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Application of image processing techniques for analysis of nano- and micro-spaces in carbon materials
Synthetic Metals 125 (2002) 223±230
Application of image processing techniques for analysis of nano- and micro-spaces in carbon materials K. Oshidaa,*, T. Nakazawaa, T. Miyazakia, M. Endob a
Nagano National College of Technology, 716 Tokuma, Nagano 381-8550, Japan b Faculty of Engineering, Shinshyu University, Nagano 380-8553, Japan
Received 7 May 2001; received in revised form 2 June 2001; accepted 9 July 2001
Abstract Transmission electron microscopy (TEM) is one of the most useful methods to clarify the structure in carbon materials. We developed quantitative analysis methods for the texture and structure of carbon materials containing the micro- and nano-spaces by using electron microscopy combined with image processing technique. The relations between phase transfer functions and TEM images of amorphous carbon ®lms which consist of random arrangement of carbon layers were investigated using image processing. The similar patterns as the laser diffraction are obtained by the two-dimensional (2D) fast Fourier transform (FFT) of the digitized TEM images. The details of frequency distribution can be analyzed by integration around the central point of the power spectrum images. We applied this new technique to the study of microtexture and structure of graphite intercalation compounds (GICs). As a result of application of the frequency analysis using 2D FFT to the CuCl2-GIC, a characteristic power spectrum pattern called streak, which was similar to the electron diffraction pattern, was obtained. The images corresponding to the speci®c frequencies were reconstructed by 2D inverse FFT (IFFT). The stage structure of CuCl2-GICs was discussed by using this technique. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Amorphous carbon ®lms; Graphite intercalation compounds; Transmission electron microscopy; Image analysis; Fast Fourier transform
1. Introduction Many kinds of carbon-based materials have been contributing to develop the current engineering technology, which have been reinforced by analysis techniques of their structures. X-ray diffraction, various spectroscopy and transport measurements have been widely used as quantitative techniques for analyzing carbon-based materials [1]. However, it is dif®cult to attain results with atomic resolution. On the other hand, whole and partial images of materials can be observed by means of transmission electron microscopy (TEM), though it is not quantitative by itself. In this study, we tried to analyze microtexture and structure of carbon materials, using TEM combined with image analysis. Contrast in TEM image mainly consists of two elements, extinction contrast and phase difference one. In high resolution region, the phase difference contrast is more effective. Therefore, arbitrary magni®cation image is obtained by modulating acceleration voltage and defocus value Df on real high resolution TEM observation. We report here the investigation of TEM image of amorphous carbon * Corresponding author. Tel.: 81-26-295-7092; fax: 81-26-295-4950. E-mail address: [email protected] (K. Oshida).
®lm, which does not have any particular oriented structure, under the different conditions of Df. The results of characterization of the materials structure by using image analysis of the TEM image are also reported. A new approach to the study of microtexture and structure of acceptor-type graphite intercalation compounds (GICs) with CuCl2 was shown using the technique of high resolution TEM combined with image analysis. We used a twodimensional (2D) fast Fourier transform (FFT) for our frequency analysis. From the analysis of the power spectrum obtained by the 2D FFT, we extracted some speci®c frequencies. The power spectrum was then analyzed by 2D inverse FFT (IFFT), and real space image associated with the speci®c frequencies was reproduced. The relationship between the electron diffraction streak patterns and the microstructure of the GICs was further analyzed. 2. Relation between phase transfer function and TEM image of amorphous carbon films 2.1. Experimental We surveyed quantitative analysis method for random structure by using amorphous carbon ®lm. Amorphous
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carbon ®lms have random structure without any orientation, of which structure studies by using TEM were reported [2± 4]. In general, quantitative analysis of the TEM image is dif®cult and therefore the detailed structure of amorphous carbon ®lms has not been clari®ed quantitatively yet. Amorphous carbon ®lm is, however, suitable for inspection of TEM observation on different conditions of Df because of following reasons. It is very thin (several tens of nanometers) and can be easily transmitted by electron beam, and the TEM image of amorphous carbon ®lm can be formatted at arbitrary magni®cation because it has non-oriented and random structure. Amorphous carbon ®lm was observed by TEM under 100 kV acceleration. Optical diffraction patterns were obtained by exposing laser beam on the resultant TEM image negative ®lms. For the digital analysis, the TEM images were converted to digital data. The resolution of the digitized image was 512 512 pixels (8 bit depth per pixel), and the area of one pixel corresponded to 0:0867 nm 0:0867 nm. The optical diffraction patterns of the TEM images were compared with power spectra which were obtained by 2D FFT of the digitized TEM images. Furthermore, the power spectra were represented by graphs obtained by integration around their central points [5]. A transfer function of the objective lens of TEM, cos(w), is given by the following equation [6]: " # p 2p 2y4 2p 2y2 cos w cos Cs Df ; (1) 2 l l 4 2 where y is the Bragg angle, Cs the spherical aberration constant of the lens, Df the underfocus value, and l the de Broglie wavelength of the electrons. For obtaining a reliable image, it is necessary to maintain a constant phase shift cos w constant over the region where the scattered beams interfere. For obtaining maximum contrast, it is necessary for w p so that jcos wj 1. The transfer function of TEM under the condition of each Dfs was calculated and the relations with the power spectra were investigated. From the results of the calculation of the power spectra, distribution of frequency under the condition of each Dfs was analyzed [5]. 2.2. Results and discussion TEM images and optical diffraction patterns under the conditions of various Dfs of: (a) 500 nm, (b) 200 nm, (c) 0, (d) 200 nm and (e) 500 nm are shown in Fig. 1. The TEM image shows a rough pattern at Df 500 nm, and the relatively ®ne pattern at Df 200 nm. Under the condition Df 0, contrast of the image is weak and not clear. The images at Df s 500 and 200 nm are similar to that at Df s 500 and 200 nm, respectively. In the TEM image, the area where mass of carbon atoms exists is bright and where nothing exists is dark on the condition that Df is plus, and vice versa when Df is minus. The parts
Fig. 1. TEM images of the amorphous carbon film for different defocus values Dfs: (a) 500 nm, (b) 200 nm, (c) 0 nm, (d) 200 nm and (e) 500 nm. The insets on the right are the optical diffraction patterns of each TEM image.
corresponding to bulk of carbon are generally observed as dark area by the selection of minus Df. But quantitative evaluation of the sample structure is still dif®cult with the knowledge above, because the amorphous carbon ®lm has a quite random structure. Since each optical diffraction pattern of corresponding TEM image is concentric, the texture of the sample has no orientation on the surface. Three or fourfold thin rings appear around the center spot in the diffraction pattern at Df 500 nm. A wide ring is seen around the center at Df 200 nm, as observed at Df 200 nm. At the condition of Df 0, the diffraction pattern appears only in the central area. These optical diffraction patterns are closely correlated to the transfer function as will be discussed later. Since the TEM images at Df s 500 and 200 nm are similar to that at Df s 500 and 200 nm, respectively, as
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Fig. 2. Digitized TEM images of the amorphous carbon film and the power spectra obtained from them by FFT operation. The defocus values Dfs are: (a) 500 nm, (b) 200 nm and (c) 0 nm.
mentioned above, we analyzed the TEM images at Df s 500, 200 and 0 nm by image processing. Digitized images under the different condition of Dfs, which were obtained from the TEM images of Fig. 1(a)±(c), and their power spectra obtained by 2D FFT are shown in Fig. 2(a)±(c), respectively. The central area of the power spectra corresponds to low frequency, and the frequencies become higher as the location moves further from the center. Consequently, both the power spectrum and the optical diffraction pattern appear as coaxial circles and similar to each other. The advantage of power spectrum is, however, the adjustability of brightness in the image. The optical diffraction patterns of which intensity is wholly weak, as shown in Fig. 1(a) and (c), are usually dif®cult to be clear. But the change of power spectrum with Df is shown clearly in Fig. 2 of which brightness is regulated. The transfer functions obtained by Eq. (1) at Df s 500, 200 and 0 nm are shown in Fig. 3. The plus peaks of the transfer function correspond to the bright rings which appear in the optical diffraction pattern and in the power spectrum. In order to discuss the relation between the power spectrum and transfer function, the power spectrum in Fig. 2 was represented as a graph obtained by integration around its central point. Perpendicular axis in the graphs in Fig. 4 shows the spectrum intensity in logarithmic scale. The peaks and downs of wave at Df 500 nm in Fig. 4(a) correspond
Fig. 3. Phase transfer functions for different defocus values Dfs: (a) 500 nm, (b) 200 nm and (c) 0 nm.
to the peaks and downs of the transfer function in Fig. 3(a), respectively. The same relation can be seen at Df 200 nm in Fig. 4(b) and Fig. 3(b). In order to avoid the reverse of contrast and to get wellcontrasted TEM images, it is better to put an aperture which contains one peak of transfer function. As seen in the range from 1 to 5 nm in Figs. 3(b) and 4(b) at Df 200 nm, the brightness of image is not reversed because the transfer function has one minus peak in this range. At Df 0, it is understood that the power spectrum of Fig. 4(c) scarcely contains frequency components, and the image is not formed. The relation between power spectrum and transfer function was discussed so far. Since the TEM image is formed in the range of space frequency where the peak of transfer function exists, it is thought that the image signal is contained in each peaks of the power spectrum of logarithm indication. In order to show the peaks clearly, vertical axis of the power spectrum of Fig. 4(b) was replotted in Fig. 5 with linear scale. The power spectrum of Df 200 nm has many peaks of frequency distribution in wide range as shown in Fig. 5. These peaks correspond to the cycles of brightness
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is carried out on them, the real space images corresponding to the selected space frequencies can be obtained and it is possible to analyze in detail how the TEM images change corresponding to the speci®c frequency range [5]. 3. Microtexture and structure of graphite intercalation compounds studied by TEM and image analysis 3.1. Materials and their TEM images for the study
Fig. 4. The integration of the power spectra with different defocus values Dfs around the central points.
which appear frequently in the TEM image and show the characteristics of structure of the amorphous carbon ®lm sample. The highest peak in power spectrum, which shows the dominant repetition intervals of bright and dark regions in the TEM image, appears at 1.9 nm of space length. This shows that the sample has certain repeating structure with 1.9 nm intervals extending over a large area. Furthermore, if the peak frequency components are extracted from the results of 2D FFT operation and then 2D IFFT operation
Fig. 5. Replot of Fig. 4(b) with linear scale vertical axis. The peaks corresponding to the real space image are shown clearly.
In the present study, we take an acceptor-type GICs with CuCl2 intercalates as a target material, because they are usually well-staged. Vapor grown carbon ®bers (VGCFs) were used as pristine materials for GICs. Because of their small diameter (about 1 mm), VGCFs served as excellent host materials for the analysis of structural change induced by intercalation. VGCFs have been synthesized by the thermal decomposition of benzene [7]. When heat-treated to temperatures as high as 28008C, the VGCFs exhibit highly crystalline characteristics, which consist of concentrically stacked layers of graphite planes around the ®ber axis, similar to the annular rings of a tree [8]. Acceptor-type CuCl2-GICs were synthesized by using VGCFs heat-treated at temperatures around 29008C [9]. The staging of GICs were observed in TEM lattice fringe images of the ®bers. In the TEM image, the 0 0 l lattice planes appeared to be extremely ¯at and the ®bers were known to be well-staged. The electron diffraction pattern of the sample presented a characteristic shape which extends perpendicular to the 0 0 l lattice plane, and was called a ``streak'' or ``spike'' pattern [10]. A 0 0 l lattice fringe image obtained from VGCFs intercalated with CuCl2 (CuCl2-GICs) is shown in Fig. 6, the inset being the selected area electron diffraction (SAD) pattern. A streak pattern which is thought to be strongly related to staging is seen in the diffraction pattern. From spacing of lattice fringe, this GIC is supposed to be composed of regions of graphite stacking, stage-1, stage-2, and higher stage structures. 3.2. Image analysis For convenience to the successive processing, the 0 0 l lattice planes were directed horizontally when the TEM images were converted to the digital data. We carried out the 2D FFT on the digitized TEM images and calculated the 2D power spectrum for analysis of the spatial frequencies of the images. In order to suppress the in¯uence of the peripheral regions of the images on the power spectra, Hamming window was used in operating the 2D FFT. The power spectra were represented by integration along the direction parallel to the 0 0 l lattice planes, for the purpose of analyzing the frequency distribution along the direction perpendicular to the lattice planes [11]. The speci®c frequencies in the integrated power spectrum of CuCl2-GICs were
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Fig. 6. Lattice fringe image of a CuCl2-GIC sample. An electron diffraction pattern of the TEM image is shown in the inset.
3.3. Results and discussion
more disturbed than that of the heat-treated VGCFs, especially along the horizontal axis, i.e., ®ber axis. In addition, there is a cloud of spots located near the center of the power spectrum in Fig. 7(a). The cloud indicates the existence of
3.3.1. Host VGCFs The digitized TEM images of the lattice fringes for asprepared VGCFs and VGCFs heat-treated to 29008C are shown in Fig. 7(a) and (b), respectively, together with power spectra. VGCFs became highly ordered graphite ®bers after heat treatment to 29008C. The improvement in structural perfection of these VGCFs by the heat treatment is evidenced by comparison of these two lattice fringe images. The lattice image of the heat-treated VGCF exhibits long straight 0 0 2 lattice fringes, while those of the as-prepared VGCFs shows short fringes. In the power spectrum of Fig. 7(b), the two bright spots that are symmetrically positioned around the central point correspond to the 0 0 2 lattice planes in the image. This feature of the power spectrum pattern was the same as that of the laser diffraction pattern obtained from the original TEM image. The central point corresponds to the brightness of the image. Since the two 0 0 2 spots and the center spot appear to be sharp, it is found that the 0 0 2 lattice planes are consistently parallel and the interlayer spacing is uniform. The repetition distance of 0 0 2 lattice planes in the heat-treated VGCFs is 0.336 nm [9]. The 0 0 2 spots in the power spectrum of the as-prepared VGCFs are extended, in comparison with that of the heattreated VGCFs, as shown in the inset of Fig. 7(a). The extension of the spots along the horizontal axis indicates the presence of a perturbation in the orientation of 0 0 2 lattice planes, whereas the extension along the vertical axis corresponds to a spread in the interlayer spacings. It is, therefore, indicated that the structure of the as-prepared VGCFs is
Fig. 7. Digitized lattice fringe images for: (a) the as-prepared VGCF sample and (b) the pristine VGCF sample heat treated to 29008C. The corresponding power spectra are shown in the insets.
extracted and real space images were reconstructed by using a 2D IFFT.
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¯uctuation in the magnitude of brightness at long spatial intervals appearing in the image. The distribution range of the spots provides a measure for the region sizes of a group of lattice planes with similar orientation, and for that with the different orientations within the lattice image under analysis. On the other hand, all the lattice planes in Fig. 7(b) have a common direction, and there is no extension of the center spot. The distribution of interlayer spacing obtained by integration along the horizontal axis of the power spectra in Fig. 7(a) and (b) are shown in Fig. 8(a) and (b), respectively. From these integrated power spectra, we can get detailed and quantitative information about the distribution of interlayer spacings. The strong peak, which appears in the range between 0.3 and 0.5 nm in the integrated power spectrum, corresponds to the 0 0 2 lattice planes. By means of the Xray diffraction analysis, the 0 0 2 interlayer spacing (d0 0 2) of as-prepared and 29008C-treated VGCFs were determined as 0.348 and 0.336 nm, respectively, as reported in literature [9]. While the plot for the heat-treated VGCFs shows single peak at 0.336 nm, the peak for the as-prepared VGCFs spreads from 0.34 to 0.40 nm in both sides of the peak position of 0.348 nm. The right-hand side of the spread indicates the partial existence of shorter 0 0 2 interlayer spacing than 0.348 nm. Interlayer spacings wider than 0.348 nm contributes to the left-hand side spread of the peak, which also contains the effect of an inclination of the 0 0 2 lattice planes. Other small peaks, appear between 0.96 and 1.57 nm in Fig. 8(a), are related to the stacking thickness of the 0 0 2 lattice layers. We can derive the number of layers per stacking is about 3±5 from the position of the peaks. We can ®nd three or four layers stack continuously (see Fig. 7(a)), indeed, in the TEM image of the as-prepared VGCFs. 3.3.2. Intercalated VGCFs (GICs) The digitized lattice fringe image for CuCl2-GIC is shown in Fig. 9(a) with the inset indicating its power spectrum
Fig. 8. The distribution of interlayer repeat distances for: (a) the asprepared VGCF sample obtained from the power spectrum of Fig. 7(a) and (b) the pristine VGCF sample heat treated to 29008C obtained from the power spectrum of Fig. 7(b). The values of 0.348 and 0.336 nm are peak tops determined by X-ray diffraction analysis.
obtained by the 2D FFT, and a reconstructed image of CuCl2-GIC, which is mentioned later, is shown in Fig. 9(b). The pattern appearing in the power spectrum in Fig. 9(a) is very similar to the streaking, which is found in the electron diffraction pattern, as shown in Fig. 6. Its characteristic pattern is distributed in a line perpendicular to the original image of 0 0 l lattice planes. The spectrum is very sharp for CuCl2-GICs. This is because the transverse width of the FFT power spectrum pattern is very small, indicating large lateral regions with the same stage.
Fig. 9. (a) Digitized lattice fringe image of a CuCl2-GIC sample. The corresponding power spectrum is shown in the inset, (b) Image of the IFFT for the CuCl2-GIC sample reconstructed from specific frequencies shown in Fig. 10.
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Fig. 10. The distribution of interlayer repeat distances for the CuCl2-GIC sample obtained from the power spectrum of Fig. 9(a).
Fig. 10 shows the distribution of interlayer spacings obtained by integration along the horizontal axis of the power spectrum in Fig. 9(a). Since the spectrum is distributed only in one direction, the 2D power spectrum image can be graphed by integration perpendicular to the distribution of the spectrum, using the same approach as applied to the TEM images of the as-prepared VGCFs (see Figs. 7(a) and 8(a)) and of the heat-treated VGCFs (see Figs. 7(b) and 8(b)). There are many peaks in the integrated power spectrum in Fig. 10 in the region between 0.3 and 4 nm. The large peak at 0.336 nm corresponds to the 0 0 2 graphite lattice planes. Stage-1, stage-2, and higher stage regions as well as graphite stacking appear in Fig. 9(a). We observe a fairly small stage-1 peak around 0.93 nm in Fig. 10. There is another peak between 1.21 and 1.65 nm (the highest point located at 1.396 nm). This peak is thought to be a complex peak which consist of two peaks of a stage-2 component (peak at 1.27 nm) and a stage-3 component (peak at 1.61 nm). A small peak of 0.27 nm in Fig. 10 corresponds to the frequency component which helps to de®ne the shape of the 0 0 2 graphite lattice planes clearly in Fig. 9(a). From this frequency analysis, it is clear that the TEM image for CuCl2-GICs shows the existence of stage-1, stage2, and stage-3 regions, and graphite stacking. However, the presence of the stage-1 region, which is represented by the peak at 0.93 nm, is not as evident in the digitized image shown in Fig. 9(a) as in the Fourier analysis in Fig. 10. There are several unidenti®ed peaks between the graphite and stage-1 peaks which may contribute to the construction of the digitized image. These peaks have the possibility of containing the two kinds of components; one is a fundamental component from which the shape of the wave is formed, and the other is associated with harmonic components. Since the brightness of the TEM image of the CuCl2GICs changes smoothly in the micrographs used (Fig. 6), very low intensity for the harmonic components is expected, except for the harmonic component of the 0 0 2 lattice planes, as mentioned above. Many elemental images that correspond to the each frequency component constitute the TEM image. Some of the elemental images cancel one
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another, which causes dark spaces to appear in the TEM image for the CuCl2 intercalate layers, while some other elemental images reinforce one another, and contribute to construction of the shape of the stage layers. In order to verify the staging of the CuCl2-GICs discussed above, real space images were reconstructed by using the 2D IFFT method. Fig. 9(b) is the image obtained by 2D IFFT reconstruction from the speci®c frequencies corresponding to the interlayer spacings of 0.336 nm (graphite 0 0 2), 0.358, 0.478 and 1.396 nm (corresponds to a complex peak of the stage-2 and stage-3) in Fig. 10. We can see that the peculiar features of the digitized TEM image appear clearly in Fig. 9(b). The layers of Fig. 9(b) appear to be sharper than those in the digitized image (Fig. 9(a)) because the selection of speci®c frequencies acts as a noise reduction operation. If all of the frequencies existing in the digitized image can be identi®ed and selected, a perfect reconstruction of the digitized image can be achieved. Comparing with Fig. 9(a), some lines appear in faint form in the CuCl2 intercalate layers in the reconstructed image (Fig. 9(b)). This is caused by a lack of data when the speci®c frequencies were selected. Fig. 9(a), however, already contains some faint lines where the intercalates exist. These faint features also appear in the original TEM image as a result of the in¯uence of the aperture setting when the TEM image was taken. Therefore, the aperture setting of TEM observation may also act as a frequency selection of the electron diffraction. The image analysis technique of a frequency extract can set the mask patterns, equivalent to the aperture to TEM, in the arbitrary con®guration to a free positions. 4. Conclusions We could obtain a power spectrum image, which is almost the same as optical diffraction pattern of TEM image, by image analysis. The relation between underfocus value Df and the transfer function of TEM image was investigated by integration of the power spectrum around its center. It was shown that the image analysis method was effective for analysis of TEM images. The structural analysis of the carbon materials was investigated by means of the digital image processing of high resolution TEM images. The detailed structure of GIC was revealed through the technique by which rather quanti®ed data was obtained, compared to the conventional methods of the electron diffraction and the laser diffraction. Spatial frequency analysis method according to a 2D FFT was used mainly as the analyzing technique. The characteristic peaks appear in the graph, which made from the power spectrum image obtained by the image processing of the digitized image, were studied quantitatively. The relation between some of the peaks among those and each stage structures of the GICs were discussed. Furthermore, the analytical results were veri®ed by the reconstitution of the real space image using a 2D IFFT technique.
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The target material of CuCl2-GIC was suitable for the discussion on the adequacy of the image processing of TEM image, since this material has complicated but exact stage structures, and therefore the evaluation of analyzed result was considered to be comparatively easy. A great possibility was shown that the detailed material analysis could be performed by the image processing method. The digitized 2D power spectrum image showed a pattern equivalent to the conventional electron diffraction or laser diffraction showing the characteristic feature of a detailed material structure. Especially, the streak pattern which appears as a series of spots in a straight line of the conventional electron diffraction spots can be reproduced in the power spectrum image which was obtained by the image processing of CuCl2-GIC. The frequency extract technique in the image analysis is thought as equivalent to the application of the aperture to TEM observation with the possibility of free mask pattern setting, free positions and arbitrary con®guration. We also expect that this approach is useful for the analysis of the structural characteristics of GICs, as well as the clari®cation of their electrical characteristics. Acknowledgements This work is supported by a grant-in-aid for `Research for the Future' Program No. JSPS-RFTF96R11701 from the
Japan Society for the Promotion of Science. The authors are indebted to them. The authors are indebted to Prof. M.S. Dresselhaus of Massachusetts Institute of Technology, Cambridge, MA 02139, USA for useful discussions and suggestions.
References [1] M.S. Dresselhaus, G. Dresselhaus, K. Sugihara, I.L. Spain, H.A. Goldberg, Graphite Fibers and Filaments, Springer, Berlin, 1988, pp. 35±229. [2] J. Goma, M. Oberlin, Thin Solid Films 65 (1980) 221±232. [3] J.N. Rouzaud, A. Oberlin, C. Beny-Bassez, Thin Solid Films 105 (1983) 75±96. [4] N. Yoshizawa, Y. Yamada, M. Shiraishi, Carbon 31 (1993) 1049± 1055. [5] K. Oshida, K. Kogiso, K. Matsubayashi, K. Takeuchi, S. Kobori, M. Endo, M.S. Dresselhaus, G. Dresselhaus, J. Mater. Res. 10 (1995) 2507±2517. [6] M. Huttepain, A. Oberlin, Carbon 28 (1990) 103±111. [7] M. Endo, Chemtech 18 (1988) 568±576. [8] T. Koyama, M. Endo, Jpn. J. Appl. Phys. 13 (1974) 1175±1176. [9] M. Endo, T.C. Chieu, G. Timp, M.S. Dresselhaus, Synth. Met. 8 (1983) 251±260. [10] P.B. Hirsh, A. Howie, R.B. Ncholson, D.W. Pashley, M.J. Whelan, Electron Microscopy of Thin Crystals, Robert E. Krieger Publishing, Florida, 1977 (Chapter 6). [11] K. Oshida, M. Endo, T. Nakajima, S.L. di Vittorio, M.S. Dresselhaus, G. Dresselhaus, J. Mater. Res. 8 (1993) 512±522.
Application of image processing techniques for analysis of nano- and micro-spaces in carbon materials K. Oshidaa,*, T. Nakazawaa, T. Miyazakia, M. Endob a
Nagano National College of Technology, 716 Tokuma, Nagano 381-8550, Japan b Faculty of Engineering, Shinshyu University, Nagano 380-8553, Japan
Received 7 May 2001; received in revised form 2 June 2001; accepted 9 July 2001
Abstract Transmission electron microscopy (TEM) is one of the most useful methods to clarify the structure in carbon materials. We developed quantitative analysis methods for the texture and structure of carbon materials containing the micro- and nano-spaces by using electron microscopy combined with image processing technique. The relations between phase transfer functions and TEM images of amorphous carbon ®lms which consist of random arrangement of carbon layers were investigated using image processing. The similar patterns as the laser diffraction are obtained by the two-dimensional (2D) fast Fourier transform (FFT) of the digitized TEM images. The details of frequency distribution can be analyzed by integration around the central point of the power spectrum images. We applied this new technique to the study of microtexture and structure of graphite intercalation compounds (GICs). As a result of application of the frequency analysis using 2D FFT to the CuCl2-GIC, a characteristic power spectrum pattern called streak, which was similar to the electron diffraction pattern, was obtained. The images corresponding to the speci®c frequencies were reconstructed by 2D inverse FFT (IFFT). The stage structure of CuCl2-GICs was discussed by using this technique. # 2001 Elsevier Science B.V. All rights reserved. Keywords: Amorphous carbon ®lms; Graphite intercalation compounds; Transmission electron microscopy; Image analysis; Fast Fourier transform
1. Introduction Many kinds of carbon-based materials have been contributing to develop the current engineering technology, which have been reinforced by analysis techniques of their structures. X-ray diffraction, various spectroscopy and transport measurements have been widely used as quantitative techniques for analyzing carbon-based materials [1]. However, it is dif®cult to attain results with atomic resolution. On the other hand, whole and partial images of materials can be observed by means of transmission electron microscopy (TEM), though it is not quantitative by itself. In this study, we tried to analyze microtexture and structure of carbon materials, using TEM combined with image analysis. Contrast in TEM image mainly consists of two elements, extinction contrast and phase difference one. In high resolution region, the phase difference contrast is more effective. Therefore, arbitrary magni®cation image is obtained by modulating acceleration voltage and defocus value Df on real high resolution TEM observation. We report here the investigation of TEM image of amorphous carbon * Corresponding author. Tel.: 81-26-295-7092; fax: 81-26-295-4950. E-mail address: [email protected] (K. Oshida).
®lm, which does not have any particular oriented structure, under the different conditions of Df. The results of characterization of the materials structure by using image analysis of the TEM image are also reported. A new approach to the study of microtexture and structure of acceptor-type graphite intercalation compounds (GICs) with CuCl2 was shown using the technique of high resolution TEM combined with image analysis. We used a twodimensional (2D) fast Fourier transform (FFT) for our frequency analysis. From the analysis of the power spectrum obtained by the 2D FFT, we extracted some speci®c frequencies. The power spectrum was then analyzed by 2D inverse FFT (IFFT), and real space image associated with the speci®c frequencies was reproduced. The relationship between the electron diffraction streak patterns and the microstructure of the GICs was further analyzed. 2. Relation between phase transfer function and TEM image of amorphous carbon films 2.1. Experimental We surveyed quantitative analysis method for random structure by using amorphous carbon ®lm. Amorphous
0379-6779/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 9 - 6 7 7 9 ( 0 1 ) 0 0 5 3 5 - 5
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carbon ®lms have random structure without any orientation, of which structure studies by using TEM were reported [2± 4]. In general, quantitative analysis of the TEM image is dif®cult and therefore the detailed structure of amorphous carbon ®lms has not been clari®ed quantitatively yet. Amorphous carbon ®lm is, however, suitable for inspection of TEM observation on different conditions of Df because of following reasons. It is very thin (several tens of nanometers) and can be easily transmitted by electron beam, and the TEM image of amorphous carbon ®lm can be formatted at arbitrary magni®cation because it has non-oriented and random structure. Amorphous carbon ®lm was observed by TEM under 100 kV acceleration. Optical diffraction patterns were obtained by exposing laser beam on the resultant TEM image negative ®lms. For the digital analysis, the TEM images were converted to digital data. The resolution of the digitized image was 512 512 pixels (8 bit depth per pixel), and the area of one pixel corresponded to 0:0867 nm 0:0867 nm. The optical diffraction patterns of the TEM images were compared with power spectra which were obtained by 2D FFT of the digitized TEM images. Furthermore, the power spectra were represented by graphs obtained by integration around their central points [5]. A transfer function of the objective lens of TEM, cos(w), is given by the following equation [6]: " # p 2p 2y4 2p 2y2 cos w cos Cs Df ; (1) 2 l l 4 2 where y is the Bragg angle, Cs the spherical aberration constant of the lens, Df the underfocus value, and l the de Broglie wavelength of the electrons. For obtaining a reliable image, it is necessary to maintain a constant phase shift cos w constant over the region where the scattered beams interfere. For obtaining maximum contrast, it is necessary for w p so that jcos wj 1. The transfer function of TEM under the condition of each Dfs was calculated and the relations with the power spectra were investigated. From the results of the calculation of the power spectra, distribution of frequency under the condition of each Dfs was analyzed [5]. 2.2. Results and discussion TEM images and optical diffraction patterns under the conditions of various Dfs of: (a) 500 nm, (b) 200 nm, (c) 0, (d) 200 nm and (e) 500 nm are shown in Fig. 1. The TEM image shows a rough pattern at Df 500 nm, and the relatively ®ne pattern at Df 200 nm. Under the condition Df 0, contrast of the image is weak and not clear. The images at Df s 500 and 200 nm are similar to that at Df s 500 and 200 nm, respectively. In the TEM image, the area where mass of carbon atoms exists is bright and where nothing exists is dark on the condition that Df is plus, and vice versa when Df is minus. The parts
Fig. 1. TEM images of the amorphous carbon film for different defocus values Dfs: (a) 500 nm, (b) 200 nm, (c) 0 nm, (d) 200 nm and (e) 500 nm. The insets on the right are the optical diffraction patterns of each TEM image.
corresponding to bulk of carbon are generally observed as dark area by the selection of minus Df. But quantitative evaluation of the sample structure is still dif®cult with the knowledge above, because the amorphous carbon ®lm has a quite random structure. Since each optical diffraction pattern of corresponding TEM image is concentric, the texture of the sample has no orientation on the surface. Three or fourfold thin rings appear around the center spot in the diffraction pattern at Df 500 nm. A wide ring is seen around the center at Df 200 nm, as observed at Df 200 nm. At the condition of Df 0, the diffraction pattern appears only in the central area. These optical diffraction patterns are closely correlated to the transfer function as will be discussed later. Since the TEM images at Df s 500 and 200 nm are similar to that at Df s 500 and 200 nm, respectively, as
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Fig. 2. Digitized TEM images of the amorphous carbon film and the power spectra obtained from them by FFT operation. The defocus values Dfs are: (a) 500 nm, (b) 200 nm and (c) 0 nm.
mentioned above, we analyzed the TEM images at Df s 500, 200 and 0 nm by image processing. Digitized images under the different condition of Dfs, which were obtained from the TEM images of Fig. 1(a)±(c), and their power spectra obtained by 2D FFT are shown in Fig. 2(a)±(c), respectively. The central area of the power spectra corresponds to low frequency, and the frequencies become higher as the location moves further from the center. Consequently, both the power spectrum and the optical diffraction pattern appear as coaxial circles and similar to each other. The advantage of power spectrum is, however, the adjustability of brightness in the image. The optical diffraction patterns of which intensity is wholly weak, as shown in Fig. 1(a) and (c), are usually dif®cult to be clear. But the change of power spectrum with Df is shown clearly in Fig. 2 of which brightness is regulated. The transfer functions obtained by Eq. (1) at Df s 500, 200 and 0 nm are shown in Fig. 3. The plus peaks of the transfer function correspond to the bright rings which appear in the optical diffraction pattern and in the power spectrum. In order to discuss the relation between the power spectrum and transfer function, the power spectrum in Fig. 2 was represented as a graph obtained by integration around its central point. Perpendicular axis in the graphs in Fig. 4 shows the spectrum intensity in logarithmic scale. The peaks and downs of wave at Df 500 nm in Fig. 4(a) correspond
Fig. 3. Phase transfer functions for different defocus values Dfs: (a) 500 nm, (b) 200 nm and (c) 0 nm.
to the peaks and downs of the transfer function in Fig. 3(a), respectively. The same relation can be seen at Df 200 nm in Fig. 4(b) and Fig. 3(b). In order to avoid the reverse of contrast and to get wellcontrasted TEM images, it is better to put an aperture which contains one peak of transfer function. As seen in the range from 1 to 5 nm in Figs. 3(b) and 4(b) at Df 200 nm, the brightness of image is not reversed because the transfer function has one minus peak in this range. At Df 0, it is understood that the power spectrum of Fig. 4(c) scarcely contains frequency components, and the image is not formed. The relation between power spectrum and transfer function was discussed so far. Since the TEM image is formed in the range of space frequency where the peak of transfer function exists, it is thought that the image signal is contained in each peaks of the power spectrum of logarithm indication. In order to show the peaks clearly, vertical axis of the power spectrum of Fig. 4(b) was replotted in Fig. 5 with linear scale. The power spectrum of Df 200 nm has many peaks of frequency distribution in wide range as shown in Fig. 5. These peaks correspond to the cycles of brightness
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is carried out on them, the real space images corresponding to the selected space frequencies can be obtained and it is possible to analyze in detail how the TEM images change corresponding to the speci®c frequency range [5]. 3. Microtexture and structure of graphite intercalation compounds studied by TEM and image analysis 3.1. Materials and their TEM images for the study
Fig. 4. The integration of the power spectra with different defocus values Dfs around the central points.
which appear frequently in the TEM image and show the characteristics of structure of the amorphous carbon ®lm sample. The highest peak in power spectrum, which shows the dominant repetition intervals of bright and dark regions in the TEM image, appears at 1.9 nm of space length. This shows that the sample has certain repeating structure with 1.9 nm intervals extending over a large area. Furthermore, if the peak frequency components are extracted from the results of 2D FFT operation and then 2D IFFT operation
Fig. 5. Replot of Fig. 4(b) with linear scale vertical axis. The peaks corresponding to the real space image are shown clearly.
In the present study, we take an acceptor-type GICs with CuCl2 intercalates as a target material, because they are usually well-staged. Vapor grown carbon ®bers (VGCFs) were used as pristine materials for GICs. Because of their small diameter (about 1 mm), VGCFs served as excellent host materials for the analysis of structural change induced by intercalation. VGCFs have been synthesized by the thermal decomposition of benzene [7]. When heat-treated to temperatures as high as 28008C, the VGCFs exhibit highly crystalline characteristics, which consist of concentrically stacked layers of graphite planes around the ®ber axis, similar to the annular rings of a tree [8]. Acceptor-type CuCl2-GICs were synthesized by using VGCFs heat-treated at temperatures around 29008C [9]. The staging of GICs were observed in TEM lattice fringe images of the ®bers. In the TEM image, the 0 0 l lattice planes appeared to be extremely ¯at and the ®bers were known to be well-staged. The electron diffraction pattern of the sample presented a characteristic shape which extends perpendicular to the 0 0 l lattice plane, and was called a ``streak'' or ``spike'' pattern [10]. A 0 0 l lattice fringe image obtained from VGCFs intercalated with CuCl2 (CuCl2-GICs) is shown in Fig. 6, the inset being the selected area electron diffraction (SAD) pattern. A streak pattern which is thought to be strongly related to staging is seen in the diffraction pattern. From spacing of lattice fringe, this GIC is supposed to be composed of regions of graphite stacking, stage-1, stage-2, and higher stage structures. 3.2. Image analysis For convenience to the successive processing, the 0 0 l lattice planes were directed horizontally when the TEM images were converted to the digital data. We carried out the 2D FFT on the digitized TEM images and calculated the 2D power spectrum for analysis of the spatial frequencies of the images. In order to suppress the in¯uence of the peripheral regions of the images on the power spectra, Hamming window was used in operating the 2D FFT. The power spectra were represented by integration along the direction parallel to the 0 0 l lattice planes, for the purpose of analyzing the frequency distribution along the direction perpendicular to the lattice planes [11]. The speci®c frequencies in the integrated power spectrum of CuCl2-GICs were
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Fig. 6. Lattice fringe image of a CuCl2-GIC sample. An electron diffraction pattern of the TEM image is shown in the inset.
3.3. Results and discussion
more disturbed than that of the heat-treated VGCFs, especially along the horizontal axis, i.e., ®ber axis. In addition, there is a cloud of spots located near the center of the power spectrum in Fig. 7(a). The cloud indicates the existence of
3.3.1. Host VGCFs The digitized TEM images of the lattice fringes for asprepared VGCFs and VGCFs heat-treated to 29008C are shown in Fig. 7(a) and (b), respectively, together with power spectra. VGCFs became highly ordered graphite ®bers after heat treatment to 29008C. The improvement in structural perfection of these VGCFs by the heat treatment is evidenced by comparison of these two lattice fringe images. The lattice image of the heat-treated VGCF exhibits long straight 0 0 2 lattice fringes, while those of the as-prepared VGCFs shows short fringes. In the power spectrum of Fig. 7(b), the two bright spots that are symmetrically positioned around the central point correspond to the 0 0 2 lattice planes in the image. This feature of the power spectrum pattern was the same as that of the laser diffraction pattern obtained from the original TEM image. The central point corresponds to the brightness of the image. Since the two 0 0 2 spots and the center spot appear to be sharp, it is found that the 0 0 2 lattice planes are consistently parallel and the interlayer spacing is uniform. The repetition distance of 0 0 2 lattice planes in the heat-treated VGCFs is 0.336 nm [9]. The 0 0 2 spots in the power spectrum of the as-prepared VGCFs are extended, in comparison with that of the heattreated VGCFs, as shown in the inset of Fig. 7(a). The extension of the spots along the horizontal axis indicates the presence of a perturbation in the orientation of 0 0 2 lattice planes, whereas the extension along the vertical axis corresponds to a spread in the interlayer spacings. It is, therefore, indicated that the structure of the as-prepared VGCFs is
Fig. 7. Digitized lattice fringe images for: (a) the as-prepared VGCF sample and (b) the pristine VGCF sample heat treated to 29008C. The corresponding power spectra are shown in the insets.
extracted and real space images were reconstructed by using a 2D IFFT.
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¯uctuation in the magnitude of brightness at long spatial intervals appearing in the image. The distribution range of the spots provides a measure for the region sizes of a group of lattice planes with similar orientation, and for that with the different orientations within the lattice image under analysis. On the other hand, all the lattice planes in Fig. 7(b) have a common direction, and there is no extension of the center spot. The distribution of interlayer spacing obtained by integration along the horizontal axis of the power spectra in Fig. 7(a) and (b) are shown in Fig. 8(a) and (b), respectively. From these integrated power spectra, we can get detailed and quantitative information about the distribution of interlayer spacings. The strong peak, which appears in the range between 0.3 and 0.5 nm in the integrated power spectrum, corresponds to the 0 0 2 lattice planes. By means of the Xray diffraction analysis, the 0 0 2 interlayer spacing (d0 0 2) of as-prepared and 29008C-treated VGCFs were determined as 0.348 and 0.336 nm, respectively, as reported in literature [9]. While the plot for the heat-treated VGCFs shows single peak at 0.336 nm, the peak for the as-prepared VGCFs spreads from 0.34 to 0.40 nm in both sides of the peak position of 0.348 nm. The right-hand side of the spread indicates the partial existence of shorter 0 0 2 interlayer spacing than 0.348 nm. Interlayer spacings wider than 0.348 nm contributes to the left-hand side spread of the peak, which also contains the effect of an inclination of the 0 0 2 lattice planes. Other small peaks, appear between 0.96 and 1.57 nm in Fig. 8(a), are related to the stacking thickness of the 0 0 2 lattice layers. We can derive the number of layers per stacking is about 3±5 from the position of the peaks. We can ®nd three or four layers stack continuously (see Fig. 7(a)), indeed, in the TEM image of the as-prepared VGCFs. 3.3.2. Intercalated VGCFs (GICs) The digitized lattice fringe image for CuCl2-GIC is shown in Fig. 9(a) with the inset indicating its power spectrum
Fig. 8. The distribution of interlayer repeat distances for: (a) the asprepared VGCF sample obtained from the power spectrum of Fig. 7(a) and (b) the pristine VGCF sample heat treated to 29008C obtained from the power spectrum of Fig. 7(b). The values of 0.348 and 0.336 nm are peak tops determined by X-ray diffraction analysis.
obtained by the 2D FFT, and a reconstructed image of CuCl2-GIC, which is mentioned later, is shown in Fig. 9(b). The pattern appearing in the power spectrum in Fig. 9(a) is very similar to the streaking, which is found in the electron diffraction pattern, as shown in Fig. 6. Its characteristic pattern is distributed in a line perpendicular to the original image of 0 0 l lattice planes. The spectrum is very sharp for CuCl2-GICs. This is because the transverse width of the FFT power spectrum pattern is very small, indicating large lateral regions with the same stage.
Fig. 9. (a) Digitized lattice fringe image of a CuCl2-GIC sample. The corresponding power spectrum is shown in the inset, (b) Image of the IFFT for the CuCl2-GIC sample reconstructed from specific frequencies shown in Fig. 10.
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Fig. 10. The distribution of interlayer repeat distances for the CuCl2-GIC sample obtained from the power spectrum of Fig. 9(a).
Fig. 10 shows the distribution of interlayer spacings obtained by integration along the horizontal axis of the power spectrum in Fig. 9(a). Since the spectrum is distributed only in one direction, the 2D power spectrum image can be graphed by integration perpendicular to the distribution of the spectrum, using the same approach as applied to the TEM images of the as-prepared VGCFs (see Figs. 7(a) and 8(a)) and of the heat-treated VGCFs (see Figs. 7(b) and 8(b)). There are many peaks in the integrated power spectrum in Fig. 10 in the region between 0.3 and 4 nm. The large peak at 0.336 nm corresponds to the 0 0 2 graphite lattice planes. Stage-1, stage-2, and higher stage regions as well as graphite stacking appear in Fig. 9(a). We observe a fairly small stage-1 peak around 0.93 nm in Fig. 10. There is another peak between 1.21 and 1.65 nm (the highest point located at 1.396 nm). This peak is thought to be a complex peak which consist of two peaks of a stage-2 component (peak at 1.27 nm) and a stage-3 component (peak at 1.61 nm). A small peak of 0.27 nm in Fig. 10 corresponds to the frequency component which helps to de®ne the shape of the 0 0 2 graphite lattice planes clearly in Fig. 9(a). From this frequency analysis, it is clear that the TEM image for CuCl2-GICs shows the existence of stage-1, stage2, and stage-3 regions, and graphite stacking. However, the presence of the stage-1 region, which is represented by the peak at 0.93 nm, is not as evident in the digitized image shown in Fig. 9(a) as in the Fourier analysis in Fig. 10. There are several unidenti®ed peaks between the graphite and stage-1 peaks which may contribute to the construction of the digitized image. These peaks have the possibility of containing the two kinds of components; one is a fundamental component from which the shape of the wave is formed, and the other is associated with harmonic components. Since the brightness of the TEM image of the CuCl2GICs changes smoothly in the micrographs used (Fig. 6), very low intensity for the harmonic components is expected, except for the harmonic component of the 0 0 2 lattice planes, as mentioned above. Many elemental images that correspond to the each frequency component constitute the TEM image. Some of the elemental images cancel one
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another, which causes dark spaces to appear in the TEM image for the CuCl2 intercalate layers, while some other elemental images reinforce one another, and contribute to construction of the shape of the stage layers. In order to verify the staging of the CuCl2-GICs discussed above, real space images were reconstructed by using the 2D IFFT method. Fig. 9(b) is the image obtained by 2D IFFT reconstruction from the speci®c frequencies corresponding to the interlayer spacings of 0.336 nm (graphite 0 0 2), 0.358, 0.478 and 1.396 nm (corresponds to a complex peak of the stage-2 and stage-3) in Fig. 10. We can see that the peculiar features of the digitized TEM image appear clearly in Fig. 9(b). The layers of Fig. 9(b) appear to be sharper than those in the digitized image (Fig. 9(a)) because the selection of speci®c frequencies acts as a noise reduction operation. If all of the frequencies existing in the digitized image can be identi®ed and selected, a perfect reconstruction of the digitized image can be achieved. Comparing with Fig. 9(a), some lines appear in faint form in the CuCl2 intercalate layers in the reconstructed image (Fig. 9(b)). This is caused by a lack of data when the speci®c frequencies were selected. Fig. 9(a), however, already contains some faint lines where the intercalates exist. These faint features also appear in the original TEM image as a result of the in¯uence of the aperture setting when the TEM image was taken. Therefore, the aperture setting of TEM observation may also act as a frequency selection of the electron diffraction. The image analysis technique of a frequency extract can set the mask patterns, equivalent to the aperture to TEM, in the arbitrary con®guration to a free positions. 4. Conclusions We could obtain a power spectrum image, which is almost the same as optical diffraction pattern of TEM image, by image analysis. The relation between underfocus value Df and the transfer function of TEM image was investigated by integration of the power spectrum around its center. It was shown that the image analysis method was effective for analysis of TEM images. The structural analysis of the carbon materials was investigated by means of the digital image processing of high resolution TEM images. The detailed structure of GIC was revealed through the technique by which rather quanti®ed data was obtained, compared to the conventional methods of the electron diffraction and the laser diffraction. Spatial frequency analysis method according to a 2D FFT was used mainly as the analyzing technique. The characteristic peaks appear in the graph, which made from the power spectrum image obtained by the image processing of the digitized image, were studied quantitatively. The relation between some of the peaks among those and each stage structures of the GICs were discussed. Furthermore, the analytical results were veri®ed by the reconstitution of the real space image using a 2D IFFT technique.
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The target material of CuCl2-GIC was suitable for the discussion on the adequacy of the image processing of TEM image, since this material has complicated but exact stage structures, and therefore the evaluation of analyzed result was considered to be comparatively easy. A great possibility was shown that the detailed material analysis could be performed by the image processing method. The digitized 2D power spectrum image showed a pattern equivalent to the conventional electron diffraction or laser diffraction showing the characteristic feature of a detailed material structure. Especially, the streak pattern which appears as a series of spots in a straight line of the conventional electron diffraction spots can be reproduced in the power spectrum image which was obtained by the image processing of CuCl2-GIC. The frequency extract technique in the image analysis is thought as equivalent to the application of the aperture to TEM observation with the possibility of free mask pattern setting, free positions and arbitrary con®guration. We also expect that this approach is useful for the analysis of the structural characteristics of GICs, as well as the clari®cation of their electrical characteristics. Acknowledgements This work is supported by a grant-in-aid for `Research for the Future' Program No. JSPS-RFTF96R11701 from the
Japan Society for the Promotion of Science. The authors are indebted to them. The authors are indebted to Prof. M.S. Dresselhaus of Massachusetts Institute of Technology, Cambridge, MA 02139, USA for useful discussions and suggestions.
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