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Reconstruction of Thickness and Composition of Stratified Materials by Means of 3D Micro X-ray Fluorescence Spectroscopy Ioanna Mantouvalou,*,† Wolfgang Malzer,† Ina Schaumann,‡ Lars Lu 1 hl,† Rainer Dargel,‡ ‡ † Carla Vogt, and Birgit Kanngiesser
Institute for Optics and Atomic Physics, Technische Universita¨t Berlin, Hardenbergstrasse 36, 10623 Berlin, Germany, and Institute for Inorganic Chemistry, Leibniz Universita¨t Hannover, Callinstrasse 9, 30167 Hanover, Germany
The recently developed 3D micro X-ray fluorescence spectroscopy (3D Micro-XRF) enables three-dimensional resolved, nondestructive investigation of elemental distribution in samples in the micrometer regime. Establishing a reliable quantification procedure is the precondition to render this spectroscopic method into a true analytical tool. One prominent field of application is the investigation of stratified material. A procedure for the quantitative reconstruction of the composition of stratified material by means of 3D Micro-XRF is proposed and validated. With the procedure, it is now possible to determine nondestructively the chemical composition and the thickness of layers. As no adequate stratified reference samples were available for validation, stratified reference material has been developed that is appropriate for 3D Micro-XRF or other depth-sensitive X-ray techniques. 3D micro X-ray fluorescence spectroscopy (Micro-XRF) is a recent development in X-ray fluorescence analysis with which it is possible to investigate samples into the depth with a spatial resolution in the tens of micrometers. 3D Micro-XRF experiments have been carried out at synchrotron radiation sources1-3 and with X-ray tubes.4-6 The depth resolving capability is realized by a confocal setup with X-ray optics. While the usefulness of this method has already been shown for a number of applications, reliable quantification procedures are still a topic for further development. Establishing a reliable quantification procedure is the precondition to render this spectroscopic method into a true analytical tool. * To whom correspondence should be addressed. E-mail: IM@atom. physik.tu-berlin.de. † Technical University Berlin. ‡ Leibniz University Hannover. (1) Woll, A. R.; Mass, J.; Bisulca, C.; Huang, R.; Bilderback, D. H.; Gruner, S.; Gao, N. Appl. Phys. A 2006, 83, 2, 235-238. (2) Janssens, K.; Proost, K.; Falkenberg, G. Spectrochim. Acta, Part B 2004, 59, 1637-1645. (3) Kanngieβer, B.; Malzer, W.; Reiche, I. Nucl. Instrum. Methods Phys. Res. B 2003, 211, 259-264. (4) Kanngieβer, B.; Malzer, W.; Fuentes Rodriguez, A.; Reiche, I. Spectrochim. Acta, Part B 2005, 60, 41-47. (5) Tsuji, K.; Nakano, K.; Ding, X. Spectrochim. Acta, Part B. In press, DOI 10.101/j.sab.2007.02.014. (6) Patterson, B. M.; Havrilla, G. J. Am. Lab. 2006, 38, 8, 15-20. 10.1021/ac701774d CCC: $40.75 Published on Web 00/00/0000
© 2008 American Chemical Society
With fluorescence tomography, it is also possible to carry out nondestructive three-dimensional microanalysis.7,8 Though this technique may have a resolution on the nanometer scale, its major disadvantage is the size restriction allowing one to investigate only objects with dimensions of a few hundreds of micrometers. One prominent field of application for 3D Micro-XRF is the investigation of stratified material, as, for example, paint layers or biological samples.1,9-10 The samples have a light matrix with traces or major contents of high Z elements and structures in the micrometer regime. With a typical depth resolution of 10-30 µm, at the moment, 3D Micro-XRF is capable of contributing to nondestructive investigation of the elemental distribution in these samples. With respect to quantification for 3D Micro-XRF in general, two papers have been published. Smit et al.10 proposed a quantification approach for layered systems, which has not been validated up to now. Vekemans et al.11 reported a treatment of three-dimensional data sets by K-means clustering. In a previous study,12 we presented a calibration procedure based on an expression for the primary fluorescence intensity for bulk material using monochromatic excitation. In this paper, this intensity expression is expanded for the case of stratified material. The mathematical description of the count rate as a function of depth is the nucleus of a reconstruction algorithm. Its correctness and accuracy is validated by means of measurements of reference materials. As no adequate stratified reference material was available for validation, stratified polymer samples were manufactured as well as characterized by the analytical chemistry research group of the Leibniz University of Hanover. These polymer layer systems are made of ethylene-propylene-diene rubber (EPDM), which was vulcanized with dicumyl peroxide. Silica and zinc oxide were (7) Golosio B.; Simionovici A.; Somogyi A.; Lemelle L.; Chukalina M.; Brunetti A. J. Appl. Phys. 2003, 94, 145-156. (8) Golosio B.; Somogyi A.; Simionovici A.; Bleuet P.; Susini J.; Lemelle L. Appl. Phys. Lett. 2004, 84, 12, 2199-2201 (9) Kanngieβer, B.; Malzer, W.; Pagels, M.; Lu ¨ hl, L.; Weseloh, G. Anal. Bioanal. Chem. 2007, 389, 1171-1176. (10) Smit, Z.; Janssens, K.; Proost, K.; Langus, I. Nucl. Instrum. Methods Phys., Res. B 2004, 219-220, 35-40. (11) Vekemans, B.; Vincze, L.; Brenker, F. E.; Adams, F. J. Anal. At. Spectrom. 2004, 19, 1302-1308. (12) Malzer, W.; Kanngiesser, B. Spectrochim. Acta, Part B 2005, 60, 13341341.
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The used theoretical expression includes instrumental parameters characterizing the probing volume, and the properties of the specimen, that are the thickness of the layers and their composition. Fundamental atomic parameters are used to calculate the attenuation of X-rays in the specimen; i.e., effects of selfabsorption are taken into account. We developed this expression adapting the fundamental parameter approach for monochromatic excitation to the new confocal geometry.12 For a single homogeneous layer with thickness D ) d2 - d1 and layer boundaries at d1 and d2, the count rate profile Φ(x) of a specific X-ray emission line in dependence on the probing depth x can be written as
Φ(x) ) Figure 1. Net peak intensity profile of zinc for sample A. Though the weight percent distribution of the Zn content is rectangular shaped, the fluorescence intensity profile shows absorption and resolution effects.
added as inorganic fillers. They are widely used in rubber chemistry as additives to change the materials’ properties. Silica is responsible for improved abrasion resistance and tear resistance of the polymers, whereas ZnO is used as pigment or vulcanization support. Polymer systems with different thicknesses of individual layers as well as with different Zn or Si concentrations have been produced. This paper introduces the reconstruction algorithm for stratified materials and presents its validation with thick glass standards and well-characterized, stratified polymer materials. On these reference samples, we show the capabilities of 3D Micro-XRF to determine thickness and composition of stratified materials. THEORY AND ALGORITHMS FOR RECONSTRUCTION In order to introduce our reconstruction algorithm, the main objectives are discussed by means of a measured intensity depth profile. Figure 1 shows the net peak intensity profile of Zn obtained by scanning a stack of polymer slabs with alternating high and zero Zn content. The objective of a quantitative evaluation of such depth profiles is to reconstruct the layer thicknesses and to determine the composition of the layers. Two problems have to be addressed: absorption of the X-rays inside the sample and the limited spatial resolution of the instrument. Both effects can be observed in the profile depicted in Figure 1. The peak intensities representing the high Zn concentration decrease with depth, whereas the respective Zn concentration is constant. Due to the above-mentioned effects of absorption and limited spatial resolution, intensity profiles are not rectangular shaped like the weight fraction profiles. These effects become more serious with increasing sample complexity and absorption inside the sample. Intensity Equations. The approach used for the quantitative reconstruction of stratified materials from depth-sensitive microXRF experiments relies on a theoretical expression for the primary X-ray fluorescence intensity as a function of probing depth. As in conventional XRF, the synchrotron beam is assumed to be parallel and the sample is considered flat. Up to now, secondary fluorescence is not included in the model as it is negligible for a lot of samples. Alloys, where secondary fluorescence has to be taken into account, are not suitable samples for this technique due to the small information depth of the X-rays. 820
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( ) ) (
(µ/linσx)2 Φ0ησFF exp(-µ/linx) exp 2 2
[( erf
d2 + µ/linσx2 - x
x2σx
- erf
)]
d1 + µ/linσx2 - x
x2σx
(1)
Φ0 is the intensity of the X-rays impinging onto the specimen. For practical reasons, we do not measure Φ0 but the current I0 of the ionization chamber (see section 3D Micro-XRF Measurements), which is proportional to the X-ray flux Φ0 ) kI0, with k a conversion constant. The fluorescence production cross section σF accounts for all atomic processes leading to the emission of the X-ray fluorescence line and µ/lin is the so-called effective linear mass attenuation coefficient. It takes into account the attenuation of the incoming beam and of the fluorescence radiation, including the geometry of the setup. The instrument is characterized by two parameters per chemical element, the integral sensitivity η and the width σx of the probing volume in the scanning direction. Both depend on the fluorescence energy of the detected chemical element. The specimen property, which determines the count rate of an X-ray line, is the local density of the respective chemical element. The local density must not be confused with the density of the element. It is the density of the element in the sample. In other words, it is the product of its weight fraction and the mass density of the sample. It is important to note that, unlike in classical XRF, the mass density of the specimen plays an important role in depth-sensitive Micro-XRF. The consequences will be discussed below. The composition and meaning of eq 1 becomes clearer, if we subdivide it into four factors: (a) The product of the first four factors including the local density F represents the intensity one would obtain with the probing volume completely inside the sample and with negligible absorption. (b) The first exponential function, a Lambert-Beer term, stands for the decrease of intensity at probing depth x due to absorption. Absorption of the impinging beam and absorption of the characteristic radiation are taken into account. This absorption correction would be sufficient for an infinitesimal small confocal volume. (c) The second exponential function corrects for its actual extension. Radiation originating from deeper parts of the probing volume is absorbed stronger than radiation from parts of the volume closer to the surface of the sample. (d) The error functions are important if the probing volume intersects the layer boundaries.
For each element detected, such an equation exists. They are coupled via the effective linear mass attenuation coefficient µ/lin, which is influenced by all elements present in the specimen. For stratified materials, the intensity expression 1 for a certain layer must be extended by a factor for the attenuation by the layers on top of it. If we symbolize the intensity contribution from a specific layer at probing depth x with an index l as Φl(x), the overall intensity detected for a stack of n layers can be written as the sum of the contribution from all n layers: n
Φ(x) )
l-1
∑ ∏ exp(- µ
/ lin,kDk)Φl(x)
(2)
l)1 k)1
Algorithms for Calibration and Quantification. For calibration and quantification, respectively, the system of eq 1 or 2 has to be solved with respect to the unknown quantities. This is achieved by using least-squares fitting. For the calibration, the complete composition and the mass density of the reference material must be known. For thick, homogeneous material, eq 1 is valid. The integral sensitivity η multiplied with the conversion constant k, and the profile width σx must be determined for each chemical element. Gaps in the succession of elements can be bridged by interpolation. The selfdeveloped algorithm for calibration based on least-squares fitting is very stable and unambiguous, yielding k‚η and σx from measured depth profiles. On the other hand, quantification can be a demanding task in the case of complex systems of layers. For stratified materials, eq 2 holds. For each layer, the local densities of the chemical compounds are calculated. Layer thicknesses are determined, as well. These two types of parameters are the free parameters of the least-squares fitting. Initial values for the composition for each layer and the number and succession of layers must be given in advance. In the case of samples with small self-absorption or with a plain layered structure, the values for the layer boundaries can be directly derived from the count rate profiles. In these cases, the accuracy of the initial values for the concentration of the elements does not influence the result. In contrast, for samples with thin layers or strong absorption, it may require extensive trials, computing, and judging the quality of the fits to find adequate initial values. As mentioned above, the quantity determined is the local density. For the calculation of weight fractions, this quantity must be known for all the elements present in the specimen. This causes problems for light elements from which no fluorescence is detected. This “dark matrix” problem is not yet solved and is now the most serious limitation. Thus, the content of light elements must be given as an input value. Computation schemes have been developed for calculation via stoichiometry or direct setting weight fraction values for elements not detected. EXPERIMENTAL SECTION Reference Materials. For calibration and as bulk reference samples, thick glass reference materials were used (Breitla¨nder GmbH, universal glass set for XRF (BR A4-F3)). Each reference sample contains 20-30 elements in the concentration range of 0.1 ppm to 10%. Suitable stratified reference material was not available. Typical for various kinds of applications are metals in
an organic matrix. As reference material for this type of sample, metals in polymers have been proposed and applied. An IRMM reference material made of polymer granules with trace amounts of a few elements is commericially available.13 Nakano and Nakamura produced disks of polyurethane and polyester with trace amounts of metals for the calibration of XRF spectrometer.14 For the validation of the reconstruction algorithm, the availability of stratified reference material is essential. The layer thicknesses are required to be in the region of some 10 µm. Such stratified materials were manufactured and characterized by the analytical chemistry research group at the Leibniz University of Hanover. As an amorphous organic material, commercially available Keltan-512 was chosen. It consists of EPDM with ethylidennorbornen as the diene. One percent of dicumyl peroxide was added as vulcanizing agent. Thirteen different matrixes with ZnO (1.55, 3.08, 4.52, 5.92, and 7.22% Zn) and silica (2, 3.8, 5.4, 6.9, and 8.2% Si) as well as a matrix without additive were fabricated. These were then vulcanized and pressed into thin films with varying thicknesses. Five of these thin films were stacked together to attain stratified samples. Each polymer as well as the layer systems have been characterized by scanning Micro-XRF to analyze the homogeneity of the filler dispersion and by light microscopy to determine the layer thicknesses. The layer thickness of one layer in a stack of five shows deviations of 3-10%, while the Micro-XRF intensity of Zn shows a stability of 3-8% averaging ∼5000 single measurements in the latter case. Both relative standard deviation values are within the typical range of the applied method. For Micro-XRF, variations of layer thicknesses are the main source for increased deviations of the intensities measured while the highest standard deviation for measurements by light microscopy was induced by layers with comparable composition, which means adjacent layers with additives in different concentrations. In this case, the identification of the boundary between two adjacent layers, which was used to measure the thickness in the stratified samples, was complicated. This led to higher errors (∼10%) in the determination of layer thicknesses of those materials in comparison to the materials with alternating layers with and without additives. Additionally, the layer systems containing silica as an infraredactive substance were analyzed by microinfrared spectroscopy in transmission mode. Samples containing layers with 2 and 8.2% silicon were cut into microsections using a microtome. These were placed on polished BaF2 substrates, which are not infraredactive in the region of silica. Analysis was carried out using the FT-IR spectrometer Thermo Nicolet Nexus 870 and the IR microscope Thermo Nicolet Continuµm at the Infrared Initiative Synchrotron Radiation-Beamline (IRIS-Beamline) at the electron storage ring BESSY in Berlin. In order to determine the layer thicknesses, line scans were measured with a step size of 5-10 µm and a spot size of the infrared beam of 15 µm. It was possible to distinguish different layers, as the signals ideally originate only from the layer of interest and are not influenced from neighboring layers. Fifty-five scans on seven different systems with alternating ZnO concentrations and layer thicknesses between 30 and 130 µm have been performed by 3D Micro-XRF. Two examples, samples A and (13) Quevauviller, Ph. Trends Anal. Chem. 2001, 20, 446-456. (14) Nakano, K.; Nakamura, T. X-Ray Spectrom. 2003, 32, 452-457.
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Figure 2. Left: Schematic sketch of the confocal setup. The overlap of the foci of the two polycapillary optics form the probing volume. Right: Intensity profile of Zn-KR fluorescence line. The intensity increases as the probing volume is moved into the sample in part one. Part two shows the decrease due to absorption of the excitation as well as the fluorescence radiation.
B, will be discussed in the following. Sample A consists of three layers with a Zn concentration of 5.92% and two layers without any additive in between. In sample B, layers of 3.08% Zn alternate with 3.8% Si. 3D Micro-XRF Measurements. The confocal setup was assembled at the new microfocus beamline of the electron storage ring BESSY in Berlin. A polycapillary half-lens in the excitation channel produced a spot size on the sample with a fwhm of 24 µm at energy of 18 keV of the monochromatized synchrotron radiation. The fluorescence and scattered radiation coming from the sample was detected by a seven-element Si(Li) detector. In front of one of the seven elements, a second polycapillary halflens was situated with a fwhm of 12 µm at energy of 18 keV. The second X-ray optic was aligned in such a way that its focal spot was overlapping with the focus of the first X-ray optic in the excitation channel. The overlap of the two foci defined a microvolume for probing the sample. When the sample was moved through this probing volume perpendicular to its surface depth, sensitive information on the elemental composition could be obtained. The remaining six elements of the detector were used without an X-ray optic to monitor the overall radiation coming from the sample. The flux of the monochromatic radiation falling onto the first X-ray optic was measured by an ionization chamber. The position of the probing volume on the sample was optically controlled along the focal distance by an optical long focal distance microscope with a resolution of ∼3 µm. RESULTS OF VALIDATION Calibration. For the calibration of the setup, the thick glass reference samples were used. Three standards were measured with excitation energy of 18 keV, step widths of 3 µm, and acquisition time of 250 s per point. In addition to the standard calibration procedure with an angle Ψ of 45° between beam axis and sample normal, two scans with angles Ψ of 30° and 60°, respectively, have been carried out (see Figure 2, left) in order to test the angle dependency of the width of the probing volume. Five scans ensured sufficient data in order to test the standard calibration procedure. Net peak areas are extracted from the 822
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spectra using a deconvolution software. The count rate depth profiles were fitted with eq 1 as shown for the example of zinc in Figure 2, right panel. The count rate profile can be divided into two parts. Part one is the increase of the fluorescence intensity as the sample is moved into the probing volume. The slope of this rising is determined by the shape of the probing volume. In the second part of the profile, the fluorescence intensity drops due to self-absorption. The information depth depends on the energy of the exciting and of the fluorescence radiation, on the matrix composition of the sample, and on the incoming flux. In this example, we were able to detect fluorescence from a low Z element into a depth of ∼100 µm. For elements like strontium, the information depth was twice as high in this glass matrix. The fitting routine immediately yields the integral sensitivity η multiplied with the conversion constant k and the width σx of the probing volume for the respective fluorescence energy from the depth profiles measured. Thus, the parameters for the integral sensitivity η times k and the width of the probing volume σx for the energies of the fluorescence lines of major elements (concentration above 0.3 wt %) in the samples were obtained; see Figure 3. The values of the integral sensitivity multiplied with k show a statistical spread of up to 10%; see right of Figure 3. The maximum lies between fluorescence energies of 5-10 keV. It decreases to lower and to higher energies. The decrease to smaller energies can be explained by the decrease of reflectivity of the glass capillaries with lower energies. The decrease to higher energies is due to large losses at the capillary entrance, because of the decreasing critical angles for total reflection.15 The full width of half-maximum of the focal spot size drops with rising energy due to the decreasing critical angle, which is inversely proportional to the reflected energy. The minimal fwhm of 18 µm is obtained for energies above 15 keV. The values for σx show a statistical spread of ∼5%. In contrast to the integral sensitivity η, the width σx is expected to depend on the scanning (15) Arkadiev, V. A; Kumakhov, M. A; Fayazov, R. F. Pisma Zh. Tech. Phys. 1988, 14 (3), 226-230 (Sov. Tech. Phys. Lett. 1988, 14, 101).
Figure 3. Left: Angle dependency of the width of the sensitivity profile. A theoretical treatment shows that one may imagine the threedimensional shape of the probing volume as an ellipsoid. The extensions are determined by the focal spot sizes of both optics employed.12 A variation of the scanning direction, i.e., a variation of the angle Ψ between beam axis and sample normal, results in a variation of the width σx of the probing volume in the scanning direction. Right: The integral sensitivity η times k is independent of the scanning direction. Table 1. Validation by Means of Thick Glass Reference Samplea
element K Ca Ti Cr Mn Fe Zn
weight fractions/ % reference quantification 1.8 0.59 2.3 0.1 16 0.8 6
0.87 0.30 2.5 0.023 13.6 0.86 5.8
deviation, % 52 49 8.7 77 15 7 3.3
element Ge Rb Sr Zr Ba Th
weight fractions/ % reference quantification 0.055 0.037 0.6 0.1 1.8 0.035
0.058 0.031 0.79 0.073 1.5 0.03
deviation, % 5.4 16 32 27 15 13
a The weight fractions for selected elements as given by the manufacturer, as fitted with the analytical model, and their deviation in percent are listed.
direction. The probing volume is not a sphere, due to the fact that the foci of the two optics are not equal; see Figure 2 (left). With a smaller angle Ψ between sample normal and beam axis, the profile width σx is more and more dominated by the width of the focal spot in the detection channel. The left panel of Figure 3 depicts this dependency of the scan direction. The calibration values for missing elements can be obtained by interpolation between the fitted values. K-Emission as well as L-emission can be mixed as the calibration holds for both within the whole energy range of detected elements. A comparison with values obtained by scanning thin foils shows an agreement within the calibration uncertainties of the proposed calibration method with thick glass reference material. The glass standards should be chosen according to the elements of the objects to be analyzed. As a rule of thumb, one calibration scan requires ∼2 h of beamtime, which leads to ∼6-8 h for a satisfactory calibration of the full range of elements. Quantification of Bulk Glass Material. To validate this calibration, one of the reference standard materials was removed from the calibration procedure. This standard was then quantified with weight fractions as free parameters in the fitting algorithm. For nondetectable elements, the manufacturers’ values were implemented as fixed parameters. The elements were fitted via direct fit. The integral sensitivity η times k and the width of the probing volume σx obtained with the other standards were used. Table 1 compares the weight fractions for a representative selection of elements as given by the manufacturer and as obtained by the quantification.
All elements are fitted simultaneously. Therefore, errors in the calculation of one element affect all the others. In general, the deviation from the reference values is ∼20-30%. Higher concentrations of elements yield smaller errors. The deviations may increase for minor and trace elements as well as for low Z elements. In the case of calcium or potassium, the absorption influences the ratio of KR to Kβ fluorescence with depth. This induces distortions in the intensity profiles. These problems are of particular importance if regions deep inside the specimen are probed. Furthermore, the reference material is a XRF monitor standard. It is not certified to be homogeneous in the micrometer regime. Considering a probing volume of (20 µm)3 only 30 pg of glass is probed. Thus, inhomogeneities may contribute to the overall error as well. Errors due to the fitting routine were tested by varying the initial values of the concentrations and by weighting procedures in the routine. They are less than 3% and, thus, negligible compared to the uncertainties caused by the spectral processing mechanism and the inhomogeneity of the reference material. Quantification of Zn Containing Polymer Layers. As the final step of the validation of the quantitative reconstruction for stratified materials, the self-manufactured Zn-containing polymer layers were investigated. In Figure 4, measured count rate profiles and the reconstructed weight percent values as a function of thickness for two polymer systems are shown. The dotted line shows the nominal weight percent of zinc for the layers one, three, and five; layers two and four are polymer Analytical Chemistry, Vol. 80, No. 3, February 1, 2008
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Figure 4. Top: Example for reconstruction of composition and layer thickness of sample A: The measured data in counts/(s µA) (dots) and the fit in counts/(s µA) (black line) with eq 2 are depicted as well as the reconstructed weight percent profile in weight percent (dashed line) and the nominal values in weight percent for the Zn concentration in layers one, three, and five (dotted line). Bottom: Example for Zn concentration variation. In this sample (sample B), a lump of Zn could be detected in the fifth layer.
layers without ZnO. The deviation of the fitted values is below 13% compared to the reference values. The precision of the zinc concentrations in this sample is excellent; the relative standard deviation is smaller than 5%. Whereas the top example in Figure 4 of sample A is a typical depth profile of the measured series, significant variations of the concentration of Zn were observed in one scan of sample B, lower panel of Figure 4. As stated previously, ∼5000 individual intensity values have been used to obtain the average zinc intensities for each polymer system by scanning Micro-XRF (see chapter Reference Materials). If small lumps of ZnO produce significantly higher intensities at only few measuring points, the total number of averaged data will smooth this effect with respect to the resulting average value. Thus, inhomogeneous distribution of the filler material will eventually only show in a higher standard deviation of the average intensity. Hence, we show the result for sample B in Figure 4 as an example that 3D Micro-XRF is capable of determining changes in the concentration of elements into the depth in the micrometer regime. 824
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The depth profiles at different points among the seven samples investigated in this work were measured with step widths of 3-5 µm with live times of 5 s. Figure 5 shows the results of the thickness determination of the five layers of sample A. As a reference method, thicknesses were determined with a light microscope after the 3D measurements at BESSY. They are compared with the results of the reconstruction computation. Finally, for comblike systems with moderate absorption, the boundaries between successive layers can be determined as half values between peaks and valleys. The error bars are derived from multiple measurements. The results obtained by the various methods agree within their uncertainties of ∼10-15%. For the light microscopy experiments, a cross section was prepared in the vicinity of the spots of the 3D scans by slicing the samples with a razor blade. In order to test the homogeneity of the samples, measurements were carried out in an area of ∼1 mm2 around the 3D scan spots. The values for the layer thicknesses obtained by light microscopy and by 3D Micro-XRF agree within their standard deviation for all samples. The thick-
Figure 5. Example of reconstruction of layer thickness. The thicknesses of the five layers of sample A were measured with light microscopy, reconstructed via examination of the count rate profiles and by means of the fitting algorithm.
nesses obtained by repeated scans on the same sample scatter with 10-15% for both techniques. As a result, the variation of thicknesses is sufficiently small for this validation. Improvements for the thickness determination should be expected if both measurements were performed at exactly the same position, and a scatter of the values of both methods below 10% is likely for this case. The weight percent of Zn obtained by the reconstruction algorithm shows a mean standard deviation in all samples smaller than 5%. The comparison with the reference value exhibits a systematic deviation of 9-13% toward lower values. Altogether, the deviations range between 5 and 30%, which lies in the range of the expected uncertainties. The Zn weight fractions computed for the layers made of pure EPDM vary around zero. However, they can reach values of almost 0.1%. This can be explained by the very nature of a deconvolution procedure with limited resolution. A layer of pure EPDM surrounded by two layers with additives represents a difficulty for a fit procedure, especially when the layer thicknesses are in the scale of the resolution of the setup: the thinner the layer, the higher the uncertainties of the computed weight fractions. The dynamic range of weight fractions, which can be accommodated by this method and this setup, is ∼60 (6% Zn for layers one and three, 0.1% Zn for layer 2) for layer thicknesses of 40 µm. DISCUSSION AND PERSPECTIVES A procedure for the quantitative reconstruction of the composition of stratified materials by means of 3D Micro-XRF has been proposed and validated. We have shown that chemical composition as well as the thicknesses of the layers of stratified materials can be determined by the method proposed. Validity and the accuracy of the reconstruction were tested with stratified and bulk reference materials. In general, the deviation from the reference values was found to be ∼20-30%. Higher uncertainties, which may reach into the region of 50%, occur for trace elements or for cases where the absorption of the fluorescence radiation is very strong. This may be the case either for low Z elements or for elements deep inside the specimen. The uncertainty of the thicknesses of layers determined by the
reconstruction was found to be ∼10%. The dynamic range of weight fractions, that is the ratio of weight fractions of adjacent layers, which can be dealt with is ∼60 for layer thickness down to 40 µm. The accuracy of the weight fractions determined by means of 3D Micro-XRF is lower than the one achievable with fundamental parameter calculations for classical XRF. In particular, for trace elements in heavy matrixes like, for example, glass or ceramics, the method provides rather semiquantitative than quantitative results. In comparison to conventional XRF or MicroXRF, the properties of the confocal setup and of the reconstruction complicate precise quantification: The first property is that the overall detected intensity of a confocal measurement is lower than by using Micro-XRF. Due to the restricted probing volume, the investigated mass is small. One may consider this as a measurement of a layer with a thickness of ∼20 µm. In addition, the solid angle of detection is limited by the acceptance of the capillary lens in front of the detector. Finally, the transmission of these lenses usually is below 20%. The second property that complicates precise quantification is the use of a reconstruction algorithm for the determination of the weight fractions. Mathematically, the main procedure for the reconstruction is a deconvolution, which inherently has higher uncertainties. In particular, if the attenuation of the radiation is strong, errors in the determination of the layer boundaries, the calibration of the sensitivity profile, and the composition and the density of the matrix may severely affect the value obtained for the weight fraction. In comparison to classical Micro-XRF, the quantification is more laborious and the results are less accurate. Nevertheless, 3D Micro-XRF as a tool for the investigation of stratified materials is an alternative, if sectioning of the sample has serious disadvantages or nondestructive characterization is the only option. For many scientific issues from art and archeology, geology, biology, or materials science, relative concentration profiles or quantitative analysis with lower precision provides valuable and important information. Further improvements concerning the instrumentation as well as the calibration will contribute to a wider applicability of this method and the quantification of complex stratified materials. As further outcome, a stratified reference material has been developed, appropriate not only for the validation for 3D MicroXRF but also for other depth-sensitive X-ray techniques. These polymer-stratified samples consist of a light matrix filled with inorganic additives and can be considered as representative for a wide range of typical applications. The thicknesses of the individual layers can be as low as 30 µm, and the weight fractions of the additives can be up to the 10% region. The thicknesses of the layers vary by 15% in the investigated area. In 1 out of 55 scans, a lump of ZnO could be detected. Apart from this scan, the precision of the weight fraction values, which is ∼5%, is sufficient for this kind of investigations. However, the manufacturing method of the multilayered samples shows a low reproducibility as the layer thicknesses differ even if the production conditions are unchanged. Besides, the preparation of the layer systems is very time-consuming as every sample is handmade. Therefore, other more efficient and automated production methods will be tested in the near future. Analytical Chemistry, Vol. 80, No. 3, February 1, 2008
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These well-characterized stratified materials are interesting for the development of confocal X-ray techniques with sources other than the synchrotron, e.g., for the use of X-ray tubes4-6 and particle beams.16 With this work, we could establish and validate an experimental and computational scheme for the determination of the chemical composition and the thicknesses of layers of stratified materials by means of 3D Micro-XRF. This renders this nondestructive technique into a quantitative analytical tool for a wide range of samples like paintings or lacquers, paper, biological materials, etc., and can help to control their quality and identify their origin. In some cases, such as art objects, 3D Micro-XRF is a unique method (16) Karydas, A. G.; Sokaras, D.; Zarkadas, Chapter; Grlj, N.; Pelicon, P.; Zitnik, M.; Schu ¨ tz, R.; Malzer, W.; Kanngiesser, B. J. Anal. At. Spectrom. In press; DOI 10.1039/b700851c.
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due to its nondestructive character. In the future, the main focus will be on the application of 3D Micro-XRF in different fields of research and the dedicated development of quantification strategies. ACKNOWLEDGMENT This work was funded by the Federal Ministry for Education and Research (BMBF) of Germany, grant 05KS4KT1/6, and by the German Research Foundation (DFG), grant KA925/7-13004607. We thank the staff of BESSY for their support.
Received for review August 21, 2007. Accepted November 7, 2007. AC701774D
