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Site-specific electronic structure analysis by channeling EELS and first-principles calculations
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Ultramicroscopy 106 (2006) 1019–1023 www.elsevier.com/locate/ultramic
Site-specific electronic structure analysis by channeling EELS and first-principles calculations Kazuyoshi Tatsumia,, Shunsuke Mutoa, Yu Yamamotoa, Hirokazu Ikenob, Satoru Yoshiokab, Isao Tanakab a
Department of Materials, Physics and Energy Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan b Department of Materials Science and Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan Received 12 July 2005; received in revised form 18 October 2005; accepted 6 April 2006
Abstract Site-specific electronic structures were investigated by electron energy loss spectroscopy (EELS) under electron channeling conditions. The Al-K and Mn-L2,3 electron energy loss near-edge structure (ELNES) of, respectively, NiAl2O4 and Mn3O4 were measured. Deconvolution of the raw spectra with the instrumental resolution function restored the blunt and hidden fine features, which allowed us to interpret the experimental spectral features by comparing with theoretical spectra obtained by first-principles calculations. The present method successfully revealed the electronic structures specific to the differently coordinated cationic sites. r 2006 Elsevier B.V. All rights reserved. PACS: 61.14.Rq; 61.85.+p; 71.20.b; 71.27.+a Keywords: Electron energy loss spectroscopy (EELS); Electron channeling; First-principles calculations; Site-specific chemical states
1. Introduction Recent advances in (scanning) transmission electron microscopy ((S)TEM), such as the combination of a field emission gun and a spherical aberration corrector, have enabled atomic column-by-column electron energy loss spectroscopy (EELS) analysis [1–5]. Another site-by-site EELS analysis can be performed under a specific electron channeling condition [6]. Channeling EELS is performed in a manner similar to the well-known ALCHEMI (Atom Location by Channeling-Enhanced Microanalysis) method. While ALCHEMI is used for quantitative elemental analysis, channeling EELS can give the chemical state of an excited atom at a specific site using the electron energy loss near-edge structure (ELNES) in the core loss spectra. Tafto et al. [6] were the first to perform such an analysis. They studied the valence of iron ions in a chromite spinel. Although channeling EELS has the potential for siteCorresponding author. Tel.: +81 527895135; fax: +81 527895137.
E-mail address: [email protected] (K. Tatsumi). 0304-3991/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2006.04.015
specific measurements in crystals, few applications have been reported [7–9]. To the best of our knowledge, there have been no chemical state analyses except those conducted by Tafto et al. [9] and our recent report. This is partly because the signal-to-noise (S/N) ratio is typically very low under the channeling conditions because the EELS entrance aperture has to be placed off-axis under the two-beam excitation condition [6], which smeared out the fine features of ELNES. Another factor was the lack of a reliable theory for interpreting ELNES data. To overcome the first difficulty, several algorithms have been developed to deconvolute the raw spectra and are currently available. These algorithms restore the spectra with muchimproved S/N ratio and instrumental energy spread. The second difficulty has been overcome by the recent firstprinciples calculations, which have been reported to successfully reproduce ELNES [10–16]. In the present paper, we demonstrate atomic site-specific analyses of ELNES under electron channeling conditions. We have tried to reveal the fine spectral features using our newly developed software deconvolution method based on
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the Pixon algorithm [17]. The spectral features are interpreted using the theoretical spectra obtained through first principles. NiAl2O4 and Mn3O4 spinels are targeted. Valuable experimental and theoretical information on the complex ELNES of spinels have been reported [10,11,18–22]. However, experimental site-specific ELNES and their first principles calculation have not been combined thus far. Our results would clearly confirm the origin of the complex spectral features discussed in these reports.
itself to the distribution of information content in the data and processes it locally. The explicit formula of the method is described in detail in Refs. [17,24]. The criterion parameter for distinguishing between noise and signal was carefully set so as to reveal the finest features that the experimental noise level allows. The method requires an instrumental resolution function (point-spread function) like other similar methods [25,26]. For this purpose, a low-loss spectrum was taken from the same area as the core-loss spectrum recording.
2. Experimental and theoretical procedures
2.3. First-principles calculations of ELNES
2.1. Sample preparation
Theoretical spectra of Al-K were obtained using the firstprinciples APW+lo (augmented plane-wave+local orbital) band method based on the density functional theory (DFT) [27]. Before the ELNES calculation, the atom positions were fully optimized within the NiAl2O4 primitive cell with the first-principles PAW (projector augmentedwave) method so as to save the computational costs [28,29]. The cut-off energy of the plane wave basis was chosen to be 500 eV.125 k-points were used for the primitive cell of 14 atoms. Optimization was performed until the maximum residual force on atoms dropped below 0.05 eV/A˚. Both in the geometry optimation and ELNES calculation, spinpolarized electronic structures were calculated with the exchange correlation potential of the generalized gradient approximation [30]. Since ELNES reflects the electronic transition from core states to unoccupied states, accurate treatment of core states, as done in the APW+lo method, is needed for the ELNES calculation. A 56-atom supercell with one coreholed Al atom was used, as was done in Ref. [18]. Spectral intensity was calculated by the product of the radial transition probability and unoccupied Al p-like density of states, according to the dipole transition approximation [31]. 27 k-points in the whole Brillouin zone of the supercell were used. Muffin–tin radii (RMT) of Ni, Al and O were set to 1.9, 1.9 and 1.7 bohr, respectively. The number of plane waves for the basis set was truncated by RKmax (product of minimum RMT and maximum wave number of plane waves) equals 5.1. We set RMT non-overlapping and as large as possible with the size difference smaller than 20%. The larger radii are preferable for the computational cost and the orthogonality of the core states [27,31]. It was confirmed that the spectral shape and peak position were well converged with respect to the supercell size, number of k-points and size of basis set. The Mn-L2,3 spectra were calculated using first principles. Since strong correlation of Mn 3d and relativistic effects on Mn 2p is critical on the spectra, we adopted the totally relativistic first-principles molecular orbital calculation beyond DFT [15,16]. Electronic correlations among the Mn 2p1/2, 2p3/2 and 3d electrons were calculated rigorously as the configuration interaction (CI) incorporated with the Slater determinants of these molecular orbitals. The integration of the dipole transition matrix was
The samples used in the present study were NiAl2O4 and Mn3O4. To prepare the NiAl2O4 samples, commercially available NiO and Al2O3 powders were mixed thoroughly, and sintered at 1600 1C for 20 h. In the case of Mn3O4, a commercial Mn3O4 powder was sintered at 1100 1C for 24 h. From the sintered bodies, TEM specimens were prepared by mechanical grinding, dimpling and ion milling. To avoid charging-up of the specimens, we carbon-coated (ca. 10 nm) each specimen with its edge area masked. 2.2. EELS data acquisition and deconvolution Al-K and Mn-L2,3 ELNES of NiAl2O4 and Mn3O4 were recorded under electron channeling conditions. TEMEELS measurements were performed using a Jeol JEM3010FEF with an O-type Energy Filter. Grains showing good visibility of Kikuchi lines, as large as 500–1000 nm, were selected for EEL spectra measurements. The thickness of these regions was estimated to be approximately 50–100 nm from the thickness contours. The thickness by the low loss spectrum was comparable. When a systematic orientation was chosen to observe the stacking sequence ABABABy along the [h 0 0] direction, the thickness-averaged electron intensity could be maximized on the atomic planes A and B, for example, under the 100 reflection excitation condition with positive and negative excitation errors, S. The entrance aperture of the EELS detector should be placed off axis, which increases the localization of the inelastic excitation and enhances the channeling effect [6]. The magnitude of the excitation errors was selected so as to maximize the difference between the corresponding ELNES. Typical data acquisition time was 1 min. Deconvolution of the raw spectra was performed using the Pixon algorithm [23]. The Pixon method is one of the most powerful image reconstruction algorithms based on the Bayesian estimation [17,24], similar to the maximum entropy method (MEM) and its family [25,26]. However, MEM must inevitably oversmooth the spectrum in some regions and undersmooth it in others, because it assumes that each pixel value in the data pixel grid carrying information equally. In contrast, the Pixon method adapts
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done directly using the total wave functions. For both Mn L2,3 and Al K edge, the final spectrum was broadened by a Gaussian function with a FWHM of 1.5 eV. 3. Results and discussion 3.1. Al-K of NiAl2O4 NiAl2O4 has a spinel-type crystal structure, which has two kinds of cationic sites, namely, tetrahedral and octahedral sites, as shown in Figs. 1a and b. In these figures, the occupancy of Al at the tetrahedral sites (fT) was set to unity for simplicity, though fT was reported to range from 0.80 to 0.86 [32]. The tetrahedral and octahedral sites are alternately aligned on the {4 0 0} planes. Hence, the 400 reflection excitation conditions with positive and negative S enhance the ELNES signal of the tetrahedral and the octahedral sites, respectively. The Al-K spectra are compared in Fig. 2. Fig. 2a–c show the experimental raw, deconvoluted, and theoretical spectra, respectively. In Fig. 2a and b we show the spectra measured at three different conditions: So0, S40 and the normal TEM mode. The normal TEM mode does not employ the channeling conditions. Thus, in this mode, the tetrahedral and octahedral sites are excited to the same extent. Comparing the raw spectra, we find that the shoulder at around 1552 eV is enhanced for S40, and that the feature is less conspicuous for So0. The normal spectrum has the feature between the two. The differences are observed better in Fig. 2b among the deconvoluted spectra. In these spectra, we can see three major peaks, labeled A, B, and C. The intensity of A relative to B decreases in the order S40, normal, and So0. Positive S values enhance the signal of the tetrahedral site, thus peak A is assigned to the tetrahedral site. Similarly, peak B is due mainly to the octahedral site. The theoretical spectra obtained from
Fig. 2. Experimental raw (a), deconvoluted (b) and theoretical (c) Al K ELNES of NiAl2O4. The horizontal axes are aligned so as to give the same peak energies.
Fig. 1. Model atomic arrangement of NiAl2O4 spinel: unit cell (a) and primitive cell (b).
the two different Al sites are shown at Fig. 2c. The spectra of Altet and Aloct are drawn with an intensity ratio of 1:1, which is equal to the number ratio of the tetrahedral and octahedral sites occupied by Al. It is supposed that the difference in energy between peaks A and B reflects the difference in electronic structure between Altet and Aloct. Fig. 3 shows the partial densities of states (PDOS) of Altet and Aloct. We show the results for the non-core-holed, ground state electronic structure, because it would be simpler to correlate the ELNES difference and the chemical bonding around each site on the basis of the ground state electronic structure.
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0.3 Aloct p
Aloct PDOS
Aloct d
Partial Density of States (states / eV atom)
0.2
Aloct s
0.1
0.0 Altet PDOS
0.2
Altet p Altet s Altet d
0.1
-10
-5
0
5
10
15
20
Energy rel. to EF (eV) Fig. 3. Electron partial densities of states of NiAl2O4, with no holes introduced in Al 1s. Energies are expressed relative to the Fermi level.
In the low-energy region of the conduction band, from 3 to 15 eV above the Fermi level, Altet p PDOS exhibits significant intensities. On the other hand, p PDOS of the octahedral sites is mainly located at the higher-energy region of 10–18 eV. This roughly corresponds to the energy difference between peaks A and B of the Al-K ELNES. All the Al s and p PDOS have larger intensities in the conduction band than in the valence band. This trend is more conspicuous for Aloct. This means that octahedral Al is more ionic, as confirmed by the effective charges of +2.55 and +2.38 for Aloct and Altet, respectively, calculated by the Bader’s method [33]. Because of the more ionic character of the octahedral site, the Aloct p states contribute to the higher energy region of the conduction band. We found that this electronic mechanism is one of the main reasons for the site-specific difference of the Al-K ELNES. Since the calculated 1s level of the Aloct is only 0.17 eV lower than that of the Altet, the chemical shift between the different sites plays a minor role. 3.2. Mn-L2,3 spectra of Mn3O4 Experimental ELNES of Mn-L2,3 of Mn3O4 spinel are compared on the basis of XANES (X-ray absorption nearedge structure) data [34] and the results of the multielectron calculation (Fig. 4). Unlike the case of NiAl2O4, the two kinds of cationic sites are fully occupied by one cationic
Fig. 4. Comparison of Mn L2,3 spectra. The theoretical spectra of Mn2þ tet and Mn3þ oct are plotted with weighting factor of 1:2, equal to the number ratio of the tetrahedral and octahedral sites.
element, namely Mn. For the multielectron calculation, we used the atomic positions of the Mn ions as experimentally reported that the tetrahedral and octahedral sites are occupied by Mn2+ and Mn3+, respectively [35,36]. In the calculations, we used model clusters of (MnO4)6 and (MnO6)10 for the tetrahedral and octahedral Mn, respectively. In order to take the effective Madelung potential into account, point charges were put at the external atomic sites. Overall, the theoretical results are consistent with the experimental XANES. There are four
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peaks, viz., A and B at the L3 edge, C and D at the L2 edge. The site-specific theoretical spectra indicate that peaks A 3þ and B are mainly from the Mn2þ tet , and Mnoct , respectively. This peak assignment is experimentally examined in the deconvoluted spectra of the channeling ELNES, shown in the second panel of Fig. 4. The deconvolution procedure reveals the detailed features of these spectra. We see two distinct peaks (A and B) in the second panel. Clearly, negative S values enhance peak B, while peak A predominates in the case of positive S. Thus, peaks A and B are assigned to Mntet and Mnoct, respectively, which is consistent with the theoretical results. 4. Summary Electronic structures around the two cationic sites in NiAl2O4 and Mn3O4 have been investigated with a combination of Al-K and Mn-L2,3 ELNES under electron channeling conditions and their first-principles calculations. In the case of NiAl2O4, the lower (higher) energy peak could be assigned to the tetrahedral (octahedral) Al site, which qualitatively agreed with the theoretical Al-K ELNES at the corresponding site in NiAl2O4. The theoretical electronic structures showed that the increased ionic character of Aloct is mainly ascribable to the energy difference between the two peaks. In the experimental ELNES of Mn-L2,3, two distinct peaks were successfully resolved in the L3 region. Each peak was enhanced by a different channeling condition. The first and second peak was assigned to Mntet and Mnoct, respectively. The fully relativistic multielectron calculation of Mn-L2,3 ELNES showed that the first (second) peak was attributed to the Mn2+ (Mn3+) at the tetrahedral (octahedral) site, which was consistent with experimental results. As shown in the case of Mn3O4, combination of the channeling EELS experiment and the multielectron calculation can provide the site-specific electronic states of transition metal ions in strongly correlated systems, particularly effective for the charge-ordered systems of transition metal chalcogenides. Diffraction technique such as neutron diffraction or electron diffraction methods can imply the charge ordering from the corresponding superlattice reflections, rather than its direct evidence. The present channeling ELNES is arguably one of the most effective methods to obtain its direct information not only on its presence but also on detailed electronic structures of key elements, and we will proceed in this direction. Acknowledgments This work was partly supported by the Grants-in-Aid for Scientific Research of JSPS, the Nanotechnology Support Project (Kyushu University) of MEXT, Japan and DAIKO foundation. KT thanks Dr. Iwasaki at Nagoya University for kindly helping with sample preparation.
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References [1] R.F. Klie, Y. Zhu, Micron 36 (2005) 219. [2] P.D. Nellist, N. Dellby, O.L. Krivanek, M.F. Murifitt, Z. Szilagyi, A.R. Lupini, S.J. Pennycook, in: Electron Microscopy and Analysis 2003: Institute of Physics Conference Series, vol. 179, 2004, p. 159. [3] R.F. Klie, I. Arslan, N.D. Browning, J. Electron Microsc. Related Phenomena 143 (2005) 105. [4] G. Duscher, N.D. Browning, S.J. Pennycook, Phys. Stat. Sol. (a) 166 (1998) 327. [5] M. Varela, S.S. Findlay, A.R. Lupini, H.M. Christen, A.Y. Borisevich, N. Dellby, O.L. Krivanek, P.D. Nellist, M.P. Oxley, L.J. Allen, S.J. Pennycook, Phys. Rev. Lett. 92 (2004) 095502. [6] J. Tafto, O.L. Krivanek, Phys. Rev. Lett. 48 (1982) 560. [7] K. Leifer, P.A. Buffat, Inst. Phys. Ser. 157 (1997) 381. [8] P.G. Self, P.R. Buseck, Philos. Mag. A 48 (1983) L21. [9] S. Arai, S. Muto, T. Sasaki, K. Tatsumi, Y. Ukyo, K. Kuroda, H. Saka, Solid State Commun. 135 (2005) 664. [10] S.D. Mo, W.Y. Ching, Phys. Rev. B 62 (2000) 7901. [11] I. Tanaka, T. Mizoguchi, T. Sekine, H. He, K. Kimoto, T. Kobayashi, S.D. Mo, W.Y. Ching, Appl. Phys. Lett. 78 (2001) 2134. [12] T. Mizoguchi, I. Tanaka, S. Yoshioka, M. Kunisu, T. Yamamoto, W.Y. Ching, Phys. Rev. B 70 (2004) 045103. [13] M. Mogi, T. Yamamoto, T. Mizoguchi, K. Tatsumi, S. Yoshioka, S. Kameyama, I. Tanaka, H. Adachi, Mater. Trans. 45 (2004) 2031. [14] C. He´bert-Souche, P.-H. Louf, P. Blaha, M. Nelhiebel, J. Luitz, P. Schattschneider, K. Schwarz, B. Jouffrey, Ultramicroscopy 83 (2000) 9. [15] K. Ogasawara, T. Iwata, Y. Koyama, T. Ishii, I. Tanaka, H. Adachi, Phys. Rev. B 64 (2001) 115413. [16] H. Ikeno, I. Tanaka, T. Miyamae, T. Mishima, H. Adachi, K. Ogasawara, Mater. Trans. 45 (2004) 1414. [17] R.C. Puetter, Ann. N.Y. Acad. Sci. 808 (1997) 160. [18] K. Tatsumi, T. Mizoguchi, S. Yoshioka, T. Yamamoto, T. Suga, T. Sekine, I. Tanaka, Phys. Rev. B 71 (2005) 033202. [19] S.D. Mo, W.Y. Ching, Phys. Rev. B 54 (2000) 16555. [20] S. Kostlmeier, C. Elsasser, B. Meyer, Ultramicroscopy 80 (1999) 145. [21] F.T. Docherty, A.J. Craven, D.W. McComb, J. Skakle, Ultramicroscopy 86 (2001) 273. [22] K. van Benthem, H. Kohl, Micron 31 (2000) 347. [23] S. Muto, R.C. Puetter, K. Tatsumi, J. Electron Microsc., 2006, submitted. [24] R.C. Puetter, T.R. Gosnell, A. Yahil, Annu. Rev. Astron. Astrophys. 43 (2005) 139–194. [25] A. Gloter, A. Douiri, M. Tence, C. Colliex, Ultramicroscopy 96 (2003) 385–400. [26] K. Kimoto, K. Ishizuka, T. Mizoguchi, I. Tanaka, Y. Matsui, J. Electron Microsc. 52 (2003) 299–303. [27] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, in: K. Schwarz, T.U. Wien (Eds.), WIEN2K, An Augmented Plane Wave+Local Orbitals Program for Calculating Crystal Properties, Austria, 2001, ISBN 3-9501031-1-2. [28] G. Kresse, J. Furthmu¨ller, Phys. Rev. B 54 (1996) 11169. [29] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [30] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [31] M. Nelhiebel, P.-H. Louf, P. Schattshneider, P. Blaha, K. Schwarz, B. Jouffrey, Phys. Rev. B 59 (1999) 12807. [32] J.N. Roelofsen, R.C. Peterson, M. Raudsepp, Am. Miner. 77 (1992) 522. [33] R.F.W. Bader, Atoms in Molecules—A Quantum Theory, Oxford University Press, Oxford, ISBN 0198558651, 1990. [34] B. Gilbert, B.H. Frazer, A. Belz, P.G. Conrad, K.H. Nealson, D. Haskel, J.C. Lang, G. Srajer, G. De Stasio, J. Phys. Chem. A 107 (2003) 2839. [35] B. Boucher, R. Buhl, M. Perrin, J. Phys. Chem. Solids 32 (1971) 2429. [36] G. Jensen, O. Nielsen, J. Phys. C 7 (1974) 409.
Ultramicroscopy 106 (2006) 1019–1023 www.elsevier.com/locate/ultramic
Site-specific electronic structure analysis by channeling EELS and first-principles calculations Kazuyoshi Tatsumia,, Shunsuke Mutoa, Yu Yamamotoa, Hirokazu Ikenob, Satoru Yoshiokab, Isao Tanakab a
Department of Materials, Physics and Energy Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan b Department of Materials Science and Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan Received 12 July 2005; received in revised form 18 October 2005; accepted 6 April 2006
Abstract Site-specific electronic structures were investigated by electron energy loss spectroscopy (EELS) under electron channeling conditions. The Al-K and Mn-L2,3 electron energy loss near-edge structure (ELNES) of, respectively, NiAl2O4 and Mn3O4 were measured. Deconvolution of the raw spectra with the instrumental resolution function restored the blunt and hidden fine features, which allowed us to interpret the experimental spectral features by comparing with theoretical spectra obtained by first-principles calculations. The present method successfully revealed the electronic structures specific to the differently coordinated cationic sites. r 2006 Elsevier B.V. All rights reserved. PACS: 61.14.Rq; 61.85.+p; 71.20.b; 71.27.+a Keywords: Electron energy loss spectroscopy (EELS); Electron channeling; First-principles calculations; Site-specific chemical states
1. Introduction Recent advances in (scanning) transmission electron microscopy ((S)TEM), such as the combination of a field emission gun and a spherical aberration corrector, have enabled atomic column-by-column electron energy loss spectroscopy (EELS) analysis [1–5]. Another site-by-site EELS analysis can be performed under a specific electron channeling condition [6]. Channeling EELS is performed in a manner similar to the well-known ALCHEMI (Atom Location by Channeling-Enhanced Microanalysis) method. While ALCHEMI is used for quantitative elemental analysis, channeling EELS can give the chemical state of an excited atom at a specific site using the electron energy loss near-edge structure (ELNES) in the core loss spectra. Tafto et al. [6] were the first to perform such an analysis. They studied the valence of iron ions in a chromite spinel. Although channeling EELS has the potential for siteCorresponding author. Tel.: +81 527895135; fax: +81 527895137.
E-mail address: [email protected] (K. Tatsumi). 0304-3991/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultramic.2006.04.015
specific measurements in crystals, few applications have been reported [7–9]. To the best of our knowledge, there have been no chemical state analyses except those conducted by Tafto et al. [9] and our recent report. This is partly because the signal-to-noise (S/N) ratio is typically very low under the channeling conditions because the EELS entrance aperture has to be placed off-axis under the two-beam excitation condition [6], which smeared out the fine features of ELNES. Another factor was the lack of a reliable theory for interpreting ELNES data. To overcome the first difficulty, several algorithms have been developed to deconvolute the raw spectra and are currently available. These algorithms restore the spectra with muchimproved S/N ratio and instrumental energy spread. The second difficulty has been overcome by the recent firstprinciples calculations, which have been reported to successfully reproduce ELNES [10–16]. In the present paper, we demonstrate atomic site-specific analyses of ELNES under electron channeling conditions. We have tried to reveal the fine spectral features using our newly developed software deconvolution method based on
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the Pixon algorithm [17]. The spectral features are interpreted using the theoretical spectra obtained through first principles. NiAl2O4 and Mn3O4 spinels are targeted. Valuable experimental and theoretical information on the complex ELNES of spinels have been reported [10,11,18–22]. However, experimental site-specific ELNES and their first principles calculation have not been combined thus far. Our results would clearly confirm the origin of the complex spectral features discussed in these reports.
itself to the distribution of information content in the data and processes it locally. The explicit formula of the method is described in detail in Refs. [17,24]. The criterion parameter for distinguishing between noise and signal was carefully set so as to reveal the finest features that the experimental noise level allows. The method requires an instrumental resolution function (point-spread function) like other similar methods [25,26]. For this purpose, a low-loss spectrum was taken from the same area as the core-loss spectrum recording.
2. Experimental and theoretical procedures
2.3. First-principles calculations of ELNES
2.1. Sample preparation
Theoretical spectra of Al-K were obtained using the firstprinciples APW+lo (augmented plane-wave+local orbital) band method based on the density functional theory (DFT) [27]. Before the ELNES calculation, the atom positions were fully optimized within the NiAl2O4 primitive cell with the first-principles PAW (projector augmentedwave) method so as to save the computational costs [28,29]. The cut-off energy of the plane wave basis was chosen to be 500 eV.125 k-points were used for the primitive cell of 14 atoms. Optimization was performed until the maximum residual force on atoms dropped below 0.05 eV/A˚. Both in the geometry optimation and ELNES calculation, spinpolarized electronic structures were calculated with the exchange correlation potential of the generalized gradient approximation [30]. Since ELNES reflects the electronic transition from core states to unoccupied states, accurate treatment of core states, as done in the APW+lo method, is needed for the ELNES calculation. A 56-atom supercell with one coreholed Al atom was used, as was done in Ref. [18]. Spectral intensity was calculated by the product of the radial transition probability and unoccupied Al p-like density of states, according to the dipole transition approximation [31]. 27 k-points in the whole Brillouin zone of the supercell were used. Muffin–tin radii (RMT) of Ni, Al and O were set to 1.9, 1.9 and 1.7 bohr, respectively. The number of plane waves for the basis set was truncated by RKmax (product of minimum RMT and maximum wave number of plane waves) equals 5.1. We set RMT non-overlapping and as large as possible with the size difference smaller than 20%. The larger radii are preferable for the computational cost and the orthogonality of the core states [27,31]. It was confirmed that the spectral shape and peak position were well converged with respect to the supercell size, number of k-points and size of basis set. The Mn-L2,3 spectra were calculated using first principles. Since strong correlation of Mn 3d and relativistic effects on Mn 2p is critical on the spectra, we adopted the totally relativistic first-principles molecular orbital calculation beyond DFT [15,16]. Electronic correlations among the Mn 2p1/2, 2p3/2 and 3d electrons were calculated rigorously as the configuration interaction (CI) incorporated with the Slater determinants of these molecular orbitals. The integration of the dipole transition matrix was
The samples used in the present study were NiAl2O4 and Mn3O4. To prepare the NiAl2O4 samples, commercially available NiO and Al2O3 powders were mixed thoroughly, and sintered at 1600 1C for 20 h. In the case of Mn3O4, a commercial Mn3O4 powder was sintered at 1100 1C for 24 h. From the sintered bodies, TEM specimens were prepared by mechanical grinding, dimpling and ion milling. To avoid charging-up of the specimens, we carbon-coated (ca. 10 nm) each specimen with its edge area masked. 2.2. EELS data acquisition and deconvolution Al-K and Mn-L2,3 ELNES of NiAl2O4 and Mn3O4 were recorded under electron channeling conditions. TEMEELS measurements were performed using a Jeol JEM3010FEF with an O-type Energy Filter. Grains showing good visibility of Kikuchi lines, as large as 500–1000 nm, were selected for EEL spectra measurements. The thickness of these regions was estimated to be approximately 50–100 nm from the thickness contours. The thickness by the low loss spectrum was comparable. When a systematic orientation was chosen to observe the stacking sequence ABABABy along the [h 0 0] direction, the thickness-averaged electron intensity could be maximized on the atomic planes A and B, for example, under the 100 reflection excitation condition with positive and negative excitation errors, S. The entrance aperture of the EELS detector should be placed off axis, which increases the localization of the inelastic excitation and enhances the channeling effect [6]. The magnitude of the excitation errors was selected so as to maximize the difference between the corresponding ELNES. Typical data acquisition time was 1 min. Deconvolution of the raw spectra was performed using the Pixon algorithm [23]. The Pixon method is one of the most powerful image reconstruction algorithms based on the Bayesian estimation [17,24], similar to the maximum entropy method (MEM) and its family [25,26]. However, MEM must inevitably oversmooth the spectrum in some regions and undersmooth it in others, because it assumes that each pixel value in the data pixel grid carrying information equally. In contrast, the Pixon method adapts
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done directly using the total wave functions. For both Mn L2,3 and Al K edge, the final spectrum was broadened by a Gaussian function with a FWHM of 1.5 eV. 3. Results and discussion 3.1. Al-K of NiAl2O4 NiAl2O4 has a spinel-type crystal structure, which has two kinds of cationic sites, namely, tetrahedral and octahedral sites, as shown in Figs. 1a and b. In these figures, the occupancy of Al at the tetrahedral sites (fT) was set to unity for simplicity, though fT was reported to range from 0.80 to 0.86 [32]. The tetrahedral and octahedral sites are alternately aligned on the {4 0 0} planes. Hence, the 400 reflection excitation conditions with positive and negative S enhance the ELNES signal of the tetrahedral and the octahedral sites, respectively. The Al-K spectra are compared in Fig. 2. Fig. 2a–c show the experimental raw, deconvoluted, and theoretical spectra, respectively. In Fig. 2a and b we show the spectra measured at three different conditions: So0, S40 and the normal TEM mode. The normal TEM mode does not employ the channeling conditions. Thus, in this mode, the tetrahedral and octahedral sites are excited to the same extent. Comparing the raw spectra, we find that the shoulder at around 1552 eV is enhanced for S40, and that the feature is less conspicuous for So0. The normal spectrum has the feature between the two. The differences are observed better in Fig. 2b among the deconvoluted spectra. In these spectra, we can see three major peaks, labeled A, B, and C. The intensity of A relative to B decreases in the order S40, normal, and So0. Positive S values enhance the signal of the tetrahedral site, thus peak A is assigned to the tetrahedral site. Similarly, peak B is due mainly to the octahedral site. The theoretical spectra obtained from
Fig. 2. Experimental raw (a), deconvoluted (b) and theoretical (c) Al K ELNES of NiAl2O4. The horizontal axes are aligned so as to give the same peak energies.
Fig. 1. Model atomic arrangement of NiAl2O4 spinel: unit cell (a) and primitive cell (b).
the two different Al sites are shown at Fig. 2c. The spectra of Altet and Aloct are drawn with an intensity ratio of 1:1, which is equal to the number ratio of the tetrahedral and octahedral sites occupied by Al. It is supposed that the difference in energy between peaks A and B reflects the difference in electronic structure between Altet and Aloct. Fig. 3 shows the partial densities of states (PDOS) of Altet and Aloct. We show the results for the non-core-holed, ground state electronic structure, because it would be simpler to correlate the ELNES difference and the chemical bonding around each site on the basis of the ground state electronic structure.
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0.3 Aloct p
Aloct PDOS
Aloct d
Partial Density of States (states / eV atom)
0.2
Aloct s
0.1
0.0 Altet PDOS
0.2
Altet p Altet s Altet d
0.1
-10
-5
0
5
10
15
20
Energy rel. to EF (eV) Fig. 3. Electron partial densities of states of NiAl2O4, with no holes introduced in Al 1s. Energies are expressed relative to the Fermi level.
In the low-energy region of the conduction band, from 3 to 15 eV above the Fermi level, Altet p PDOS exhibits significant intensities. On the other hand, p PDOS of the octahedral sites is mainly located at the higher-energy region of 10–18 eV. This roughly corresponds to the energy difference between peaks A and B of the Al-K ELNES. All the Al s and p PDOS have larger intensities in the conduction band than in the valence band. This trend is more conspicuous for Aloct. This means that octahedral Al is more ionic, as confirmed by the effective charges of +2.55 and +2.38 for Aloct and Altet, respectively, calculated by the Bader’s method [33]. Because of the more ionic character of the octahedral site, the Aloct p states contribute to the higher energy region of the conduction band. We found that this electronic mechanism is one of the main reasons for the site-specific difference of the Al-K ELNES. Since the calculated 1s level of the Aloct is only 0.17 eV lower than that of the Altet, the chemical shift between the different sites plays a minor role. 3.2. Mn-L2,3 spectra of Mn3O4 Experimental ELNES of Mn-L2,3 of Mn3O4 spinel are compared on the basis of XANES (X-ray absorption nearedge structure) data [34] and the results of the multielectron calculation (Fig. 4). Unlike the case of NiAl2O4, the two kinds of cationic sites are fully occupied by one cationic
Fig. 4. Comparison of Mn L2,3 spectra. The theoretical spectra of Mn2þ tet and Mn3þ oct are plotted with weighting factor of 1:2, equal to the number ratio of the tetrahedral and octahedral sites.
element, namely Mn. For the multielectron calculation, we used the atomic positions of the Mn ions as experimentally reported that the tetrahedral and octahedral sites are occupied by Mn2+ and Mn3+, respectively [35,36]. In the calculations, we used model clusters of (MnO4)6 and (MnO6)10 for the tetrahedral and octahedral Mn, respectively. In order to take the effective Madelung potential into account, point charges were put at the external atomic sites. Overall, the theoretical results are consistent with the experimental XANES. There are four
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peaks, viz., A and B at the L3 edge, C and D at the L2 edge. The site-specific theoretical spectra indicate that peaks A 3þ and B are mainly from the Mn2þ tet , and Mnoct , respectively. This peak assignment is experimentally examined in the deconvoluted spectra of the channeling ELNES, shown in the second panel of Fig. 4. The deconvolution procedure reveals the detailed features of these spectra. We see two distinct peaks (A and B) in the second panel. Clearly, negative S values enhance peak B, while peak A predominates in the case of positive S. Thus, peaks A and B are assigned to Mntet and Mnoct, respectively, which is consistent with the theoretical results. 4. Summary Electronic structures around the two cationic sites in NiAl2O4 and Mn3O4 have been investigated with a combination of Al-K and Mn-L2,3 ELNES under electron channeling conditions and their first-principles calculations. In the case of NiAl2O4, the lower (higher) energy peak could be assigned to the tetrahedral (octahedral) Al site, which qualitatively agreed with the theoretical Al-K ELNES at the corresponding site in NiAl2O4. The theoretical electronic structures showed that the increased ionic character of Aloct is mainly ascribable to the energy difference between the two peaks. In the experimental ELNES of Mn-L2,3, two distinct peaks were successfully resolved in the L3 region. Each peak was enhanced by a different channeling condition. The first and second peak was assigned to Mntet and Mnoct, respectively. The fully relativistic multielectron calculation of Mn-L2,3 ELNES showed that the first (second) peak was attributed to the Mn2+ (Mn3+) at the tetrahedral (octahedral) site, which was consistent with experimental results. As shown in the case of Mn3O4, combination of the channeling EELS experiment and the multielectron calculation can provide the site-specific electronic states of transition metal ions in strongly correlated systems, particularly effective for the charge-ordered systems of transition metal chalcogenides. Diffraction technique such as neutron diffraction or electron diffraction methods can imply the charge ordering from the corresponding superlattice reflections, rather than its direct evidence. The present channeling ELNES is arguably one of the most effective methods to obtain its direct information not only on its presence but also on detailed electronic structures of key elements, and we will proceed in this direction. Acknowledgments This work was partly supported by the Grants-in-Aid for Scientific Research of JSPS, the Nanotechnology Support Project (Kyushu University) of MEXT, Japan and DAIKO foundation. KT thanks Dr. Iwasaki at Nagoya University for kindly helping with sample preparation.
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