Interpretation of heterogeneity effects in synchrotron X-ray fluorescence microprobe data
© The Royal Society of Chemistry and the Division of Geochemistry of the American Chemical Society 2002
Received: 08 May 2002
Accepted: 25 July 2002
Published: 20 August 2002
Heterogeneity effects often limit the accuracy of synchrotron X-ray fluorescence microprobe elemental analysis data to ± 30%. The difference in matrix mass absorption at Kα and Kβ fluorescence energies of a particular element can be exploited to yield information on the average depth-position of the element or account for heterogeneity effects. Using this technique, the heterogeneous distribution of Cu in a simple layered sample could be resolved to a 2 × 2 × 10 (x, y, z, where z is the depth coordinate) micrometer scale; a depth-resolution limit was determined for the first transition metal series and several other elements in calcite and iron oxide matrices. For complex heterogeneous systems, determination of average element depth may be computationally limited but the influence of heterogeneity on fluorescence data may still be assessed. We used this method to compare solid-state diffusion with sample heterogeneity across the Ni-serpentine/calcite boundary of a rock from Panoche Creek, California. We previously reported that Ni fluorescence data may indicate solid state diffusion; in fact, sample heterogeneity in the depth dimension can also explain the Ni fluorescence data. Depth heterogeneity in samples can lead to misinterpretation of synchrotron X-ray microprobe results unless care is taken to account for the influence of heterogeneity on fluorescence data.
A synchrotron X-ray fluorescence microprobe (SXRFM) has been in use at the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory, since March 1986. New higher flux third generation synchrotron X-ray sources such as the Advanced Photon Source (APS), Argonne National Laboratory, and several others have more recently become available for SXRFM studies. Due to the high brightness of these sources, elemental mapping can be accomplished at the sub-ppm level. In addition, focusing techniques (e.g. multilayer Kirkpatrick-Baez mirrors,[2, 3] zone plates and tapered capillaries) can now reduce the beam to < 1 μm2 spot sizes to achieve unprecedented spatial resolutions. Though techniques such as the electron microprobe, secondary ion mass spectro-metry, and others may have similar spatial resolution or similar detection limits in some cases, one of the most appealing aspects of the SXRFM is that samples can be run at atmospheric pressures and temperatures which is particularly important for characterization of environmentally sensitive samples. SXRFM can also provide information on element speciation when fluorescence is measured as a function of primary X-ray energy. These advantages make SXRFM an ideal tool for 2-D elemental mapping of environmental samples.
The use of SXRFM in the analysis of environmental samples has been particularly popular due to the low detection limits for environmentally significant elements and little sample treatment which reduces the possibility for sample preparation effects. Geological investigations have included trace element analysis of extraterrestrial materials, sediments, and fluid inclusions,[1, 5] as well as oxidation state analysis of minerals. SXRFM has also been used in quantification of various environmental problems such as radionuclide migration through sediments, redox-controlled mobility of toxic metals in soils, and plant–metal interactions.[7, 8] However, due to the highly heterogeneous matrix that usually composes "real" environmental samples, precise quantification of metal concentrations is difficult, as will be discussed below.
In traditional XRF elemental analysis, the effect of sample heterogeneity on the apparent concentration of trace elements in a sample has been widely studied.[9–16] Though there have been many techniques that have improved the accuracy of traditional XRF elemental analysis (scattered radiation, internal standards, standard addition, dilution methods, several mathematical methods, and dual measurement methods),[17–22] most require sample homogenization and are, thus, inappropriate for 2-D elemental mapping. SXRFM encounters the same problem as XRF analysis; this typically limits SXRFM accuracy to ± 30% in thick heterogeneous samples. The accuracy can be improved by ensuring relative homogeneity of the sample or by carefully choosing standards of similar composition to the unknown; ultimately, heterogeneity effects are best minimized by reducing sample thickness (typically to 10–30 μm) which drastically improves SXRFM accuracy.[1, 23, 24]
The basic behavior of the primary X-rays and fluorescence X-rays in a homogeneous and simple heterogenous sample is described in the Appendix. More detailed descriptions of X-ray interaction with homogeneous/heterogeneous samples can be found in other sources.[12, 25] For a simple heterogeneous sample in which a trace element is buried within a matrix (equation derived in the Appendix),
Synchrotron X-ray fluorescence microprobe set-up
Samples were run both at the Advanced Light Source (ALS), Lawrence Berkeley National Laboratory, microprobe beam line 10.3 (for Cu wedge and Panoche Creek samples) and NSLS beam line X26A (for Sn wedge samples). The ALS microprobe was configured with 10 keV multi-layer Kirkpatrick–Baez mirrors focused to 3 by 5 μm at the surface while the NSLS beam line was configured with slits set to approximately 50 by 50 μm. Beam spots as small as 25 μm2 have been achieved using slits and pinholes at NSLS while Kirkpatrick–Baez mirrors can reduce beam spots to 1 μm2 or less.[2, 3] Sample fluorescence was measured at 90° to the primary beam to reduce background radiation at the detector. Counting times per position were held between 10 and 20 seconds in all samples.
Simple heterogeneous sample fluorescence experiments
Ni heterogeneity analysis across a serpentine–calcite interface
A Ni-serpentine rock which had secondary calcite accumulations on its surface was collected from the Panoche Creek area of California. It was previously thought that the sample showed possible solid state diffusion of Ni from the serpentine to the overlain calcite. The rock sample was sectioned and polished; the sample thickness was approximately 5 mm. The Ni concentratiosn in the serpentine was 1500 mg kg-1.
Results and discussion
Fig. 2 illustrates the effect of sample heterogeneity on quantitative analysis by SXRFM. The overlayer thickness drastically changes the apparent Cu concentration in the sample. In fact, the fluorescence signal varies by more than an order of magnitude across this sample. From Cu Kα fluorescence data alone, depth-heterogeneity and homogeneous changes in metal concentration cannot be distinguished. However, the Cu Kα and Kβ fluorescence signals are influenced by depth heterogeneity to different degrees; this relationship can be used to distinguish between variation in average Cu depth (heterogeneity) and homogeneous concentration changes.
Figs. 2, 3, 4 illustrate the potential for using Kα/Kβ ratios to investigate sample heterogeneity in the depth dimension though the technique's accuracy will be dependent on the element of interest and the matrix mass absorption at Kα and Kβ fluorescence energies. Eqn. 1 can be used to examine the sensitivity of this technique for these simple two-layered systems. The ratio of Kα to Kβ fluorescence is:
where S accounts for the relative intensity of Kα and Kβ fluorescence originating from the fluorescing underlayer and d( (λβ) - (λα)) accounts for the overlayer effect. If the difference between λα and λβ is very small, or if the overlayer thickness, d, approaches 0,
The depth resolution can be approximated by relating the change in element depth to a detectable change in the Kα/Kβ ratio. Assuming that a 5% change in the Kα/Kβ ratio is detectable and assuming that the matrix mass absorption as a function of energy is smooth and negative between Kα and Kβ energies, then:
The effect of interface orientation on fluorescence results can be compared to model calculations. Assuming Ni (1500 ppm) was only found in the serpentine fraction of the sample, the fluorescence across the interface will change depending on sample orientation. By comparing the Panoche Creek sample results to predicted ln(Ni Kα/Ni Kβ) fluorescence for a variety of sample orientations, we conclude that the fluorescence data could be qualitatively explained by a calcite–serpentine interface orientation as shown in Fig. 6. Solid state diffusion is, therefore, not necessary to explain the Ni fluorescence data across the interface boundary. This result illustrates the danger of directly relating SXRFM fluorescence intensity to element concentration. It is of paramount importance that the potential for heterogeneity effects be accounted for when quantifying element concentrations; the fluorescence ratio method can, in some cases, be used to help interpret the SXRFM results. In Fig. 6, fluorescence data are shown for Ni and Ca along with ln(Ni Kα/Ni Kβ). Other transition elements could show a similar trend as Ni, i.e., if Co were present in high enough concentrations in the serpentine, it should also show the "apparent" diffusion into calcite. But, when corrected for depth, it would result in the same interpretation as for Ni.
The difference in calcite mass absorption at Cu Kα and Kβ fluorescence energies, coupled with a focused synchrotron beam, was used to resolve the position of Cu to a 2 × 2 × 10 (x, y, z, where z is the depth coordinate) micrometer scale in a simple layered system. This technique could be used for a variety of elements. The resolution is dependent on the fluorescing element and the nature of the matrix material. For the first transition metal series elements in a calcite or iron oxide matrix, the depth resolution will fall in the 10–25 μm range. For complex heterogeneous systems, determination of average element depth may be computationally limited. The technique can, nevertheless, be used to investigate heterogeneity effects; we showed that the steady decrease of Ni across a calcite–serpentine boundary could be explained equally well by sample heterogeneity instead of Ni diffusion into calcite. Depth heterogeneity in samples can lead to misinterpretation of synchrotron X-ray microprobe results unless care is taken to account for the influence of heterogeneity on fluorescence data.
Fluorescence from a homogeneous sample
A close-up view of (1) a homogeneous sample and its interaction with the beam and (2) a simple heterogeneous sample
The change in primary X-ray intensity as it travels through a short length of sample (labeled dx in Fig. 7) can be described by:
dI(λp) = - ρfμf(λp)I(λp,x)dx (a1)
where: dI(λp) is the change in intensity of primary energy (cm-2); μf(λp) is the sample mass absorption coefficient at primary energy (cm2 g-1); ρf is the density of sample (g cm-3); and I(λp,x) is the intensity of primary energy at depth x (cm-2). The sample mass absorption coefficient at the primary X-ray energy, μf(λp) is
where: μ(λp) is the mass absorption coefficient of element i at the primary energy (cm2 g-1); C i is the concentration of element i with respect to mass (g g -1); and n is the number of elements. The intensity of the primary energy at depth x in the sample, I(λp,x), can be calculated from Beer's law:
Where I0(λp) is the primary intensity per area (cm-2). The local secondary beam or fluorescence beam, I(λs), will be a function of the local intensity of the primary energy, the fluorescence yield, and the fraction of absorption due to the fluorescing compound:
where: k is the fluorescence yield; Ce is the concentration of the fluorescing element (g g-1); and μe(λp) is the mass absorption coefficient of fluorescing element (cm2 g-1). The actual fluorescence intensity that reaches the surface of the sample will be a function of the distance from the point of fluorescence to the surface by way of Beer's law:
Eqns. al-a5 can be combined to form:
which can be integrated with respect to the sample parameters (integrated from 0 to L):
where 0.707 L is the thickness of the sample (cm). Note that the sample is effectively infinitely thick when L > 5(ρf(μf(λp) + μf(λs)))-1.
Fluorescence from a simple heterogeneous sample
Fig. 7 presents a very simple 2-D sample which is heterogeneous with respect to sample depth dimension. In this case, the primary X-ray intensity loss and the secondary fluorescence X-ray intensity loss due to the overlying non-fluorescing portion of the sample must be added to eqn. a7. The loss of fluorescence intensity can be taken into account by adding a Beer's Law factor for the primary energy loss and another for secondary energy loss. Eqn. a7 then becomes:
where: μ' is the mass absorption of the non-fluorescing over-layer (cm2 g-1); ρ' is the density of the overlayer (g cm-3); d is the thickness of the overlayer (cm); (λs) is the fluorescence intensity from the heterogeneous sample (cm-2); and Il(λs) is eqn. a7 calculated for the fluorescing layer of the sample (cm-2).
Courendlin limestone was donated by Rudy Wenk of the Geology and Geophysics Department, U.C. Berkeley. Limestone wedges were constructed with the help of Tim Teague and John Donovan of the Geology and Geophysics Department, U.C. Berkeley. Karen Chapman and Albert C. Thompson helped run samples at the ALS microprobe beam line 10.3.1. Patt Nuessle ran Sn and Cu wedges at the NSLS beam line X26A. We also wish to thank Tetsu K. Tokunaga for helpful suggestions and draft review. Research was supported by the Lawrence Berkeley National Laboratory, Laboratory Directed Research and Development Program and the Kearney Foundation of Soil Science. This work was performed under the auspices of the US Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.
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