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Electron diffraction structure analysis for amorphous materials
Materials Chemistry and Physics 81 (2003) 360–363
Electron diffraction structure analysis for amorphous materials Y. Hirotsu a,∗ , T. Ohkubo b , I.-T. Bae c , M. Ishimaru a b
a The Institute of Scientific and Industrial Research, Osaka University, Osaka 567-0047, Japan Materials Engineering Laboratory, National Institute for Materials Science, Tsukuba 305-0047, Japan c Department of Materials Science and Engineering, Osaka University, Osaka 565-0871, Japan
Abstract Amorphous structures of liquid-quenched Fe90 Zr7 B3 and ion-bombarded SiC were studied using modern electron diffraction structure analysis techniques. From a reverse Monte-Carlo (RMC) structural simulation on the experimental atomic pair distribution function (PDF) of amorphous Fe90 Zr7 B3 , “nano-scale phase separation” was found to occur in this structure with spatial distributions of body-centered cubic-like, icosahedral and trigonal prism clusters. In amorphous SiC, the network includes not only heteronuclear (Si–C) bonds but also homonuclear (Si–Si and C–C) bonds. The ratio of homonuclear to heteronuclear bonds changes due to structural relaxation. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Electron diffraction; Amorphous structure analysis; Fe–Zr–B alloy; SiC; Ion bombardment
1. Introduction In amorphous structures, atomic short-range order (SRO) which defines the nearest-neighbor atomic arrangement [1] is important to understand atomic correlations and the correlation distances. The SRO analysis can be achieved by the atomic pair distribution function (PDF) analysis using X-ray, neutron and electron diffraction techniques [1]. In the structure analysis electron diffraction has an advantage to study atomic correlations concerned with lighter atoms and also to obtain scattering information up to high scattering angles. Nano-beam diffraction is another advantage of electron diffraction in the case of local area amorphous structure analysis. Recent advances in electron intensity recording systems like imaging-plate (IP) and slow-scan CCD have made it possible to measure electron intensities precisely for electron diffraction intensity analysis. Recent electron energy loss spectroscopy (EELS) and energy-filtering techniques which can remove the inelastic part of intensity help precise diffraction intensity analysis. In these days, these new techniques in addition to nano-diffraction and high-resolution transmission electron microscopy (TEM) techniques are becoming necessary for understanding the atomic structures of non-equilibrium materials comprehensively. We have applied the IP, EELS and energy-filtering techniques to the electron diffraction PDF analysis of various amorphous alloys [2–5] and ceramics [6] to understand ∗ Corresponding author. Tel.: +81-6-6879-8430; fax: +81-6-6879-8434. E-mail address: [email protected] (Y. Hirotsu).
their local atomic arrangements through SRO structures. In this paper some important aspects of amorphous Fe–Zr–B (a-Fe–Zr–B) and amorphous silicon carbide (a-SiC) structures revealed by electron diffraction structure analyses are presented together with the analysis method. The a-Fe–Zr–B alloy is one of the fundamental magnetic alloys to form a soft-magnetic nanostructure on annealing [7], and a-SiC is now attracting much interests for the future electronics materials.
2. Experimental An amorphous Fe90 Zr7 B3 (a-Fe90 Zr7 B3 ) alloy ribbon, about 20 m thick and 15 mm wide, was prepared by a single-roll rapid quenching technique, while a-SiC was produced by ion irradiation into a single crystalline 6H–SiC wafer to a fluence of 1016 cm−2 with a 150 keV Ar+ beam. For TEM observation and electron diffraction, the specimens were thinned by ion-milling. TEM and electron diffraction studies were performed using 200 kV electron microscopes, JEM-2010 and JEM-2010F. Electron diffraction patterns were recorded on IPs and were read using a IP reader (FDL-5000). In the PDF analysis the intensity recorded was divided into 16,384 gray levels and were digitized using a computer. To decrease the multiple scattering, thin specimen areas were selected. In the case of a-Fe90 Zr7 B3 , the inelastic part of intensities was removed using an energy filter. The width of the energy slit was 15 eV. In electron diffraction, the camera lengths
0254-0584/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0254-0584(03)00022-1
Y. Hirotsu et al. / Materials Chemistry and Physics 81 (2003) 360–363
were corrected by using reference diffraction patterns from fine gold particles. On the other hand, SiC consists of light element, so we did not remove the inelastic scattering.
3. Electron diffraction structure analysis According to diffraction theory [1], a reduced interference function can be obtained as F(Q) =
[Iobs (Q) − BG(Q)]Qf 2 BG(Q)f 2
(1)
where Iobs (Q) is the observed elastic scattering intensity and Q the scattering vector (Q = 4π sin θ/λ; θ is the half scattering angle and λ, in the present case, the electron wave length). BG(Q) is the background intensity which smoothly links the middle points between the intensity maxima and minima of the halo-intensity profile almost along the f 2 curve. The square-mean and mean-square atomic scattering factors for electrons, f 2 and f 2 , are expressed as f 2 = 2 Nj fj2 /N and f 2 = Nj fj /N 2 , where N = Nj and Nj and fj are the atom number and atomic scattering factor for element j, respectively. The function f (Q) is related to the reduced distribution function G(r) by the Fourier transform as ∞ G(r) = (2/π) F(Q) sin(Qr) dQ = 4πr[ρ(r) − ρ0 ] (2)
361
the most important procedure is to obtain diffraction intensity profiles as close as that of kinematical intensity with less inelastic scattering and multiple scattering, and with good linearity in intensity recording. In the case of intensity close to the kinematical one, the background BG(Q) can be drawn almost along the f 2 curve. In making a final plausible structure model which can explain the experimental PDF profile very well, the reverse Monte-Carlo (RMC) simulation [8] was used especially for the a-Fe90 Zr7 B3 alloy. It is noted that the RMC simulation can be an effective procedure to obtain partial PDFs for constituting atoms (in electron diffraction there is no way to obtain experimental partial PDFs). As an indication for a convergence of the simulation, the χ2 criterion [8] was taken χ2 =
(gexp (r) − gcal (r))2 N
(3)
where gexp (r) is the experimental total PDF, gcal (r) the RMC-calculated total PDF and N the number of data points. To minimize the χ2 value at least 105 iterations were necessary for a model of 2500 atoms. After obtaining a preferable structure model, Voronoi polyhedral analysis [9] was also performed to the local structure analysis of the structure model.
4. Results and discussion
0
where ρ(r) is the atomic density and ρ0 the average atomic density. The atomic PDF g(r) (= ρ(r)/ρ0 ) and the RDF 4πr2 ρ(r) can be obtained by G(r). The average atomic density ρ0 can be obtained from the specimen density. It should be noted that in a precise electron diffraction PDF analysis
4.1. Amorphous Fe90 Zr7 B3 structure Fig. 1 shows the RMC-PDF fitting to the experimental PDF for the a-Fe90 Zr7 B3 alloy. The fitting of gcal (r) to gexp (r) is very good, and the partial PDFs for the Fe–Fe,
Fig. 1. Experimental and RMC-calculated g(r) profiles for as-quenched Fe90 Zr7 B3 . Partial gFe–Fe (r), gFe–Zr (r) and gFe–B (r) calculated are also shown together with the calculated total g(r).
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Fig. 2. Deformed-bcc (dark), icosahedra (light) and trigonal prism (semi-dark) clusters found in the RMC-simulated structure.
Fe–Zr and Fe–B correlations can be seen in the figure. As the initial structure model a dense-random-packing model with 2500 atoms in a cubic space of (3.192 nm)3 was constructed, followed by a static relaxation using Lenard–Jones potentials. The density of the a-Fe90 Zr7 B3 alloy was measured by the Archimedean method. According to the Voronoi polyhedral analysis of the final RMC-simulated structure with central Fe, Zr and B, deformed body-centered cubic (bcc) clusters with indices such as “028400” and “036400” were frequently observed. The bcc-like clusters are mostly composed of Fe atoms and the amount of Fe atoms concerning with the bcc-related clusters in the model structure are about 40 at.%. Icosahedral (00 12 000) polyhedra were observed with high density. The trigonal prisms and Archimedean anti-prisms are also observed around the B atoms. These different types of atomic clusters are arranged in space as shown in Fig. 2. Zr and B atoms were found to be distributed almost randomly. As in the eutectic amorphous Fe–B alloy [10], regions of atomic medium range order (MRO) as small as 1 nm which were identified as bcc MROs were observed by high-resolution TEM imaging in an a-Fe90 Zr7 B3 alloy [3], which corresponds well to the local formation of the bcc Fe-like atomic region as shown in Fig. 2. It has been thus demonstrated from the present PDF and TEM studies that a “nano-scale phase separation” exists in the a-Fe90 Zr7 B3 alloy. The local formation of the bcc Fe clusters is supposed to cause nucleation sites for the formation of bcc Fe nanocrystals in the later annealing stage. A detailed process of structural development of such bcc Fe nanocrystals on annealing has been argued [3].
Fig. 3. (a) Reduced interference functions f (Q) and (b) pair-distribution functions g(r) of as-irradiated (broken line) and 800 ◦ C annealed a-SiC (solid line).
4.2. Amorphous SiC formed by ion bombardment and structural change on annealing Fig. 3a indicates the reduced interference function f (Q) of the sample annealed at 800 ◦ C (solid line), compared to the f (Q) of the as-irradiated sample (broken line). Very weak intensity profiles up to high scattering angles as high as Q ≈ 220 nm−1 can be recorded well above the background intensity level of the imaging plate. This scattering vector is much larger than that measured by previous electron diffraction [11,12] and X-ray diffraction experiments [13] for a-SiC. The measured f (Q) exhibits clear differences both in the height and width of the first and second peaks. These peaks become more pronounced with annealing. Reduced radial distribution functions, g(r), were calculated via Fourier transformation of f (Q). The resulting g(r) are shown in Fig. 3b. Fig. 3b also shows the atomic distances in crystalline SiC (marked with the arrows in the bottom part of Fig. 3b). The first and second nearest neighbors are centered at 0.188(±0.002) and 0.307 nm, respectively. These values correspond to the bond lengths of Si–C (the first nearest neighbor) and Si–Si (the second nearest neighbor) in crystalline SiC. In addition to these peaks, subpeaks appear in the both sides of the first peak in Fig. 3b. Their positions are assignable to C–C and Si–Si bond lengths [14,15],
Y. Hirotsu et al. / Materials Chemistry and Physics 81 (2003) 360–363
suggesting that a-SiC networks contain not only heteronuclear bonds but also homonuclear bonds. The g(r) obtained here is in good agreement with molecular-dynamics simulations of a-SiC quenched from the liquid [14,15] or produced by ion irradiation [16]. Substantial changes in the g(r) function were observed during annealing. The major differences between as-irradiated and annealed a-SiC are apparent within the second coordination shell (<0.4 nm); only small differences are observed beyond the second peak. This implies that the largest variations in atomic configurations are in the SRO range. The locations of the first and second nearest neighbors are not affected by annealing. The peak of the heteronuclear bonds (0.188 nm) become more pronounced, whereas the homonuclear bonds (0.151 and 0.238 nm) decrease during annealing. Our present study is the first to provide an evidence of structural changes due to relaxation of a-SiC by means of diffraction analysis.
Acknowledgements The authors express their thanks to Dr. S.A. Makino and K.E. Sickagus for preparing specimens for this study. The present study was partly supported by the Special Coordination Funds for Promoting Science and Technology on “Nanohetero metallic materials” from the Ministry of Education, Science, Sports and Culture, Japan.
363
References [1] S.R. Elliott, Physics of Amorphous Materials, Section 3, Longman Science and Technology, Essex, 1990. [2] T. Ohkubo, Y. Hirotsu, M. Matsushita, J. Electr. Microsc. 48 (1999) 1005. [3] T. Ohkubo, H. Kai, A. Makino, Y. Hirotsu, Mater. Sci. Eng. A 312 (2001) 274. [4] T. Ohkubo, T. Hiroshima, Y. Hirotsu, A. Inoue, T. Oikawa, Mater. Trans. JIM 41 (2000) 1385. [5] T. Takagi, T. Ohkubo, Y. Hirotsu, B.S. Murty, K. Hono, D. Shindo, Appl. Phys. Lett. 79 (2001) 485. [6] Y. Hirotsu, M. Ishimaru, T. Ohkubo, T. Hanada, M. Sugiyama, J. Electr. Microsc. 50 (2001) 435. [7] K. Suzuki, N. Kataoka, A. Inoue, A. Makino, T. Matsumoto, Mater. Trans. JIM 31 (1990) 743. [8] P.A. Duine, J. Sietsma, B.J. Thijsse, L. Pusztai, Phys. Rev. B 50 (1994) 13240. [9] T. Kondo, K. Tsumuraya, J. Chem. Phys. 94 (1991) 8220. [10] Y. Hirotsu, R. Akada, Jpn. J. Appl. Phys. 23 (1984) L479. [11] J. Bentley, P. Angelini, A.P. Gove, P.S. Sklad, A.T. Fisher, Inst. Phys. Conf. Ser. 98 (1989) 107. [12] A. Sproul, D.R. McKenzie, D.J.H. Cookayne, Phil. Mag. B 54 (1986) 113. [13] C. Meneghini, S. Pascarelli, F. Boscherini, S. Mobilio, F. Evangelisti, J. Non-Cryst. Solids 137/138 (1991) 75. [14] F. Finocchi, G. Galli, M. Parrinello, C.M. Bertoni, Phys. Rev. Lett. 68 (1992) 3044. [15] D. Mura, L. Colombo, R. Bertoncini, G. Mula, Phys. Rev. B 58 (1998) 10357. [16] F. Gao, W.J. Weber, J. Appl. Phys. 89 (2001) 4275.
Electron diffraction structure analysis for amorphous materials Y. Hirotsu a,∗ , T. Ohkubo b , I.-T. Bae c , M. Ishimaru a b
a The Institute of Scientific and Industrial Research, Osaka University, Osaka 567-0047, Japan Materials Engineering Laboratory, National Institute for Materials Science, Tsukuba 305-0047, Japan c Department of Materials Science and Engineering, Osaka University, Osaka 565-0871, Japan
Abstract Amorphous structures of liquid-quenched Fe90 Zr7 B3 and ion-bombarded SiC were studied using modern electron diffraction structure analysis techniques. From a reverse Monte-Carlo (RMC) structural simulation on the experimental atomic pair distribution function (PDF) of amorphous Fe90 Zr7 B3 , “nano-scale phase separation” was found to occur in this structure with spatial distributions of body-centered cubic-like, icosahedral and trigonal prism clusters. In amorphous SiC, the network includes not only heteronuclear (Si–C) bonds but also homonuclear (Si–Si and C–C) bonds. The ratio of homonuclear to heteronuclear bonds changes due to structural relaxation. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Electron diffraction; Amorphous structure analysis; Fe–Zr–B alloy; SiC; Ion bombardment
1. Introduction In amorphous structures, atomic short-range order (SRO) which defines the nearest-neighbor atomic arrangement [1] is important to understand atomic correlations and the correlation distances. The SRO analysis can be achieved by the atomic pair distribution function (PDF) analysis using X-ray, neutron and electron diffraction techniques [1]. In the structure analysis electron diffraction has an advantage to study atomic correlations concerned with lighter atoms and also to obtain scattering information up to high scattering angles. Nano-beam diffraction is another advantage of electron diffraction in the case of local area amorphous structure analysis. Recent advances in electron intensity recording systems like imaging-plate (IP) and slow-scan CCD have made it possible to measure electron intensities precisely for electron diffraction intensity analysis. Recent electron energy loss spectroscopy (EELS) and energy-filtering techniques which can remove the inelastic part of intensity help precise diffraction intensity analysis. In these days, these new techniques in addition to nano-diffraction and high-resolution transmission electron microscopy (TEM) techniques are becoming necessary for understanding the atomic structures of non-equilibrium materials comprehensively. We have applied the IP, EELS and energy-filtering techniques to the electron diffraction PDF analysis of various amorphous alloys [2–5] and ceramics [6] to understand ∗ Corresponding author. Tel.: +81-6-6879-8430; fax: +81-6-6879-8434. E-mail address: [email protected] (Y. Hirotsu).
their local atomic arrangements through SRO structures. In this paper some important aspects of amorphous Fe–Zr–B (a-Fe–Zr–B) and amorphous silicon carbide (a-SiC) structures revealed by electron diffraction structure analyses are presented together with the analysis method. The a-Fe–Zr–B alloy is one of the fundamental magnetic alloys to form a soft-magnetic nanostructure on annealing [7], and a-SiC is now attracting much interests for the future electronics materials.
2. Experimental An amorphous Fe90 Zr7 B3 (a-Fe90 Zr7 B3 ) alloy ribbon, about 20 m thick and 15 mm wide, was prepared by a single-roll rapid quenching technique, while a-SiC was produced by ion irradiation into a single crystalline 6H–SiC wafer to a fluence of 1016 cm−2 with a 150 keV Ar+ beam. For TEM observation and electron diffraction, the specimens were thinned by ion-milling. TEM and electron diffraction studies were performed using 200 kV electron microscopes, JEM-2010 and JEM-2010F. Electron diffraction patterns were recorded on IPs and were read using a IP reader (FDL-5000). In the PDF analysis the intensity recorded was divided into 16,384 gray levels and were digitized using a computer. To decrease the multiple scattering, thin specimen areas were selected. In the case of a-Fe90 Zr7 B3 , the inelastic part of intensities was removed using an energy filter. The width of the energy slit was 15 eV. In electron diffraction, the camera lengths
0254-0584/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0254-0584(03)00022-1
Y. Hirotsu et al. / Materials Chemistry and Physics 81 (2003) 360–363
were corrected by using reference diffraction patterns from fine gold particles. On the other hand, SiC consists of light element, so we did not remove the inelastic scattering.
3. Electron diffraction structure analysis According to diffraction theory [1], a reduced interference function can be obtained as F(Q) =
[Iobs (Q) − BG(Q)]Qf 2 BG(Q)f 2
(1)
where Iobs (Q) is the observed elastic scattering intensity and Q the scattering vector (Q = 4π sin θ/λ; θ is the half scattering angle and λ, in the present case, the electron wave length). BG(Q) is the background intensity which smoothly links the middle points between the intensity maxima and minima of the halo-intensity profile almost along the f 2 curve. The square-mean and mean-square atomic scattering factors for electrons, f 2 and f 2 , are expressed as f 2 = 2 Nj fj2 /N and f 2 = Nj fj /N 2 , where N = Nj and Nj and fj are the atom number and atomic scattering factor for element j, respectively. The function f (Q) is related to the reduced distribution function G(r) by the Fourier transform as ∞ G(r) = (2/π) F(Q) sin(Qr) dQ = 4πr[ρ(r) − ρ0 ] (2)
361
the most important procedure is to obtain diffraction intensity profiles as close as that of kinematical intensity with less inelastic scattering and multiple scattering, and with good linearity in intensity recording. In the case of intensity close to the kinematical one, the background BG(Q) can be drawn almost along the f 2 curve. In making a final plausible structure model which can explain the experimental PDF profile very well, the reverse Monte-Carlo (RMC) simulation [8] was used especially for the a-Fe90 Zr7 B3 alloy. It is noted that the RMC simulation can be an effective procedure to obtain partial PDFs for constituting atoms (in electron diffraction there is no way to obtain experimental partial PDFs). As an indication for a convergence of the simulation, the χ2 criterion [8] was taken χ2 =
(gexp (r) − gcal (r))2 N
(3)
where gexp (r) is the experimental total PDF, gcal (r) the RMC-calculated total PDF and N the number of data points. To minimize the χ2 value at least 105 iterations were necessary for a model of 2500 atoms. After obtaining a preferable structure model, Voronoi polyhedral analysis [9] was also performed to the local structure analysis of the structure model.
4. Results and discussion
0
where ρ(r) is the atomic density and ρ0 the average atomic density. The atomic PDF g(r) (= ρ(r)/ρ0 ) and the RDF 4πr2 ρ(r) can be obtained by G(r). The average atomic density ρ0 can be obtained from the specimen density. It should be noted that in a precise electron diffraction PDF analysis
4.1. Amorphous Fe90 Zr7 B3 structure Fig. 1 shows the RMC-PDF fitting to the experimental PDF for the a-Fe90 Zr7 B3 alloy. The fitting of gcal (r) to gexp (r) is very good, and the partial PDFs for the Fe–Fe,
Fig. 1. Experimental and RMC-calculated g(r) profiles for as-quenched Fe90 Zr7 B3 . Partial gFe–Fe (r), gFe–Zr (r) and gFe–B (r) calculated are also shown together with the calculated total g(r).
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Y. Hirotsu et al. / Materials Chemistry and Physics 81 (2003) 360–363
Fig. 2. Deformed-bcc (dark), icosahedra (light) and trigonal prism (semi-dark) clusters found in the RMC-simulated structure.
Fe–Zr and Fe–B correlations can be seen in the figure. As the initial structure model a dense-random-packing model with 2500 atoms in a cubic space of (3.192 nm)3 was constructed, followed by a static relaxation using Lenard–Jones potentials. The density of the a-Fe90 Zr7 B3 alloy was measured by the Archimedean method. According to the Voronoi polyhedral analysis of the final RMC-simulated structure with central Fe, Zr and B, deformed body-centered cubic (bcc) clusters with indices such as “028400” and “036400” were frequently observed. The bcc-like clusters are mostly composed of Fe atoms and the amount of Fe atoms concerning with the bcc-related clusters in the model structure are about 40 at.%. Icosahedral (00 12 000) polyhedra were observed with high density. The trigonal prisms and Archimedean anti-prisms are also observed around the B atoms. These different types of atomic clusters are arranged in space as shown in Fig. 2. Zr and B atoms were found to be distributed almost randomly. As in the eutectic amorphous Fe–B alloy [10], regions of atomic medium range order (MRO) as small as 1 nm which were identified as bcc MROs were observed by high-resolution TEM imaging in an a-Fe90 Zr7 B3 alloy [3], which corresponds well to the local formation of the bcc Fe-like atomic region as shown in Fig. 2. It has been thus demonstrated from the present PDF and TEM studies that a “nano-scale phase separation” exists in the a-Fe90 Zr7 B3 alloy. The local formation of the bcc Fe clusters is supposed to cause nucleation sites for the formation of bcc Fe nanocrystals in the later annealing stage. A detailed process of structural development of such bcc Fe nanocrystals on annealing has been argued [3].
Fig. 3. (a) Reduced interference functions f (Q) and (b) pair-distribution functions g(r) of as-irradiated (broken line) and 800 ◦ C annealed a-SiC (solid line).
4.2. Amorphous SiC formed by ion bombardment and structural change on annealing Fig. 3a indicates the reduced interference function f (Q) of the sample annealed at 800 ◦ C (solid line), compared to the f (Q) of the as-irradiated sample (broken line). Very weak intensity profiles up to high scattering angles as high as Q ≈ 220 nm−1 can be recorded well above the background intensity level of the imaging plate. This scattering vector is much larger than that measured by previous electron diffraction [11,12] and X-ray diffraction experiments [13] for a-SiC. The measured f (Q) exhibits clear differences both in the height and width of the first and second peaks. These peaks become more pronounced with annealing. Reduced radial distribution functions, g(r), were calculated via Fourier transformation of f (Q). The resulting g(r) are shown in Fig. 3b. Fig. 3b also shows the atomic distances in crystalline SiC (marked with the arrows in the bottom part of Fig. 3b). The first and second nearest neighbors are centered at 0.188(±0.002) and 0.307 nm, respectively. These values correspond to the bond lengths of Si–C (the first nearest neighbor) and Si–Si (the second nearest neighbor) in crystalline SiC. In addition to these peaks, subpeaks appear in the both sides of the first peak in Fig. 3b. Their positions are assignable to C–C and Si–Si bond lengths [14,15],
Y. Hirotsu et al. / Materials Chemistry and Physics 81 (2003) 360–363
suggesting that a-SiC networks contain not only heteronuclear bonds but also homonuclear bonds. The g(r) obtained here is in good agreement with molecular-dynamics simulations of a-SiC quenched from the liquid [14,15] or produced by ion irradiation [16]. Substantial changes in the g(r) function were observed during annealing. The major differences between as-irradiated and annealed a-SiC are apparent within the second coordination shell (<0.4 nm); only small differences are observed beyond the second peak. This implies that the largest variations in atomic configurations are in the SRO range. The locations of the first and second nearest neighbors are not affected by annealing. The peak of the heteronuclear bonds (0.188 nm) become more pronounced, whereas the homonuclear bonds (0.151 and 0.238 nm) decrease during annealing. Our present study is the first to provide an evidence of structural changes due to relaxation of a-SiC by means of diffraction analysis.
Acknowledgements The authors express their thanks to Dr. S.A. Makino and K.E. Sickagus for preparing specimens for this study. The present study was partly supported by the Special Coordination Funds for Promoting Science and Technology on “Nanohetero metallic materials” from the Ministry of Education, Science, Sports and Culture, Japan.
363
References [1] S.R. Elliott, Physics of Amorphous Materials, Section 3, Longman Science and Technology, Essex, 1990. [2] T. Ohkubo, Y. Hirotsu, M. Matsushita, J. Electr. Microsc. 48 (1999) 1005. [3] T. Ohkubo, H. Kai, A. Makino, Y. Hirotsu, Mater. Sci. Eng. A 312 (2001) 274. [4] T. Ohkubo, T. Hiroshima, Y. Hirotsu, A. Inoue, T. Oikawa, Mater. Trans. JIM 41 (2000) 1385. [5] T. Takagi, T. Ohkubo, Y. Hirotsu, B.S. Murty, K. Hono, D. Shindo, Appl. Phys. Lett. 79 (2001) 485. [6] Y. Hirotsu, M. Ishimaru, T. Ohkubo, T. Hanada, M. Sugiyama, J. Electr. Microsc. 50 (2001) 435. [7] K. Suzuki, N. Kataoka, A. Inoue, A. Makino, T. Matsumoto, Mater. Trans. JIM 31 (1990) 743. [8] P.A. Duine, J. Sietsma, B.J. Thijsse, L. Pusztai, Phys. Rev. B 50 (1994) 13240. [9] T. Kondo, K. Tsumuraya, J. Chem. Phys. 94 (1991) 8220. [10] Y. Hirotsu, R. Akada, Jpn. J. Appl. Phys. 23 (1984) L479. [11] J. Bentley, P. Angelini, A.P. Gove, P.S. Sklad, A.T. Fisher, Inst. Phys. Conf. Ser. 98 (1989) 107. [12] A. Sproul, D.R. McKenzie, D.J.H. Cookayne, Phil. Mag. B 54 (1986) 113. [13] C. Meneghini, S. Pascarelli, F. Boscherini, S. Mobilio, F. Evangelisti, J. Non-Cryst. Solids 137/138 (1991) 75. [14] F. Finocchi, G. Galli, M. Parrinello, C.M. Bertoni, Phys. Rev. Lett. 68 (1992) 3044. [15] D. Mura, L. Colombo, R. Bertoncini, G. Mula, Phys. Rev. B 58 (1998) 10357. [16] F. Gao, W.J. Weber, J. Appl. Phys. 89 (2001) 4275.