Sample Preparation for Evaluation of Detection Limits in X-ray Fluorescence Spectrometry

2005 The Japan Society for Analytical Chemistry 143 Sample Preparation for Evaluation of Detection Limits in X-ray Fluorescence Spectrometry M. K. TIWARI, A. K. SINGH, and K. J. S. SAWHNEY Synchrotron Utilization Division, Centre for Advanced Technology, Indore-452 013, India The influence of analyte mass concentration on determination of detection limits in X-ray fluorescence spectrometry has been investigated experimentally. Both the total reflection X-ray fluorescence (TXRF) and the conventional energydispersive X-ray fluorescence techniques have been used to derive the dependence of analyte mass concentration on the values of detection limits. Results obtained indicate that values of detection limits are optimum, or in other words, they are closer to the true detection limit of the technique, when analyte concentrations are in the range of 10 times of the detection limit. (Received June 30, 2004; Accepted September 10, 2004) Introduction X-ray fluorescence spectrometry is one of the widely used techniques for elemental analysis of materials. Using the energy-dispersive X-ray fluorescence (EDXRF) analysis technique, non-destructive multielement analysis at ppm levels can be performed for elements ranging from sodium to uranium in the periodic table. 1,2 The technique finds several applications to a variety of fields such as archeological, geological and environmental. 3 6 Total reflection X-ray fluorescence (TXRF) technique is a variant of the conventional EDXRF technique, 7 9 where the principle of total external reflection is used to restrict the penetration of the primary beam into the specimen substrate. This yields a substantial reduction of scattered background, which improves the detection limit of the system to subppm/ppb levels. The term detection limit (DL) is an important aspect of any technique because it is an indication of the sensitivity of the technique. As the name itself indicates, the detection limit is a measure of the minimum quantity that can be detected by an instrument or technique under the given experimental conditions (sample geometry, sample matrix, analysis time, etc.). A through description about detection limits can be obtained from publications of Currie et al. 10 14 The detection values for an element are largely influenced by these parameters. For example, in a multielement sample, the presence of several peaks in the fluorescence spectrum can modify the spectral background and hence change the DL value of the element of interest. Such a limitation sometimes results in non-detects i.e. some concentrations that cannot be measured directly. 15 The problem of non-detects often occurs for biological and geological samples where the sample matrix strongly influences the spectral background. The presence of non-detects in XRF and TXRF analysis techniques has been To whom correspondence should be addressed. E-mail: mktiwari@cat.ernet.in K. J. S. S. present address: Diamond Light Source Ltd., Rutherford Appleton Laboratory, Chilton, Didcto-OX11 0QX, UK. described in detail by Pajek et al. They employed the process of Censoring for determining the detection sensitivities in TXRF. The parameters that improve the detection limits of various X-ray spectrometric techniques, such as PIXE, WDXRF, synchrotron excited XRF and γ-ray spectroscopy, have been discussed thoroughly by several workers. 16 19 Furthermore, it has also shown that in X-ray tube excited XRF, the detection limit can be improved by properly selecting the primary filters. 20 Moreover, a more elaborate theoretical description for detection limit calculation in TXRF with various modes of analysis, viz. grazing incidence (TXRF) and grazing emission (GE-XRF) conditions, has been given by Sanchez. 21 With developments/innovations in the fields of X-ray sources, sample preparation, nuclear electronics, detection systems and data processing procedures in the last decades, the XRF techniques have also been refined to give better and better DLs. Synchrotron radiation based X-ray fluorescence (SR-XRF) and total reflection X-ray fluorescence (SR-TXRF) techniques are the examples of such trends, where parts per trillion (ppt) level or, in absolute mass, femto gram detection sensitivities have been achieved. 22 24 Normally, XRF techniques are comparative in nature and type-standards are generally used to calibrate the spectrometers. Similarly, synthetic standards are employed to determine the DLs. In the literature, no guidelines are available for the selection of analyte concentration to be used for detection limit determination. Our experience, over the years, has been that the DLs tend to depend on the analyte concentration in the synthetic standard employed to determine the DLs. We have undertaken a systematic study to resolve this issue; our results give guidelines for what the analyte mass concentrations should be for achieving the best possible DLs under the given experimental conditions. This study indicates that, to derive the optimum detection limit values, one should locate the analyte mass concentration in the synthetic standards in the range of 10 times the detection limit. Theoretical Background Mathematically, as per the IUPAC recommendation, the

144 ANALYTICAL SCIENCES FEBRUARY 2005, VOL. 21 Fig. 1 Variation of Zn detection limits with analyte concentration determined using EDXRF technique for different acquisition times. Excitation source: Cd 109. a, Solid square (s); b, solid circle (s); c, solid triangle (g) show the measurements performed for acquisitions time 1000, 5000 and 10000 s, respectively whereas a solid line (m) shows the polynomial fit. detection limit has been defined in terms of standard counting error of the background intensity. 1 If σ P and σ B are the counting errors of the individual peak and the background, respectively, then the standard counting error for a net count can be expressed as, σ = In the limit of detection one can assume σ P σ B. Therefore σ For 95% confidence level, the counting error would be 2σ 3ρ B = 3 N B By taking into account the counting time T and the slope m of fluorescence intensity vs. analyte concentration curve, one can write the expression for minimum detectable concentration for an analyte element as or 2σ B C DL = 3 m σ P2 + σ B 2 C DL = 3 I B I A C A N B T where, I B = background intensity (N B/T); I A = net area intensity; C A = mass concentration of analyte; N B = background counts in a given time T; m = I A/C A, i.e., slope of analyte countsconcentration curve; C DL = minimum detectable concentration (1) of analyte. From Eq. (1), it is clear that, for a specified counting time, the minimum detectable concentration of analyte or detection limit depends mainly on two parameters: the background intensity I B and the net area intensity per unit analyte mass (I A/C A). Experimental Both the EDXRF and TXRF techniques have been used to perform X-ray fluorescence measurements. For EDXRF, an inhouse developed EDXRF spectrometer 25 has been employed that comprises of a Si(Li) detector of energy resolution 155 ev at 5.9 kev and an EG&G ORTEC 92X spectrum master that has a built-in spectroscopy amplifier, a multi channel analyzer and a HV bias supply. A 25 mci Cd 109 annular radioisotope is used as an excitation source. Several synthetic standards, ranging in three decades of analyte concentrations, were prepared. Zn and Cr elements were chosen as the analyte elements and their synthetic standards were prepared in the form of pellets of mass 100 mg/cm 2, by mixing their appropriate salts in cellulose matrix. Moreover, to confirm the reproducibility of system geometry, we prepared synthetic standards of various elements in various concentrations range and we analyzed them separately. The system geometry was found to reproduce within ±0.5%. To perform the same studies using the TXRF technique, researchers have used the indigenously developed TXRF spectrometer. 26 Aqueous residues of U of different concentrations were prepared from liquid solutions and polished Si substrates were used as the sample carriers. Mo X-ray tube (17.4 kev) was used as the excitation source.

145 Fig. 2 Variation of relative uncertainty for a signal at different analyte concentrations (expressed in DL units) for two different risk levels, 5% and 0.05%, calculated using Eq. (2). The variation of selfabsorption, A-factor, for Zn-K α signal at different analyte concentrations is also shown in this figure. The figure shows that for analyte mass ranging in 10 30 times of DL value, both selfabsorption and relative uncertainties are optimum. Results and Discussion Figures 1a, b and c show the variation of detection limits of Zn with various concentrations of Zn for analysis times of 1000 s, 5000 s and 10000 s, respectively. Since the DLs depend inversely on the square root of analysis time, the DLs are better for larger analysis times (Fig. 1). The figure shows that the dependency of DL on analyte mass concentration generates broad minima and that the DLs are minimum for analyte concentrations ranging from 10 30 times of DL. Moreover, one can see that the selection of an analyte concentration about 10 times that of DL is more appropriate for getting the minimum DL value. For example, for 1000 s (5000 s) analysis time, the minimum of DL for Zn is 59 ( 27) ppm which corresponds to analyte mass of 600 (300) ppm. Similarly, for analysis time of 10000 s, Zn DL is minimum ( 18 ppm) for the analyte mass of 200 ppm. The appropriateness of analyte concentration corresponding to 10 times that of DL can be explained by the Currie hypothesis of third detection limit. 10 Beside detection limit, which is a characteristic of a measurement, Currie given a concept of third detection limit, determination limit, L Q, above which the precision of a measurement can be made good enough. The relationship between determination limit L Q and detection limit C DL can be approximated by 16 L Q = C DL 2kr where, k defines the risk factor for a signal in terms of a fractile of a Gaussian distribution and r is the required relative uncertainty. If L Q is set to n times of C DL i.e. L Q = nc DL then one can derive a relation, r = 1 (2) 2nk Fig. 3 Influence of analyte concentration on the background intensity and slope m of analyte fluorescence intensity concentration calibration curve. Analysis time, 10000 s; analyte, Zn; slope m, (å); background intensity, ( ). In the limit of detection where self-absorption effects 27 for analyte elements are significantly low, L Q simply represents the smallest analyte mass that can be expected to generate a net signal intensity with a relative error less than a selected limit r. This can be understood more clearly from Fig. 2. Here, the relative uncertainty for a signal at different levels of analyte mass (expressed in DL units) has been plotted for two different risk level 5% (k = 1.645) and 0.05% (k = 3.291) along with the self absorption of Zn-K α signal. For analyte masses ranging around 10 30 times of DL, the relative uncertainties are significantly low, e.g. comparable to acceptable limits of statistical errors ( 0.5 2%) and at the same time selfabsorption effects do not affect severely the analyte signal intensity. Beyond this range, at higher analyte concentrations, though the relative uncertainties improve, the sample selfabsorption effects become dominant. Figure shows that selecting analyte concentration in the range of 10 30 times of DL would yield a fluorescence signal under acceptable uncertainties. Self-absorption effects for analyte signal can be ignored in this range. Though one can use any analyte mass between 10 30 times of DL value for detection limit measurement, it is a common practice to use an analyte mass close to the DL value i.e. 10 times of DL. The applicability of analyte mass corresponding to 10 times of DL is shown in Fig. 3. Here, the net area intensity per unit analyte concentration and the background fluorescence intensity have been plotted as a function of Zn analyte concentration. This figure shows that net area intensity of Zn-K α per unit analyte concentration, also referred to as the slope in Eq. (1), show a peaking behavior for Zn analyte concentration of 200 ppm. On the other hand, the background intensity increases monotonously, though this increase is very small. This is because, at higher analyte concentrations, apart from sample absorption effects, the tailing of the fluorescence peak increases, leading to higher background below the fluorescence peak, which in turn reduces the value of slope m. If one lowers the analyte concentration, the background that appears due to increase of tailing width of the fluorescence peak can be reduced significantly. In this case it becomes almost constant and equal to the value that one obtains in case of a blank sample. By optimizing the width of the fluorescence peak within 3σ limit and keeping background line well-known in the area of the peak, the optimum value of m can be obtained for

146 ANALYTICAL SCIENCES FEBRUARY 2005, VOL. 21 Fig. 4 X-ray fluorescence spectra recorded for various concentrations of Zn analyte. Analysis time, 10000 s; excitation source, Cd 109 radioisotope source. The figure shows that background region/intensity under a fluorescence peak increases non-linearly with increasing analyte concentrations. Fig. 5 Variation of U detection limits with analyte concentration determined using TXRF technique. Excitation source: Mo X-ray tube, 40 kv, 25 ma. Open circles (A) shows the measurements performed for an acquisition time of 500 s whereas the solid line (m) shows the polynomial fit. The inset shows the variation of net area intensity for uranium L α (slope m) and the background intensity at different analyte concentrations. analyte mass 10 times of DL. Figure 4 shows a more elaborated picture of this non-linear behavior of the background intensity, wherein fluorescence spectra for various analyte concentrations have been plotted. The figure shows that, at large analyte concentrations the background region/intensity under a fluorescence peak is higher compared to that at lower analyte concentrations, at the same time the net area intensity behaves linearly at lower concentrations, which is not strictly true at higher analyte concentrations because of sample absorption effects. Since slope m as well as the background intensity I B governs the detection limit value as defined in Eq. (1), the detection limits improve for analyte concentrations ranging in 100 500 ppm and a minimum is obtained at analyte concentration of 200 ppm. Further reduction of analyte concentration leads to poor statistics of analyte peak, resulting in less than optimum values for DL. It is often true at very low analyte concentrations that the number of counts that appears under a fluorescence peak sometimes may not be sufficient to support the Gaussian approximation i.e. the shape of the fluorescence peak no longer remains Gaussian; rather, it shifts to a Poisson distribution. This not only results in large errors in net area estimation but it also sometimes becomes difficult to define properly a window/roi for a fluorescence peak in a multichannel pulse height analyzer (MCA) spectra. Although the detection limit values determined for two analytes Cr and Zn are found to be minimum for analyte concentrations ranging from 10 30 times of DLs, the dependency of DL on analyte concentrations still shows that the selection of analyte concentration corresponding to 10 times of DLs would be better for getting optimum values of DL. To further investigate the influence of analyte concentrations on detection limit values, an independent study using TXRF technique has also been performed. The detection limit values in TXRF technique are generally determined by employing aqueous residue generated from synthetic or standard solutions. We used various concentrations of synthetic-standard solution of uranium for determining the detection limit of uranium using this technique. The dependency of detection limit on analyte concentration studied using TXRF technique, Fig. 5, reconfirmed that the best DL is obtained for analyte mass concentration corresponding to 10 times of DL value. For instance, if the true detection limit of the TXRF technique for uranium is 10 ppb, then 100 ppb (0.1 ppm) of analyte concentration would be appropriate for determining this detection limit. In TXRF, as we have used aqueous samples for determination of DLs, apart from the reasons discussed above that influences background intensity, there is a certain probability of increased surface roughness at large volumes of analyte. The inset of Fig. 5 shows the variation of net area intensity and background intensity as a function of analyte (uranium) concentration. It is found that net area intensity varies like it does in cases of conventional XRF measurements, while the increase of background is more rapid at large analyte concentrations. This is mainly due to relatively large surface roughnesses induced at higher analyte mass/volumes. We have also taken into account the total errors contributed in DL measurement as well as in preparation of analyte concentration. Since the detection limit depends linearly on analyte concentration, the net error in these two parameters has been calculated partially. We have assumed that all measurement errors; viz., errors in net area intensity, sample preparation error, statistical error, or geometry reproducibility, influence the DL value and have been determined using synthetic standards of known concentrations. The total error contributed to DL measurement has been found to vary from 2 8%. The error is higher at low analyte concentration and in this case the statistical errors are dominant. On the other hand, to estimate errors in preparation of analyte concentrations, we prepared three sets of synthetic standards and analyzed each standard for each concentration of analyte element. The net error in analyte mass concentration has been determined indirectly by measuring the fluorescence intensity. The total error in analyte concentration has been found to vary from 2 10 %. Conclusions The systematic study presented here gives guidelines for the most suitable analyte mass concentrations for achieving the best possible DLs in XRF techniques. The results obtained indicate that the optimum value of detection limit will correspond to analyte mass ~10 times of the best detection limit. The same

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