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Quantitative chemical phase analysis of EFTEM elemental maps using scatter diagrams
Pergamon PII: S0968-4328(97)00061-9
Micron Vol. 29, No. 1. pp. 43 51, 1998 ! 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0968M328/98 $19.00+0.00
Quantitative Chemical Phase Analysis of EFTEM Elemental Maps Using Scatter Diagrams WERNER GROGGER,* F E R D I N A N D HOFER and GERALD KOTHLEITNER+ Forschungsinstitut J~ir Elektronenmikroskopie, Technische Universitiit Gra:. Steyrergasse 17. A-8010. Gra:. Austria (Received 4 May 1997; accepted 16 September 1997)
Abstract--Energy-filtered transmission electron microscope (EFTEM) images can yield elemental maps of very high lateral resolution (1 2 nm) in a short time (typically less than 3 min). Additionally, correlation techniques such as scatter diagrams yield information about the intensity relationships between the various elemental maps, thus leading to the calculation of chemi)al phase maps. The application of such techniques reduces the amount of data (i.e. number of images) by compressing information of different images into only a few. This makes interpretation a lot easier and clearer since information in chemical phase maps is restricted to the chemical composition of the specimen. In this work we used a Gatan Imaging Filter (GIF) to acquire! EFTEM images of a Ba-Nd-titanate specimen. The scatter diagram technique together with quantification procedures was then ~pplied to these images in order to show the distribution of chemical phases within the specimen. First, we quantified the etemer~tal maps using atomic ratio images. Then we applied the scatter diagram technique on the atomic ratio images and calculated chemik:al phase maps. ,~ 1998 Elsevier Science Ltd. All rights reserved
Key words: energy-filtering TEM, quantitative elemental maps, phase imaging, scatter diagram, analytical electron microscopE.
1995a), the two methods work in two different ways: The three window technique yields true elemental maps which can be used directly for quantification. However, when investigating crystalline specimens diffraction effects may disturb the elemental images. On the other hand, jump ratio images (two window technique) suppress diffraction effects very well, although they are susceptible to thickness variation effects! Diffraction effects in crystalline materials can be furlher reduced by recording jump ratio images under rocking beam illumination (Hofer and Warbichler, 1996)i The result of this first step of image processing is a two-dimensional distribution of an element. If the elemental map has been recorded by using the three window technique this image can be quantified using different approaches. An absolute quantification can be performed by dividing the net intensity elemental map by a zero loss image and multiplying the result by the appropriate ionization cross section (e.g. Leapman, 1986). Alternatively a relative quantification can be i performed by dividing two elemental maps and multiplying by the appropriate k-factor (e.g. Bonnet et al., 1988). This latter approach results in an iatomic ratio image giving concentration ratios. This iprocedure is then extended to more elements to get information about the complete chemistry of the specimen (Hofer et al., 1997). Often the procedure stops at this point by making a collage of all important elemental distribution images. But what we consider even more important is to show the spatial relationship between several elemental distribution maps, and not leave it to the viewer to combine the images and detect whether or not two elements are situated together. To understand the
INTRODUCTION Energy-filtering transmission electron microscopy (EFTEM) is a well established tool for imaging elemental distributions complementing standard analytical techniques such as energy-dispersive X-ray spectrometry (EDXS) or electron energy-loss spectrometry (EELS) (Leapman and Hunt, 1992; Krahl, 1990; Mayer et al., 1994; Hofer et al., 1995a; Reimer et al., 1992)., An energy-filtered image whether centred around the zero-loss peak, a plasmon peak, or somewhere else, contains information about the specimen (e.g. elemental composition, thickness). When using EFTEM as an analytical tool, one is interested in the elemental information buried in the energy-filtered image, which is then recorded at the ionization edge of interest. An energy-filtered image, the output of the energy filter, is therefore the basic element in analytical EFTEM work. The energy-filtered image recorded at an ionization edge of interest contains element-specific information, and a non element-specific background. The first step towards an elemental distribution is the separation of all element specific information from the background. Usually this is achieved by applying either the three window (Bonnet et al., 1988; Egerton, 1996) or the two window technique (Krivanek et al., 1993; Johnson, 1979; Hofer et al., 1995a). Both methods extract elemental information from a series of two or three energy-filtered images and suppress non-elemental parts. As it has been described previously (Krivanek et al., 1993; Hofer et al., *Corresponding author. Email: [email protected]. tPresent address: Gatan Inc., Pleasanton, CA 94588, U.S.A. 43
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W. Grogger et aL
elemental composition of the specimen it is necessary to know the correlation of the elemental distributions. Several methods have been proposed for visualizing the spatial relationship of some images; two of them will be mentioned in the following, as they are rather easy to apply. Almost every image processing software offers the possibility to combine two or three images to form a colour image (RGB image) by assigning each image a colour (red, green, blue). RGB images are computed very easily, however they are limited to three elements. They look beautiful, but are sometimes difficult to interpret, because of the occurrence of mixed colours (Fig. 2(b); Hofer et al., 1995b). Alternatively, correlation analysis can be applied using scatter diagrams (Bright et al., 1988; Bright and Newbury, 1991; Bright and Marinenko, 1992). Correlation techniques are well known from other disciplines (e.g. E1 Gomati et al., 1987; Prutton et al., 1990; Browning, 1985; Latkoczy, 1994). Scatter diagrams are easily made and combined with other statistical methods such as principal component analysis and classification procedures. In principle, the number of elements used for the computation of scatter diagrams is not limited, however simple visualization is possible only in two or three dimensions, and in practical work we restrict scatter diagram analysis to two dimensions. Two dimensional scatter diagrams are not really limited to two elements. Several combinations of two elements can be used to compute scatter diagrams, from which the most suitable are selected. The aim of any method visualizing the spatial relationship between several elemental distribution maps is to show the distribution of the chemical phases in a chemical phase map. In this context specimens can be divided into two classes: 'simple' and 'complicated'. 'Simple' specimens consist of several locally well separated phases, each with a defined chemical composition. An RGB image of a 'simple' specimen can be a chemical phase map with a different colour for each phase, but with no quantitative information. The scatter diagram approach can yield both: a chemical phase map and full information about the chemical composition of each phase. On the other hand 'complicated' specimens show significant concentration gradients, which appear as smooth colour transitions in an RGB image. Scatter diagrams can be combined with quantitative information. Assigning different composition values of the gradient to a 'phase' a chemical phase map can be built, with composition ranges supplied for each part of the gradient (Hofer et al., 1997). Strictly speaking every real TEM specimen is a 'complicated' specimen because of its three dimensional nature: It shows 'gradients' due to inclined interfaces between different phases which cannot be discriminated from real concentration gradients. Fortunately, in many cases this effect is negligible and many TEM specimens can be treated as 'simple' specimens exhibiting no concentration gradients.
CALCULATION OF SCATTER DIAGRAMS AND TRACEBACKS Scatter diagrams can be considered as two dimensional histograms. The principles of the calculation are shown in Fig. 1. Every pixel (x,y) in image A is associated with the corresponding pixel in image B. The grey-levels a(x,y) and b(x,y) are then used as coordinates of the scatter diagram, where they are accumulated at (a,b). The scatter diagram usually consists of a square pixel array (image), where the abscissa corresponds to the grey-levels of image A and the ordinate corresponds to the grey-levels of image B. The grey-levels on their part may correspond to elemental concentrations of elements A and B respectively. When there is a limited number of chemical phases in the specimen, the individual dots in the scatter diagram form clusters corresponding to these phases. After calculation of a scatter diagram, the clusters can be marked digitally and traced back in order to find the pixels (area) in the original images which contributed to the clusters. If the separation of the clusters in the scatter diagram is well done, this procedure creates a map showing some phases of the specimen. Each phase is usually represented by a colour, since it is easier to distinguish colours than grey-levels. In a scatter diagram 'simple' specimens are characterized by well separated clusters. If the right combination of elemental distribution images is chosen, the clusters will not overlap and there will be only few dots lying in between the clusters. Concentration gradients will appear as significant spreading of clusters in one (or both) directions.
EXPERIMENTAL
This investigation was performed on a Philips CM20! STEM operated at 200kV (LaB 6 cathode). The instrument is equipped with a Gatan Imaging Filter (GIF) (Krivanek et al., 1991; Krivanek et al., 1992; Gubbens and Krivanek, 1993). EFTEM images and EEL-spectra were recorded with the slow-scan CCD integrated in the GIF (YAG scintillator, 1024 × 1024 pixel array). All energy-filtered images were recorded using a binning of 2 × 2 giving 512 x 512 images, for reasons of sensitivity. For the acquisition of the bright field image all 1024 x 1024 pixels were used. Since the focus for an energy-filtered image differs significantly from that of the elastic image (Berger et al., 1994; Berger and Kohl, 1993), we adjusted the focus for energy-filtered images at an energy loss of about 150 eV. The Ba-Nd-titanate specimen was not sensitive to radiation damage so we could focus the TEM spot onto the region of interest yielding approximately 15 AJcm2. Images (and spectra) were recorded with Gatan's DigitalMicrograph running on a Macintosh Quadra 840AV. All images and spectra were corrected for
Quantitative Chemical Phase Analysis of EFTEM Elemental Maps Using Scatter Diagrams 82
118
45
element A -36O 0 |~ ,
0 ,
1080 I1~ 614
1057
DO0
~ element B Fig. 1. Principles of scatter diagram calculation (two-dimensional histogram). The grey-levels of the pixels (x,y) in images A and B are used as coordinates of the scatter diagram, where they are accumulated. i
dark current and gain variation, however, they were not corrected for the blurring caused by the pointspread function of the detector (De Ruijter, 1995). Drift between successive images was automatically corrected using a cross-correlation algorithm (DigitalMicrograph). In order to enable a quantification of the crystalline specimen, elemental maps were recorded under identical electron optical conditions, i.e. the beam convergence was kept constant for the complete energy-filtered series. A changing of beam convergence would cause a considerable variation of diffraction features in the energyfiltered images and also in the corresponding elemental maps. We calculated k-factors for quantification using experimental EEL-spectra and the individual acquisition parameters. Further image processing and the calculation of scatter diagrams was performed within DigitalMicrograph. It is rather easy to implement the computation of a two-dimensional scatter diagram within DigitalMicrograph using its script language. We use a set of scripts for the calculation, annotation, traceback .... of scatter diagrams. These scripts have been written specific to our needs and are available on request. The specimen investigated was a Ba-Nd titanate ceramics prepared following the standard TEM preparation techniques with final low angle ion milling (Aldrian et al., 1996).
PRACTICAL APPLICATION OF SCATTER DIAGRAMS
i [
In order to exemplify the methods described above, a typical materials science specimen w~ts chosen: a Ba-Nd-titanate ceramics specimen consisting of three well known phases (Hofer and Warbichl~r, 1988). As these phases are 'well separated, according to the previous paragraph this specimen can be considered as a 'simple' specimen. Figure 2(a) shows a TEM bright-fiek~ image of a typical region of this specimen already ~xhibiting the three phases: Nd-titanate (needle like ~rystals), BaNd-titanate (round shaped crystals) arid a Ba-rich amorphous phase situated between the c~ystals. From the same specimen area elemental maps were acquired for the elements Ti, Ba and Nd (Fig.12(c-e)). The acquisition parameters are listed in Table l I We adjusted the position of the post-edge window and ~he slit width for optimum signal-to-noise ratio (Koth!eitner, 1996: Kothleitner and Hofer, 1996: Berger and Kohl, 1993). After acquisition the energy filtered [images were automatically cross-correlated to take ~nto account a possible specimen drift between the individual exposures. Elemental maps were calculaied using the three window technique (power law, Eger!on, 1996). The elemental maps were then spatia!ly registered with each other. In principle, this could be done using cross-correlation, but elemental maps seldom
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W. Grogger et al.
Fig. 2. TEM bright field image, RGB image and EFTEM elemental maps of a B~Nd-titanate specimen. (a) TEM bright field image showing the different phases and zones used for EEL spectrometry (colours corresponding to phases in Fig. 5). (b) RGB overlay image constructed of the elemental maps shown in (c-e): Nd (red), Ti (green) and Ba (blue). (c-e) elemental maps of Ti, Ba and Nd respectively (acquisition parameters see Table 1). Yellow: Nd-titanate; blue: Ba-Nd-titanate; red: Ba-rich phase.
show significant image features with equivalent contrast and often the signal-to-noise ratio is too low. We registered the images manually, by assembling a colour
image from image A (red) and image B (green) and shifting one image with respect to the other to reduce the displacement visually.
Quantitative Chemical Phase Analysis of EFTEM Elemental Maps Using Scatter Diagrams Table 1. Acquisition parameters of elemental maps Element- Pre-edge Pre-edge Post-edge Slit width edge 1 (eV) 2 (eV) (eV)~ (eV)~
Exposure time (s)
47
distribution (corresponding to the concentration ratio distribution) of these images. The Ba/Nd atomic ratio image (Fig. 4(c)) already
visualizes the phases present in this specimen area, because the Ba/Nd ratio differs significantly for each Ti L23 394 445 467 20 10 phase (0.014, 0.31 and 1.2 for Nd-titanate, B a - N d Ba-M45 681 763 798 30 30 titanate and the Ba-rich phase respectively). By way of Nd-M45 898 957 1000 40 30 contrast the Nd-titanate and the Ba-rict: phase blur ~These parameters were chosen to get an optimum signal-to-noise together in the Ti/Nd atomic ratio image siJ Lce they have ratio. similar concentration ratios (1.21 and 1.48, respectively). Using both atomic ratio images the three r hases can be Table 2. Phase identificationby grey-levelexamination using elemental detected and their local composition in ter: ns of atomic maps from Fig. 2(c-e) (colours correspondingto Figs 2 and 5) concentration ratios can be simply read from the computer screen by moving the cursor acro~ s the images. Ti Ba Nd elemental elemental elemental Two main problems have to be taken nto account, map map map Phase when mapping the chemical composition ~f crystalline Bright Dark Bright Nd-titanate Yellow TEM specimens: Thickness variations ai d diffraction Bright Grey Bright Ba Nd-titanate Blue effects (Schenner et al., 1996; SchattschtLeider et al., Dark Bright Dark Ba-rich phase Red 1996) may strongly influence the intendties in the elemental maps thus leading to misinterpIetable image features. Therefore we wish to suppress these effects as From the comparison of the elemental maps in far as possible. Fig. 2(c-e) three phases can be clearly distinguished (see The atomic ratio images are advantageous for the Table 2). This is well confirmed by EEL-spectra from quantification of crystalline materials, because the distinct specimen areas (Fig. 3; compare to Fig. 2(a)). diffraction and thickness variation effects cancel (comEach phase is represented by a certain grey-level combi- pare to quantitative EEL-spectrometry: B(,urdillon and nation of the three elemental maps. Stobbs, 1985; Hofer and Golob, 1988). This can be In order to quantify the elemental maps atomic ratio clearly seen by comparing the elemental rnaps in Fig. 2 images were calculated by simply dividing two images with the atomic ratio images (Fig. 4). ~lthough the followed by multiplying by the appropriate k-factor. thickness variations are rather strong and ~ome crystals These k-factors, suitable for a certain slit width, were are strongly diffracting the beam (see, e.g. Ti map), the calculated from EEL-spectra (Hofer, 1991; Hofer et al., quantifications are fairly accurate across the whole 1997). In this example the images were ratioed against specimen area. the Nd elemental map, so the k-factors were also calcuFollowing the method described above we also lated in relation to Nd: kBaNd=0.77, kTiNd=2.33. Using calculated scatter diagrams using the N o m i c ratio these k-factors two atomic ratio images could be com- images. As there are only three elements (besides puted, which are shown in Fig. 4(a,c) together with their oxygen) present in this specimen, the two atomic ratio histograms (Fig. 4(b,d)) showing the grey-level images are fully represented by a tw@dimensional
i
9o 80t
Ti_L23
I =
60
X,.!
o-K
50 ~"~40
Ba-Nd-titanate (bl~Je) Nd-titanate (yelloW)
•~ 20
i
10
Ba-rich phase (red) 0 400
I 500
I 600
I 700
I 800
I 900
I 1000
11 O0
energy [e V] Fig. 3. EEL-spectra from different phases of the Ba--Nd-titanate specimen correspondingto zones in Fig. 2(a].
48
W. Grogger
et al.
Fig. 4. Atomic ratio images and corresponding histograms. (a,c) The atomic ratio images of Ti/Nd and Ba/Nd respectively show true concentration ratios. The three phases can be seen clearly and are not disturbed by diffraction effects. (b,d) The histograms of the atomic ratio images reveal the different phases in the specimen as peaks in the concentration distribution. From (b) a separation of the Ba-rich phase and the Nd titanate is not possible, since both phases contribute to the same peak. However, the scatter diagram in Fig. 5(a) allows the separation. In (d) the Ba-rich phase cannot be seen as a sharp peak but lies above Ba/Nd ~,0.6, because a relatively small number of pixels contribute to this phase with a strongly varying Ba/Nd concentration ratio (Ba/Nd ~ 0.6-1.3). scatter diagram. The scatter d i a g r a m calculated f r o m the T i / N d and B a / N d atomic ratio images is presented in Fig. 5(a). T o illustrate the ' h i s t o g r a m ' nature o f a scatter diagram the one-dimensional histograms o f b o t h images are shown beside the scatter diagram. Scatter diagrams calculated f r o m atomic ratio images contain quantitative information: the axis o f the scatter diagrams are calibrated in atomic concentration ratios. Therefore, the position o f clusters, which can be seen in the scatter diagram, can be related to the composition o f the corresponding phases. In this example three clusters can be f o u n d in the scatter diagram: one cluster in the
upper left corner belonging to the N d - t i t a n a t e phase (yellow), one cluster at higher Ti/Nd ratio belonging to the B a - N d - t i t a n a t e phase (blue) and a rather widespread cluster in the lower half o f the scatter diagram corresponding to the Ba-rich phase (red). F o r the calculation o f a chemical phase m a p one could choose rectangles or ellipses to m a r k the clusters for traceback. Alternatively one can separate the clusters by using lines thus relating all pixels o f the original images to a certain phase. We separated the three clusters using lines (see colour coded m a s k in Fig. 5(b)) to create a phase m a p (Fig. 5(c)). In this m a p each colour represents
Quantitative Chemical Phase Analysis of EFTEM Elemental Maps Using Scatter Diagrams
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
49
TilNd
1
Ba-Nd-Titanate
Ti/Nd = 2.2, Ba/Nd = 0.3 1 Ba-rich phase Ti/Nd = 1.4, Ba/Nd = 1.2 Nd-Titanate Ti/Nd = 1.2, Ba/Nd = 0.0
BalNd
~FI
nm
|
Fig. 5. Calculation of a chemical phase map using the scatter diagram technique. (a) The scatter diagram was calculated from the two atomic ratio images shown in Fig. 4(a,c). The clusters correspond to the phases in the specimen, which can be sel~arated by drawing geometrical objects such as lines. The axes are directly calibrated in concentration ratios. (b) Using the lines drawn in (a), a mask for traceback (Bright and Newbury, 1991) was generated and colour coded. (c) Using the mask shown in (b), a traceback was calculated leading to this chemical phase map. The different phases were assigned the same colours as used in (b). In this image only information about the chemical composition and the belonging to a certain phase is visualized: thickness and ~tiffraction contrasts are completely removed. The legend besides (a) shows the three phases and the mean concentration ratios for Ti/Nd and Ba/Nd.
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W. Grogger et al.
a chemical phase with certain composition values: The Ba-Nd-titanate is coloured in blue, the Nd-titanate is shown in yellow and the amorphous Ba-rich phase is coloured red. The mean composition values (concentration ratios) are listed at the right side of the scatter diagram in Fig. 5(a). A difficulty in interpretation of chemical phase maps derived from scatter diagrams lies in relating an area in the scatter diagram to the corresponding area in the original image in the most objective way possible. One could have set the lines in Fig. 5(a) a bit more to the right or left with the same justification. The resulting phase map would not differ a lot, but pixels lying for example at grain boundaries could change their phase. This gives rise to the request for more objective methods including detailed statistical analysis (e.g. Beckers et al., 1993). One possibility is the application of an automated classification procedure, where the affiliation of a cluster to a phase can be determined by the computer. Unfortunately, EFTEM elemental maps and atomic ratio images are noisy and, as described above, the clusters are not well separated. This makes it difficult for the algorithm to establish an unambitious classification. In most cases user knowledge about the specimen (e.g. from EEL- or EDX-spectra) is needed in order to compute a realistic chemical phase map.
CONCLUSION The aim of this work was to demonstrate the application of scatter diagrams in order to yield quantitative chemical phase maps. Since in many cases more than two elements are present in a specimen the spatial relationships between elemental maps are important for image interpretation. Scatter diagrams are easily applicable and well suited to visualizing this spatial relationship in form of chemical phase maps The scatter diagram approach offers advantages over the simple calculation of RGB images in terms of easier image interpretation and fully quantitative information. Additionally in case of EFTEM elemental maps a manual cluster separation seems to be more reliable than an automatic classification procedure. This is because EFTEM elemental maps are rather noisy and in many cases the three-dimensional nature of each TEM specimen leads to continuous transitions from one cluster to another. Both effects broaden the clusters in the scatter diagram, so subjective criteria have to applied in separating clusters (i.e. selecting phases). Scatter diagram analysis works best on 'simple' specimens exhibiting no concentration gradients. However, the method can also divide concentration gradients into different regions each with a certain concentration range. If quantitative images were used for scatter diagram analysis the resulting chemical phase maps would be also fully quantitative. Therefore we calculated atomic ratio images, which are suitable for quantification of EFTEM elemental maps of crystalline materials, because thick-
ness variation and diffraction effects cancel. Using atomic ratio images scatter diagram analysis produces a chemical phase map, which yields information only about chemical composition (e.g. no diffraction and thickness variation effects) and shows directly the composition and phase distribution of the specimen within a certain area. Acknowledgements--We would like to thank Dr. Otto Fruwirth, Institut f/ir Chemische Technologie Anorganischer Stoffe, TU Graz for supplying and Dr. Peter Warbichler, FELMI, for preparing the Ba-Nd-titanate specimen and we gratefully acknowledge financial support by the Forschungsf6rderungsfonds fiir die Gewerbliche Wirtschaft, Vienna, Austria, and by the Steierm/irkische Landesregierung, Graz, Austria.
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Quantitative Chemical Phase Analysis of EFTEM Elemental Maps Using Scatter Diagrams Hofer, F. and Warbichler, P., 1988. Anwendung der Elektronenenergieverlustspektroskopie (EELS) bei der Mikrobereichsanalyse heterogen aufgebauter Werkstoffe. Prakt. Met., 25, 82-91. Hofer, F. and Warbichler, P., 1996. Improved imaging of secondary phases in solids by energy-filtering TEM. Ultramicroscopy, 63, 21 25. Hofer, F., Warbichler, P. and Grogger, W., 1995a. Imaging of nanometre sized precipitates in solids by electron spectroscopic imaging. Ultramicroscopy, 59, 15-31. Hofer, F., Warbichler, P., Grogger, W. and Lang, O., 1995b. On the Application of Energy Filtering TEM in Materials Science: I. Precipitates in a Ni/Cr-alloy. Micron, 26, 377 390. Johnson, D. E., 1979. Energy-loss spectrometry for biological research. In Introduction to Analytical Electron Microseopy, pp. 245 258. Plenum Press, New York. Kothleitner, G., 1996. Beitr~ige zur quantitativen Nanobereichsanalytik mittels Elektronenenergieverlustspektroskopie und Energiefilterung im Transmissionselektronenmikroskop. Ph.D. Thesis, TU Graz, Graz, Austria. Kothleitner, G. and Hofer, F., 1996. Optimization of the signal to noise ratio with respect to ionization edge types in EFTEM elemental maps. In llth Proc. Eur. Congr. Electron Microscopy Dublin (in press?). Krahl, D., 1990. Abbildende Energiefilterung in der Materialkunde. Mater. Wiss. Werkst. Tech., 21, 84~90. Krivanek, O. L., Gubbens, A. L. and Dellby, N., 1991. Developments in EELS instrumentation for spectroscopy and imaging. Microsc. Microanal. Mierostruct., 2, 315-332. Krivanek, O. L., Gubbens, A. J., Dellby, N. and Mayer, C. E., 1992. Design and first application of a post-column imaging filter. Microsc. Microanal. Microstruct.. 3, 187 199.
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Krivanek, O. L., Gubbens, A. L., Kundmann, M. K. and Carpenter, G. C., 1993. Elemental mapping with an energy selecting imaging filter. In Proc. 51st EMSA Meeting, eds G. W. Bailey and C. L. Rieder, pp. 586-587. San Francisco Press, San Francisco. Latkoczy, C., 1994. Klassifizierung von multivariaten Sekund/irionenmassenspektrometrie (SIMS) Bildern zur chemischen Phasenbestimmung. Dipl. Thesis, TU Vienna, Vienna, AuStria. Leapman, R. D., 1986. Quantitative electron energy loss spectroscopy and elemental mapping in biology. In Microbeami Analysis, eds A. D. Romig and W. F. Chambers, pp. 187 191i San Francisco Press, San Francisco. Leapman, R. D. and Hunt, J. A., 1992. Compositiorlal imaging with electron energy-loss spectrometry. In Micros~'opy: The Key Research Tool, eds C. E. Lyman, L. D. Peachey afld R. M. Fisher, pp. 3949. EMSA, Woods Hole. Mayer, J., Berger, A. and Kohl, H., 1994. Electr6n spectroscopic imaging and its application to thin film analysis. ~n Proc. 13th Int. Congress Electron Microscopy, Paris, Vol. 1, pp. 615 618. Prutton, M., El Gomati, M. M. and Kenny, P. G., 1990. Scatter diagrams and hotelling transforms: application to surface analytical microscopy. J. Electron. Spectrose. Re,at. Phenom., 52, 197 219. Reimer, L., Fromm, I., Milk, C. and Rennekamp, R4., 1992. Energyfiltering transmission electron microscopy in materials science. Micros~. Microanal. Microstruet., 3, 14t 157. Schattschneider, P., Nelhiebk M., Schenner, M., ~rogger, W. and Hofer, F., 1996. Diffraction effects in inner-shell ionization edges. J. Microscopy, 183, 18-26. Schenner, M., Nelhiebl, M. and Schattschneider, P., i996. Diffraction effects in electron spectroscopic imaging. UltrOmicroscop),. 65, 95 99.
Micron Vol. 29, No. 1. pp. 43 51, 1998 ! 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0968M328/98 $19.00+0.00
Quantitative Chemical Phase Analysis of EFTEM Elemental Maps Using Scatter Diagrams WERNER GROGGER,* F E R D I N A N D HOFER and GERALD KOTHLEITNER+ Forschungsinstitut J~ir Elektronenmikroskopie, Technische Universitiit Gra:. Steyrergasse 17. A-8010. Gra:. Austria (Received 4 May 1997; accepted 16 September 1997)
Abstract--Energy-filtered transmission electron microscope (EFTEM) images can yield elemental maps of very high lateral resolution (1 2 nm) in a short time (typically less than 3 min). Additionally, correlation techniques such as scatter diagrams yield information about the intensity relationships between the various elemental maps, thus leading to the calculation of chemi)al phase maps. The application of such techniques reduces the amount of data (i.e. number of images) by compressing information of different images into only a few. This makes interpretation a lot easier and clearer since information in chemical phase maps is restricted to the chemical composition of the specimen. In this work we used a Gatan Imaging Filter (GIF) to acquire! EFTEM images of a Ba-Nd-titanate specimen. The scatter diagram technique together with quantification procedures was then ~pplied to these images in order to show the distribution of chemical phases within the specimen. First, we quantified the etemer~tal maps using atomic ratio images. Then we applied the scatter diagram technique on the atomic ratio images and calculated chemik:al phase maps. ,~ 1998 Elsevier Science Ltd. All rights reserved
Key words: energy-filtering TEM, quantitative elemental maps, phase imaging, scatter diagram, analytical electron microscopE.
1995a), the two methods work in two different ways: The three window technique yields true elemental maps which can be used directly for quantification. However, when investigating crystalline specimens diffraction effects may disturb the elemental images. On the other hand, jump ratio images (two window technique) suppress diffraction effects very well, although they are susceptible to thickness variation effects! Diffraction effects in crystalline materials can be furlher reduced by recording jump ratio images under rocking beam illumination (Hofer and Warbichler, 1996)i The result of this first step of image processing is a two-dimensional distribution of an element. If the elemental map has been recorded by using the three window technique this image can be quantified using different approaches. An absolute quantification can be performed by dividing the net intensity elemental map by a zero loss image and multiplying the result by the appropriate ionization cross section (e.g. Leapman, 1986). Alternatively a relative quantification can be i performed by dividing two elemental maps and multiplying by the appropriate k-factor (e.g. Bonnet et al., 1988). This latter approach results in an iatomic ratio image giving concentration ratios. This iprocedure is then extended to more elements to get information about the complete chemistry of the specimen (Hofer et al., 1997). Often the procedure stops at this point by making a collage of all important elemental distribution images. But what we consider even more important is to show the spatial relationship between several elemental distribution maps, and not leave it to the viewer to combine the images and detect whether or not two elements are situated together. To understand the
INTRODUCTION Energy-filtering transmission electron microscopy (EFTEM) is a well established tool for imaging elemental distributions complementing standard analytical techniques such as energy-dispersive X-ray spectrometry (EDXS) or electron energy-loss spectrometry (EELS) (Leapman and Hunt, 1992; Krahl, 1990; Mayer et al., 1994; Hofer et al., 1995a; Reimer et al., 1992)., An energy-filtered image whether centred around the zero-loss peak, a plasmon peak, or somewhere else, contains information about the specimen (e.g. elemental composition, thickness). When using EFTEM as an analytical tool, one is interested in the elemental information buried in the energy-filtered image, which is then recorded at the ionization edge of interest. An energy-filtered image, the output of the energy filter, is therefore the basic element in analytical EFTEM work. The energy-filtered image recorded at an ionization edge of interest contains element-specific information, and a non element-specific background. The first step towards an elemental distribution is the separation of all element specific information from the background. Usually this is achieved by applying either the three window (Bonnet et al., 1988; Egerton, 1996) or the two window technique (Krivanek et al., 1993; Johnson, 1979; Hofer et al., 1995a). Both methods extract elemental information from a series of two or three energy-filtered images and suppress non-elemental parts. As it has been described previously (Krivanek et al., 1993; Hofer et al., *Corresponding author. Email: [email protected]. tPresent address: Gatan Inc., Pleasanton, CA 94588, U.S.A. 43
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W. Grogger et aL
elemental composition of the specimen it is necessary to know the correlation of the elemental distributions. Several methods have been proposed for visualizing the spatial relationship of some images; two of them will be mentioned in the following, as they are rather easy to apply. Almost every image processing software offers the possibility to combine two or three images to form a colour image (RGB image) by assigning each image a colour (red, green, blue). RGB images are computed very easily, however they are limited to three elements. They look beautiful, but are sometimes difficult to interpret, because of the occurrence of mixed colours (Fig. 2(b); Hofer et al., 1995b). Alternatively, correlation analysis can be applied using scatter diagrams (Bright et al., 1988; Bright and Newbury, 1991; Bright and Marinenko, 1992). Correlation techniques are well known from other disciplines (e.g. E1 Gomati et al., 1987; Prutton et al., 1990; Browning, 1985; Latkoczy, 1994). Scatter diagrams are easily made and combined with other statistical methods such as principal component analysis and classification procedures. In principle, the number of elements used for the computation of scatter diagrams is not limited, however simple visualization is possible only in two or three dimensions, and in practical work we restrict scatter diagram analysis to two dimensions. Two dimensional scatter diagrams are not really limited to two elements. Several combinations of two elements can be used to compute scatter diagrams, from which the most suitable are selected. The aim of any method visualizing the spatial relationship between several elemental distribution maps is to show the distribution of the chemical phases in a chemical phase map. In this context specimens can be divided into two classes: 'simple' and 'complicated'. 'Simple' specimens consist of several locally well separated phases, each with a defined chemical composition. An RGB image of a 'simple' specimen can be a chemical phase map with a different colour for each phase, but with no quantitative information. The scatter diagram approach can yield both: a chemical phase map and full information about the chemical composition of each phase. On the other hand 'complicated' specimens show significant concentration gradients, which appear as smooth colour transitions in an RGB image. Scatter diagrams can be combined with quantitative information. Assigning different composition values of the gradient to a 'phase' a chemical phase map can be built, with composition ranges supplied for each part of the gradient (Hofer et al., 1997). Strictly speaking every real TEM specimen is a 'complicated' specimen because of its three dimensional nature: It shows 'gradients' due to inclined interfaces between different phases which cannot be discriminated from real concentration gradients. Fortunately, in many cases this effect is negligible and many TEM specimens can be treated as 'simple' specimens exhibiting no concentration gradients.
CALCULATION OF SCATTER DIAGRAMS AND TRACEBACKS Scatter diagrams can be considered as two dimensional histograms. The principles of the calculation are shown in Fig. 1. Every pixel (x,y) in image A is associated with the corresponding pixel in image B. The grey-levels a(x,y) and b(x,y) are then used as coordinates of the scatter diagram, where they are accumulated at (a,b). The scatter diagram usually consists of a square pixel array (image), where the abscissa corresponds to the grey-levels of image A and the ordinate corresponds to the grey-levels of image B. The grey-levels on their part may correspond to elemental concentrations of elements A and B respectively. When there is a limited number of chemical phases in the specimen, the individual dots in the scatter diagram form clusters corresponding to these phases. After calculation of a scatter diagram, the clusters can be marked digitally and traced back in order to find the pixels (area) in the original images which contributed to the clusters. If the separation of the clusters in the scatter diagram is well done, this procedure creates a map showing some phases of the specimen. Each phase is usually represented by a colour, since it is easier to distinguish colours than grey-levels. In a scatter diagram 'simple' specimens are characterized by well separated clusters. If the right combination of elemental distribution images is chosen, the clusters will not overlap and there will be only few dots lying in between the clusters. Concentration gradients will appear as significant spreading of clusters in one (or both) directions.
EXPERIMENTAL
This investigation was performed on a Philips CM20! STEM operated at 200kV (LaB 6 cathode). The instrument is equipped with a Gatan Imaging Filter (GIF) (Krivanek et al., 1991; Krivanek et al., 1992; Gubbens and Krivanek, 1993). EFTEM images and EEL-spectra were recorded with the slow-scan CCD integrated in the GIF (YAG scintillator, 1024 × 1024 pixel array). All energy-filtered images were recorded using a binning of 2 × 2 giving 512 x 512 images, for reasons of sensitivity. For the acquisition of the bright field image all 1024 x 1024 pixels were used. Since the focus for an energy-filtered image differs significantly from that of the elastic image (Berger et al., 1994; Berger and Kohl, 1993), we adjusted the focus for energy-filtered images at an energy loss of about 150 eV. The Ba-Nd-titanate specimen was not sensitive to radiation damage so we could focus the TEM spot onto the region of interest yielding approximately 15 AJcm2. Images (and spectra) were recorded with Gatan's DigitalMicrograph running on a Macintosh Quadra 840AV. All images and spectra were corrected for
Quantitative Chemical Phase Analysis of EFTEM Elemental Maps Using Scatter Diagrams 82
118
45
element A -36O 0 |~ ,
0 ,
1080 I1~ 614
1057
DO0
~ element B Fig. 1. Principles of scatter diagram calculation (two-dimensional histogram). The grey-levels of the pixels (x,y) in images A and B are used as coordinates of the scatter diagram, where they are accumulated. i
dark current and gain variation, however, they were not corrected for the blurring caused by the pointspread function of the detector (De Ruijter, 1995). Drift between successive images was automatically corrected using a cross-correlation algorithm (DigitalMicrograph). In order to enable a quantification of the crystalline specimen, elemental maps were recorded under identical electron optical conditions, i.e. the beam convergence was kept constant for the complete energy-filtered series. A changing of beam convergence would cause a considerable variation of diffraction features in the energyfiltered images and also in the corresponding elemental maps. We calculated k-factors for quantification using experimental EEL-spectra and the individual acquisition parameters. Further image processing and the calculation of scatter diagrams was performed within DigitalMicrograph. It is rather easy to implement the computation of a two-dimensional scatter diagram within DigitalMicrograph using its script language. We use a set of scripts for the calculation, annotation, traceback .... of scatter diagrams. These scripts have been written specific to our needs and are available on request. The specimen investigated was a Ba-Nd titanate ceramics prepared following the standard TEM preparation techniques with final low angle ion milling (Aldrian et al., 1996).
PRACTICAL APPLICATION OF SCATTER DIAGRAMS
i [
In order to exemplify the methods described above, a typical materials science specimen w~ts chosen: a Ba-Nd-titanate ceramics specimen consisting of three well known phases (Hofer and Warbichl~r, 1988). As these phases are 'well separated, according to the previous paragraph this specimen can be considered as a 'simple' specimen. Figure 2(a) shows a TEM bright-fiek~ image of a typical region of this specimen already ~xhibiting the three phases: Nd-titanate (needle like ~rystals), BaNd-titanate (round shaped crystals) arid a Ba-rich amorphous phase situated between the c~ystals. From the same specimen area elemental maps were acquired for the elements Ti, Ba and Nd (Fig.12(c-e)). The acquisition parameters are listed in Table l I We adjusted the position of the post-edge window and ~he slit width for optimum signal-to-noise ratio (Koth!eitner, 1996: Kothleitner and Hofer, 1996: Berger and Kohl, 1993). After acquisition the energy filtered [images were automatically cross-correlated to take ~nto account a possible specimen drift between the individual exposures. Elemental maps were calculaied using the three window technique (power law, Eger!on, 1996). The elemental maps were then spatia!ly registered with each other. In principle, this could be done using cross-correlation, but elemental maps seldom
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W. Grogger et al.
Fig. 2. TEM bright field image, RGB image and EFTEM elemental maps of a B~Nd-titanate specimen. (a) TEM bright field image showing the different phases and zones used for EEL spectrometry (colours corresponding to phases in Fig. 5). (b) RGB overlay image constructed of the elemental maps shown in (c-e): Nd (red), Ti (green) and Ba (blue). (c-e) elemental maps of Ti, Ba and Nd respectively (acquisition parameters see Table 1). Yellow: Nd-titanate; blue: Ba-Nd-titanate; red: Ba-rich phase.
show significant image features with equivalent contrast and often the signal-to-noise ratio is too low. We registered the images manually, by assembling a colour
image from image A (red) and image B (green) and shifting one image with respect to the other to reduce the displacement visually.
Quantitative Chemical Phase Analysis of EFTEM Elemental Maps Using Scatter Diagrams Table 1. Acquisition parameters of elemental maps Element- Pre-edge Pre-edge Post-edge Slit width edge 1 (eV) 2 (eV) (eV)~ (eV)~
Exposure time (s)
47
distribution (corresponding to the concentration ratio distribution) of these images. The Ba/Nd atomic ratio image (Fig. 4(c)) already
visualizes the phases present in this specimen area, because the Ba/Nd ratio differs significantly for each Ti L23 394 445 467 20 10 phase (0.014, 0.31 and 1.2 for Nd-titanate, B a - N d Ba-M45 681 763 798 30 30 titanate and the Ba-rich phase respectively). By way of Nd-M45 898 957 1000 40 30 contrast the Nd-titanate and the Ba-rict: phase blur ~These parameters were chosen to get an optimum signal-to-noise together in the Ti/Nd atomic ratio image siJ Lce they have ratio. similar concentration ratios (1.21 and 1.48, respectively). Using both atomic ratio images the three r hases can be Table 2. Phase identificationby grey-levelexamination using elemental detected and their local composition in ter: ns of atomic maps from Fig. 2(c-e) (colours correspondingto Figs 2 and 5) concentration ratios can be simply read from the computer screen by moving the cursor acro~ s the images. Ti Ba Nd elemental elemental elemental Two main problems have to be taken nto account, map map map Phase when mapping the chemical composition ~f crystalline Bright Dark Bright Nd-titanate Yellow TEM specimens: Thickness variations ai d diffraction Bright Grey Bright Ba Nd-titanate Blue effects (Schenner et al., 1996; SchattschtLeider et al., Dark Bright Dark Ba-rich phase Red 1996) may strongly influence the intendties in the elemental maps thus leading to misinterpIetable image features. Therefore we wish to suppress these effects as From the comparison of the elemental maps in far as possible. Fig. 2(c-e) three phases can be clearly distinguished (see The atomic ratio images are advantageous for the Table 2). This is well confirmed by EEL-spectra from quantification of crystalline materials, because the distinct specimen areas (Fig. 3; compare to Fig. 2(a)). diffraction and thickness variation effects cancel (comEach phase is represented by a certain grey-level combi- pare to quantitative EEL-spectrometry: B(,urdillon and nation of the three elemental maps. Stobbs, 1985; Hofer and Golob, 1988). This can be In order to quantify the elemental maps atomic ratio clearly seen by comparing the elemental rnaps in Fig. 2 images were calculated by simply dividing two images with the atomic ratio images (Fig. 4). ~lthough the followed by multiplying by the appropriate k-factor. thickness variations are rather strong and ~ome crystals These k-factors, suitable for a certain slit width, were are strongly diffracting the beam (see, e.g. Ti map), the calculated from EEL-spectra (Hofer, 1991; Hofer et al., quantifications are fairly accurate across the whole 1997). In this example the images were ratioed against specimen area. the Nd elemental map, so the k-factors were also calcuFollowing the method described above we also lated in relation to Nd: kBaNd=0.77, kTiNd=2.33. Using calculated scatter diagrams using the N o m i c ratio these k-factors two atomic ratio images could be com- images. As there are only three elements (besides puted, which are shown in Fig. 4(a,c) together with their oxygen) present in this specimen, the two atomic ratio histograms (Fig. 4(b,d)) showing the grey-level images are fully represented by a tw@dimensional
i
9o 80t
Ti_L23
I =
60
X,.!
o-K
50 ~"~40
Ba-Nd-titanate (bl~Je) Nd-titanate (yelloW)
•~ 20
i
10
Ba-rich phase (red) 0 400
I 500
I 600
I 700
I 800
I 900
I 1000
11 O0
energy [e V] Fig. 3. EEL-spectra from different phases of the Ba--Nd-titanate specimen correspondingto zones in Fig. 2(a].
48
W. Grogger
et al.
Fig. 4. Atomic ratio images and corresponding histograms. (a,c) The atomic ratio images of Ti/Nd and Ba/Nd respectively show true concentration ratios. The three phases can be seen clearly and are not disturbed by diffraction effects. (b,d) The histograms of the atomic ratio images reveal the different phases in the specimen as peaks in the concentration distribution. From (b) a separation of the Ba-rich phase and the Nd titanate is not possible, since both phases contribute to the same peak. However, the scatter diagram in Fig. 5(a) allows the separation. In (d) the Ba-rich phase cannot be seen as a sharp peak but lies above Ba/Nd ~,0.6, because a relatively small number of pixels contribute to this phase with a strongly varying Ba/Nd concentration ratio (Ba/Nd ~ 0.6-1.3). scatter diagram. The scatter d i a g r a m calculated f r o m the T i / N d and B a / N d atomic ratio images is presented in Fig. 5(a). T o illustrate the ' h i s t o g r a m ' nature o f a scatter diagram the one-dimensional histograms o f b o t h images are shown beside the scatter diagram. Scatter diagrams calculated f r o m atomic ratio images contain quantitative information: the axis o f the scatter diagrams are calibrated in atomic concentration ratios. Therefore, the position o f clusters, which can be seen in the scatter diagram, can be related to the composition o f the corresponding phases. In this example three clusters can be f o u n d in the scatter diagram: one cluster in the
upper left corner belonging to the N d - t i t a n a t e phase (yellow), one cluster at higher Ti/Nd ratio belonging to the B a - N d - t i t a n a t e phase (blue) and a rather widespread cluster in the lower half o f the scatter diagram corresponding to the Ba-rich phase (red). F o r the calculation o f a chemical phase m a p one could choose rectangles or ellipses to m a r k the clusters for traceback. Alternatively one can separate the clusters by using lines thus relating all pixels o f the original images to a certain phase. We separated the three clusters using lines (see colour coded m a s k in Fig. 5(b)) to create a phase m a p (Fig. 5(c)). In this m a p each colour represents
Quantitative Chemical Phase Analysis of EFTEM Elemental Maps Using Scatter Diagrams
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
49
TilNd
1
Ba-Nd-Titanate
Ti/Nd = 2.2, Ba/Nd = 0.3 1 Ba-rich phase Ti/Nd = 1.4, Ba/Nd = 1.2 Nd-Titanate Ti/Nd = 1.2, Ba/Nd = 0.0
BalNd
~FI
nm
|
Fig. 5. Calculation of a chemical phase map using the scatter diagram technique. (a) The scatter diagram was calculated from the two atomic ratio images shown in Fig. 4(a,c). The clusters correspond to the phases in the specimen, which can be sel~arated by drawing geometrical objects such as lines. The axes are directly calibrated in concentration ratios. (b) Using the lines drawn in (a), a mask for traceback (Bright and Newbury, 1991) was generated and colour coded. (c) Using the mask shown in (b), a traceback was calculated leading to this chemical phase map. The different phases were assigned the same colours as used in (b). In this image only information about the chemical composition and the belonging to a certain phase is visualized: thickness and ~tiffraction contrasts are completely removed. The legend besides (a) shows the three phases and the mean concentration ratios for Ti/Nd and Ba/Nd.
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W. Grogger et al.
a chemical phase with certain composition values: The Ba-Nd-titanate is coloured in blue, the Nd-titanate is shown in yellow and the amorphous Ba-rich phase is coloured red. The mean composition values (concentration ratios) are listed at the right side of the scatter diagram in Fig. 5(a). A difficulty in interpretation of chemical phase maps derived from scatter diagrams lies in relating an area in the scatter diagram to the corresponding area in the original image in the most objective way possible. One could have set the lines in Fig. 5(a) a bit more to the right or left with the same justification. The resulting phase map would not differ a lot, but pixels lying for example at grain boundaries could change their phase. This gives rise to the request for more objective methods including detailed statistical analysis (e.g. Beckers et al., 1993). One possibility is the application of an automated classification procedure, where the affiliation of a cluster to a phase can be determined by the computer. Unfortunately, EFTEM elemental maps and atomic ratio images are noisy and, as described above, the clusters are not well separated. This makes it difficult for the algorithm to establish an unambitious classification. In most cases user knowledge about the specimen (e.g. from EEL- or EDX-spectra) is needed in order to compute a realistic chemical phase map.
CONCLUSION The aim of this work was to demonstrate the application of scatter diagrams in order to yield quantitative chemical phase maps. Since in many cases more than two elements are present in a specimen the spatial relationships between elemental maps are important for image interpretation. Scatter diagrams are easily applicable and well suited to visualizing this spatial relationship in form of chemical phase maps The scatter diagram approach offers advantages over the simple calculation of RGB images in terms of easier image interpretation and fully quantitative information. Additionally in case of EFTEM elemental maps a manual cluster separation seems to be more reliable than an automatic classification procedure. This is because EFTEM elemental maps are rather noisy and in many cases the three-dimensional nature of each TEM specimen leads to continuous transitions from one cluster to another. Both effects broaden the clusters in the scatter diagram, so subjective criteria have to applied in separating clusters (i.e. selecting phases). Scatter diagram analysis works best on 'simple' specimens exhibiting no concentration gradients. However, the method can also divide concentration gradients into different regions each with a certain concentration range. If quantitative images were used for scatter diagram analysis the resulting chemical phase maps would be also fully quantitative. Therefore we calculated atomic ratio images, which are suitable for quantification of EFTEM elemental maps of crystalline materials, because thick-
ness variation and diffraction effects cancel. Using atomic ratio images scatter diagram analysis produces a chemical phase map, which yields information only about chemical composition (e.g. no diffraction and thickness variation effects) and shows directly the composition and phase distribution of the specimen within a certain area. Acknowledgements--We would like to thank Dr. Otto Fruwirth, Institut f/ir Chemische Technologie Anorganischer Stoffe, TU Graz for supplying and Dr. Peter Warbichler, FELMI, for preparing the Ba-Nd-titanate specimen and we gratefully acknowledge financial support by the Forschungsf6rderungsfonds fiir die Gewerbliche Wirtschaft, Vienna, Austria, and by the Steierm/irkische Landesregierung, Graz, Austria.
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