Article pubs.acs.org/ac
Reconstruction of Confocal Micro-X-ray Fluorescence Spectroscopy Depth Scans Obtained with a Laboratory Setup Ioanna Mantouvalou,*,† Timo Wolff,†,‡ Christian Seim,† Valentin Stoytschew,†,§ Wolfgang Malzer,† and Birgit Kanngießer† †
Technische Universität Berlin, 10623 Berlin, Germany S Supporting Information *
ABSTRACT: Depth profiling with confocal micro-X-ray fluorescence spectroscopy (confocal micro-XRF) is a nondestructive analytical method for obtaining elemental depth profiles in the micrometer region. Up until now, the quantitative reconstruction of thicknesses and elemental concentration of stratified samples has been only possible with monochromatic, thus, synchrotron radiation. In this work, we present a new calibration and reconstruction procedure, which renders quantification in the laboratory feasible. The proposed model uses the approximation of an effective spot size of the optic in the excitation channel and relies on the calibration of the transmission of this lens beforehand. Calibration issues are discussed and validation measurements on thick multielement reference material and a stratified system are presented. he first XRF measurements in a confocal geometry were reported in 2003 by Kanngießer et al.1 The setup was realized at the synchrotron facility BESSY II with monochromatic excitation radiation. By overlapping the foci of two X-ray optics, one in the excitation channel and a second one in the detection channel, a probing volume is formed. By moving this volume through a sample, or vice versa, three-dimensionally resolved fluorescence information can be obtained. In the past decade, different experimental setups have been developed at synchrotron facilities as well as in laboratories with X-ray tubes and the technique has proven to be useful for various analytical questions. Although full 3D maps are possible,2,3 in most applications, only 1- or 2-dimensional data are collected due to long measuring times. Depth profiling can be most suitably applied to stratified samples where the lateral structures are large compared to the size of the probing volume and, thus, homogeneous layers can be assumed. Examples of measurements on paintings,1,4 decorated glass objects5,6 or ceramics7 have been reported. The quantitative reconstruction of layer composition and thicknesses of such depth profiles with monochromatic excitation has been developed, validated8 and used for the investigation of, for example, historical glass objects5 or fragments of the Dead Sea Scrolls.9 Several other quantification procedures have been reported10 based on simplified analytical expressions11 or Monte Carlo methods.12 The transfer of such a reconstruction methodology to depth profiles obtained with polychromatic excitation though has not yet been published. In this paper, we present a procedure for the calibration of a laboratory confocal micro-X-ray fluorescence spectroscopy
T
© 2014 American Chemical Society
(confocal micro-XRF) setup and show the reconstruction of depth profiles on two kinds of reference samples as validation. With this procedure, quantitative depth profiling becomes accessible for a significantly broader community, allowing experiments to become independent of synchrotron facilities.
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THEORY
Similar to conventional XRF, an analytical description of measured fluorescence intensities can be developed for confocal micro-XRF. The usage of this model requires access to the fundamental parameters, an accurate knowledge of the spectrometer configuration and, in practice, calibration parameters, which have to be obtained from measurements of well-known reference materials. The equation for primary X-ray fluorescence produced in a setup with confocal geometry and monochromatic excitation was given by Malzer and Kanngießer13 in 2005. With this model, the reconstruction of depth profiles of stratified samples with homogeneous layers becomes feasible, which was validated in Mantouvalou et al.8 The net peak intensity Φi of a fluorescence line i of an element in a layer with thickness D, with center point position xn of the probing volume and a surface position of the sample x0 can be written as Received: June 26, 2014 Accepted: August 26, 2014 Published: August 27, 2014 9774
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Analytical Chemistry Φi(xn) =
Φ0σF, iηi 2
Article
⎧ (μ * σ x)2 ⎫ * xn} × exp⎨ lin i ⎬ ρi × exp{−μ lin 2 ⎩ ⎭ ⎪
⎪
⎪
⎪
Here, practical problems arise. First, monochromatizing Xray tube spectra for a wide range of energies is experimentally complex. Second and more important, the transmission of a polycapillary optic is not a global one,16 but depends on the specific setup and geometry. The usage and alignment of the optic lead to variations in the spot size and transmission functions and therefore a calibration is mandatory with all components aligned as in the later measurements. Hence, by placing for example a monochromator in front of the first polycapillary optic, the transmission is altered. A precalibration at a synchrotron facility is not feasible for exactly the same reason. Therefore, a simplification for the calibration procedure is necessary. A simple experiment was performed in order to investigate the effect of different excitation energy distributions on the size of the probing volume. Depth profiles on six different thin foils were measured with the setup described below. For depth profiles on thin foils, the probing volume size σxi can easily be extracted by fitting the profile with a Gaussian function. The standard deviation equals the probing volume size. The results are displayed in Figure 1 for four different tube
⎛ ⎧ ⎫ x2 ⎪ x 0 + D + μ * σi − xn ⎪ lin ⎜ ⎨ ⎬ × erf x ⎪ ⎜ ⎪ 2 σ i ⎭ ⎝ ⎩ ⎫⎞ ⎧ x + μ * σ x2 − x ⎪ 0 n ⎟ lin i ⎬ − erf⎨ ⎪ ⎪⎟ 2 σix ⎩ ⎭⎠ ⎪
(1)
where ρi is the local density of the element with fluorescence line i, Φ0 the intensity of the exciting radiation, σF,i the fluorescence production cross section and μ*lin the effective linear mass attenuation coefficient. The intensity eq 1 is discussed in detail in Mantouvalou et al.8 The parameters η and σ are the two new calibration parameters, which describe the integral sensitivity of the setup for a certain fluorescence energy and the size of the probing volume in the direction of the sample normal, respectively. These parameters can be attributed to the transmission and spot size of the two involved lenses: σix(E0 , Ei) =
ηi(E0 , Ei) =
σE(E0)2 cos2(ψ ) + σD(Ei)2 sin 2(ψ )
ΩTE(E0)TD(Ei) 8π
(2)
σD(Ei)2 σE(E0)2 + σD(Ei)2
(3)
where Ω is the solid angle of detection, Ψ the angle between excitation direction and sample normal, σE/D the size of the intensity distribution of the excitation and detection optic and TE/D their transmission functions. For polychromatic excitation, the integration over the primary spectrum for eq 1 is required, from the corresponding absorption edge EABS of the line i to the energy maximum of the i excitation spectrum Emax: 1 Φi(xn) = ρi 2
∫E
E max
ABS i
Figure 1. Probing volume size derived with thin foils at four X-ray tube voltage settings. The deviations of the size for the different voltages are in first approximation negligible.
* (E)xn} Φ0(E)ηi(E)σF, i(E)×exp{−μ lin
⎧ (μ * (E)σ x(E))2 ⎫ i ⎬ × exp⎨ lin 2 ⎩ ⎭ ⎪
⎪
⎪
⎪
voltages, step widths of 5 μm and measuring times of 5 to 200 s per spectrum. By changing the X-ray tube’s high voltage, the excitation spectrum was modified and, thus, changes in the probing volume size as a function of the energetic distribution could be investigated. It is expected that the higher the tube voltage, the smaller the probing volume size. This is due to the fact that the excitation spectrum is shifted to higher energies, and the spot size of the excitation lens decreases for increasing energies. The deviations of the probing volume size for the different excitation spectra are approximately 1% for all investigated foils. The only higher deviation (7%) for the lowest energy at 4.51 keV and 50 kV tube voltage shows the expected dependency. Nevertheless, the differences in probing volume size are small and thus these results suggest that for the used setup the dependency of the probing volume size on the excitation energy is in first approximation negligible. The measurement was performed with a microfocus X-ray tube, two sets of polycapillary lenses with transmission maxima in the range between 5 and 12 keV and a 90° angle between the two optics. For all measurements, the assumption of a negligible dependency was confirmed.
⎛ ⎧ x + D + μ * (E)σ x(E)2 − x ⎫ 0 i n lin ⎬ × ⎜⎜erf⎨ x E 2 ( ) σ ⎩ ⎭ i ⎝ ⎪
⎪
⎪
⎪
⎧ x + μ * (E)σ x(E)2 − x ⎫⎞ 0 i n ⎟ lin ⎬⎟dE − erf⎨ x E 2 ( ) σ ⎩ ⎭⎠ i ⎪
⎪
⎪
⎪
(4)
The excitation spectrum can be calculated14 and the effective linear mass attenuation coefficient and the fluorescence production cross section can be extracted from fundamental parameter databases, such as the Elam database.15 The difficulty though is the determination of the two calibration parameters. As seen from eqs 2 and 3, they are both functions of excitation and fluorescence energy. For monochromatic excitation, they simplify to functions of fluorescence energy and can therefore be readily calibrated with a set of reference samples. For polychromatic excitation on the other hand, the whole set of reference samples would have to be measured at different selected energies in order to calibrate the transmission and spot size functions of the two lenses. 9775
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It is assumed that the most crucial factor for the approximation is that the excitation is dominated by the characteristic lines of the X-ray tube material. If these lines are suppressed, for example, by the transmission of the lens in the excitation channel and thus the Bremsstrahlung radiation is responsible for the fluorescence excitation only, the uncertainties resulting from the approximation might be larger. This scenario though will typically not occur in practice, as the excitation would be substantially less effective. Nevertheless, it is advisable to repeat the measurements for other experimental arrangements, like, for example, different angles between excitation and detection, larger anode spots, optics adapted to lower or higher energy ranges, in order to verify the assumption for each setup individually. As a result, an effective spot size of the lens in the excitation channel, which is dependent on the fluorescence line only, is proposed:
Φi(xn) =
ηĩ 2
ρi
∫E
E max
ABS i
* (E)xn} Φ̃0(E)σF, i(E)×exp{−μ lin
⎧ (μ * (E)σ ̃ x)2 ⎫ i ⎬ × exp⎨ lin 2 ⎩ ⎭ ⎪
⎪
⎪
⎪
⎛ ⎧ ⎫ x2 ⎪ x 0 + D + μ * (E)σĩ − xn ⎪ lin ⎜ ⎬ × erf⎨ ⎪ ⎜ ⎪ 2 σĩ x ⎭ ⎝ ⎩ ⎞ ⎧ x2 ⎪ x 0 + μ * (E)σĩ ⎪ − xn ⎫ lin ⎟d E ⎬ − erf⎨ x ⎪ ⎪⎟ 2 σ ̃ i ⎩ ⎭⎠
Equation 7 can be used for the calibration of the modified probing volume size and the integral sensitivity directly. For quantification of depth profiles of a stratified specimen, eq 7 has to be extended by a factor, which describes the attenuation of layers on top of the probed layer: Φi(xn) =
σE(E0 , Ei) → σEEFF(Ei)
η̃ 2
∑ ρk ∫ k
EiABS
*
This leads to two altered calibration parameters, the effective probing volume size and the modified integral sensitivity
ηĩ(Ei) =
ΩTD(Ei) 8π
j=1 *
x 2
(8)
with n being the number of layers and dk the layer boundaries. Both for calibration and quantification based on eqs 7 and 8, a C++-based software with graphical user interface was developed. The fitting of the data is performed with a Levenberg−Marquardt algorithm [http://users.ics.forth.gr/ ~lourakis/levmar/]. The crucial performance issue is the implementation of the solution of the energy integral, which has to be performed numerically. Assuming k calculations for quasi-monochromatic intervals of eq 7, for a sample with n depth profiles (respective elements/element-line combinations) with m measurement points, one calculation would require k × n × m computations of the monochromatic form. During a nonlinear fit procedure, this has to be done several times. A simple division of the integral range into equidistant intervals is inefficient, because energy intervals, which are far away from the absorption edge, contributing in relative low amounts to the fluorescence production only, would have the same computation time like intervals with lower energy, where the photo ionization cross section is much higher. Furthermore, the influence of absorption edges within the integral range would not be sufficiently taken into account in that solution. The same is true in the case of more elaborated numerical methods like Romberg integration. The integral is therefore solved by performing a subshell- and element specific division of the integral range in intervals ΔEj, contributing in similar amounts to the intensity of the corresponding fluorescence line. When creating those intervals the produced fluorescence line is calculated based on a very fine division of the excitation spectrum. Absorption effects are neglected at that point. A recalculation is required only if qualitative changes in the assumed sample composition are
(5)
σD(Ei)2 σEEFF(Ei)2 + σD(Ei)2
k−1 * Φ̃0(E)σF, i(E)[∏ e−μlin (E)(dj − dj−1)]
⎛ d + μ * (E )σ ̃ x 2 − x ⎞⎤ k−1 i n ⎟⎥ lin − erf⎜⎜ x ⎟ ⎥d E 2 σĩ ⎝ ⎠⎦
ηi(E0 , Ei) → η (̃ Ei)TE(E0)
σEEFF(Ei)2 cos2(ψ1) + σD(Ei)2 cos2(ψ2)
E max
e−(xn− dk −1)μlin (E)e(μlin (E)σĩ ) /2 2 ⎡ ⎛ * (E)σĩ x − xn ⎞ dk + μ lin ⎟ × ⎢erf⎜⎜ x ⎟ ⎢ σ 2 ̃ i ⎝ ⎠ ⎣
The transmission can then be easily excluded from the confocal parameters by a modified definition of the integral sensitivity.
σĩ x(Ei) =
(7)
(6)
which are only dependent on the fluorescence energy and can, thus, be determined with the standard calibration procedure by measuring a set of reference samples. The transmission function TE can now be treated as a factor of the primary intensity, as it is the case in the intensity equations for micro-XRF: TE(E0)Φ0(E0) → Φ̃0(E0)
The transmission of the lens in the excitation channel can thus be determined independent from the two confocal calibration parameters. There exist different possibilities for this precalibration. Either by removing the detector lens or by changing the detector channel, see the Experimental Setup section, or by using an additional second detector, it is possible to collect micro-XRF spectra, which can be used for the determination of TE(E).17−21 With the approximation of the effective spot size of the first lens and the calibration of the transmission function prior to the alignment of the confocal setup, eq 4 becomes 9776
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similar effective spot size, because the sample type of the calibration is, in general, not identical with the type of unknown samples being investigated. To verify this aspect, the calibration has been performed with three groups of sample types: (1) thin single element foils with thicknesses small compared to the expected size of the confocal volume, (2) glass standards with various minor elements (NIST 1412, Breitländer BR D3) and (3) an alloyed brass standard (BAM M387). Depth scans have been performed on all those reference materials with 5 μm step widths and measuring times between 5 and 80 s per spectrum. The measured profiles are fitted with the analytical description in eq 7. Densities, composition and thicknesses (of the foils) are known. Therefore, the modified integral sensitivity, the effective size of the probing volume and the surface position are the only free parameters to be fitted. Figure 3 shows the results of this calibration series for both, modified sensitivity and effective probing volume size. The
made. The intervals are chosen in a way that no absorption edges are present within an interval.
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EXPERIMENTAL SETUP The measurements in this work have been performed with our own laboratory setup 6,22 with a Mo-30W-Tube (rtw RÖ NTGEN-TECHNIK), a polycapillary full lens in the excitation channel (IFG Institute for Scientific Instruments), a silicon drift detector (Bruker), which can manually be switched between a micro-XRF channel and a confocal microXRF channel with a polycapillary half lens (IFG) in front of the detector, see Figure 2.
Figure 2. Photograph of the measuring head, the two polycapillary lenses can be discerned in the confocal arrangement.
For the determination of the excitation lens transmission, a set of very thin foils with defined mass deposition of various elements has been measured in micro-XRF configuration. On the basis of these measurements, the transmission curve was calculated in an iterative calibration procedure explained in Wolff et al.17 Actually, the result of the procedure is the product of transmission and solid angle of detection in micro-XRF configuration. Of course the latter parameter has no relevance for the confocal setup. This factor is corrected by the determination of the modified integral sensitivity.
Figure 3. Calibration curves for the effective probing volume size and the modified integral sensitivity derived with different standard materials.
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CALIBRATION The analytical model for polychromatic confocal micro-XRF presented in the Theory section is based on the approach of effective spot-sizes of the excitation lens for a certain tube voltage, as visible in the following simplified form of eq 8: Φi(xn) =
∫E
E max
ABS i
f (E , σE(E))dE ≈
∫E
E max
ABS i
decrease of the effective probing volume size with increasing energy, as shown in the upper diagram, is a known effect from characterization measurements on polycapillary optics.23,24,16 The critical angle of total reflection depends reciprocally on the transported photon energy. Therefore, the effective spot size of the excitation lens decreases for higher fluorescence energies, because only photons with energies above the corresponding absorption edge contribute to the signal. The collecting spot size of the detection lens decreases as well, due to the higher energies of the transported photons.16 The overlap of the two reduced focus regions leads to a reduced probing volume size (eq 5). The shape of the modified sensitivity curve is dominated by the transmission properties of the detection optic (eq 6), see the bottom diagram of Figure 3. There exists a maximal transmission between 5 and 10 keV and a wide tail to
f (E , σEEFF(Ei))dE (9)
This approach neglects the fact that the integrand changes for different sample types, because the attenuation coefficients strongly depend on the total composition. For the validity of the model, the influence of those changes within a typical range of sample types on the calculated effective spot size must be small with respect to the statistical error. In other words, for the same fluorescence line, different sample types must have a 9777
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Figure 4. Depth profiles on reference sample BR D3: experimental values (dots) and quantitative fit (lines). The surface position is zero and the sample is moved into the probing volume to higher position values.
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VALIDATION In a first step for the validation of the new reconstruction procedure, a depth profile measured on a homogeneous, thick multielement glass standard (Breitländer BR D3) was analyzed. In Figure 4, the measurement data of depth profiles with higher (left) and lower (right) maximal counts are plotted. Position zero marks the surface of the sample; higher values indicate positions of the probing volume inside the sample. The different shapes of the increasing (left) side of the profiles reflect the energy dependence of the probing volume size, while the widths of the profiles into the depth of the sample (right side) are a measure for the attenuation of the X-rays in the corresponding energy range. The set of calibrations of Figure 3 was used to perform a quantification of BR D3, see table S1 of the Supporting Information for the nominal composition. Elements with fluorescence energies outside the sensitivity of the setup were fixed as dark matrix (values marked in gray in table S1 of the Supporting Information) for the reconstruction and a density of 2.88 g/cm3 was set. The remaining depth profiles were fitted simultaneously with the position of the surface and the concentration of the oxides as fit parameters. The fits are displayed in Figure 4 as solid lines. The reconstruction software offers the possibility to perform the fitting with and without weighing of the profiles with the root of the measured counts. Especially for the reconstruction of such a large number of depth profiles with such a range of maximal intensities, weighing is mandatory in order to gain meaningful results for the profiles with low counts. The fitted curves agree very well with the measured data. Deviations are visible for the profiles with low count rates. The deviation of the quantified values from the reference values plotted vs the concentration of the elements is displayed in Figure 5. The different calibrations are indicated by different symbols. The results for Ca, Fe, Zn, W, Ga, Ge, Sb, Pb and Bi fit the reference value within a range of ±10% (squared region) for all calibrations. All other values are in the range of ±20% (dashed lines) except for the results for Sr and Zr. The K and L fluorescence lines of these two elements are at the upper respectively lower edge of the sensitivity of the setup, see Figure 3, which explains the high deviations. The effect of the different calibrations can also be seen in Figure 5. Although the calibration based solely on the thin foils yields higher uncertainties for a number of elements, the other three calibrations show no significant difference. This leads to
higher energies. Absorption effects cause the steep decrease to lower energies. As a first result, the calibration data obtained from the different types of calibration samples follow the same trend. No matrix specific deviation can be observed, which indicates the validity of the approach based on an effective spot size. The calibration data of Figure 3 were fitted with empirical equations for interpolation purposes. The effective probing volume size follows an exponential decay function and the modified integral sensitivity can be approximated by a Gumbel distribution. To estimate the influence of the number of calibration points to a latter quantification, calibration curves were fitted for various sets of calibration samples, starting with a set of 8 thin foils. By successively adding measurement points from some multielement standards (NIST 1412, BAM M387, Breitländer BR D3) to the set, four calibration curves were derived. For the effective size of the probing volume, the calibration values, and thus the curves, are in agreement for the whole energy range. Deviations between the calibration curves are only visible below 3 keV, which can partly be explained by uncertainties in the reference samples. Also, the count rates of the depth profiles are very low in this range because of the transmission of the detection lens. Nonetheless, the uncertainties between measured data and calibration curves amount to less than 10% for the whole energy range. The modified integral sensitivity shows the best results for the energy range between 6 and 12 keV with uncertainties of about 10%. There is an increased uncertainty in the peak region of the curve, which attributes up to 30%. In the low (12 keV) regions, deviations of 1 order of magnitude can occur. Such a calibration is valid for this specific setup and especially for the two optics used in the present alignment. Naturally, any change in the setup demands a new calibration. When multielement reference material is used, some calibration points usually have to be removed. This can be the case due to peak overlap uncertainties between a major and a minor element, secondary and tertiary fluorescence effects, as in the case of iron and manganese in the BAM brass standard, or due to low count rates in the depth profiles. In the following section, the four calibration curves of Figure 3 will be used for quantification in order to demonstrate the importance of a careful calibration. 9778
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Figure 5. Quantification results for the glass reference standard BR D3 for the different calibration curves of Figure 3.
Figure 6. Validation example on a polymer reference sample. The measurements data (dots) and fit (violet line) of the depth profile on point number 5 and the reconstructed samples geometries (solid lines) of all five depth scans are displayed. The nominal values for layer thickness and concentration are displayed as a gray shaded area.
the conclusion that one adequate multielement glass reference material, in addition to a set of thin foils, already includes enough interpolation points for a reliable calibration. A set of thin foils should in any case be measured regularly for a quick inspection of the setup. The depth profiles of the foils can directly be converted into probing volume sizes through Gaussian fits and the overall intensity is a second measure for the stability of the setup. As a second validation step, five depth profiles on different spots were measured on a stratified polymer sample and analyzed. The sample consists of five layers of polymer material with ZnO as additive in layers one, three and five, see Table 1,
decrease of the maximum count values of the three layers. Zn Kα radiation can be collected from the whole 215 μm thickness of the five layers. The deviation of concentration values and thicknesses of the layers are smaller than 5%, except for the thickness of the bottom layer. This might be due to diffusion processes into the substrate, which are more probable than between the layers due to the different matrixes.
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DISCUSSION AND CONCLUSIONS A reconstruction procedure for depth profiles obtained with polychromatic confocal micro-XRF has been presented using the approximation of an effective probing volume size. By using different reference materials for the calibration with different matrixes and densities, the assumption could be justified. It was also shown that it is advisable to use a set of thin foils and at least one multielement reference for an adequate calibration. Special care should be taken to include reference material in the calibration, with fluorescence lines at the energetic borders of the sensitivity of the spectrometer. The calibration introduces uncertainties in the quantification procedure. For the effective size of the probing volume the uncertainties amount to about 10% and are thus comparable to confocal micro-XRF measurements with monochromatic excitation. For the modified integral sensitivity the uncertainties are higher, especially for elements with fluorescence energies at the borders of the sensitivity of the setup. For validation purposes, a thick glass reference standard and a stratified polymer sample were analyzed and, keeping in mind the uncertainties introduced by the calibration, show satisfactory results. For the thick homogeneous sample, uncertainties smaller than 10% for most elements could be achieved. For minor or trace elements, the uncertainties are higher. Furthermore, reconstructed values for the elements with fluorescence lines at the borders of the sensitivity of the setup must be handled carefully. For the reconstruction of the stratified sample, uncertainties below 5% for thicknesses and concentrations could be obtained. Both samples must be regarded as ideal samples, as the layer boundaries are sharp and the dark matrix as well as the density of the material is known. For real samples with diffuse boundaries, unknown densities and dark matrixes, uncertainties are higher and can lead to only semiquantitative results.
Table 1. Example of the Reconstruction Results of the Depth Profile on Point Number 5 layer
certified ZnO (%)
1 2 3 4 5
3.86 0 3.86 0 3.86
reconstructed
thickness (μm) 41.5 42.3 44.9 41.0 40.9
± ± ± ± ±
ZnO (%) 0.5 0.3 0.6 0.6 0.5
4.03 0.04 3.96 0.04 3.62
thickness (μm) 43 42 43 42 47
deviation (%) ZnO
thickness
−4
3 2 4 1 16
−3 4
deposited on a paint test chart. For the exact preparation and characterization of this sample, see the dissertation of G. C. Schwartze.25 The measurements were performed with measuring times of 15 to 60 s per spectrum and step widths of 2 to 4 μm. For the reconstruction, five layers were assumed with ZnO present in each layer. The dark matrix composition and the density of the layers were fixed in the quantification routine. The results for the ZnO concentration and the thicknesses of the layers are plotted in Figure 6. The measured data (dots) and fit (purple solid line) of the depth profile of the depth scan on measurement point number 5 and the reconstructed sample’s geometries (colored solid lines) of all five depth scans are displayed. The error bars on the reconstructed concentration values are estimated to be 10%. The nominal values for layer thickness and concentration are displayed as a gray shaded area. The results for the depth profile on point number 5 are additionally displayed in Table 1. The layered structure of the sample can clearly be discerned from the measurement data though smoothing of the edges due to the extension of the probing volume can be observed. The absorption of excitation and fluorescence radiation leads to the 9779
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The performance of the fitting algorithm, both for calibration and quantification, is satisfactory. Different starting parameters, when chosen in a reasonable range, do not change the outcome of the quantification for the two reference materials. Nevertheless, when unknown samples are analyzed, the number of layers, the composition of the dark matrix and the density of the layers are critical parameters and must be chosen carefully. As usual, it is always best to use several analytical methods to gain maximal insight into the specimen. In comparison to monochromatic confocal micro-XRF performed at synchrotron facilities, the uncertainties are not significantly higher. This can be explained by the fact that the uncertainties introduced by the calibration procedure are mostly due to the heterogeneity of the reference material and this error outweighs even the approximation of the effective spot size. Furthermore, in the laboratory, more time can be used for a thorough calibration of the setup and regular monitoring measurements on, for example, thin foils. The complete formalism relies on the assumption of homogeneous layers, where depth profiling is well suited for analysis. For a laterally heterogeneous specimen, full 3D mapping is mandatory and a different analytical strategy must be utilized. With the new procedure presented in this work, the quantitative reconstruction of stratified samples with lateral structures larger than the probing volume size becomes feasible in the laboratory. Unknown samples can be analyzed and reconstructed quantitatively or, depending on the complexity of the specimen, semiquantitatively. Thus, the access to the nondestructive depth resolved XRF analysis is facilitated, rendering polychromatic confocal micro-XRF into a valuable analytical tool for a broader community.
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ASSOCIATED CONTENT
S Supporting Information *
Certified concentration values of the glass reference standard BR D3. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*I. Mantouvalou. E-mail:
[email protected]. Present Addresses ‡
Bruker Nano GmbH, Berlin, Germany Ruđer Bošković Institute, Zagreb, Croatia
§
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank Gregor Schwartze and the Arbeitskreis Analytik from the Institut für Anorganische Chemie at the Leibniz Universität Hannover for the preparation of the stratified polymer sample. This work was conducted in the frame of a transfer project together with the company Bruker Nano GmbH supported by the German science foundation, grant no. KA925/8-1.
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REFERENCES
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dx.doi.org/10.1021/ac502342t | Anal. Chem. 2014, 86, 9774−9780
