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Mg 2p shallow core-level and local atomic structure of i-ZnMgRE quasicrystals
Applied Surface Science 252 (2006) 5411–5414 www.elsevier.com/locate/apsusc
Mg 2p shallow core-level and local atomic structure of i-ZnMgRE quasicrystals V. Karpus a,*, A. Suchodolskis a,b, U.O. Karlsson b, G. Le Lay c, L. Giovanelli d, W. Assmus e, S. Bru¨hne e, E. Uhrig e a
Semiconductor Physics Institute, A. Gosˇtauto 11, LT-01108 Vilnius, Lithuania b Materials Physics, KTH, P.O. Box Electrum 229, S-16440 Kista, Sweden c CRMC2-CNRS, Campus de Luminy, Case 913, F-13288 Marseille Cedex 9, France d L2MP, UMR CNRS 6137, Unive´rsite´ Paul Ce´zanne, F-13397 Marseille, France e Physikalisches Institut, J.W. Goethe-Universita¨t, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany Available online 23 January 2006
Abstract We present a detailed analysis of the Mg 2p shallow core-levels measured on icosahedral single-grain ZnMgY, ZnMgHo, and ZnMgEr quasicrystals during a photoelectron microscopy study. The synchrotron radiation photoemission measurements were performed on in situ cleaved samples at a pressure of 1010 mbar and at low temperature, typically 90–150 K. The Mg 2p photoemission lines are essentially broadened as compared to those of the Mg 2p spin–orbit doublet recorded on the Zn2Mg crystalline Laves phase. The broadening is associated to the coordination shifts of the Mg 2p level due to the inequivalent magnesium sites in the quasicrystalline lattice. The coordination shifts are calculated on the basis of i-ZnMg(Ho, Y) atomic structure data, recently determined from the pair distribution function analysis. The coordination shifts obtained are up to 0.2 eV. The Mg 2p experimental spectral intensity is nicely reproduced by a superposition of coordination-shifted Mg 2p spin–orbit doublets. # 2005 Elsevier B.V. All rights reserved. PACS: 71.23.F Keywords: Quasicrystals; Photoemission spectroscopy; Coordination shift
1. Introduction The distinguishing features of the atomic arrangement of quasicrystals (QCs), the long-range order and the ‘‘forbidden’’ five-fold orientational symmetry, can be combined only in aperiodic structures. As a result, there are no equivalent sites in a quasicrystalline lattice, i.e., each atom is surrounded by all others in a unique way. However, the number of inequivalent sites, with respect to the local atomic surrounding due to the nearest neighbours, is finite in quasicrystals, as is evidently illustrated by the Penrose tilings [1]. In principle, the local atomic surrounding of inequivalent sites should affect the localized electron states of the shallow atomic core-levels. In the present paper we will show that the effect can be traced in photoemission (PE) spectra of the Mg 2p
* Corresponding author. Tel.: +370 5 2619475; fax: +370 5 2627123. E-mail address: [email protected] (V. Karpus). 0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.12.059
core-levels in icosahedral ZnMgRE (RE = Y, Ho, Er) quasicrystals. 2. Experimental The face-centred icosahedral Zn62Mg29Y9, Zn65Mg25Ho10, and Zn65Mg24Er11 single-grain quasicrystals were grown by the liquid-encapsulated top-seeded solution growth method [2]. In addition to the i-ZnMg(Y, Ho, Er) QCs, we investigated, as a reference system, the usual crystalline (hexagonal) compound Zn2Mg, in which all magnesium atoms are in equivalent sites. Photoemission measurements were performed with the angle-resolved scanning photoelectron microscope, at beamline BL31 of the Swedish synchrotron-radiation facility MAX-lab (Lund). The single-grain i-ZnMg(Y, Ho, Er) and Zn2Mg samples for the PE measurements were prepared in the form of small, 0.5 cm long, rods with 1 mm2 cross-section. The samples were cleaved in situ at about 2 1010 mbar and low,
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V. Karpus et al. / Applied Surface Science 252 (2006) 5411–5414
90–150 K, temperature. The cleanliness of the cleaved surfaces was routinely monitored following by photoemission the evolution of the O 2p states [3]. The best attainable total instrumental energy resolution was about 0.1 eV; it varied depending on the photon energy and the chosen pass energy of the analyser. 3. Results and discussion The photoemission spectra of the Mg 2p core-levels on i-ZnMg(Y, Ho, Er) quasicrystals recorded at several different photon energies are presented by open dots in Fig. 1. The
underlying structure of the Mg 2p PE lines in the QCs is a spin– orbit doublet, as is evident from a comparison with the Mg 2p spectra from Zn2Mg, which are presented in full-symbols. The Mg 2p spin–orbit splitting in Zn2Mg is Ds–o = 0.28 eV in agreement with the Ds–o value in pure Mg [4]; the full width at half maximum (FWHM) of the doublet components is G = 0.12 eV, and the branching ratio of the doublet is equal to the statistical value b = 2. As seen from Fig. 1, the Mg 2p line in i-ZnMg(Y, Ho, Er) quasicrystals is much broader than that in Zn2Mg. A preliminary analysis of the Mg 2p PE spectra in i-ZnMgEr [5] indicated that the experimental Mg 2p PE spectra can be
Fig. 1. Photoemission spectra of the Mg 2p shallow core-levels in (a) i-ZnMgY (T = 90–140 K), (b) i-ZnMgHo (T = 90–100 K), (c) i-ZnMgEr (T = 140–150 K) quasicrystals (open dots) and in crystalline Zn2Mg (T 100 K, full-dotted curves), and (d) the theoretical inner structure of the Mg 2p spectrum in the QCs.
V. Karpus et al. / Applied Surface Science 252 (2006) 5411–5414
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jellium due to the redistribution of the valence electrons, and a constant term, which was determined from the condition V R 0 is d3 r VðrÞ ¼ 0. The Madelung potential field VM(r) was calculated following the Ewald–Fuchs method [8]. The atomic potentials were assumed to correspond to the empty-core model [9]
vk ðrÞ ¼ Fig. 2. The local atomic coordination polyhedra of the magnesium Mg4 and Mg8 sites in i-ZnMgY.
well approximated by several binding-energy shifted spin–orbit doublets with the same intensity ratio for all photon energies used hn = 60–130 eV. The small changes in the Mg 2p PE lineshapes at increasing photon energies (Fig. 1) are solely due to the variation of instrumental energy resolution. This supports the assumption that the broad Mg 2p lineshapes in quasicrystals are related to the different inequivalent magnesium sites in the quasicrystalline lattice. Due to different atomic surroundings at the sites, the magnesium atoms experience different potentials, which give rise to the ‘coordination shifts’ of the atomic levels. The local atomic surroundings in face-centred icosahedral ZnMgHo [6] and ZnMgY [7] quasicrystals have been determined recently on the basis of the analysis of the atomic pair distribution function deduced from diffraction data. The ˚ ) model of the QC analysis indicates that in a local (Dr = 27 A atomic structure there are at least six different magnesium sites. The local atomic structure of i-ZnMgRE was determined for the model cubic ZnMg(Ho, Y) 2/1-approximants, the primitive cell of which contains 680 atoms. The 144 magnesium atoms evenly occupy six inequivalent sites denoted as Mg1, Mg3, Mg4, Mg7, Mg8, and Mg9 [7]. The atomic coordinations of the Mg4 and Mg8 sites are illustrated in Fig. 2. 3.1. Calculations of the local atomic potential To determine the coordination shift of the core levels of the atom positioned at site Rk, we calculated the local potential ˜ k Þ, which acts on the test electron and which is due to all VðR charges in the system, except the ion at the Rk site ˜ k Þ ¼ lim ½VðrÞ vk ðr Rk Þ; VðR r ! Rk
(1)
where vk ðr Rk Þ is the atomic potential of the ion. The total potential field V(r) in a metallic solid can be presented as the sum VðrÞ ¼ VM ðrÞ þ dVion ðrÞ þ dVel ðrÞ þ V0 ;
(2)
where VM(r) is the electrostatic Madelung potential field, which is due to the point-ion charges and to the uniform valence electron jellium; the dVion(r) field accounts for a deviation of the atomic potentials vk ðr Rk Þ from those due to pointcharges –Zke2/jr Rkj; the dVel(r) term corresponds to the deviation of the electron charge density from the uniform
8 <0
for r < ac;k ;
Z e2 : k r
(3)
for r > ac;k ;
where ac,k are the core radii. The potential field dVel(r) due to the redistribution of the valence electrons was calculated within the framework of self-consistent screening
dVel ðrÞ ¼
X g 6¼ 0
Vgbare
Vgbare
1 1 expðigrÞ; eðgÞ
1 X ¼ va;g expðigra Þ; Vcell a
(4)
where va;g is the Fourier amplitude of the atomic potential (3), g are the reciprocal lattice vectors, Vcell is the cell volume, ra are the cell atomic-basis vectors, and e(g) is the static dielectric function of the valence electrons
eðgÞ ¼ 1 þ
Fðg=2kF Þ ; g2 a2s
1 1 x2 1 þ x : ln FðxÞ ¼ þ 2 1 x 4x (5) 1/2
Here kF is the Fermi wavevector, as = (paB/4kF) is the screening radius, and aB is the Bohr radius. Formulas (1)–(5) allow for calculations of the local potential on the chosen atomic site at given set of atomic positions Rk (or ra) and values of the core radii ac,k. The calculations were carried out for the Rk set, which was determined in [7] for i-ZnMgY and was assumed to be a prototype for all three i-ZnMg(Y, Ho, Er) QCs studied, and for ˚ values of the core the known ac,Zn = 0.67 and ac,Mg = 0.74 A radii [10]. The core radius of the RE atom was taken to be equal ˚ [11]. to the Y3+ ionic radius, ac,RE = 0.9 A The results of the calculations of the local atomic potential on the magnesium sites are presented in Table 1. As seen, the difference in potentials on inequivalent Mg sites in i-ZnMgRE quasicrystals is spread within the interval of about 0.25 eV. The differences in potentials correspond to the coordination shifts of the atomic levels. Therefore, the inner structure of the Mg 2p spectrum in the quasicrystals should have the form presented in Fig. 1(d). 3.2. PE spectral intensity of the Mg 2p levels The PE spectral intensity of Mg 2p core-level was calculated as the sum of six spin–orbit doublets, shifted on the energy axis by the determined coordination shifts Dc,i, convoluted with a
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Table 1 The local potential on the inequivalent magnesium sites in i-ZnMgRE quasicrystals and the coordination shift of atomic core levels (with respect to the Mg4 atom)
˜ k Þ (Ry) VðR Dc (eV)
Mg1
Mg3
Mg4
Mg7
Mg8
Mg9
1.644 0.110
1.652 0.211
1.636 0
1.636 0.006
1.639 0.033
1.633 0.044
Gaussian function, which accounts for the total instrumental energy resolution of the photoelectron microscope Z 1 X 6 IðeÞ ¼ de0 Fðe0 ; e0 þ Dc;i ; G ; a; Dso ; bÞ Gðe e0 Þ: 1
i¼1
(6) The parameters of the spin–orbit doublets, the width G, the asymmetry parameter a, the spin–orbit splitting Ds–o = 0.28 eV, and the branching ratio b = 2, were taken to be the same for all six coordination-shifted Mg 2p doublets. The results of the calculations are shown by the curves through the experimental dots in Fig. 1(a)–(c). As seen, they nicely fit the experimental PE lineshapes of the Mg 2p corelevels in the i-ZnMg(Y, Ho, Er) quasicrystals. The asymmetry parameter a and the width G of the spin– orbit components were determined by the least square method. The asymmetry parameter deduced experiences a sharp variation with photon energy: its value changes from a = 0 at about hn < 65 eV to a 0.08 at hn > 65 eV. A similar a ‘jump’ of Da 0.1 at hn 65 eV was revealed also in the analysis of the Mg 2p PE spectra of Zn2Mg. Most probably, the jump is due to the transition from the adiabatic to the sudden regime of photoionization. The transition is related to polarization effects of Zn 3d electrons, as was previously revealed for the Zn 3p core-level in pure zinc [12]. The FWHM of the spin–orbit components in the i-ZnMg(Y, Ho, Er) quasicrystals was determined to be G = 0.22 eV, which exceeds the G = 0.12 eV value in magnesium dizinc. The additional broadening can be due to the fact that all Mg sites are in principle inequivalent in a quasicrystalline lattice with respect to the far-away neighbours, while the six inequivalent sites accounted for in the present analysis correspond only to the local atomic surrounding. The additional broadening of the
Mg 2p spin–orbit components can be due as well to a small asymmetry of the potential field V(r), which can lead to a splitting of the j = 3/2 and j = 1/2 components. 4. Conclusions Summarizing, we conclude that the photoemission spectra of the Mg 2p shallow core-levels in face-centred icosahedral ZnMgRE quasicrystals indicate a correlation between the quasicrystalline local atomic structure and the localized electron states. The different local atomic surroundings of the inequivalent sites induce the coordination shifts of the core electron levels. The calculated coordination shifts at the magnesium sites are up to 0.2 eV. The simulated spectral intensity of the Mg 2p photoemission spectra taking into account of the coordination shifts nicely fits experimental data. Acknowledgements Support by the EC Access to Research Infrastructure Programme, by the EC PRAMA Programme, and by the Swedish Institute is gratefully acknowledged. References [1] M. Gardner, Sci. Am. 236 (1977) 110–121. [2] A. Langsdorf, W. Assmus, J. Cryst. Growth 192 (1998) 152–156. ˇ echavicˇius, J. Dalmas, L. Giovanelli, [3] A. Suchodolskis, W. Assmus, B. C M. Go¨thelid, U.O. Karlsson, V. Karpus, G. Le Lay, R. Sterzel, E. Uhrig, Appl. Surf. Sci. 212/213 (2003) 485–490. [4] P.H. Citrin, G.H. Wertheim, Y. Baer, Phys. Rev. B 16 (1977) 4270–4282. [5] A. Suchodolskis, W. Assmus, G.-J. Babonas, L. Giovanelli, U.O. Karlsson, V. Karpus, G. Le Lay, A. Re˙za, E. Uhrig, Acta Physica Polonica A 107 (2005) 412–419. [6] S. Bru¨hne, R. Sterzel, E. Uhrig, C. Gross, W. Assmus, Z. Kristallogr. 219 (2004) 245–258. [7] S. Bru¨hne, E. Uhrig, C. Gross, W. Assmus, A.S. Masadeh, S.J.L. Billinge, J. Phys.: Condens. Matter 17 (2005) 1561–1572. [8] K. Fuchs, Proc. R. Soc. A 151 (1935) 585–602. [9] N.W. Ashcroft, Phys. Lett. 23 (1966) 48–51. [10] N.W. Ashcroft, D.C. Langreth, Phys. Rev. 155 (1967) 682–684. [11] C. Kittel, Introduction to Solid State Physics, Wiley, 1996. [12] F.J. Himpsel, D.E. Eastman, E.E. Koch, Phys. Rev. Lett. 44 (1980) 214– 217.
Mg 2p shallow core-level and local atomic structure of i-ZnMgRE quasicrystals V. Karpus a,*, A. Suchodolskis a,b, U.O. Karlsson b, G. Le Lay c, L. Giovanelli d, W. Assmus e, S. Bru¨hne e, E. Uhrig e a
Semiconductor Physics Institute, A. Gosˇtauto 11, LT-01108 Vilnius, Lithuania b Materials Physics, KTH, P.O. Box Electrum 229, S-16440 Kista, Sweden c CRMC2-CNRS, Campus de Luminy, Case 913, F-13288 Marseille Cedex 9, France d L2MP, UMR CNRS 6137, Unive´rsite´ Paul Ce´zanne, F-13397 Marseille, France e Physikalisches Institut, J.W. Goethe-Universita¨t, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany Available online 23 January 2006
Abstract We present a detailed analysis of the Mg 2p shallow core-levels measured on icosahedral single-grain ZnMgY, ZnMgHo, and ZnMgEr quasicrystals during a photoelectron microscopy study. The synchrotron radiation photoemission measurements were performed on in situ cleaved samples at a pressure of 1010 mbar and at low temperature, typically 90–150 K. The Mg 2p photoemission lines are essentially broadened as compared to those of the Mg 2p spin–orbit doublet recorded on the Zn2Mg crystalline Laves phase. The broadening is associated to the coordination shifts of the Mg 2p level due to the inequivalent magnesium sites in the quasicrystalline lattice. The coordination shifts are calculated on the basis of i-ZnMg(Ho, Y) atomic structure data, recently determined from the pair distribution function analysis. The coordination shifts obtained are up to 0.2 eV. The Mg 2p experimental spectral intensity is nicely reproduced by a superposition of coordination-shifted Mg 2p spin–orbit doublets. # 2005 Elsevier B.V. All rights reserved. PACS: 71.23.F Keywords: Quasicrystals; Photoemission spectroscopy; Coordination shift
1. Introduction The distinguishing features of the atomic arrangement of quasicrystals (QCs), the long-range order and the ‘‘forbidden’’ five-fold orientational symmetry, can be combined only in aperiodic structures. As a result, there are no equivalent sites in a quasicrystalline lattice, i.e., each atom is surrounded by all others in a unique way. However, the number of inequivalent sites, with respect to the local atomic surrounding due to the nearest neighbours, is finite in quasicrystals, as is evidently illustrated by the Penrose tilings [1]. In principle, the local atomic surrounding of inequivalent sites should affect the localized electron states of the shallow atomic core-levels. In the present paper we will show that the effect can be traced in photoemission (PE) spectra of the Mg 2p
* Corresponding author. Tel.: +370 5 2619475; fax: +370 5 2627123. E-mail address: [email protected] (V. Karpus). 0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2005.12.059
core-levels in icosahedral ZnMgRE (RE = Y, Ho, Er) quasicrystals. 2. Experimental The face-centred icosahedral Zn62Mg29Y9, Zn65Mg25Ho10, and Zn65Mg24Er11 single-grain quasicrystals were grown by the liquid-encapsulated top-seeded solution growth method [2]. In addition to the i-ZnMg(Y, Ho, Er) QCs, we investigated, as a reference system, the usual crystalline (hexagonal) compound Zn2Mg, in which all magnesium atoms are in equivalent sites. Photoemission measurements were performed with the angle-resolved scanning photoelectron microscope, at beamline BL31 of the Swedish synchrotron-radiation facility MAX-lab (Lund). The single-grain i-ZnMg(Y, Ho, Er) and Zn2Mg samples for the PE measurements were prepared in the form of small, 0.5 cm long, rods with 1 mm2 cross-section. The samples were cleaved in situ at about 2 1010 mbar and low,
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V. Karpus et al. / Applied Surface Science 252 (2006) 5411–5414
90–150 K, temperature. The cleanliness of the cleaved surfaces was routinely monitored following by photoemission the evolution of the O 2p states [3]. The best attainable total instrumental energy resolution was about 0.1 eV; it varied depending on the photon energy and the chosen pass energy of the analyser. 3. Results and discussion The photoemission spectra of the Mg 2p core-levels on i-ZnMg(Y, Ho, Er) quasicrystals recorded at several different photon energies are presented by open dots in Fig. 1. The
underlying structure of the Mg 2p PE lines in the QCs is a spin– orbit doublet, as is evident from a comparison with the Mg 2p spectra from Zn2Mg, which are presented in full-symbols. The Mg 2p spin–orbit splitting in Zn2Mg is Ds–o = 0.28 eV in agreement with the Ds–o value in pure Mg [4]; the full width at half maximum (FWHM) of the doublet components is G = 0.12 eV, and the branching ratio of the doublet is equal to the statistical value b = 2. As seen from Fig. 1, the Mg 2p line in i-ZnMg(Y, Ho, Er) quasicrystals is much broader than that in Zn2Mg. A preliminary analysis of the Mg 2p PE spectra in i-ZnMgEr [5] indicated that the experimental Mg 2p PE spectra can be
Fig. 1. Photoemission spectra of the Mg 2p shallow core-levels in (a) i-ZnMgY (T = 90–140 K), (b) i-ZnMgHo (T = 90–100 K), (c) i-ZnMgEr (T = 140–150 K) quasicrystals (open dots) and in crystalline Zn2Mg (T 100 K, full-dotted curves), and (d) the theoretical inner structure of the Mg 2p spectrum in the QCs.
V. Karpus et al. / Applied Surface Science 252 (2006) 5411–5414
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jellium due to the redistribution of the valence electrons, and a constant term, which was determined from the condition V R 0 is d3 r VðrÞ ¼ 0. The Madelung potential field VM(r) was calculated following the Ewald–Fuchs method [8]. The atomic potentials were assumed to correspond to the empty-core model [9]
vk ðrÞ ¼ Fig. 2. The local atomic coordination polyhedra of the magnesium Mg4 and Mg8 sites in i-ZnMgY.
well approximated by several binding-energy shifted spin–orbit doublets with the same intensity ratio for all photon energies used hn = 60–130 eV. The small changes in the Mg 2p PE lineshapes at increasing photon energies (Fig. 1) are solely due to the variation of instrumental energy resolution. This supports the assumption that the broad Mg 2p lineshapes in quasicrystals are related to the different inequivalent magnesium sites in the quasicrystalline lattice. Due to different atomic surroundings at the sites, the magnesium atoms experience different potentials, which give rise to the ‘coordination shifts’ of the atomic levels. The local atomic surroundings in face-centred icosahedral ZnMgHo [6] and ZnMgY [7] quasicrystals have been determined recently on the basis of the analysis of the atomic pair distribution function deduced from diffraction data. The ˚ ) model of the QC analysis indicates that in a local (Dr = 27 A atomic structure there are at least six different magnesium sites. The local atomic structure of i-ZnMgRE was determined for the model cubic ZnMg(Ho, Y) 2/1-approximants, the primitive cell of which contains 680 atoms. The 144 magnesium atoms evenly occupy six inequivalent sites denoted as Mg1, Mg3, Mg4, Mg7, Mg8, and Mg9 [7]. The atomic coordinations of the Mg4 and Mg8 sites are illustrated in Fig. 2. 3.1. Calculations of the local atomic potential To determine the coordination shift of the core levels of the atom positioned at site Rk, we calculated the local potential ˜ k Þ, which acts on the test electron and which is due to all VðR charges in the system, except the ion at the Rk site ˜ k Þ ¼ lim ½VðrÞ vk ðr Rk Þ; VðR r ! Rk
(1)
where vk ðr Rk Þ is the atomic potential of the ion. The total potential field V(r) in a metallic solid can be presented as the sum VðrÞ ¼ VM ðrÞ þ dVion ðrÞ þ dVel ðrÞ þ V0 ;
(2)
where VM(r) is the electrostatic Madelung potential field, which is due to the point-ion charges and to the uniform valence electron jellium; the dVion(r) field accounts for a deviation of the atomic potentials vk ðr Rk Þ from those due to pointcharges –Zke2/jr Rkj; the dVel(r) term corresponds to the deviation of the electron charge density from the uniform
8 <0
for r < ac;k ;
Z e2 : k r
(3)
for r > ac;k ;
where ac,k are the core radii. The potential field dVel(r) due to the redistribution of the valence electrons was calculated within the framework of self-consistent screening
dVel ðrÞ ¼
X g 6¼ 0
Vgbare
Vgbare
1 1 expðigrÞ; eðgÞ
1 X ¼ va;g expðigra Þ; Vcell a
(4)
where va;g is the Fourier amplitude of the atomic potential (3), g are the reciprocal lattice vectors, Vcell is the cell volume, ra are the cell atomic-basis vectors, and e(g) is the static dielectric function of the valence electrons
eðgÞ ¼ 1 þ
Fðg=2kF Þ ; g2 a2s
1 1 x2 1 þ x : ln FðxÞ ¼ þ 2 1 x 4x (5) 1/2
Here kF is the Fermi wavevector, as = (paB/4kF) is the screening radius, and aB is the Bohr radius. Formulas (1)–(5) allow for calculations of the local potential on the chosen atomic site at given set of atomic positions Rk (or ra) and values of the core radii ac,k. The calculations were carried out for the Rk set, which was determined in [7] for i-ZnMgY and was assumed to be a prototype for all three i-ZnMg(Y, Ho, Er) QCs studied, and for ˚ values of the core the known ac,Zn = 0.67 and ac,Mg = 0.74 A radii [10]. The core radius of the RE atom was taken to be equal ˚ [11]. to the Y3+ ionic radius, ac,RE = 0.9 A The results of the calculations of the local atomic potential on the magnesium sites are presented in Table 1. As seen, the difference in potentials on inequivalent Mg sites in i-ZnMgRE quasicrystals is spread within the interval of about 0.25 eV. The differences in potentials correspond to the coordination shifts of the atomic levels. Therefore, the inner structure of the Mg 2p spectrum in the quasicrystals should have the form presented in Fig. 1(d). 3.2. PE spectral intensity of the Mg 2p levels The PE spectral intensity of Mg 2p core-level was calculated as the sum of six spin–orbit doublets, shifted on the energy axis by the determined coordination shifts Dc,i, convoluted with a
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Table 1 The local potential on the inequivalent magnesium sites in i-ZnMgRE quasicrystals and the coordination shift of atomic core levels (with respect to the Mg4 atom)
˜ k Þ (Ry) VðR Dc (eV)
Mg1
Mg3
Mg4
Mg7
Mg8
Mg9
1.644 0.110
1.652 0.211
1.636 0
1.636 0.006
1.639 0.033
1.633 0.044
Gaussian function, which accounts for the total instrumental energy resolution of the photoelectron microscope Z 1 X 6 IðeÞ ¼ de0 Fðe0 ; e0 þ Dc;i ; G ; a; Dso ; bÞ Gðe e0 Þ: 1
i¼1
(6) The parameters of the spin–orbit doublets, the width G, the asymmetry parameter a, the spin–orbit splitting Ds–o = 0.28 eV, and the branching ratio b = 2, were taken to be the same for all six coordination-shifted Mg 2p doublets. The results of the calculations are shown by the curves through the experimental dots in Fig. 1(a)–(c). As seen, they nicely fit the experimental PE lineshapes of the Mg 2p corelevels in the i-ZnMg(Y, Ho, Er) quasicrystals. The asymmetry parameter a and the width G of the spin– orbit components were determined by the least square method. The asymmetry parameter deduced experiences a sharp variation with photon energy: its value changes from a = 0 at about hn < 65 eV to a 0.08 at hn > 65 eV. A similar a ‘jump’ of Da 0.1 at hn 65 eV was revealed also in the analysis of the Mg 2p PE spectra of Zn2Mg. Most probably, the jump is due to the transition from the adiabatic to the sudden regime of photoionization. The transition is related to polarization effects of Zn 3d electrons, as was previously revealed for the Zn 3p core-level in pure zinc [12]. The FWHM of the spin–orbit components in the i-ZnMg(Y, Ho, Er) quasicrystals was determined to be G = 0.22 eV, which exceeds the G = 0.12 eV value in magnesium dizinc. The additional broadening can be due to the fact that all Mg sites are in principle inequivalent in a quasicrystalline lattice with respect to the far-away neighbours, while the six inequivalent sites accounted for in the present analysis correspond only to the local atomic surrounding. The additional broadening of the
Mg 2p spin–orbit components can be due as well to a small asymmetry of the potential field V(r), which can lead to a splitting of the j = 3/2 and j = 1/2 components. 4. Conclusions Summarizing, we conclude that the photoemission spectra of the Mg 2p shallow core-levels in face-centred icosahedral ZnMgRE quasicrystals indicate a correlation between the quasicrystalline local atomic structure and the localized electron states. The different local atomic surroundings of the inequivalent sites induce the coordination shifts of the core electron levels. The calculated coordination shifts at the magnesium sites are up to 0.2 eV. The simulated spectral intensity of the Mg 2p photoemission spectra taking into account of the coordination shifts nicely fits experimental data. Acknowledgements Support by the EC Access to Research Infrastructure Programme, by the EC PRAMA Programme, and by the Swedish Institute is gratefully acknowledged. References [1] M. Gardner, Sci. Am. 236 (1977) 110–121. [2] A. Langsdorf, W. Assmus, J. Cryst. Growth 192 (1998) 152–156. ˇ echavicˇius, J. Dalmas, L. Giovanelli, [3] A. Suchodolskis, W. Assmus, B. C M. Go¨thelid, U.O. Karlsson, V. Karpus, G. Le Lay, R. Sterzel, E. Uhrig, Appl. Surf. Sci. 212/213 (2003) 485–490. [4] P.H. Citrin, G.H. Wertheim, Y. Baer, Phys. Rev. B 16 (1977) 4270–4282. [5] A. Suchodolskis, W. Assmus, G.-J. Babonas, L. Giovanelli, U.O. Karlsson, V. Karpus, G. Le Lay, A. Re˙za, E. Uhrig, Acta Physica Polonica A 107 (2005) 412–419. [6] S. Bru¨hne, R. Sterzel, E. Uhrig, C. Gross, W. Assmus, Z. Kristallogr. 219 (2004) 245–258. [7] S. Bru¨hne, E. Uhrig, C. Gross, W. Assmus, A.S. Masadeh, S.J.L. Billinge, J. Phys.: Condens. Matter 17 (2005) 1561–1572. [8] K. Fuchs, Proc. R. Soc. A 151 (1935) 585–602. [9] N.W. Ashcroft, Phys. Lett. 23 (1966) 48–51. [10] N.W. Ashcroft, D.C. Langreth, Phys. Rev. 155 (1967) 682–684. [11] C. Kittel, Introduction to Solid State Physics, Wiley, 1996. [12] F.J. Himpsel, D.E. Eastman, E.E. Koch, Phys. Rev. Lett. 44 (1980) 214– 217.