Checking of XRF Observations with Matrix Terms Involved in Sample Analysis

In X-Ray Fluorescence (XRF) studies of samples, the relative absorption terms for an analyte in a sample with respect to its standard (the analyte itself or its compound) have been empirically related to analyte amount as well as to next enhanced element amount in the sample. The terms along with these empirical relations have been used to cross check the XRF observations for the analysis work. One such an attempt has been made in the present work for bulk measurements on rice saplings and a disparity in observations has been caught.


Introduction
X-ray fluorescence has been a powerful analytical tool since the beginning of its application to elemental analysis.The working principle of XRF analysis is the measurement of energy and intensity of the X-rays emitted from the sample.The energies of the emitted X-rays are the characteristic of elements present in the sample and thus provide the knowledge about the composition of sample, hence form the basis of qualitative analysis.Whereas the measurement of the intensities of the X-rays provides information about the concentration of the elements present, thereby forms the basis of quantitative analysis.In XRF analysis of samples, the presence of substrate matrix effects (absorption and enhancement) disturbs the proportionality between the elemental characteristic X-ray intensity and its amount [1][2][3][4].For the correction and compensation of these effects, different analytical methods [5][6][7][8][9][10] exist in literature.While evaluating the absorption and enhancement terms, Bansal [11] established that the relative absorption and enhancement terms for an analyte in a sample with respect to its standard (the analyte itself or its compound) are related to analyte amount in the sample and its characteristic X-ray counts under the photo peak in each sample and standard spectra respectively.The absorption terms were empirically related to the determined analyte amounts irrespective of its X-ray counts.Similarly, the enhancement terms for the analyte were empirically related, in turn, with the analyte amount and with enhancer amount [12].For a specific category of substrate, these relations give absorption and enhancement terms direct from the known amounts of analyte and enhancer elements or vice versa i.e. with known absorption and enhancement terms and the amount of enhancer element, the analyte amount can be predicted.Moreover, these empirical relations along with the terms can cross check the XRF observations of the analysis.In the present work, the bulk measurements on rice saplings have been checked following the said procedure for absorption terms.

Methodology
In a sample S, if X-rays of an analyte a excite the X-rays of other element c, it causes the absorption of a X-rays and enhancement of c X-rays called matrix effects that disturb the linearity between the analyte X-ray intensity and analyte amount.When S is irradiated with photons i a from a source for selective excitation of a and the resulting a X-rays are counted in a detector (Figure 1), the

counts "
" under the X-ray photo peak of analyte a from the sample can be expressed in terms of basic and the experimental set up parameters as [11]: where, the number of incident photons at the sample sur-  of detector at emitted X-ray energy are experimental setup parameters.The X-ray production cross-section of a X-rays at incident energy i a , , Avogadro's number A v, atomic weight of analyte element M a (g) and the factor in terms of absorption coefficients, 's (cm 2 /g), of sample S at incident (i a ) and emitted (e a ) photon energies and sample thickness t (g/cm 2 ) are basic parameters. is the fractional analyte amount in target material.
In case of symmetrical geometry (θ 1 = θ 2 = θ) and for thick samples , the Equation (1) reduces to Similarly, if the S is replaced by standard A, a compound of analyte a with its molecular weight M A that comprises n atoms of a and the relation (2) reduces to

Absorption Effects
Under selective excitation of analyte, a, absorption term of sample, S, relative to that of first standard, A, i.e.
in terms of analyte amount  and X-ray counts under the analyte photo peak in S and A comes as

Empirical Relations
For empirical relations of matrix terms in rice saplings, rements [13] for Ca were ents, material of first te the earlier rice sapling measu used in relation ( 4).In the measurem standard was CaCO 3 for Ca detection.
For selective excitation of calcium K X-rays with Ti K X-rays in double reflection set-up [13], the absorption where Acof j 's are coefficients of fit for abs For the fit, care was taken that the number fitted must be greater than the number of Acof 's that    orption terms. of values to be j ensured optimization of the coefficients.Moreover, the uniqueness of the relations [14] was checked with different permutations and combinations of a data set so that the same closeness of fitted values with the actual ones was there for each combination.
For the derived relation, the mean absolute percent deviation D p is measure of the analysis error.It was calculated according to the relation 100 where C i and i C  C are the evaluated and act fractions and im is the mean of C i 's.values for the relation is also listed in Table 1.

Results and Discussion
From the studies of effect of KCl and CaSO 3.92 on the contents K and Ca in rice pla , ata r nine pot samples is considered, where a pot numbered of nts [13] the d fo 1 was left untreated.Four pots (numbered 2 -5) were treated with CaSO 4 solutions; 50, 100, 150 and 200 mg/200 ml of water.The remaining four pots (numbered 6 -9) were treated with KCl solutions; 50, 100, 150 and 200 mg of KCl per 200 ml of water.
In the processing for absorption terms for rice saplings, a polynomial in analyte Ca amount with its power varying for p = 1 and q = 2 was found appropriate for the nine sample data.The percentage deviation of fitted values from the actual ones is shown in the Table 2(a).Here the deviation is <10% for most of the samples except for one with fractional analyte amount 0.041, it is 19%.To reduce the overall error, that particular sample was excluded for the polynomial fitting.It was observed (in Table 2(b)) that by excluding the sample, the deviation reduced to a remarkable extent.
To certify these findings, the data on evaluated amounts of potassium in 9 samples [13] were tried for empirical relations of Ca absorption terms with potassium amounts as potassium in rice plants leads to strong absorption of Ca K X-rays.The absorption term and K fractional amounts, , were found t t a polynomial with p = 2 and q = 3 for the nine (Table 3).Again a large deviation for the same sample was observed and with exclusion of the data of same troubling sample, the deviation reduces significantly (Tables 4(a) & (b)).
In order to find the reason behind this disparity,      [2] B. J. Mitchell, "Encyclopedia of X-Rays and Gamma Rays," Reinho [3] R. Jenkins, "An Introduction Spectrometry," mber of X-ounts d und eak.ow at wit meth tting, the di er After rectifying th s c omb e odd, the ratios for both the cases are found to be within the error < 1%.

Figure 1 .
Figure 1.Arrangement of source, sample S and detector.
with Equation (4) using the observed counts of analyte (Ca) X-rays and deteramounts saplings.The derived terms were empirically related to mined of the analyte in different samples of rice the calcium amounts irrespective of their X-ray counts.Judged from the pattern of absorption term variations with determined amounts, different order polynomial fits were tried to find the closeness of generated terms with the actual ones.The polynomial fits in amounts of  Ca From the plot, the determined value of  term ponds to  value ~0.196 and vice-versa etermined i.e. the d

Figure 2 .Table 4 .
Figure 2. Plot of relative absorption terms versus concentration  and  in rice saplings.Table 4. Comparison of empirically generated relative e

Table 3 . Listing of relative absorption terms for Ca K X-rays, their empirical relations with potassium amounts, , and mean absolute percent deviation D p in rice saplings.
of project grant (ref No. 2007/37/ 6/BRNS) for this work and from DST in the form of Inn Deep is highly acknowl- w York, 1960.