Local Structures of Equiatomic CoTi Alloy Films with Various Degrees of Structural Order

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1 Journal of the Korean Physical Society, Vol. 43, No. 2, August 2003, pp Local Structures of Equiatomic CoTi Alloy Films with Various Degrees of Structural Order Y. S. Lee Division of Information Communication & Computer Engineering, Hanbat National University, Daejeon J. Y. Rhee Department of Physics, Hoseo University, Asan Y. V. Kudryavtsev Institute of Metal Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine Y. Jeon Department of Physics, Jeonju University, Jeonju C. N. Whang Atomic-scale Surface Science Research Center and Department of Physics, Yonsei University, Seoul Y. P. Lee Quantum Photonic Science Research Center and Department of Physics, Hanyang University, Seoul (Received 30 December 2002) The microstructures of ordered B2-phase and amorphous-like equiatomic CoTi alloy films have been investigated by using X-ray absorption spectroscopy. Analysis of the extended X-ray absorption fine structure (EXAFS) data elucidates, at least in a local sense, that both Co and Ti atoms are arranged in an ordered cubic-b2 structure for the film deposited on a heated substrate (730 K) while the film deposited on a the substrate cooled down to 150 K is amorphous-like. The film deposited at 150 K has the same main peak position as the pure Co film in the Co K-edge Fourier transform EXAFS spectrum. This indicates that the radial distance is the same as for a pure Co film, and reflects the formation of Co clusters, which is attributed to an increase in the number of nearest Co-Co bondings and implies the formation of a considerable amount of antistructure Co atoms (Co atoms at Ti sites) and nearest-neighbor clustering of Co atoms. These results are consistent with recent observations and interpretation of a weakly ferromagnetic behavior in CoTi films deposited at 150 K [Y. P. Lee et al, Phys. Rev. B 60, 8067 (1999)] and their other peculiar physical properties. PACS numbers: Gm, Th, Be, q, i Keywords: EXAFS, CoTi I. INTRODUCTION The equiatomic CoTi alloy and its related compounds, such as FeTi and NiTi, exhibit some peculiar physical properties. The equiatomic FeTi and CoTi alloys have a cubic CsCl structure (B2 phase) at room temperature while the NiTi alloy has a monoclinic structure (B19 phase). NiTi undergoes the famous martensitic transformation from the austenitic B2 phase at high temperature yslee@hanbat.ac.kr ( 333 K) to the martensitic B19 phase upon cooling [1]. This transition is accompanied by the so-called shapememory effect [2]. CoTi and FeTi do not show such a transformation. Both perfectly ordered equiatomic CoTi and FeTi alloys are paramagnetic; however, pseudobinary Fe 1 x Co x Ti alloys with 0.15 < x < 0.65 are weakly ferromagnetic with T c < 70 K [3,4]. According to an experimental study of [5] and a theoretical calculation [6] for disordered bulk alloys, the magnetic moment of the Co atoms must be equal to zero. However, the magnetic properties of disordered equiatomic CoTi alloy films are different from those of the ordered one; that is, a fer

2 Local Structures of Equiatomic CoTi Alloy Films Y. S. Lee et al romagnetic ordering of the disordered equiatomic CoTi alloy film has been observed near 100 K [7]. On the other hand, the origin of the magnetic properties is not clearly resolved yet. Among the many parameters that determine the physical properties of these alloys, the degree of ordering plays a very important role. Many researchers have undertaken investigations to elucidate the ordering dependence of the physical properties of equiatomic CoTi alloys [7,8,10]. The optical properties of the ordered and the disordered CoTi alloys were measured ellipsometrically, and a peak, was observed at 0.6 ev in the optical conductivity spectrum [7]. This peak was theoretically predicted [11], but had not been observed previously [11, 12]. The evolution in the optical conductivity spectra due to the order-disorder transition has also discussed in the framework of lattice symmetry and the electronic structure of the ordered CoTi compound [7]. The temperature-dependent electrical resistivity was measured [8, 9]. The temperature coefficient of resistivity (TCR) strongly depends on the degree of ordering, and a significantly disordered alloy film even has a negative TCR. The TCR change with the degree of ordering was explained by the loss of translational symmetry, and the observed temperature dependence of resistivity for a partially disordered alloy film was ascribed to partial localization of the electronic states near the Fermi level. For an ordered film, electron-phonon scattering is the main contribution to the resistivity while partial structural disordering enhances the role of electron-phononvibrating impurity scattering and makes spin-diffusive scattering rather noticeable [8]. As aforementioned, one of the very interesting effects of structural disordering on the physical properties of CoTi alloy films is the appearance of a weakly ferromagnetic behavior of the disordered film [7]. The observed magnetic behavior was different from an early investigation [5] in which the disordered CoTi bulk alloys never exhibited any magnetic behavior even at very low temperatures. According to the theoretical calculations [10], electron localization and the magnetic behavior of the disordered alloy film result from the appearance of antistructure Co atoms (AS-Co atoms; Co atoms at Ti sites). One should note that the calculations in Ref. 9 were done for the bulk disordered alloy. A sharp peak in the density-of-states (DOS) curve near the Fermi level grows as the AS-Co atoms are formed. Since the sharp peak in the DOS curve is dominantly composed of the minorityspin d character of the AS-Co atoms, the ferromagnetic behavior of the disordered film naturally emerges. Not only the investigations of the CoTi alloy films but also a series of investigations of transition-metal aluminides was performed by Lee and his coworkers [13] and changes in the various physical properties due to the structural disorder were attributed to the appearance of AS -transition-metal atoms and their nearestneighbor-clustering (NNC) transition-metal atoms. Although the various changes were successfully explained by the structural disorder and some indirect information about the structural disorder was obtained from X-ray diffraction and electron microscopy measurements, more direct evidence for the structural disorder is still lacking, especially, a direct signature of the formation of AS -transition-metal atoms and their NNC transition-metal atoms. Thus, it is natural to choose X-ray absorption spectroscopy (XAS) or, more specifically, extended X-ray absorption fine structure (EXAFS), as a tool for obtaining information about the local structure microscopically since XAS or EXAFS is element-specific and, more importantly, extremely sensitive to the local environment, yielding reliable information on the near-neighbor distance and coordination number [14]. In this research, we employed XAS to understand the local structure of equiatomic CoTi alloy films with various degrees of ordering. II. EXPERIMENTAL Co 0.5 Ti 0.5 alloy films, both ordered and disordered, were prepared by flash evaporation onto singlecrystalline Si and NaCl substrates heated to 730 K and cooled to 150 K by using liquid nitrogen in a high vacuum of better than Pa. The thicknesses of the Co 0.5 Ti 0.5 alloy films were about 100 nm. X-ray fluorescence of the prepared samples confirmed their equiatomic compositions. Structural analysis of the films was performed by using transmission electron microscopy (TEM). In order to have more direct local structural information of the films, we employed XAS. By analyzing the X-ray absorption near-edge spectroscopy (XANES) and the EXAFS spectra, we were able to understand how the chemical ordering was altered as the substrate temperature was changed during deposition. The Co and Ti K-edge XAS spectra were obtained at the 3C1 EXAFS beam line of the Pohang Light Source. The X-ray energy was controlled by using a Si(111) double-crystal monochromator. The spectra were collected at room temperature in the total-electron-yield mode, which is particularly suitable for thin-film materials. III. RESULTS AND DISCUSSION The results of the TEM study on the obtained Co 0.5 Ti 0.5 alloy films are presented in Fig. 1. The TEM pattern for the film deposited onto the substrate at 730 K [Fig. 1(a)] exhibits a mixture of diffraction rings typical of the bcc lattice and a series of additional superstructure rings, which are attributed to the reflections from the (100), (111), and (210) atomic planes. The mean grain size was estimated to be about 50 nm [Fig. 1(b)].

3 -248- Journal of the Korean Physical Society, Vol. 43, No. 2, August 2003 Fig. 1. TEM (a) diffraction pattern and (b) dark-field image of the CoTi film deposited at 730 K and (c) diffraction pattern and (d) dark-field image of the CoTi film deposited at 150 K. Fig. 2. (a) Normalized Co K-edge absorption spectra and (b) the derivative spectra of the ordered and disordered CoTi alloy films. All the spectra are aligned to the edge jump. This result shows that a stable phase of the equiatomic B2 CoTi alloy with a high degree of ordering is formed when the substrate is held at a high temperature during deposition. However, as shown in Figs. 1(c) and 1(d), the film deposited at 150 K turns out to be a considerably disordered polycrystalline film which does not show any visible superstructure ring. The mean grain size was estimated to be less than 5 nm. The β-phase(b2) CoTi alloy has a CsCl-type crystal structure which is stable up to the melting point (1508 K) [15]. Due to this high thermal stability, all our preliminary attempts to obtain a bulk CoTi disordered alloy by quenching from high temperature had no success. However, as shown in Fig. 1(c), we could obtain the disordered state of the equiatomic CoTi alloy through growth of an alloy film by vapor-quenching deposition. The TEM results [Fig. 1(b) and 1(d)] indicate that the disordered CoTi alloy film has a much smaller grain size than the ordered one. Previous reports [7] stated that the ordered CoTi film samples had finer grain structures than bulk samples. The grain boundaries were usually highly disordered or even amorphous. Therefore, it was possible to produce an equiatomic CoTi alloy film with a significantly increased degree of ordering by deposition at an elevated temperature of 730 K and a substantially disordered film by maintaining the substrate at a temperature as low as 150 K during deposition. Since the TEM diffraction pattern shows both a smeared halo, typical of an amorphous sample, and very weak but discernible ring outside the halo, we could not completely resolve the structural characteristics of the film deposited at low temperature, i.e., whether it was an amorphous or a very fine-grained polycrystalline (or even nanocrystalline) sample. However, the XAS results showed that it was rather amorphous-like (see below). It was also possible to increase the degree of ordering by subsequent heat treatment at 730 K for 45 m after lowtemperature deposition [7]. The degree of ordering for the annealed film was not as high as it was for the films deposited at high temperatures. Fig. 3. (a) Normalized Ti K-edge absorption spectra and (b) the derivative spectra of the ordered and disordered CoTi alloy films. All the spectra are aligned to the edge jump. Figures 2(a) and 3(a) show the normalized Co and Ti K-edge absorption spectra for the films deposited at 730 K and 150 K, respectively. The spectra have had the background subtracted and were normalized as follows: The extrapolation of the linear fit of pre-edge absorption coefficient was subtracted from each raw spectrum. Then, the resultant curves were normalized by multiplying by the factor that made the continuum step equal to unity at higher energy [16,17]. For the alloy film deposited at 730 K, oscillations in the Co [Fig. 2(a)] and the Ti [Fig. 3(a)] K-edge spectra were clearly seen, even in the high-energy region. On the other hand, in case of the film deposited at 150 K, the oscillation in the Co K -edge spectrum [Fig. 2(a)] gradually died away as the photon energy was increased. In addition, no significant oscillation was observed in the Ti K-edge spectrum [Fig. 3(a)]. Generally, an X-ray absorption spectrum can be divided into two region: the XANES region up to 50 ev from the absorption edge and the EXAFS region from 50 ev to over 1000 ev. The small oscillations in the EXAFS region are referred to as fine structure (FS) features [14]. This oscillation, especially, the shape and magnitude, contain information on the local

4 Local Structures of Equiatomic CoTi Alloy Films Y. S. Lee et al Fig. 4. FEFF6 multiple scattering calculations for the FS of the (a) Co K-edge spectra and (b) Ti K-edge spectra of B2- CoTi, together with the corresponding experimental results for the CoTi alloy film deposited at 703 K. Note that the principle FS features above 20 ev are well aligned despite the background difference. The simulated spectra for (c) the Co K-edge and (d) the Ti K-edge of B2-CoTi alloys with different lattice constants are also included. environment around the absorbing atoms. The magnitude change of oscillatory part can be due to thermal broadening [18], film thickness effects [19], and so on. In this study, we can safely disregard the thermal and the thickness effects because all the absorption spectra were obtained at the same temperature, i.e., room temperature; moreover, the samples had the same compositions and thicknesses. Therefore, the decrease and/or disappearance of the oscillation in the spectrum of the film deposited at 150 K [Fig. 2(a)] implies that the ordering around the absorbing atoms is broken compared to that at 730 K. These results reconfirm, at least in a local sense, the arguments deduced from the TEM analysis. Particularly, it should be noted that the ordering at the Ti site of the film deposited at 150 K is weaker than the ordering at the Co site. This Ti spectrum [Fig. 3(a)], containing no oscillation, may indicate a local amorphous structure. However, the amorphous-phase formation of the Ti atoms was not observed in the TEM study since generally TEM does not give information on microscopic local structures. The derivative spectra in Figs. 2 and 3 will be discussed later. The FS features are caused by interference between the outgoing photoelectrons and the backscattered ones from the near-neighbor atoms. The details of this process can involve both single and multiple scattering and is quite complicated. However, it is well established, both empirically and theoretically, that the locations and/or frequencies of the FS are sensitive to the near-neighbor distances around the absorbing atom. It would be useful to quantitatively correlate the FS feature shifts with lattice parameter changes. In Figs. 4(a) and 4(b), we present the results of a multiple scattering calculation including 10 atomic shells for cubic B2-CoTi with a = nm (the 1st shell of 8 Co-Ti : nm, the 2nd shell of 6 Co-Co or Ti-Ti : nm, etc.) using the FEFF6 computer code developed by the University of Washington [20, 21]. No Debye-Waller damping was included in the calculated spectrum, which implies a greater FS amplitude in the calculation. Comparison of the calculated FS peak positions with our experiment shows a very good correlation in the energy range above 20 ev [see Fig. 4(a)]. The results indicate that the CoTi film deposited at 730 K clearly has a cubic B2 structure with a lattice parameter of a = nm. In comparison with the simulation for the ideal cubic B2-CoTi bulk alloy with a = nm [22], the experimental FS turns out to be shifted to higher photon energy, as shown in Figs. 4(c) and 4(d). These shifts may be expected due to the lattice compression in thin films [16], although sometimes they might be due to an asymmetric radial distribution function in the calculation [23]. The resultant electronic effects are presumably responsible for the disparity near the edge between the simulation and the experiment. From the EXAFS results, we can suggest that the local structure of the alloy film deposited at 730 K is well ordered, but in a compressed cubic B2 phase, and the degree of ordering is higher than that at 150 K. The Ti atoms in the film deposited at 150 K form an amorphous phase, at least locally. In this result, we obtained ordered and disordered equiatomic CoTi film alloys which differed from the bulk alloys. A number of spectral features in the vicinity of the edge can be seen more clearly in the derivative spectra shown in Figs. 2(b) and 3(b). For the film deposited at 730 K, several distinct peaks were observed in both the Co and the Ti K-edge spectra. The features in the region of 0 20 ev above the inflection peak (peak I) [insets in Fig. 2(b) and Fig. 3(b)] are XANES-related. Generally, peak I corresponds to the dipole forbidden 1s 3d transition, peak II is assigned to the 1s 4p transition by the selection rule, and the peaks in region III are most likely due to multiple-scattering effects [18,24]. As the insets of Figs. 2(b) and 3(b) show, the film deposited at 730 K presents distinct peaks in region III while the one deposited at 150 K has only a broad peak. This may reflect the fact that the film deposited at 730 K has a substantial long-range order (LRO) as compared with that at 150 K because XANES, as opposed to EXAFS, is usually considered to be due to a LRO [19]. We may not say explicitly that a film has LRO or short-range order (SRO) based only on the XAS data even though EXAFS and XANES usually reflect SRO and LRO, respectively [19]. However, by considering the XAS results together with the TEM results, we can argue that, for the film deposited at 730 K, both Co and Ti atoms form the ordered structure of B2 phase, but for the alloy film at 150 K, both Co and Ti atoms form an amorphous-like phase, implying a considerable amount of segregation and clustering of the Co atoms. The clustering of Co atoms results in a weakly ferromagnetic be-

5 -250- Journal of the Korean Physical Society, Vol. 43, No. 2, August 2003 Fig. 6. Fourier transforms of the k 3 χ(k) EXAFS spectra for the CoTi alloy films deposited at 730 K and 150 K, and the respective pure elements: the (a) Co K-edge and the (b) Ti K-edge radial structure functions. Fig. 5. k 3 χ(k) EXAFS spectra of the CoTi alloy films deposited at 730 K and 150 K at the (a) Co K-edge and the (b) Ti K-edge. The amplitudes are normalized to the edge jump. havior [7,10]. In order to obtain more detailed structural information, we display the k 3 -weighted EXAFS spectra, k 3 χ(k), at the Co and the Ti sites of the films in Fig. 5. The pre-edge background was extracted using the AUTOBK code [25,26]. The Co K-edge k 3 χ(k) spectrum of the film deposited at 730 K reveals multiple oscillations of large amplitude while that of the film deposited at 150 K is dominated by a single oscillation. It is well known that, in general, the k 3 χ(k) spectrum of an ordered sample includes multiple oscillations with large amplitudes and that of a completely disordered one shows only a single oscillation [27]. Although the Ti K-edge k 3 χ(k) spectrum of the film prepared at 730 K also exhibits multiple oscillations, they are less evident in the Co K-edge k 3 χ(k) spectrum in which only minor oscillations are clearly discernible. This may indicate that, even for the ordered film, the degree of ordering seen at the Co sites is much greater than that seen at the Ti sites. We call the film deposited at an elevated temperature an ordered film, but a small, but non-negligible, amount of structural disorder still exists because of the polycrystalline character of the film. At the same time, it is noted that there might be other reasons for this difference in the order seen at the Ti and the Co sites, which should be investigated further. The argument given above is also consistent with the case of the film deposited at 150 K. The Ti K-edge k 3 χ(k) spectrum of the film deposited at 150 K exhibits random oscillations, but the assignment of the peak positions is almost impossible, indicating that a nearly amorphous phase is formed. Thus, the analyses of the weighted EXAFS spectra further support the previous arguments that the Co and the Ti atoms form an ordered structure in the film deposited at 730 K while, in the deposited film at 150 K, the Co atoms form a disordered structure and the Ti atoms form an amorphous phase. In Fig. 6, the Fourier transforms of the EXAFS (FT- EXAFS) spectra for the Co and Ti K-edges are presented. The FT-EXAFS at the Co sites of the CoTi films are different from that of pure Co [Fig. 6(a)]. The main peak corresponding to the first shell of FT-EXAFS for the film deposited at 730 K is shifted toward a larger radial distance with respect to the peak for pure Co. However, for the film deposited at 150 K, the main-peak stays at the same position as for pure Co, and the peaks at larger radial distances corresponding to the second shell and other subshells disappear. This result can be interpreted as follows: There are only Co-Co bonds in pure Co, while not only the Co-Co bonds but also Co-Ti and Ti-Ti bonds are possible in the alloy. Since the ionic radius of Ti (0.146 nm) is larger than that of Co (0.125 nm), the bond length of Co-Ti (0.271 nm) is greater than that of Co-Co (0.250 nm) when a similar argument to the one given in Ref. 25 is employed. Therefore, the shift of the main peak toward a larger radial distance reflects the fact that the main peak of FT-EXAFS for the film deposited at 730 K is predominantly due to Co-Ti bonds, which might be naturally understood by the formation of the equiatomic B2 phase. In a perfectly ordered B2- phase equiatomic alloy, each atom is surrounded by 8 nearest-neighbor atoms of a different kind. Meanwhile,

6 Local Structures of Equiatomic CoTi Alloy Films Y. S. Lee et al the film deposited at 150 K has its main FT-EXAFS peak at the same radial distance as the pure Co film does. This is another manifestation of the formation of the Co clusters, that is, AS-Co atoms and their NNC Co atoms. As seen in Fig. 6(b), the main peak corresponding to the first shell of the Ti K-edge FT-EXAFS of the film deposited at 730 K is shifted toward a smaller radial distance compared to that for pure Ti, which is consistent with the Co K-edge FT-EXAFS in Fig. 6(a), which indicates the formation of Co-Ti bonds in the film deposited at 730 K. For the film deposited at 150 K, however, the spectrum shows no major peak, indicating that an amorphous phase is formed. It is interesting to note that the Co K-edge XAS spectrum of the film deposited at 150 K is very similar to that in Ref. 27. The Co K-edge FT-EXAFS shown in Fig. 6(a) has a shape typical of an amorphous structure: shorter distance, lower intensity for the first shell, and quasiabsence of more distant shells. From this resemblance, we may conclude that the film deposited at 150 K is amorphous. However, from the results of the TEM study, we cannot completely exclude the possibility of the presence of a very fine-grained polycrystalline, or even nanocrystalline, structure. Therefore, we have to say that the film deposited at 150 K is amorphous-like. Concerning the absorption spectra of both the CoTi films deposited at 730 K and 150 K, the Co K-edge spectrum is composed of modulations due to Co-Ti and Co- Co bonds, and the Ti K-edge spectrum is produced by Ti-Co and Ti-Ti bonds. The shift of the main peak in the FT-EXAFS of Co (Ti) toward a larger (smaller) radial distance for the film deposited at 730 K indicates that the nearest-neighbor bonds are mostly Co-Ti bonds; thus, the film is close to a perfect B2 phase. On the other hand, the constancy of the main peak of Co FT-EXAFS and the absence of the main peak in the Ti FT-EXAFS for the film deposited at 150 K may be interpreted as an indication that the film is amorphous-like and that its the amorphous-like nature is predominantly caused by formation of AS-Co atoms with their NNC Co atoms (i.e., Co clusters). This Co-cluster formation in the film deposited at 150 K is sufficiently supported by the transport properties [7,8,10,29] of these alloy films: the number of Co clusters increases as the degree of ordering is weakened, and the clustering of Co atoms results in a weakly ferromagnetic behavior of the film. IV. CONCLUSIONS An amorphous-like phase can be obtained in equiatomic CoTi alloy films by means of vapor quenching deposition onto glass substrates cooled by liquid nitrogen. According to the analyses of the EXAFS spectra, the Co and the Ti atoms are arranged in the ordered equiatomic B2 phase for the film deposited at 730 K while in the film deposited at 150 K, both Co and Ti atoms form an amorphous-like structure, at least, locally. The Co K-edge FT-EXAFS spectrum for the film deposited at 150 K has its main peak at the same radial distance as the pure Co film, indicating more directly the formation of Co clusters, which is consistent with the conclusions drawn in other works; The Ti K-edge x- ray absorption spectrum shows no major peak, implying that the Ti atoms form an amorphous net. ACKNOWLEDGMENTS This work was supported by the Korea Science Engineering Foundation through the Quantum Photonic Science Research Center at Hanyang University and grant No. R , and by the Korea Research Foundation grants (Nos DP0193 and DS0015). REFERENCES [1] G. M. Michal and R. Sinclair, Acta Crystallogr. B 37, 1803 (1981). [2] F. E. Wang, W. J. Buehler and S. J. Pickart, J. Appl. Phys. 36, 3232 (1965). [3] Y. Asada and H. Nose, J. Phys. Soc. Jpn. 35, 409 (1973). [4] G. Hilscher, N. Buis and J. J. M. Franse, Physica B 91, 170 (1977). [5] K. Endo, I. An and A. Shinogi, J. Phys. F: Metal Phys. 7, L99 (1977). [6] A. Jezierski and G. Gorstel, Physica B 205, 397 (1995). [7] Y. P. Lee, K. W. Kim, J. Y. Rhee, Y. V. Kudryavtsev and V. V. Nemoshkalenko, Phys. Rev. B 60, 8067 (1999). [8] Y. P. Lee, K. W. Kim, J. Y. Rhee, Yu V. Kudryavtsev, V. V. Nemoshkalenko and V. G. Prokhorov, Eur. Phys. J. B (2000). [9] A. Suzuki and S. Matsutani, J. Korean Phys. Soc. 38, 540 (2001). [10] J. Y. Rhee, Yu V. Kudryavtsev, K. W. Kim and Y. P. Lee, IEEE Trans. Mag. 35, 3745 (1999). [11] J. Y. Rhee, B. N. Harmon and D. W. Lynch, Phys. Rev. B 55, 4124 (1997). [12] I. I. Sasovskaya, Phys. Met. Metall. 69, 72 (1990); I. I. Sasovskaya, Phys. Status Solidi B 164, 327 (1990). [13] See, for example, Y. P. Lee, K. W. Kim, J. Y. Rhee and Yu V. Kudryavtsev, Phys. Rev. B 59, 546 (1999). [14] B. K. Teo, Basic Principles and Data Analysis (Springer- Verlag, Berlin, 1986), Ch. 2. [15] T. B. Massalski, Binary Alloy Phase Diagrams (American Society for Metals, Metals Park, Ohio, 1986), Vol. I, p [16] K. H. Chae, S. M. Jung, Y. S. Lee, C. N. Whang, Y. Jeon, M. Croft, D. Sills, P. H. Ansari and K. Mack, Phys. Rev. B 53, (1996). [17] T. Sikora, G. Hug, M. Jaouen and J. J. Rehr, Phys. Rev. B 62, 1723 (2000). [18] J. Wong and H. H. Liebermann, Phys. Rev. B 29, 651 (1984).

7 -252- Journal of the Korean Physical Society, Vol. 43, No. 2, August 2003 [19] See Advances in Catalysis, edited by D. D. Eley, H. Pines and P. B. Weisz (Academic Press, New York, 1986), Vol. 34. [20] J. J. Rehr and R. C. Albers, Phys. Rev. B 41, 8139 (1990). [21] J. J. Rehr, S. I. Zabinsky and R. C. Albers, Phys. Rev. Lett. 69, 3397 (1992). [22] P. Villars and L. D. Calvert, Pearson s Handbook of Crystallographic Data for Intermetallic Phases (American Society for Metal, Metals Park, Ohio, 1989). [23] P. Eisenberger and G. S. Brown, Solide State Commun. 29, 481 (1979). [24] P. J. Durham, J. B. Pendry and C. H. Hodges, Solide State Commun. 38, 159 (1981). [25] J. Newville, P. Livins, Y. Yacoby, J. J. Rehr and E. A. Stern, Phys. Rev. B 47, (1993). [26] J. J. Rehr, C. H. Booth, F. Bridges and S. I. Zabinsky, Phys. Rev. B 49, (1994). [27] T. K. Sham, Y. M. Yiu, M. Kuhn and K. H. Tan, Phys. Rev. B 41, (1990). [28] H. Magnan, D. Chandesris, G. Rossi, G. Jesquel, K. Hricovini and J. Lecante, Phys. Rev. B 40, R9989 (1989). [29] H.-J. Yeon and J.-S. Kim, J. Korean Phys. Soc. 41, 265 (2002).

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