Rapid X-Ray Fluorescence Determination
of Traces of Strontium in Samples of Biological and Geological Origin K.
P.
CHAMPION, J. C. TAYLOR,’ and R. N. WHITTEM
Australian Afomic Energy Commission, Sufherland,
b
A mathematical expression i s derived, relating the ratio of line peak to background intensities with sample composition. The treatment is generally similar to that of Kalman and Heller, but leads to a matrix effect, which can conveniently be called a “sample scattering factor.” This factor can be simply calculated from an approximate knowledge of the composition of the sample, and published values of coherent and Compton scattering functions. From this a rapid analytical method is developed which employs no standards other than aqueous solutions of strontium nitrate. Examples are quoted of strontium determinations in a variety of samples, analyzed by other methods.
A
method was required to determine the concentration of strontium in a wide range of biological materials, including aqueous solutions of separated strontium and various ashed samples such as oyster shell, oyster flesh, milk, and grasses. The so-called external standard method, or calibration standards, used by Roberts (23) to determine the strontium content of bone ash was discarded because of the large number of matrices for which standards would need to be prepared, and also because many of the matrix types-for instance, grass ash-could not be considered reproducible in corn, wition and packing density. Internal s+andard methods (3) and standard addition techniques (4) were discarded because of effort in sample preparation, analysis time, and the need for destruction of the sample (in some cases the sample was required intact for other analyses). The use, as internal standard, of radiation scattered by the sample has been proposed by Bndermann and Kemp ( I ) and by Kalman and Heller (9) for this type of analysis, and seemed to offer promise. It was therefore decided to RAPID
N .S.W.,
minimum wavelength from exciting source XE = absorption edge for element x xk = K , wavelength for element x J = photon flux from exciting source p, p / p = linear and mass absorption coefficients, respectively ;1.I = matrix X = element x el, e1 = angles of incidence and exit (from normal t o sample surface) K1, K 2 , etc. = constants involving instrumental details, fluorescence efficiency of element 2, etc. C = concentration, expressed as weight fraction
investigate the potentialities of this technique. The above authors studied the radiation scattered a t some arbitrary wavelength, but in our case an interpolation was used to determine the (scattered) intensity a t the wavelength of the strontium K , line. This wavelength was chosen because an accurate correction for the background intensity a t the peak position was considered essential, a t least for samples containing less than 100 p.p.m. of strontium. Once the background intensity was measured, this could be simply used as internal standard using the formula:
R
=
(n,/nd
THEORY
Intensity of Fluorescence. Several authors (9, 14) have shown that the intensity of fluorescence from an “infinitely thick” sample can be represented by
X
=
=
A,
-1
where R is the ratio of net peak to background, n, is the count rate a t the peak position, and nb is the interpolated background count rate a t the peak position. By using a theoretical treatment similar to that of Kalman and Heller (9), but different simplifying assumptions, an expression relating R to strontium concentration is derived. This treatment shows that if a wide range of sample types is encountered, the matrix composition must be known, a t least approximately, and the results corrected by an appropriate factor, relating the matrix scattering powers of sample and standard. The method is generally limited to light element matrices-that is, samples containing only traces of elements heavier than bromine (Z = 35) *
where P , Present address, Argonne National Laboratory, Argonne, Ill.
Australia
intensity of fluorescence peak of element z above background wavelength, which is variable
=
Kalman and Heller (9) simplified this expression by defining an effective exciting wavelength, X, such that
P,
=
Kz X n
We have verified the constancy of X in the case of strontium K , excited by 50-kv. x-rays emitted by a tungsten tube using :
el
=
2 7 O , e2 = 55’ (Philips geometry)
Values of p / p used were a more or less consistent set extracted from the literature; J X was derived from data measured by Ulrey (15); and a simple numerical integration of Equation 1 was used to provide values of X for the range
of matrices given in Table I. These values show the high degree of reliance that can be placed on the simplifying assumptions used to derive Equation 2 from Equation 1 for the range of VOL. 38, NO. 1, JANUARY 1966
109
matrices likely to be encountered in biological and siliceous rock samples. Intensity of Background. The background may arise from many phenomena; but if a pulse height analyzer is used in the detector circuit t o eliminate photons of energy remote from the strontium K , energy, the background generally comprises :
A. Coherent scattering of photons of wavelength A k by the sample. B. Compton scattering of photons of wavelength A, ( = A k - 0.03 -4.) by the sample. C. Scatter of radiation = by the analyzing crystal. D. Fluorescence by the crystal. With LiF or topaz analyzing crystals, factor D can be neglected. In comparison with factors A and B, C will be small, with a reasonable analyzing crystal and, in any case, intensities arising from C can be regarded as proportional increases in X and B. (The main exception is the “tailing” of a
strong line adjacent to the measurement wavelength, but this can be detected in the measurement scheme outlined below.) With these assumptions, the background underneath a peak can be expressed (6) by an equation analogous to Equation 1.
of N for Rb and Y are included in Table I, and show large deviations, as would be expected, since their K edges lie between X and Xk. However, unless these elements are present in high concentration, their effect is minor, as shown 10 by the values calculated for Ca weight % Y and Ca 10 weight % Rb.
+
+
B , = Ka X
where A = atomic weight 2 = atomic number F = atomic scattering power f 1 2 = incoherent scattering power r = recoil factor [(6)p. 1391 = summation over-all atomic components of the matrix Equation 3 can be simplified by noting that since Ak - A, = 0.03 A. = 0 J
A
= J h k and
(P/P)x,
=
Use of Aqueous Solution Standards. The use of aqueous solutions as standards has obvious practical advantages, such as ease of preparation, assurance of homogeneity, and high degree of reproducibility for interlaboratory comparisons. Within the range [Sr] > 1 mg. per ml., highly linear calibration curves are obtained, so it is generally necessary to use only one standard. Under these conditions,
(M/P)x~.
Thus Table 1. Values of Effective Exciting Wavelength, and Absorption Coefficient Term, N
x,
Matrix H Li C 0
Na Si
Ca
Fe
Br
Rb
Y H,O Ci:Y::lO:l Ca: Rb: :10: 1
K, =
X, A.
N
0.505 0.500 0.495 0.495 0.493 0.493 0.492 0.492 0.490 0.467 0.490 0.496 0.489 0.488
1.30 1.18 1.05 0.98 1.00 0.99 0.99 0.99 1.01 2.10 1.84 0.98 1.07 1.06
+
( K d , = [Ft2 r ( Z , - flz)l/A,
1 H 3 Li 4 Be
1.60 0.73 0.78 0.83 0.94 0.92 0.92 0.89 0.98 1.08 1.12 1.31
5B
6C
7N
80 9F
11 Na 12 Mg 13 A1 14 Si
Matrix
s
Element l5P 16s 17 C1 19K 20 Ca 21 Sc 22Ti 23 V 23 Cr 25Mn 26 Fe
Matrix
S 1.40 1.62 1.70 1.97 2.10 2.02 2.02 2.01 2.06 2.06 2.15
S
1.00 Cellulose 0.96 1 .04 (CHzL Stearin 1.03 1.51 Milk ash Grass ash 1 . 3 2 Oyster ash 1.32 Sulfur 1.62
HzO
110
*
ANALYTICAL CHEMISTRY
(5)
(6)
Values of ( K J t for each element of interest can be tabulated from values of F and f 2 available in standard texts (2, ‘7, IO). From these one can quickly calculate values of K , for a given matrix composition. Peak-Background Relationship. By combining Equations 2 and 4 we obtain
>
S
Cl(C,( K J , ]
and
Table II. Values of S (Scattering Factor Relative to Water) for Elements Z 26 and Various Common Matrices
Element
where
C, = KS(P/B). K , N
(7)
where
N =
x I
(~/P)M,
(P/P)M, Xk
sec el sec @z
(8)
AT can be considered a constant if for all matrices ( p / p ) ~ 0: An, where n is independent of the matrix [(6) p. 533 ff.], over the range X t o Ak. (In general the absorption term is about l/g the constant geometric term, so that the constant tends t o swamp minor variations in the absorption.) To verify this assumption, values of this expression were calculated as explained above, and appear as a normalized set in Table I. Inspection of these values indicates that for the type of matrix likely to be encountered, N can be regarded as constant. (Minor variations in N probably derive from errors in the absorption data, and from the rather crude method of numerical integration used.) Values
Thus S is the sample scattering factor, relative to water. Values of S for the first 26 elements and for some common matrices are given in Table 11. EXPERIMENTAL
Apparatus. Philips (Eindhoven) equipment Type PW1520 was used. (This is generally similar to Norelco equipment but is limited t o 1-kv. amp. output.) A tungsten target tube was operated a t 40 kv. and 20 ma. Analyzing crystals were LiF or topaz. Detector was a NaI (Tl) scintillation counter followed by a single-channel pulse height analyzer set to exclude higher orders. Sampling Procedure. Samples were simply poured (after rough grinding of solids to ensure homogeneity) into plastic sample holders equipped with 0.0005-inch Mylar windows. For most work, a strontium standard of 250 pg. per gram was prepared by dissolving analytical reagent grade SrCOa in dilute HX03 and making to volume with water. Choice of Background Positions. Since the background intensity is as important as the line intensity, some care is required in the choice of the background measurement position. It should be sufficiently far from the line that, in samples with the highest strontium content, no spread of the Sr line to the background position is incurred. Also it is important that no other line-e.g., Rb, which may occur in appreciable quantitiesinterferes with the background measure-
ment. For these reasons the higher dispersion of the topaz crystal, achieved with some loss of line intensity, is to be preferred. Rather than scanning each sample to check for lines which may interfere with the background measurements, the following scheme is used. First, statistically accurate measurements are made a t the three chosen angles using water as sample. From these, two factors are calculated relating count rates a t the selected background position to true background. In subsequent measurements on samples and standard, the background counts are equally shared between the two background positions, and two individual estimates are made of the true background. If on inspection these agree, no background interference has occurred. If, on the other hand, they disagree, one can either accept the lower count rate as the better estimate or investigate the nature of the interference and thus select a better background position. I n practice, for most samples when a topaz crystal is used, background positions =!=lo 2 e from the strontium peak have proved satisfactory. Counting Strategy. It can be shown that the precision obtained from taking fixed equal counts a t peak and background positions approaches closely that which can be obtained by the optimum count rate strategy. The strategy adopted was to accumulate LV counts a t the peak position and N / 2 counts a t each background position. The statistical significance of the result can then be determined using the formula: Relative standard deviation = (2/N)1/2X ( R l ) / R X loo%, where R is the ratio of net peak to background.
+
RESULTS AND DISCUSSION
Inorganic Matrices. Table I11 shows a number of results for a wide range of samples with mineral and ashed biological matrices. I n general the results agree favorably with the referee method, particularly in view of the wide difference between sample and standard matrix. The results also show the necessity of applying the matrix scattering factorfor instance, if this factor were neglected, the KCl result would be approximately 45555 low. Occasionally, samples occur with very little information regarding their matrix composition, and it is difficult to assign a sample scattering factor. Such a case is the crab ash in Table 111. For this analysis, the ash was diluted tenfold with sulfur, which by reference t o Table I1 can be seen to have an S value intermediate in the range of the elements one might expect in the sample, and the composite sample was then regarded as sulfur.
Table 111.
Matrix 1M HCl 5M HCl Fe(N0a)a.9Hz0 (350 g./l.) KC1 CaC03, A.R.
Results Obtained with Inorganic Matrices
Strontium, p.p.m. This method Referee 198 20 1
200 200
Diabase W.I.
205 266 90 88 183
Granite G.I.
22 1 165 45 29 543 146 52 4360
200 271 77 100 180 172 236 252 173 38.5 31.3 570 147.5 51.8 4600
114 43 128 125 139 149
114 38 119 124 144 150
LMicrocline Granite Trachyte Microd,iorite Rhyolitic tuff Crab ash Milk ash 62/51 62/116 62/212 621213 62/214 62/215
S.I.D. Stable isotope dilution. S. Synthesis S.A. Standard addition.
Organic Matrices. Frequently it is possible, and may even be advisable, to carry out analyses of dried, rather than ashed, biological materials. Refrence t o Table I1 shows t h a t the scattering factors for organic materials fortunately lie very close to that for water, so t h a t direct analysis of the dried material eliminates to a large degree the uncertainty of the ash composition and hence of the scattering factor for the ash. Examples of several such analyses are given in Table IV, together with published referee figures. Agreement is generally as good as that between the referee analyses. With such light matrices, it is often difficult t o ensure infinite sample thickness. In fact, frequently the spectrom-
Table IV.
Matrix Rye grass Milk powder Pine needles Wheat straw Clover Forest litter Oat straw Oat grain
Ref. method0
S S S S S.I.D. ( 1 2 ) F.P. S.I.D. (11) N.A. S.I.D. (11) N.A. S.I.D. ( 5 ) S.I.D. S.I.D. ( 5 ) S.I.D. ( 5 ) S.I.D. (5) S.I.D. ( 5 ) S.A.
F.P. F.P. F.P. F.P. F.P. F.P.
F.P. Flame photometery. N.A. Neutron activation.
eter geometry, rather than the sample thickness, limits the “infinite” intensity. Since the theoretical aspects of the method were based on infinite sample thickness, a series of measurements was made using varying weights of the forest litter sample used in Table IV. The results shown in Figure 1 indicate that the method is applicable where sample thicknesses are such that only 20% of infinite thickness intensity is obtained. Sensitivity, Precision, and Accuracy. When a topaz crystal is used, and 100,000 counts are accumulated for both peak and background estimations, the sensitivity for aqueous solutions is 1 p.p.m. (based on 50% relative standard deviation), and 1 to 2 p.p.m. for other matrices.
Results Obtained with Organic Matrices
This method 13.3 9.3 1.9, 2.4, 1.9 36.2 85.2 148 13.1 3.2
Strontium, p.p.m. Referee methods (8) A B 13.5 9.8 1.8 36.6 88.2 165 14.3 3.6
13.6 9.7 1.3 35.9 87.6 160 16.0 3.0
C 13.1 9.4
