent peak ratios to measure hydrogen and carbon in light element matrices such as hydrocarbons (17), and in other reports, to estimate average atomic numbers (18) and absorption corrections for environmental samples of similar composition (19).
THEORY
10
The x-ray spectrum in Figure 1 schematicallyillustrates the basis for analyzing the heavy elements (2 > 13) which are observed by their characteristic x-rays, and the light elements (H, C, N, 0, Na, etc.) which must be estimated by difference from the scattered x-ray peaks. Since the major elements in biological and environmental samples are light elements, the resulting scatter peaks are fortunately large and provide a precise basis for the light element measurement. Self-absorption, enhancement, and particle size corrections all utilize both the heavy and light element concentrations, along with published elemental mass absorption coefficients and related parameters. Since the concentrations and corrections are interdependent, correction is accomplished by iteration. Concentrations of heavy elements determined from the thin film spectrometer calibration are first used to estimate the incoherent and coherent scatter they have caused. The remaining fractions of the scatter peak areas are then used to determine the quantity of two representative light elements. The heavy and light element concentrations are then used in computing self-absorption, enhancement, and particle size corrections for the heavy elements, from which new heavy element concentrations are determined. The iteration process continues until further corrections are insignificant. It should be noted that particle size corrections additionally require an estimate of the mean particle size and density which are not available from spectral parameters. The quantity, Qi, of an element is computed in terms of its mass per unit area (pg/cm2) to permit use of an x-ray fluorescence calibration based on thin, single element standards. It is computed as Ai -Fi Pi Qi = (1) tKi 1 - e - F a E i 1 with the symbol definitions as listed in Table I. The calibration factors Ki are the net counts per unit time and mass resulting from analyses of thin film standards under identical instrumental conditions to those used for the sample. Equation l is a common thin sample calculation method ( 2 , 3 )with correction terms added for particle size effects and enhancement. The self-absorption factor is defined as
1.
ELEMENTAL S E N S I T I V I T I E S
Rb
Ka X-RAYS
I
L Sr
CI
EXCITATION: Zr SECONDARY
SOURCE
STANDARDS: THIN FILMS, I N VACUO
0.01
5
0
10
15
X-RAY ENERGY IkeVl
Flgure 2. X-ray sensitlvity curves for zirconium exciting radiation
element pairs often satisfy Equations 3, the pair is chosen whose incoherenthoherent scattering cross-section ratios lie immediately on either side of the ratio of the observed scatter attributable to light elements,
h A ~ /t
w
