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Electronic characterization of quasicrystalline surface transformations
Surface Science 454–456 (2000) 453–457 www.elsevier.nl/locate/susc
Electronic characterization of quasicrystalline surface transformations A. Hensch *, B. Bolliger, M. Erbudak, R.F. Willis 1 Laboratorium fu¨r Festko¨rperphysik, Eidgeno¨ssische Technische Hochschule Zu¨rich, CH-8093 Zu¨rich, Switzerland
Abstract When ion bombarded at room temperature, the surface of the icosahedral quasicrystal Al Pd Mn converts to 70 20 10 a cubic structure. Bombarded at elevated temperatures, the surface remains quasicrystalline but converts to a tenfoldsymmetric structure. In this paper, we search for a change in the electronic properties as the structure is modified and argue a case against the Hume-Rothery rule for these alloys. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Alloys; Electron energy loss spectroscopy ( EELS ); Low energy electron diffraction (LEED); X-ray photoelectron spectroscopy
1. Introduction Much research has been devoted to elucidate the nature of chemical bonding in quasicrystals, in particular with the aim of finding the driving force which assembles atoms in a fivefold symmetric environment. In classical crystal theory, a strong relationship between the electronic and the crystalline structure has been postulated [1]. Therefore, the investigation of the electronic structure of a crystalline material may supply a fingerprint to determine its atomic arrangement. An analogous relationship between the electronic and the extraordinary atomic structure of the quasicrystals has long been sought. A possible approach relies on the earlier ideas of HumeRothery for crystalline alloys [2]. He pointed out * Corresponding author. Fax: +41-1-6331096. E-mail address: [email protected] (A. Hensch) 1 Also at: Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA.
a correlation between the average number of valence electrons per atom (e/a) and the crystal structure of binary alloys of mainly sp band metals. Many quasicrystalline alloys have an e/a ratio in the range of 2.1–2.4 [3], whereas close-packed structures fall in the range of 1.4–1.8, suggesting that quasicrystals have a higher electron density than the close-packed structures. In general, experimental investigations determining both the atomic structure of surfaces and their electronic properties provide a critical test ground for possible models describing a relationship between the electronic and the quasicrystalline structure of such materials. The icosahedral quasicrystal Al Pd Mn is known to undergo a 70 20 10 reversible structural phase transition in the nearsurface region. Either cubic or decagonal quasicrystalline structures can routinely be induced by Ar+ ion sputtering at 1 keV while maintaining the sample at different temperatures [4,5]. Consequently, the investigation of the electronic properties of these different surfaces on the same
0039-6028/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 00 ) 0 02 1 8 -1
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A. Hensch et al. / Surface Science 454–456 (2000) 453–457
quasicrystalline bulk material might furnish a connection between the electronic and the atomic structure. The following describes such an effort.
2. Experimental The surface of the icosahedral quasicrystal Al Pd Mn , having the dimensions of approxi70 20 10 mately 4 mm×5 mm, is oriented perpendicular to one of the fivefold symmetry axes by means of X-ray diffraction. After mechanically polishing this surface with diamond paste of coarseness down to 0.3 mm, the sample is inserted into an ultrahigh vacuum chamber with a total pressure in the lower 10−10 Torr region. Repeated heat treatment and sputtering (Ar+, 1 keV, 10−7 A mm−2) is then performed to clean the samples surface. Annealing at 400°C for 30 min, followed by a brief flashing at 600°C, restores the quasicrystalline surface structure. This is directly determined using secondary electron imaging (SEI ) [6 ]. The SEI technique is based on the fact that electrons with an energy in the keV range show forward focusing when scattering at atoms [7]. By directing an electron beam of 2 keV onto the sample surface and collecting the secondary electrons with a retarding field display system, which is concentric with the sample, the local atomic arrangement in the sample is revealed as a central projection of the interatomic rows. Therefore, the secondary electron pattern contains information on the symmetry properties as well as the relative orientations of the symmetry axes in direct space. The central portion of the pattern, which is covered by the shadow of the electron gun used for the excitation, coincides with the surface normal representing the zero polar angle, while the outer edge of the pattern corresponds to a polar angle of approximately 52°. Low-energy electron diffraction (LEED) observations from the same sample surface, performed by simply reducing the primary electron energy while maintaining all other experimental settings, ensures the presence of structural long-range order. Scanning the primary electron beam over the entire surface both in the SEI and LEED modes, does not change the quality of the
pattern proving that the sample consists of one single grain. Subsequently, studies of the electronic structure by means of X-ray photoelectron ( XPS) and electron energy-loss spectroscopy ( EELS ) experiments are performed in order to investigate the density of occupied states near the Fermi level, E , as well as to observe single-electron and collecF tive excitations. Additionally, core-level spectra are recorded in XPS with the aim of determining the chemical composition in the near-surface region of the sample and of measuring the corelevel energy shifts that signal electron transfer processes between the alloy constituents. For the XPS measurements an unmonochromatized Mg Ka source is used. The binding energy is referred to E which is determined by measuring F the high-energy end of the 4d electrons distribution in Pd metal placed in ohmic contact with the quasicrystal. The total energy resolution in XPS is 1 eV. For the EELS measurements, a stabilized electron beam with a primary electron energy of 1.5 keV is used. The loss energy is referred to the energy of elastically scattered electrons. The total energy resolution in EELS is 0.7 eV. The SEI patterns are generated with a primary electron energy of 2 keV in order to ensure that the electronic information accessible in XPS and EELS originates from the same near-surface region. After the investigation of the pentagonal surface structure, first the cubic and then the decagonal quasicrystalline surface structures are induced as described below and are then investigated the same way as the pentagonal surface.
3. Results The SEI pattern obtained from the prepared sample surface is displayed in Fig. 1, center panel. The pattern is dominated by five bright patches at a polar angle of 31.5° placed in equal-azimuthal distribution. These are the corners of the pentagon with its symmetry axis in the center. In addition to this pentagon, several twofold and threefold symmetry axes are identified. These data correspond to the icosahedral point group symmetry [8]. This SEI pattern, therefore, represents the
A. Hensch et al. / Surface Science 454–456 (2000) 453–457
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Fig. 1. Secondary electron patterns recorded from the icosahedral quasicrystal at a primary electron energy of 2 keV. The left panel displays the cubic and the right panel the decagonal quasicrystalline surface phases, while the bulk-terminated structure is depicted in the middle.
pentagonal surface of the bulk-terminated icosahedral quasicrystal. To obtain a near-surface structure that is cubic, the same surface is bombarded with 1 keV Ar+ for 30 min at room temperature (RT ). The resulting SEI pattern is shown in Fig. 1, left panel. The orthogonal symmetry is typical of the (110) face of a cubic structure. If, however, the sputtering is performed while the sample is maintained at 400°C, the surface structure becomes decagonal quasicrystalline (cf. Fig. 1, right panel ). In both cases, cubic as well as decagonal, these structures remain stable during the course of our measurements performed at RT. These two surface phases are epitaxial with the aperiodic quasicrystalline bulk [4,5]. All three surface structures show LEED patterns, confirming that long-range order prevails over the entire surface area. We can deduce a twodimensional cell from the LEED data. The areas of the 2D Brillouin zones have the ratio 1:1.05:0.95 for the cubic, fivefold, and tenfold structures. Fig. 2 shows the results of the XPS measurements in the valence-band region obtained from the three different surface structures shown in Fig. 1. For the fivefold symmetric surface ( lower curve), the predominant peak is centered at E =4.2 eV. There is a shoulder located near E . B F Previous photoemission measurements on the same material using synchrotron radiation at a photon energy of 35 eV [9] and soft X-ray emission experiments [10] have indicated that the main peak has
predominantly Pd 4d character. Similarly, the emission band near E is due to Mn 3d-derived F states [11]. Both surfaces with a cubic and a decagonal structure have their main emission
Fig. 2. XPS spectra from the valence band of the Al Pd Mn quasicrystal recorded at hn=1253 eV for three 70 20 10 different surface structures. Zero binding energy refers to the Fermi level.
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energy-loss region of one-electron and collective excitations. For the fivefold symmetric surface ( lower curve), an energy-loss channel at 17 eV ( labeled d) is observed. In Pd, the 3d and 4d core levels are equally accompanied by a similar loss [12]. Therefore, the loss channel (d ) has been ascribed to excitations localized at the Pd site. Two other dominant energy losses can be observed at 10.3 and 5.3 eV, labeled (c) and (b), respectively. In the cubic as well as in the decagonal structure, the same loss channels can be identified (d∞, c∞, b∞ and d◊, c◊, b◊). We note that the cubic as well as the decagonal near-surface structures possess an additional loss channel placed at 2.5 eV (a∞, a◊). Therefore, the energy-loss spectra provide a clue to distinguish the pentagonal surface structure from the two Ar+-bombarded surfaces.
4. Conclusions
Fig. 3. EELS spectra from three different surface structures generated on the Al Pd Mn quasicrystal, excited with primary 70 20 10 electrons of 1.5 keV energy. Zero energy loss corresponds to the energy of elastically backscattered electrons.
intensity located at E =3.7 eV, therefore exhibitB ing a shift of 0.5 eV towards lower binding energies compared with the icosahedral phase. Measured core-level spectra (not shown) reveal that the Pd 3d levels in the quasicrystal are more tightly bound than in Pd metal. The binding energies of the Al and Mn states remain unchanged. Between the different surface phases, in contrast, no significant core-level shifts could be observed. However, we observe significant changes in the Mn 2p core-level line shapes indicating strong many-body effects, similar to those previously reported [12]. The emission intensity near E is increased slightly in F both the cubic and the tenfold symmetric structure compared with the pentagonal surface structure. There is a change in the stoichiometry of the analyzed surfaces induced by preferential sputtering [4,5]. This change in the surface chemistry can be the cause of the observed shifts in the density of states. Fig. 3 displays the EELS measurements in the
The Hume-Rothery scheme to stabilize a structure had success in sp band metals. The electron gas density e/a for the quasicrystalline surface increases to a value of 2.2 which is well above that of cubic close-packed phases. In order to explore the driving force which assembles atoms in a quasicrystalline environment, we have systematically modified the surface structure of an Al–Pd– Mn quasicrystal. We have taken the electronic distribution in the valence band, determined in XPS, as a measure for the density of the electron gas. Together with the nonsignificant change in the area of the Brillouin zone, determined by LEED, our measurements on icosahedral and decagonal surface structures as well as on the cubic surface structure failed to indicate a significant dependence of e/a on these structural changes. Hence we conclude that the Hume-Rothery rule is not the driving force for the assembly of the extraordinary structure of quasicrystals [13]. In fact, so far, including in the present work with the given energy resolution, no special property could be detected in the electronic density of states which is typical and characteristic of the quasicrystalline structure. However, the Al–Pd–Mn alloy shows electronic properties which can be reconciled with localized
A. Hensch et al. / Surface Science 454–456 (2000) 453–457
d bands. In particular, the Mn 3d electrons are located at and near the E and are responsible for F the anomalously low conductivity. Therefore, we question the general applicability of the HumeRothery rule to d electron systems.
Acknowledgements The authors thank A.R. Kortan and D.D. Vvedensky for their valuable interest as well as ETH Zu¨rich and Schweizerischer Nationalfonds for financial support.
References [1] H.L. Skriver, Phys. Rev. B 31 (1985) 1909. [2] W. Hume-Rothery, G.V. Raynor, in: The Structure of
457
Metals and Alloys, The Institute of Metals, London, 1954, p. 196. [3] J. Friedel, F. Denoyer, C. R. Acad. Sci. Paris, Ser. II 305 (1987) 171. [4] B. Bolliger, M. Erbudak, D.D. Vvedensky, M. Zurkirch, Phys. Rev. Lett. 80 (1998) 5369. [5] B. Bolliger, M. Erbudak, D.D. Vvedensky, M. Zurkirch, Phys. Rev. Lett. 82 (1999) 763. [6 ] M. Erbudak, M. Hochstrasser, E. Wetli, M. Zurkirch, Surf. Rev. Lett. 4 (1997) 179. [7] H.C. Poon, S.Y. Tong, Phys. Rev. B 30 (1984) 6211. [8] M. Zurkirch, M. Erbudak, H.-U. Nissen, M. Hochstrasser, E. Wetli, Philos. Mag. Lett. 72 (1995) 199. [9] G.W. Zhang, Z.M. Stadnik, A.-P. Tsai, A. Inoue, Phys. Lett. A 186 (1994) 345. [10] E. Belin, Z. Danhka´zi, J. Non-Cryst. Solids 153–154 (1993) 298. [11] M. Zurkirch, M. De Crescenzi, M. Erbudak, M. Hochstrasser, Phys. Rev. B 55 (1997) 8808. [12] M. Zurkirch, A. Atrei, M. Hochstrasser, M. Erbudak, A.R. Kortan, J. Electron Spectrosc. Relat. Phenom. 77 (1996) 233. [13] Z.M. Stadnik, G.W. Zhang, A.-P. Tsai, A. Inoue, Phys. Lett. A 198 (1995) 237.
Electronic characterization of quasicrystalline surface transformations A. Hensch *, B. Bolliger, M. Erbudak, R.F. Willis 1 Laboratorium fu¨r Festko¨rperphysik, Eidgeno¨ssische Technische Hochschule Zu¨rich, CH-8093 Zu¨rich, Switzerland
Abstract When ion bombarded at room temperature, the surface of the icosahedral quasicrystal Al Pd Mn converts to 70 20 10 a cubic structure. Bombarded at elevated temperatures, the surface remains quasicrystalline but converts to a tenfoldsymmetric structure. In this paper, we search for a change in the electronic properties as the structure is modified and argue a case against the Hume-Rothery rule for these alloys. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Alloys; Electron energy loss spectroscopy ( EELS ); Low energy electron diffraction (LEED); X-ray photoelectron spectroscopy
1. Introduction Much research has been devoted to elucidate the nature of chemical bonding in quasicrystals, in particular with the aim of finding the driving force which assembles atoms in a fivefold symmetric environment. In classical crystal theory, a strong relationship between the electronic and the crystalline structure has been postulated [1]. Therefore, the investigation of the electronic structure of a crystalline material may supply a fingerprint to determine its atomic arrangement. An analogous relationship between the electronic and the extraordinary atomic structure of the quasicrystals has long been sought. A possible approach relies on the earlier ideas of HumeRothery for crystalline alloys [2]. He pointed out * Corresponding author. Fax: +41-1-6331096. E-mail address: [email protected] (A. Hensch) 1 Also at: Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA.
a correlation between the average number of valence electrons per atom (e/a) and the crystal structure of binary alloys of mainly sp band metals. Many quasicrystalline alloys have an e/a ratio in the range of 2.1–2.4 [3], whereas close-packed structures fall in the range of 1.4–1.8, suggesting that quasicrystals have a higher electron density than the close-packed structures. In general, experimental investigations determining both the atomic structure of surfaces and their electronic properties provide a critical test ground for possible models describing a relationship between the electronic and the quasicrystalline structure of such materials. The icosahedral quasicrystal Al Pd Mn is known to undergo a 70 20 10 reversible structural phase transition in the nearsurface region. Either cubic or decagonal quasicrystalline structures can routinely be induced by Ar+ ion sputtering at 1 keV while maintaining the sample at different temperatures [4,5]. Consequently, the investigation of the electronic properties of these different surfaces on the same
0039-6028/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 00 ) 0 02 1 8 -1
454
A. Hensch et al. / Surface Science 454–456 (2000) 453–457
quasicrystalline bulk material might furnish a connection between the electronic and the atomic structure. The following describes such an effort.
2. Experimental The surface of the icosahedral quasicrystal Al Pd Mn , having the dimensions of approxi70 20 10 mately 4 mm×5 mm, is oriented perpendicular to one of the fivefold symmetry axes by means of X-ray diffraction. After mechanically polishing this surface with diamond paste of coarseness down to 0.3 mm, the sample is inserted into an ultrahigh vacuum chamber with a total pressure in the lower 10−10 Torr region. Repeated heat treatment and sputtering (Ar+, 1 keV, 10−7 A mm−2) is then performed to clean the samples surface. Annealing at 400°C for 30 min, followed by a brief flashing at 600°C, restores the quasicrystalline surface structure. This is directly determined using secondary electron imaging (SEI ) [6 ]. The SEI technique is based on the fact that electrons with an energy in the keV range show forward focusing when scattering at atoms [7]. By directing an electron beam of 2 keV onto the sample surface and collecting the secondary electrons with a retarding field display system, which is concentric with the sample, the local atomic arrangement in the sample is revealed as a central projection of the interatomic rows. Therefore, the secondary electron pattern contains information on the symmetry properties as well as the relative orientations of the symmetry axes in direct space. The central portion of the pattern, which is covered by the shadow of the electron gun used for the excitation, coincides with the surface normal representing the zero polar angle, while the outer edge of the pattern corresponds to a polar angle of approximately 52°. Low-energy electron diffraction (LEED) observations from the same sample surface, performed by simply reducing the primary electron energy while maintaining all other experimental settings, ensures the presence of structural long-range order. Scanning the primary electron beam over the entire surface both in the SEI and LEED modes, does not change the quality of the
pattern proving that the sample consists of one single grain. Subsequently, studies of the electronic structure by means of X-ray photoelectron ( XPS) and electron energy-loss spectroscopy ( EELS ) experiments are performed in order to investigate the density of occupied states near the Fermi level, E , as well as to observe single-electron and collecF tive excitations. Additionally, core-level spectra are recorded in XPS with the aim of determining the chemical composition in the near-surface region of the sample and of measuring the corelevel energy shifts that signal electron transfer processes between the alloy constituents. For the XPS measurements an unmonochromatized Mg Ka source is used. The binding energy is referred to E which is determined by measuring F the high-energy end of the 4d electrons distribution in Pd metal placed in ohmic contact with the quasicrystal. The total energy resolution in XPS is 1 eV. For the EELS measurements, a stabilized electron beam with a primary electron energy of 1.5 keV is used. The loss energy is referred to the energy of elastically scattered electrons. The total energy resolution in EELS is 0.7 eV. The SEI patterns are generated with a primary electron energy of 2 keV in order to ensure that the electronic information accessible in XPS and EELS originates from the same near-surface region. After the investigation of the pentagonal surface structure, first the cubic and then the decagonal quasicrystalline surface structures are induced as described below and are then investigated the same way as the pentagonal surface.
3. Results The SEI pattern obtained from the prepared sample surface is displayed in Fig. 1, center panel. The pattern is dominated by five bright patches at a polar angle of 31.5° placed in equal-azimuthal distribution. These are the corners of the pentagon with its symmetry axis in the center. In addition to this pentagon, several twofold and threefold symmetry axes are identified. These data correspond to the icosahedral point group symmetry [8]. This SEI pattern, therefore, represents the
A. Hensch et al. / Surface Science 454–456 (2000) 453–457
455
Fig. 1. Secondary electron patterns recorded from the icosahedral quasicrystal at a primary electron energy of 2 keV. The left panel displays the cubic and the right panel the decagonal quasicrystalline surface phases, while the bulk-terminated structure is depicted in the middle.
pentagonal surface of the bulk-terminated icosahedral quasicrystal. To obtain a near-surface structure that is cubic, the same surface is bombarded with 1 keV Ar+ for 30 min at room temperature (RT ). The resulting SEI pattern is shown in Fig. 1, left panel. The orthogonal symmetry is typical of the (110) face of a cubic structure. If, however, the sputtering is performed while the sample is maintained at 400°C, the surface structure becomes decagonal quasicrystalline (cf. Fig. 1, right panel ). In both cases, cubic as well as decagonal, these structures remain stable during the course of our measurements performed at RT. These two surface phases are epitaxial with the aperiodic quasicrystalline bulk [4,5]. All three surface structures show LEED patterns, confirming that long-range order prevails over the entire surface area. We can deduce a twodimensional cell from the LEED data. The areas of the 2D Brillouin zones have the ratio 1:1.05:0.95 for the cubic, fivefold, and tenfold structures. Fig. 2 shows the results of the XPS measurements in the valence-band region obtained from the three different surface structures shown in Fig. 1. For the fivefold symmetric surface ( lower curve), the predominant peak is centered at E =4.2 eV. There is a shoulder located near E . B F Previous photoemission measurements on the same material using synchrotron radiation at a photon energy of 35 eV [9] and soft X-ray emission experiments [10] have indicated that the main peak has
predominantly Pd 4d character. Similarly, the emission band near E is due to Mn 3d-derived F states [11]. Both surfaces with a cubic and a decagonal structure have their main emission
Fig. 2. XPS spectra from the valence band of the Al Pd Mn quasicrystal recorded at hn=1253 eV for three 70 20 10 different surface structures. Zero binding energy refers to the Fermi level.
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energy-loss region of one-electron and collective excitations. For the fivefold symmetric surface ( lower curve), an energy-loss channel at 17 eV ( labeled d) is observed. In Pd, the 3d and 4d core levels are equally accompanied by a similar loss [12]. Therefore, the loss channel (d ) has been ascribed to excitations localized at the Pd site. Two other dominant energy losses can be observed at 10.3 and 5.3 eV, labeled (c) and (b), respectively. In the cubic as well as in the decagonal structure, the same loss channels can be identified (d∞, c∞, b∞ and d◊, c◊, b◊). We note that the cubic as well as the decagonal near-surface structures possess an additional loss channel placed at 2.5 eV (a∞, a◊). Therefore, the energy-loss spectra provide a clue to distinguish the pentagonal surface structure from the two Ar+-bombarded surfaces.
4. Conclusions
Fig. 3. EELS spectra from three different surface structures generated on the Al Pd Mn quasicrystal, excited with primary 70 20 10 electrons of 1.5 keV energy. Zero energy loss corresponds to the energy of elastically backscattered electrons.
intensity located at E =3.7 eV, therefore exhibitB ing a shift of 0.5 eV towards lower binding energies compared with the icosahedral phase. Measured core-level spectra (not shown) reveal that the Pd 3d levels in the quasicrystal are more tightly bound than in Pd metal. The binding energies of the Al and Mn states remain unchanged. Between the different surface phases, in contrast, no significant core-level shifts could be observed. However, we observe significant changes in the Mn 2p core-level line shapes indicating strong many-body effects, similar to those previously reported [12]. The emission intensity near E is increased slightly in F both the cubic and the tenfold symmetric structure compared with the pentagonal surface structure. There is a change in the stoichiometry of the analyzed surfaces induced by preferential sputtering [4,5]. This change in the surface chemistry can be the cause of the observed shifts in the density of states. Fig. 3 displays the EELS measurements in the
The Hume-Rothery scheme to stabilize a structure had success in sp band metals. The electron gas density e/a for the quasicrystalline surface increases to a value of 2.2 which is well above that of cubic close-packed phases. In order to explore the driving force which assembles atoms in a quasicrystalline environment, we have systematically modified the surface structure of an Al–Pd– Mn quasicrystal. We have taken the electronic distribution in the valence band, determined in XPS, as a measure for the density of the electron gas. Together with the nonsignificant change in the area of the Brillouin zone, determined by LEED, our measurements on icosahedral and decagonal surface structures as well as on the cubic surface structure failed to indicate a significant dependence of e/a on these structural changes. Hence we conclude that the Hume-Rothery rule is not the driving force for the assembly of the extraordinary structure of quasicrystals [13]. In fact, so far, including in the present work with the given energy resolution, no special property could be detected in the electronic density of states which is typical and characteristic of the quasicrystalline structure. However, the Al–Pd–Mn alloy shows electronic properties which can be reconciled with localized
A. Hensch et al. / Surface Science 454–456 (2000) 453–457
d bands. In particular, the Mn 3d electrons are located at and near the E and are responsible for F the anomalously low conductivity. Therefore, we question the general applicability of the HumeRothery rule to d electron systems.
Acknowledgements The authors thank A.R. Kortan and D.D. Vvedensky for their valuable interest as well as ETH Zu¨rich and Schweizerischer Nationalfonds for financial support.
References [1] H.L. Skriver, Phys. Rev. B 31 (1985) 1909. [2] W. Hume-Rothery, G.V. Raynor, in: The Structure of
457
Metals and Alloys, The Institute of Metals, London, 1954, p. 196. [3] J. Friedel, F. Denoyer, C. R. Acad. Sci. Paris, Ser. II 305 (1987) 171. [4] B. Bolliger, M. Erbudak, D.D. Vvedensky, M. Zurkirch, Phys. Rev. Lett. 80 (1998) 5369. [5] B. Bolliger, M. Erbudak, D.D. Vvedensky, M. Zurkirch, Phys. Rev. Lett. 82 (1999) 763. [6 ] M. Erbudak, M. Hochstrasser, E. Wetli, M. Zurkirch, Surf. Rev. Lett. 4 (1997) 179. [7] H.C. Poon, S.Y. Tong, Phys. Rev. B 30 (1984) 6211. [8] M. Zurkirch, M. Erbudak, H.-U. Nissen, M. Hochstrasser, E. Wetli, Philos. Mag. Lett. 72 (1995) 199. [9] G.W. Zhang, Z.M. Stadnik, A.-P. Tsai, A. Inoue, Phys. Lett. A 186 (1994) 345. [10] E. Belin, Z. Danhka´zi, J. Non-Cryst. Solids 153–154 (1993) 298. [11] M. Zurkirch, M. De Crescenzi, M. Erbudak, M. Hochstrasser, Phys. Rev. B 55 (1997) 8808. [12] M. Zurkirch, A. Atrei, M. Hochstrasser, M. Erbudak, A.R. Kortan, J. Electron Spectrosc. Relat. Phenom. 77 (1996) 233. [13] Z.M. Stadnik, G.W. Zhang, A.-P. Tsai, A. Inoue, Phys. Lett. A 198 (1995) 237.