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Overlap corrected on-line PIXE imaging using the proton microprobe
Nuclear Instruments and Methods in Physics Research B 109/1 l0 (1996) 154-160
B
N
Beam Interactions with Materials & Atoms
ELSEVIER
Overlap corrected on-line PIXE imaging using the proton microprobe C.G.
Ryan
a:~ a " , E. van A c h t e r b e r g h , D.N.
• Jamleson
b
, C.L.
Churms c
aCS1RO Exploration and Mining, PO Box 136, North Ryde, NSW 2113, Australia bMicroanalytical Research Centre, School of Physics, Universi~ of Melbourne, Parkville, Vic. 3052, Australia ~Van de Graaff Group, National Accelerator Centre, PO Box 72, Faure 7131, South Africa
Abstract Conventional methods for PIXE imaging have used the counts recorded in a simple energy window set on an X-ray peak to approximate the image of an element. This method produces image artefacts due to the overlap of the X-ray lines of interfering elements, detector artefacts, such as peak-tails, pile-up and escape peaks, and continuum background. This paper reports on continuing development to solve this problem, based on the construction of a matrix transformation that transforms directly from PIXE spectrum vector to elemental concentration vector. This transformation provides a fast method for extracting on-line quantitative estimates of the concentration of a sample while still under the proton beam; the method has been called Dynamic Analysis to reflect this capability. If the spectrum is replaced by a single count in a channel, an event recorded at a point in a raster scan of the proton beam over a target, then the resultant concentration vector is the set of increments to make to all elemental images at that pixel. PIXE images accumulated in this way are inherently (i) quantitative (accumulated in ppm txC), (ii) overlap-resolved and background-subtracted, and (iii) can be formed directly on-line. The method is under development at the CSIRO and in routine use at the NAC using a simple procedure involving the fitting of a preliminary scan spectrum to build the transform matrix; spectrum fitting and matrix construction are part of the GeoPIXE software package. This paper outlines the method, reports various tests of it, and presents recent examples of its application to major and trace element imaging in geology.
1. Introduction The trace element data obtained from quantitative PIXE microanalysis of geological samples complement the major element data obtained from conventional methods such as the electron microprobe (EMP), and the sensitive yet semi-quantitative data from the ion microprobe (IMP), and open a window on the structure, chemistry and geochemical processes of the earth's crust and upper mantle. On the Ixm to cm scale, characterization of zoning of trace and major elements reveals information on the chemistry, timing and dynamics of geological processes [1,2]. On the scale of meters to hundreds of kilometers, trace element signatures reflect bulk rock chemistry and the effects of pressure and temperature on the partitioning of elements between minerals and between minerals and permeating fluids and melts [1,2]. Techniques for the detailed analysis of PIXE spectra to extract quantitative elemental concentrations are well developed. These methods generally use a non-linear leastsquares fit to the spectrum with a model function compris* Corresponding author. Tel. +61 2 887 8696, fax +61 2 887 8909, e-mail [email protected].
ing elemental line-shapes, a sum element representing pile-up contributions, and a background function (e.g. Ref. [3]). Each line-shape function may include the prominent X-ray lines, detector escape peaks, and tailing produced by incomplete charge collection and Compton scattering. The result is an accurate description of the complete PIXE spectrum from which individual elemental contributions are extracted. This approach resolves complex line-shape overlaps between elements, and distinguishes contributions from background, peak-tailing, escape peaks and pile-up. However, conventional approaches to PIXE imaging are far less refined, and commonly accept all counts within a simple software " g a t e " , defined by an energy " w i n d o w " centred on an X-ray line for an element, to provide an image of that element. For major elements on weak continuum background, this approach produces reliable elemental images. However, as the concentrations of elements fall towards the important trace levels, these images tend to suffer more from artefacts caused by contamination from continuum background and contributions from other elements due to the overlap of X-ray lines and detector artefacts with the software gate. The overlap of Sr K~ with Zr K~ (e.g. Fig. la), and As K,~ with Pb L,~ are common examples. Hence, Zr images (gate set on Zr
0168-583X/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00898-5
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become more complex and the contaminated images may be misleading. In more complex geological problems involving multiple element overlap, Ryan and Jamieson [5] demonstrated that accurate elemental images can be projected from event data in off-line analysis using a spectral decomposition transformation called the Dynamic Analysis (DA) method. The purpose of this paper is to give an update on this technique as applied to PIXE analysis and imaging, and present tests of the method using samples which exhibit complex multi-element overlaps and recent examples of its application to major and trace element microanalysis in geology.
~ Rb row
2. Quantitative true elemental imaging
0.0 -0.5 1.0
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0.5 0.0
e T ~ row
0.6 0.4 0.2 0.0 -0.2 -0.4 0.8 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0
Ba row
10
20 X-ray Energy (keV)
30
Fig. 1. (a) Total PIXE spectrum from a scan of a polished section of Roberts Victor layered-kyanite eclogite [14] analyzed using 3 MeV protons and a 160 txm A1 filter. The GeoPIXE fit to the spectrum and the SNIP background approximation are shown overlaying the spectrum. (b)-(g) Rows of the a 113matrix part of F for the indicated elements and pile-up determined from a preliminary scan. Ks) may contain features due to the spatial variation of Sr and Pb images (gate set on Pb L~) may contain artefacts due to As. Attempts can be made to set gates on weaker lines in order to avoid the dominant source of interference. However, in many cases no viable alternatives exist; all lines for an element suffer interference. And even if a minor line exists that is free of overlap interference, the resulting images will suffer from the loss of counting statistics and increased sensitivity to continuum background contributions. In cases involving simple overlap, corrections can be made during off-line post-processing of the gate images; Pallon and Knox [4] report a method for the correction of K contamination of Ca images in the analysis of biological specimens. However, in many cases element overlaps
To justify use of the term true elemental imaging, the image of an element must faithfully portray the spatial distribution of that element, and be free of artefacts due to other elements and background. For an image to be considered quantitative, the average over a region of pixels in the elemental image must provide a quantitative measure of the concentration of the element in that region and be free of contamination and accurate to -10%. The Dynamic Analysis (DA) method for PIXE imaging has been demonstrated to achieve these objectives on-line as the data accumulate and is described in detail by Ryan et al. [5,6]; accuracy may be further improved using off-line corrections. This section summarises the central elements of Dynamic Analysis and illustrates is operation using a simple example of geological imaging. 2.1. The Dynamic Analysis method
Decomposition of a PIXE spectrum Sr into contributions from component elements, can be expressed as a non-linear least-square fit to the spectrum using a model function f comprising line-shape functions for each element, together with pile-up and background terms, at each channel i. If the non-linear parameters describing detector characteristics such as energy calibration, peak width and tailing, have been determined by prior non-linear iterations, or in a preliminary fit to a prior spectrum for example, then the remaining linear parameters a k, representing major-line peak-areas and one representing background intensity (i.e. a scaling factor applied to a background model), can be found by solving the matrix equation [5,6] oLa = 13S,
(1)
where ~ and 13 are matrices in terms of the partial derivatives Of/Oa k and S is the spectrum vector: %k = ~ wi '~i]3k~,
(2)
i
~ , = wi(Of/Oaj).
(3)
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We have adopted the statistical weights w i of Awaya (wi = f i 1) [7]. As discussed in detail elsewhere [5,8], the convergence of the least-squares fit is only weakly affected by the form of the weights, provided the weights w~ = S i are not used as they introduce an error at low counting statistics [7,8]. Indeed, acceptable results can be obtained even using unit weights (w~ = 1) [8]. The peak-areas a~ (excluding the background term) are related to element concentration (areal density in the case of thin targets) Ck by the equation [3] a~, = QO,~,TkYkCk
(4)
in terms of the integrated charge Q, detector solid-angle and efficiency/2 and e k, X-ray absorber attenuation Tk and generic X-ray yield Yk [3,9]; for the moment Yk will be assumed to be constant for element k across the image. Hence, the solution of the linear least-squares problem can be cast as a matrix equation which transforms directly from spectrum vector S to concentration vector C in terms of the matrix F, which can be precalculated [5,6]: C = Q ~FS
(5)
--I F~ = (f2ekTkY~) -1 ~ cekj ~i. J
(6)
The F matrix is calculated in a final linear least-square iteration in the program PIXE-FIT, part of the GeoPIXE software package [3,10]. The model function includes a complete set of X-ray lines for each element, detection artefacts (including tails, pile-up and Si or Ge escape peaks), and the SNIP background approximation [11] corrected for absorption [10[. The structure of the F matrix is illustrated in Figs. l b - l g which shows representative rose of the oL ~13 matrix, which is the foundation of F, calculated for silicate minerals with lists of elements typified by the spectrum in Fig. la. In this simple example, there is little element overlap and the a matrix is quite diagonal. Therefore, the rows for Fe and Ba (Figs. lb and lg), for example, are characterized by positive weights across the K B peaks (also the Fe Si-escape peaks), which act like software gates, and small negative weights across the spectrum in between X-ray lines, which sample the underlying background. However, there are two simple overlap situations. One involves the overlap of Sr K~ on the Zr K lines. This produces small negative weights in the Zr row (Fig. If) at the position of the Sr K~, which acts to subtract Sr contamination from Zr images. The Sr row (Fig. le) is more complex, having positive weights at the energies of the Sr K~,.~ lines, and negative weights at the Zr K~.~ energies. The Zr K~ is given greater weight because it is overlap free and is a good measure of the contribution of the Zr K in the vicinity of the Sr K~. Note that there are also small negative weights at the position of the Fe K~+~,~+~ pile-up peaks which compensate for Fe K~+~ contamination of the Sr K~, peak. Similar negative correc-
tions can be seen in the Rb row (Fig. lc) to compensate for overlap between the Fe K pile-up lines and Rb K (negative weights near the Fe K,~+~ energy), and also between Rb K~ and Y K,~ (seen as negative weights at the Y K~ energy). 2.2. Rapid on-line spectrum analysis
Eq. (5) permits processing of PIXE spectra to extract concentrations using a simple matrix transform. This can be performed in a fraction of a second on a small computer. Incorporated into a data acquisition system and using the instantaneous live-charge Q (integrated charge corrected for dead-time), the transform allows an on-line estimate of sample composition to be calculated, and updated continuously, as the data accumulate. This provides a useful diagnostic capability, enabling the majorelement composition to be determined in a few seconds. 2.3. Imaging
Note that if the spectrum vector in Eq. (5) is replaced by a vector with just a single count in channel e, then the resultant concentration vector represents the set of increments to make to all element concentrations for one count at that channel. If the beam is positioned at point x, y in a raster scan, each event (e,x, y) makes a contribution ~Ck(X , y) = Q(x, y) 1/kk e t o the concentration distribution of element k [5]. Therefore, a convenient procedure is to accumulate elemental images in ppm IxC units by simply incrementing each image k by F~e for each event. These images can be directly related to concentration, both online during data collection or off-line, by reference to the live-charge distribution Q(x, y). Fig. 2 shows the application of the DA matrix, containing the c~ 113 matrix rows illustrated in Fig. 1, to image major and trace element distribution in a polished section of mantle eclogite dominated by the phases kyanite (ky), clinopyroxene (cpx) and garnet (gnt). Note that the Zr image shows no evidence of artefacts due to the Sr K~ overlap with the Zr K,~ lines, through benefits from the counts recorded for both the Zr K,~ and Ka lines. Similarly, the Rb and Sr images are quite distinct and contrast with the Fe image providing some confidence that the Fe K pile-up overlaps with both Rb and Sr have been correctly rejected. Eq. (5) provides a very simple method of generating elemental distribution images with three very important properties: (i) The images are inherently element overlapresolved and background-subtracted. (ii) The images are quantitative to within a small yield correction; each pixel contains a value representing concentration times integrated charge. (iii) The images are formed directly on-line as the data accumulate. The first property means that each image is a close depiction of the distribution of a single element, discriminating against the inevitable artefacts
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157
Fig. 2. On-line PIXE elemental images (2.6 X 10 6 events) from a proton scan of the eclogite sample (Fig. 1), comprising garnet (gnt), clinopyroxene (cpx) and kyanite (ky) as the major phases, projected using the DA method; the scan area was 1800 x 1800 p~m'.
introduced by element overlaps, detection artefacts, such as tails and escape peaks, and background when using simple gates set on major X-ray lines. The second property means that by integrating an arbitrarily shaped region of a image, and dividing by the total integrated charge in the same region, a direct average of the concentration of all elements can be obtained on-line while the data accumulate. 2.4. Restrictions, approximations and corrections
There are a number of practical points and approximations to keep in mind when using the DA technique: (i) The DA matrix needs to include all anticipated elements. (ii) The energy calibrations of the spectrum and DA matrix need to be accurately aligned (~E < 20 eV). (iii) The peak width function and relative tail strengths and shapes are fixed. (iv) The background shape and X-ray relative-intensities are fixed; these are effected by the choice of X-ray filters (see Ref. [5]). (v) The pile-up " s u m " element has fixed relative intensities. (vi) The calculated yields Yk are assumed to be constant across a sample, and thick target relative-intensities are assumed. (vii) Dead-time losses must be considered separately. In practice, (i-iv) are addressed quite simply by building the DA matrix transform from a fit to a reference spectrum collected from a brief preliminary scan of the sample, or one similar, under
the same experimental conditions as the desired images. Hence, the energy calibration, X-ray relative-intensities, background shape, and peak width and tail parameters are determined during the non-linear least-squares fit to the reference spectrum. The effects of the spatial variation of PIXE yields, dead-time losses, and pile-up spectral content are more subtle and require further attention. Variation in PIXE yields can be treated in a straightforward manor as minor off-line corrections ( < 10% typically) to the images tied to major-element spatial variation reflecting the changing composition [6]. The effects of pile-up are more subtle as the intensity of pile-up can vary with count-rate on a pixel by pixel basis, and the relative-intensities of the sum element lines will change, in general, with sample composition across the scan. Therefore, care must be taken in interpreting the images of elements that suffer from pile-up overlap. However, often a single major element dominates the spectrum (e.g. Fig. l a). In these cases the pile-up is accurately described by a fixed pile-up " s u m " element, and its spatial variation is correctly described and subtracted from other elemental images. Dead-time losses depend on the scan frequency. In the limit of very low scan rates, the count-rate in a pixel determines its local deadtime [4]; image correction can be done at the pixel level. In the limit of very high scan rates and typical long shaping
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times, dead-time becomes averaged over the scan and is simply incorporated in the live-charge. Between these extremes the effects become very complex and depend on the direction of the scanning beam. No general solutions to these problems of changing pile-up and dead-time have been devised at present; these effects are discussed in more detail by Ryan et al. [6].
3. Implementation of on-line true elemental imaging The Dynamic Analysis method for on-line elemental imaging has been implemented at the CSIRO in Sydney and at the National Accelerator Centre (NAC) in Cape Town. Both installations use the GeoPIXE software package for quantitative PIXE analysis and to build the transform matrix for imaging. The method has permitted a very simple procedure for PIXE elemental imaging: (i) Perform a brief preliminary scan of a new sample, or when X-ray absorbers have been changed, to collect a reference spectrum. (ii) Fit this spectrum in the usual way using PIXE-FIT, but specifying the dynamic mapping option. The full non-linear least-squares fit is performed first, followed by a linear iteration to build the transform matrix; the matrix is output to disk. (iii) Read the matrix into the data acquisition system. Calculate energy translation, to map from spectrum to DA matrix column (if necessary), and dispersion corrections if the energy per channel differ. (iv) Start imaging; the matrix already contains the full list of elements to build images for. Once a matrix has been built it can be used for multiple scan areas on a given sample, or other samples with similar component minerals. Hence, in practice a given transform matrix can be reused for a number of scan areas. In both laboratories, the data acquisition systems have been set-up to select a column of the F matrix based on the X-ray energy of each event, and use these values to increment every elemental image at the current pixel position. At the NAC, the beam is raster scanned and data is collected through a CAMAC interface [12]. Elemental images are stored in floating point arrays (64-256 pixels square) in ppm nC units, and displayed on a VAX workstation in live-time. At the CSIRO, the beam is scanned electrostatically and data is collected through a CAMAC interface controlled by a IxVAX, and buffers are forwarded to an Amiga workstation for display, where elemental images are built up using the DA method in 32 floating point arrays (256 X 256 pixels each) in ppm ixC units and displayed in live-time [6].
4. Tests of dynamic analysis and on-line true elemental imaging A number of tests have been carried out at the NAC and CSIRO proton microprobe laboratories to evaluate the
performance of the method in demanding mineralogical applications (also see tests in Refs. [5,6,13]). The most basic tests have used PIXE point analyses within a scan area to test the accuracy of the images produced by the DA method. Ryan and Jamieson [5] used this approach to demonstrate the viability of the DA method. They showed that Au could be accurately imaged at 200 ppm in a sulphide ore despite severe overlap problems associated with major-element Zn and As in the sample [5]. In a more demanding test, a sample consisted of small fragments of BaF2, CaF 2 and ScF 3 glued to an Fe foil (containing minor Cr) and positioned between pieces of pure Ti and Cr metal. The test was to see if these distinct phases could be imaged accurately despite severe X-ray line overlaps (see Fig. 3a). A comparison was made between images produced using the DA method, and images produced using simple gates (Fig. 3a) set on the K peak of each element (or L , L~I, L~2 and L~I in the case of the Ba L lines). Most images using the simple gates (Figs. 4i-4q) show inaccuracies or artefacts due to other elements except for Ba K, when compared to the known 10e 10~ 1o~
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g) Ca row
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6 X-ray Energy(keV)
8
30 32 34 36 38 X-ray Energy (keV)
Fig. 3. (a) Total PIXE spectrum from a proton scan of the sample described in Fig. 4a, analyzed using 3 MeV protons and a 75 ~m kevlar filter. The GeoPIXE fit to the spectrum and the SNIP background approximation are shown overlaying the spectrum. The software gates are indicated. (b)-(g) Rows of the a-J[3 matrix for the indicated elements determined from a preliminary SCan.
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max
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Fig. 4. (a) Schematic map of a sample consisting of small fragments of BaF2, CaF2 and ScF 3 glued to an Fe foil (containing minor Cr) and positioned between pieces of pure Ti and Cr metal. (b)-(h) On-line elemental images (3 X 10 6 events) projected using the DA method. (i)-(q) Images produced using the software gates shown in Fig. 3a, from a repeat scan (4.5 × 106 events) of the sample. The scan area was 1800 x 1800 ~m ~-.
positions of each phase tFig. 4a). The Ba K lines are at high energy (32 keV) and free of interferences or significant underlying background. This image forms a useful point of reference for checking the Ba imaged based on the L lines. The images based on simple gates on the Ba L lines show a number of artefacts. The Ba L gate overlaps completely with the Ti K (see Fig. 3a); this image (Fig. 4i) is dominated by the Ti distribution. Similarly, the L~I gate image and L~2 image (Fig. 4q) are dominated by artefacts due to the Ti K~ lines and the Cr K tail, and the L~, gate image (Fig. 4p) shows artefacts due primarily to the Cr Ks. ~ lines. The Sc image based on a simple gate (Fig. 4n) contains artefacts due to the overlap of the Ca K~ (producing a significant Ca ghost) and the tail of the Ti K (producing a faint ghost of the Ti region). A F matrix was built simply by fitting a PIXE spectrum obtained from a - 5 rain preliminary scan; rows of the o~ 113 matrix, the important component of F, are shown in Figs. 3b-3g. The Fe row (Fig. 3b) is similar to Fe in Fig. lb showing dominant positive weights across the K ~ peaks. However, little weight is placed on the Si-escapes now; these are rendered unreliable by the presence of Sc, Ti, Ba and Cr. The Cr row (Fig. 3c) shows strong Cr K weights and negative weights, particularly on Ba L ~1, to compensate for Ba L~2 overlap on the Cr K lines. The Ti and Ba L rows (Figs. 3e and 3d) become more complex due to the overlap-coupling between Sc, Ti, Ba and Cr. The strong overlap between Ti and Ba is evident. Both the Ti and Ba L rows display interesting bipolar weights about the Ti K s and Ba L~, lines. In addition, Ti shows prominent negative weights centred on the Ba L~I and L[3 2 lines to subtract Ba contributions from Ti images. A negative weighting on the Ca K s energy is also evident in the Sc row (Fig. 3f) to subtract the effects of the Ca K~ overlap on Sc K . The benefits of the DA approach are evident in Figs. 4b-4h. In contrast to the Ba L gate images (Figs. 4i, 4p and 4q), the dynamic analysis Ba L image (Fig. 4b) matches the Ba K image (Fig. 4c), despite the complete overlap of Ba L~ and Ti K s, and the fact that all the Ba L lines are dominated by Ti and Cr in the spectrum (Fig. 3a). The DA Ca and Sc images show clearly separated phases with little evidence of overlap-derived contamination (Figs. 4g and 4h). Notwithstanding the small residual artefacts of Sc and Ba visible in the Ti image at the -0.5% level (Fig. 4d), the DA images portray realistic distributions of all elements.
5. Application of on-line true elemental imaging Successful geological applications of the DA method include the study of (1) trace Au distribution in ore from the Emperor mine in Fiji, despite extensive overlap interference on the Au L m,~2 lines [5], (2) fluid processes in the mantle [14] and (3) the development history
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of sulfide ores [15,6]. Further examples of the application of the DA method at the NAC can be found in Refs. [16-19]. A recent study by Van Achterbergh et al. [14] used DA PIXE imaging to study rare layered kyanite eclogite xenoliths from the Roberts Victor kimberlite in South Africa. PIXE microanalysis revealed clear chemical gradients (in Mn, Fe, Zn, Y and Zr, over several mm) within single garnets at the contact between the kyanite-bearing and kyanite-free zones. This gradient indicates disequilibrium between the two eclogite types, and is interpreted as indicating that the layering was created, on a geologically short time-scale prior to entrainment of the xenolith in the kimberlite [14], rather than a relict of crustal layering as suggested in previous studies [20]. The DA images (Fig. 2) revealed evidence for Sr mobility observed as heterogeneous Sr distribution through cpx and as a mantle around kyanite. Furthermore, the presence and heterogeneity of Ba is evidence for kimberlitic melt infiltration into the jadeiterich (high Na) clinopyroxene of the kyanite-bearing zones.
6. Conclusions PIXE elemental imaging can only be considered quantitative if each elemental image faithfully portrays the distribution pattern of that element with minimal misleading contributions from background or the X-ray lines or detection artefacts (tails and escape peaks) arising from other elements. The Dynamic Analysis transform outlined here provides an effective method for the routine production of true elemental images that minimize such artefacts and can be obtained on-line as the data accumulate in quantitative form, obviating the need for expensive data storage and time consuming off-line event-replay and processing. Minor off-line corrections can then be made for the variations in X-ray yields with composition ( - 1 0 % typically).
Acknowledgements The authors are indebted to Karl Springhorn of the NAC for his help, to Gary Suter for the maintenance of the CSIRO accelerator, and to David French for his constructive review of the manuscript and helpful suggestions.
References [1] C.G. Ryan, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 377.
[2] C.G. Ryan and W.L. Griffin, Nucl. Instr. and Meth. B 77 (1993) 381. [3] C.G. Ryan, D.R. Cousens, S.H. Sie, W.L. Griffin, G.F. Suter and E. Clayton, Nucl. Instr. and Meth. B 47 (1990) 55. [4] J. Pallon and J. Knox, Scanning Microscopy 7 (1993) 1207. [5] C.G. Ryan and D.N. Jamieson, Nucl. Instr. and Meth. B 77 (1993) 203. [6] C.G. Ryan, D.N. Jamieson, C.L. Churms and J.V. Pilcher, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 157. [7] T. Awaya, Nucl. Instr. and Meth. 165 (1978) 449. [8] E. Clayton and C.G. Ryan, Nucl. Instr. and Metb. B 49 (1990) 161. [9] D.R. Cousens, C.G. Ryan, S.H. Sie and W.L. Griffin, Proc. 5th Australian Conf. on Nuclear Techniques of Analysis, Lucas Heights, ISSN 0811-9422 (1987) p. 58. [10] C.G. Ryan, D.R. Cousens, S.H. Sie and W.L. Griffin, Nucl. Instr. and Meth. B 49 (1990) 271. [11] C.G. Ryan, E. Clayton, W.L. Griffin, S.H. Sie and D.R. Cousens, Nucl. Instr. and Meth. B 34 (1988) 396. [12] C.L. Churms, J.V. Pilcher, K.A. Springhom and U.A.S., Tapper, Nucl. Instr. and Meth. B 77 (1993) 56. [13] C.G. Ryan, C.L. Churms and J.V. Pilcher, NAC Annual Report (1993) 7.4.6. [14] E. van Achterbergh, C.G. Ryan, J.J. Gurney and A.P. le Roex, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 415. [15] F.M. Meyer, P. Mrller, D. de Bruin, W.J. Przybylowicz and V.M. Prozesky, Exploration and Mining Geology, in press. [16] W.J. Przybylowicz, V.M. Prozesky and F.M. Meyer, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 450. [17] V.M. Prozesky, E.J. Raubenheimer, W.P. Grotepass, W.F.P. van Heerden, W.J. Przybylowicz, C.A. Pineda and R. Swart, Proc. 4th Int. conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl, Instr. and Meth. B 104 (1995) 638. [18] W.J. Przybylowicz, C.A. Pineda, V.M. Prozesky and J. Mesjasz-Przybylowicz, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 176. [19] C.A. Pineda, A.L. Rogers, V.M. Prozesky and W.J. Przybylowicz, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. 104 (1995) 351. [20] M.B. Kirkley, B. Harte and J.J. Gurney, Crustal plagioclaserich protoliths for Roberts Victor kyanite eclogite, Contrib. Mineral. Petrol., in press.
B
N
Beam Interactions with Materials & Atoms
ELSEVIER
Overlap corrected on-line PIXE imaging using the proton microprobe C.G.
Ryan
a:~ a " , E. van A c h t e r b e r g h , D.N.
• Jamleson
b
, C.L.
Churms c
aCS1RO Exploration and Mining, PO Box 136, North Ryde, NSW 2113, Australia bMicroanalytical Research Centre, School of Physics, Universi~ of Melbourne, Parkville, Vic. 3052, Australia ~Van de Graaff Group, National Accelerator Centre, PO Box 72, Faure 7131, South Africa
Abstract Conventional methods for PIXE imaging have used the counts recorded in a simple energy window set on an X-ray peak to approximate the image of an element. This method produces image artefacts due to the overlap of the X-ray lines of interfering elements, detector artefacts, such as peak-tails, pile-up and escape peaks, and continuum background. This paper reports on continuing development to solve this problem, based on the construction of a matrix transformation that transforms directly from PIXE spectrum vector to elemental concentration vector. This transformation provides a fast method for extracting on-line quantitative estimates of the concentration of a sample while still under the proton beam; the method has been called Dynamic Analysis to reflect this capability. If the spectrum is replaced by a single count in a channel, an event recorded at a point in a raster scan of the proton beam over a target, then the resultant concentration vector is the set of increments to make to all elemental images at that pixel. PIXE images accumulated in this way are inherently (i) quantitative (accumulated in ppm txC), (ii) overlap-resolved and background-subtracted, and (iii) can be formed directly on-line. The method is under development at the CSIRO and in routine use at the NAC using a simple procedure involving the fitting of a preliminary scan spectrum to build the transform matrix; spectrum fitting and matrix construction are part of the GeoPIXE software package. This paper outlines the method, reports various tests of it, and presents recent examples of its application to major and trace element imaging in geology.
1. Introduction The trace element data obtained from quantitative PIXE microanalysis of geological samples complement the major element data obtained from conventional methods such as the electron microprobe (EMP), and the sensitive yet semi-quantitative data from the ion microprobe (IMP), and open a window on the structure, chemistry and geochemical processes of the earth's crust and upper mantle. On the Ixm to cm scale, characterization of zoning of trace and major elements reveals information on the chemistry, timing and dynamics of geological processes [1,2]. On the scale of meters to hundreds of kilometers, trace element signatures reflect bulk rock chemistry and the effects of pressure and temperature on the partitioning of elements between minerals and between minerals and permeating fluids and melts [1,2]. Techniques for the detailed analysis of PIXE spectra to extract quantitative elemental concentrations are well developed. These methods generally use a non-linear leastsquares fit to the spectrum with a model function compris* Corresponding author. Tel. +61 2 887 8696, fax +61 2 887 8909, e-mail [email protected].
ing elemental line-shapes, a sum element representing pile-up contributions, and a background function (e.g. Ref. [3]). Each line-shape function may include the prominent X-ray lines, detector escape peaks, and tailing produced by incomplete charge collection and Compton scattering. The result is an accurate description of the complete PIXE spectrum from which individual elemental contributions are extracted. This approach resolves complex line-shape overlaps between elements, and distinguishes contributions from background, peak-tailing, escape peaks and pile-up. However, conventional approaches to PIXE imaging are far less refined, and commonly accept all counts within a simple software " g a t e " , defined by an energy " w i n d o w " centred on an X-ray line for an element, to provide an image of that element. For major elements on weak continuum background, this approach produces reliable elemental images. However, as the concentrations of elements fall towards the important trace levels, these images tend to suffer more from artefacts caused by contamination from continuum background and contributions from other elements due to the overlap of X-ray lines and detector artefacts with the software gate. The overlap of Sr K~ with Zr K~ (e.g. Fig. la), and As K,~ with Pb L,~ are common examples. Hence, Zr images (gate set on Zr
0168-583X/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved SSDI 0168-583X(95)00898-5
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Fe [7 106
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become more complex and the contaminated images may be misleading. In more complex geological problems involving multiple element overlap, Ryan and Jamieson [5] demonstrated that accurate elemental images can be projected from event data in off-line analysis using a spectral decomposition transformation called the Dynamic Analysis (DA) method. The purpose of this paper is to give an update on this technique as applied to PIXE analysis and imaging, and present tests of the method using samples which exhibit complex multi-element overlaps and recent examples of its application to major and trace element microanalysis in geology.
~ Rb row
2. Quantitative true elemental imaging
0.0 -0.5 1.0
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0.5 0.0
e T ~ row
0.6 0.4 0.2 0.0 -0.2 -0.4 0.8 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0
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10
20 X-ray Energy (keV)
30
Fig. 1. (a) Total PIXE spectrum from a scan of a polished section of Roberts Victor layered-kyanite eclogite [14] analyzed using 3 MeV protons and a 160 txm A1 filter. The GeoPIXE fit to the spectrum and the SNIP background approximation are shown overlaying the spectrum. (b)-(g) Rows of the a 113matrix part of F for the indicated elements and pile-up determined from a preliminary scan. Ks) may contain features due to the spatial variation of Sr and Pb images (gate set on Pb L~) may contain artefacts due to As. Attempts can be made to set gates on weaker lines in order to avoid the dominant source of interference. However, in many cases no viable alternatives exist; all lines for an element suffer interference. And even if a minor line exists that is free of overlap interference, the resulting images will suffer from the loss of counting statistics and increased sensitivity to continuum background contributions. In cases involving simple overlap, corrections can be made during off-line post-processing of the gate images; Pallon and Knox [4] report a method for the correction of K contamination of Ca images in the analysis of biological specimens. However, in many cases element overlaps
To justify use of the term true elemental imaging, the image of an element must faithfully portray the spatial distribution of that element, and be free of artefacts due to other elements and background. For an image to be considered quantitative, the average over a region of pixels in the elemental image must provide a quantitative measure of the concentration of the element in that region and be free of contamination and accurate to -10%. The Dynamic Analysis (DA) method for PIXE imaging has been demonstrated to achieve these objectives on-line as the data accumulate and is described in detail by Ryan et al. [5,6]; accuracy may be further improved using off-line corrections. This section summarises the central elements of Dynamic Analysis and illustrates is operation using a simple example of geological imaging. 2.1. The Dynamic Analysis method
Decomposition of a PIXE spectrum Sr into contributions from component elements, can be expressed as a non-linear least-square fit to the spectrum using a model function f comprising line-shape functions for each element, together with pile-up and background terms, at each channel i. If the non-linear parameters describing detector characteristics such as energy calibration, peak width and tailing, have been determined by prior non-linear iterations, or in a preliminary fit to a prior spectrum for example, then the remaining linear parameters a k, representing major-line peak-areas and one representing background intensity (i.e. a scaling factor applied to a background model), can be found by solving the matrix equation [5,6] oLa = 13S,
(1)
where ~ and 13 are matrices in terms of the partial derivatives Of/Oa k and S is the spectrum vector: %k = ~ wi '~i]3k~,
(2)
i
~ , = wi(Of/Oaj).
(3)
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We have adopted the statistical weights w i of Awaya (wi = f i 1) [7]. As discussed in detail elsewhere [5,8], the convergence of the least-squares fit is only weakly affected by the form of the weights, provided the weights w~ = S i are not used as they introduce an error at low counting statistics [7,8]. Indeed, acceptable results can be obtained even using unit weights (w~ = 1) [8]. The peak-areas a~ (excluding the background term) are related to element concentration (areal density in the case of thin targets) Ck by the equation [3] a~, = QO,~,TkYkCk
(4)
in terms of the integrated charge Q, detector solid-angle and efficiency/2 and e k, X-ray absorber attenuation Tk and generic X-ray yield Yk [3,9]; for the moment Yk will be assumed to be constant for element k across the image. Hence, the solution of the linear least-squares problem can be cast as a matrix equation which transforms directly from spectrum vector S to concentration vector C in terms of the matrix F, which can be precalculated [5,6]: C = Q ~FS
(5)
--I F~ = (f2ekTkY~) -1 ~ cekj ~i. J
(6)
The F matrix is calculated in a final linear least-square iteration in the program PIXE-FIT, part of the GeoPIXE software package [3,10]. The model function includes a complete set of X-ray lines for each element, detection artefacts (including tails, pile-up and Si or Ge escape peaks), and the SNIP background approximation [11] corrected for absorption [10[. The structure of the F matrix is illustrated in Figs. l b - l g which shows representative rose of the oL ~13 matrix, which is the foundation of F, calculated for silicate minerals with lists of elements typified by the spectrum in Fig. la. In this simple example, there is little element overlap and the a matrix is quite diagonal. Therefore, the rows for Fe and Ba (Figs. lb and lg), for example, are characterized by positive weights across the K B peaks (also the Fe Si-escape peaks), which act like software gates, and small negative weights across the spectrum in between X-ray lines, which sample the underlying background. However, there are two simple overlap situations. One involves the overlap of Sr K~ on the Zr K lines. This produces small negative weights in the Zr row (Fig. If) at the position of the Sr K~, which acts to subtract Sr contamination from Zr images. The Sr row (Fig. le) is more complex, having positive weights at the energies of the Sr K~,.~ lines, and negative weights at the Zr K~.~ energies. The Zr K~ is given greater weight because it is overlap free and is a good measure of the contribution of the Zr K in the vicinity of the Sr K~. Note that there are also small negative weights at the position of the Fe K~+~,~+~ pile-up peaks which compensate for Fe K~+~ contamination of the Sr K~, peak. Similar negative correc-
tions can be seen in the Rb row (Fig. lc) to compensate for overlap between the Fe K pile-up lines and Rb K (negative weights near the Fe K,~+~ energy), and also between Rb K~ and Y K,~ (seen as negative weights at the Y K~ energy). 2.2. Rapid on-line spectrum analysis
Eq. (5) permits processing of PIXE spectra to extract concentrations using a simple matrix transform. This can be performed in a fraction of a second on a small computer. Incorporated into a data acquisition system and using the instantaneous live-charge Q (integrated charge corrected for dead-time), the transform allows an on-line estimate of sample composition to be calculated, and updated continuously, as the data accumulate. This provides a useful diagnostic capability, enabling the majorelement composition to be determined in a few seconds. 2.3. Imaging
Note that if the spectrum vector in Eq. (5) is replaced by a vector with just a single count in channel e, then the resultant concentration vector represents the set of increments to make to all element concentrations for one count at that channel. If the beam is positioned at point x, y in a raster scan, each event (e,x, y) makes a contribution ~Ck(X , y) = Q(x, y) 1/kk e t o the concentration distribution of element k [5]. Therefore, a convenient procedure is to accumulate elemental images in ppm IxC units by simply incrementing each image k by F~e for each event. These images can be directly related to concentration, both online during data collection or off-line, by reference to the live-charge distribution Q(x, y). Fig. 2 shows the application of the DA matrix, containing the c~ 113 matrix rows illustrated in Fig. 1, to image major and trace element distribution in a polished section of mantle eclogite dominated by the phases kyanite (ky), clinopyroxene (cpx) and garnet (gnt). Note that the Zr image shows no evidence of artefacts due to the Sr K~ overlap with the Zr K,~ lines, through benefits from the counts recorded for both the Zr K,~ and Ka lines. Similarly, the Rb and Sr images are quite distinct and contrast with the Fe image providing some confidence that the Fe K pile-up overlaps with both Rb and Sr have been correctly rejected. Eq. (5) provides a very simple method of generating elemental distribution images with three very important properties: (i) The images are inherently element overlapresolved and background-subtracted. (ii) The images are quantitative to within a small yield correction; each pixel contains a value representing concentration times integrated charge. (iii) The images are formed directly on-line as the data accumulate. The first property means that each image is a close depiction of the distribution of a single element, discriminating against the inevitable artefacts
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157
Fig. 2. On-line PIXE elemental images (2.6 X 10 6 events) from a proton scan of the eclogite sample (Fig. 1), comprising garnet (gnt), clinopyroxene (cpx) and kyanite (ky) as the major phases, projected using the DA method; the scan area was 1800 x 1800 p~m'.
introduced by element overlaps, detection artefacts, such as tails and escape peaks, and background when using simple gates set on major X-ray lines. The second property means that by integrating an arbitrarily shaped region of a image, and dividing by the total integrated charge in the same region, a direct average of the concentration of all elements can be obtained on-line while the data accumulate. 2.4. Restrictions, approximations and corrections
There are a number of practical points and approximations to keep in mind when using the DA technique: (i) The DA matrix needs to include all anticipated elements. (ii) The energy calibrations of the spectrum and DA matrix need to be accurately aligned (~E < 20 eV). (iii) The peak width function and relative tail strengths and shapes are fixed. (iv) The background shape and X-ray relative-intensities are fixed; these are effected by the choice of X-ray filters (see Ref. [5]). (v) The pile-up " s u m " element has fixed relative intensities. (vi) The calculated yields Yk are assumed to be constant across a sample, and thick target relative-intensities are assumed. (vii) Dead-time losses must be considered separately. In practice, (i-iv) are addressed quite simply by building the DA matrix transform from a fit to a reference spectrum collected from a brief preliminary scan of the sample, or one similar, under
the same experimental conditions as the desired images. Hence, the energy calibration, X-ray relative-intensities, background shape, and peak width and tail parameters are determined during the non-linear least-squares fit to the reference spectrum. The effects of the spatial variation of PIXE yields, dead-time losses, and pile-up spectral content are more subtle and require further attention. Variation in PIXE yields can be treated in a straightforward manor as minor off-line corrections ( < 10% typically) to the images tied to major-element spatial variation reflecting the changing composition [6]. The effects of pile-up are more subtle as the intensity of pile-up can vary with count-rate on a pixel by pixel basis, and the relative-intensities of the sum element lines will change, in general, with sample composition across the scan. Therefore, care must be taken in interpreting the images of elements that suffer from pile-up overlap. However, often a single major element dominates the spectrum (e.g. Fig. l a). In these cases the pile-up is accurately described by a fixed pile-up " s u m " element, and its spatial variation is correctly described and subtracted from other elemental images. Dead-time losses depend on the scan frequency. In the limit of very low scan rates, the count-rate in a pixel determines its local deadtime [4]; image correction can be done at the pixel level. In the limit of very high scan rates and typical long shaping
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times, dead-time becomes averaged over the scan and is simply incorporated in the live-charge. Between these extremes the effects become very complex and depend on the direction of the scanning beam. No general solutions to these problems of changing pile-up and dead-time have been devised at present; these effects are discussed in more detail by Ryan et al. [6].
3. Implementation of on-line true elemental imaging The Dynamic Analysis method for on-line elemental imaging has been implemented at the CSIRO in Sydney and at the National Accelerator Centre (NAC) in Cape Town. Both installations use the GeoPIXE software package for quantitative PIXE analysis and to build the transform matrix for imaging. The method has permitted a very simple procedure for PIXE elemental imaging: (i) Perform a brief preliminary scan of a new sample, or when X-ray absorbers have been changed, to collect a reference spectrum. (ii) Fit this spectrum in the usual way using PIXE-FIT, but specifying the dynamic mapping option. The full non-linear least-squares fit is performed first, followed by a linear iteration to build the transform matrix; the matrix is output to disk. (iii) Read the matrix into the data acquisition system. Calculate energy translation, to map from spectrum to DA matrix column (if necessary), and dispersion corrections if the energy per channel differ. (iv) Start imaging; the matrix already contains the full list of elements to build images for. Once a matrix has been built it can be used for multiple scan areas on a given sample, or other samples with similar component minerals. Hence, in practice a given transform matrix can be reused for a number of scan areas. In both laboratories, the data acquisition systems have been set-up to select a column of the F matrix based on the X-ray energy of each event, and use these values to increment every elemental image at the current pixel position. At the NAC, the beam is raster scanned and data is collected through a CAMAC interface [12]. Elemental images are stored in floating point arrays (64-256 pixels square) in ppm nC units, and displayed on a VAX workstation in live-time. At the CSIRO, the beam is scanned electrostatically and data is collected through a CAMAC interface controlled by a IxVAX, and buffers are forwarded to an Amiga workstation for display, where elemental images are built up using the DA method in 32 floating point arrays (256 X 256 pixels each) in ppm ixC units and displayed in live-time [6].
4. Tests of dynamic analysis and on-line true elemental imaging A number of tests have been carried out at the NAC and CSIRO proton microprobe laboratories to evaluate the
performance of the method in demanding mineralogical applications (also see tests in Refs. [5,6,13]). The most basic tests have used PIXE point analyses within a scan area to test the accuracy of the images produced by the DA method. Ryan and Jamieson [5] used this approach to demonstrate the viability of the DA method. They showed that Au could be accurately imaged at 200 ppm in a sulphide ore despite severe overlap problems associated with major-element Zn and As in the sample [5]. In a more demanding test, a sample consisted of small fragments of BaF2, CaF 2 and ScF 3 glued to an Fe foil (containing minor Cr) and positioned between pieces of pure Ti and Cr metal. The test was to see if these distinct phases could be imaged accurately despite severe X-ray line overlaps (see Fig. 3a). A comparison was made between images produced using the DA method, and images produced using simple gates (Fig. 3a) set on the K peak of each element (or L , L~I, L~2 and L~I in the case of the Ba L lines). Most images using the simple gates (Figs. 4i-4q) show inaccuracies or artefacts due to other elements except for Ba K, when compared to the known 10e 10~ 1o~
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g) Ca row
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Fig. 3. (a) Total PIXE spectrum from a proton scan of the sample described in Fig. 4a, analyzed using 3 MeV protons and a 75 ~m kevlar filter. The GeoPIXE fit to the spectrum and the SNIP background approximation are shown overlaying the spectrum. The software gates are indicated. (b)-(g) Rows of the a-J[3 matrix for the indicated elements determined from a preliminary SCan.
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max
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Fig. 4. (a) Schematic map of a sample consisting of small fragments of BaF2, CaF2 and ScF 3 glued to an Fe foil (containing minor Cr) and positioned between pieces of pure Ti and Cr metal. (b)-(h) On-line elemental images (3 X 10 6 events) projected using the DA method. (i)-(q) Images produced using the software gates shown in Fig. 3a, from a repeat scan (4.5 × 106 events) of the sample. The scan area was 1800 x 1800 ~m ~-.
positions of each phase tFig. 4a). The Ba K lines are at high energy (32 keV) and free of interferences or significant underlying background. This image forms a useful point of reference for checking the Ba imaged based on the L lines. The images based on simple gates on the Ba L lines show a number of artefacts. The Ba L gate overlaps completely with the Ti K (see Fig. 3a); this image (Fig. 4i) is dominated by the Ti distribution. Similarly, the L~I gate image and L~2 image (Fig. 4q) are dominated by artefacts due to the Ti K~ lines and the Cr K tail, and the L~, gate image (Fig. 4p) shows artefacts due primarily to the Cr Ks. ~ lines. The Sc image based on a simple gate (Fig. 4n) contains artefacts due to the overlap of the Ca K~ (producing a significant Ca ghost) and the tail of the Ti K (producing a faint ghost of the Ti region). A F matrix was built simply by fitting a PIXE spectrum obtained from a - 5 rain preliminary scan; rows of the o~ 113 matrix, the important component of F, are shown in Figs. 3b-3g. The Fe row (Fig. 3b) is similar to Fe in Fig. lb showing dominant positive weights across the K ~ peaks. However, little weight is placed on the Si-escapes now; these are rendered unreliable by the presence of Sc, Ti, Ba and Cr. The Cr row (Fig. 3c) shows strong Cr K weights and negative weights, particularly on Ba L ~1, to compensate for Ba L~2 overlap on the Cr K lines. The Ti and Ba L rows (Figs. 3e and 3d) become more complex due to the overlap-coupling between Sc, Ti, Ba and Cr. The strong overlap between Ti and Ba is evident. Both the Ti and Ba L rows display interesting bipolar weights about the Ti K s and Ba L~, lines. In addition, Ti shows prominent negative weights centred on the Ba L~I and L[3 2 lines to subtract Ba contributions from Ti images. A negative weighting on the Ca K s energy is also evident in the Sc row (Fig. 3f) to subtract the effects of the Ca K~ overlap on Sc K . The benefits of the DA approach are evident in Figs. 4b-4h. In contrast to the Ba L gate images (Figs. 4i, 4p and 4q), the dynamic analysis Ba L image (Fig. 4b) matches the Ba K image (Fig. 4c), despite the complete overlap of Ba L~ and Ti K s, and the fact that all the Ba L lines are dominated by Ti and Cr in the spectrum (Fig. 3a). The DA Ca and Sc images show clearly separated phases with little evidence of overlap-derived contamination (Figs. 4g and 4h). Notwithstanding the small residual artefacts of Sc and Ba visible in the Ti image at the -0.5% level (Fig. 4d), the DA images portray realistic distributions of all elements.
5. Application of on-line true elemental imaging Successful geological applications of the DA method include the study of (1) trace Au distribution in ore from the Emperor mine in Fiji, despite extensive overlap interference on the Au L m,~2 lines [5], (2) fluid processes in the mantle [14] and (3) the development history
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of sulfide ores [15,6]. Further examples of the application of the DA method at the NAC can be found in Refs. [16-19]. A recent study by Van Achterbergh et al. [14] used DA PIXE imaging to study rare layered kyanite eclogite xenoliths from the Roberts Victor kimberlite in South Africa. PIXE microanalysis revealed clear chemical gradients (in Mn, Fe, Zn, Y and Zr, over several mm) within single garnets at the contact between the kyanite-bearing and kyanite-free zones. This gradient indicates disequilibrium between the two eclogite types, and is interpreted as indicating that the layering was created, on a geologically short time-scale prior to entrainment of the xenolith in the kimberlite [14], rather than a relict of crustal layering as suggested in previous studies [20]. The DA images (Fig. 2) revealed evidence for Sr mobility observed as heterogeneous Sr distribution through cpx and as a mantle around kyanite. Furthermore, the presence and heterogeneity of Ba is evidence for kimberlitic melt infiltration into the jadeiterich (high Na) clinopyroxene of the kyanite-bearing zones.
6. Conclusions PIXE elemental imaging can only be considered quantitative if each elemental image faithfully portrays the distribution pattern of that element with minimal misleading contributions from background or the X-ray lines or detection artefacts (tails and escape peaks) arising from other elements. The Dynamic Analysis transform outlined here provides an effective method for the routine production of true elemental images that minimize such artefacts and can be obtained on-line as the data accumulate in quantitative form, obviating the need for expensive data storage and time consuming off-line event-replay and processing. Minor off-line corrections can then be made for the variations in X-ray yields with composition ( - 1 0 % typically).
Acknowledgements The authors are indebted to Karl Springhorn of the NAC for his help, to Gary Suter for the maintenance of the CSIRO accelerator, and to David French for his constructive review of the manuscript and helpful suggestions.
References [1] C.G. Ryan, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 377.
[2] C.G. Ryan and W.L. Griffin, Nucl. Instr. and Meth. B 77 (1993) 381. [3] C.G. Ryan, D.R. Cousens, S.H. Sie, W.L. Griffin, G.F. Suter and E. Clayton, Nucl. Instr. and Meth. B 47 (1990) 55. [4] J. Pallon and J. Knox, Scanning Microscopy 7 (1993) 1207. [5] C.G. Ryan and D.N. Jamieson, Nucl. Instr. and Meth. B 77 (1993) 203. [6] C.G. Ryan, D.N. Jamieson, C.L. Churms and J.V. Pilcher, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 157. [7] T. Awaya, Nucl. Instr. and Meth. 165 (1978) 449. [8] E. Clayton and C.G. Ryan, Nucl. Instr. and Metb. B 49 (1990) 161. [9] D.R. Cousens, C.G. Ryan, S.H. Sie and W.L. Griffin, Proc. 5th Australian Conf. on Nuclear Techniques of Analysis, Lucas Heights, ISSN 0811-9422 (1987) p. 58. [10] C.G. Ryan, D.R. Cousens, S.H. Sie and W.L. Griffin, Nucl. Instr. and Meth. B 49 (1990) 271. [11] C.G. Ryan, E. Clayton, W.L. Griffin, S.H. Sie and D.R. Cousens, Nucl. Instr. and Meth. B 34 (1988) 396. [12] C.L. Churms, J.V. Pilcher, K.A. Springhom and U.A.S., Tapper, Nucl. Instr. and Meth. B 77 (1993) 56. [13] C.G. Ryan, C.L. Churms and J.V. Pilcher, NAC Annual Report (1993) 7.4.6. [14] E. van Achterbergh, C.G. Ryan, J.J. Gurney and A.P. le Roex, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 415. [15] F.M. Meyer, P. Mrller, D. de Bruin, W.J. Przybylowicz and V.M. Prozesky, Exploration and Mining Geology, in press. [16] W.J. Przybylowicz, V.M. Prozesky and F.M. Meyer, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 450. [17] V.M. Prozesky, E.J. Raubenheimer, W.P. Grotepass, W.F.P. van Heerden, W.J. Przybylowicz, C.A. Pineda and R. Swart, Proc. 4th Int. conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl, Instr. and Meth. B 104 (1995) 638. [18] W.J. Przybylowicz, C.A. Pineda, V.M. Prozesky and J. Mesjasz-Przybylowicz, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. B 104 (1995) 176. [19] C.A. Pineda, A.L. Rogers, V.M. Prozesky and W.J. Przybylowicz, Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 1994, Nucl. Instr. and Meth. 104 (1995) 351. [20] M.B. Kirkley, B. Harte and J.J. Gurney, Crustal plagioclaserich protoliths for Roberts Victor kyanite eclogite, Contrib. Mineral. Petrol., in press.