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Multilayer relaxation of the Cu(2 1 0) surface
Surface Science 504 (2002) L201–L207 www.elsevier.com/locate/susc
Surface Science Letters
Multilayer relaxation of the Cu(2 1 0) surface Ismail a
a,b,* ,
S. Chandravakar b, D.M. Zehner
b
Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN 37996-1200, USA b Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6057, USA Received 10 September 2001; accepted for publication 21 December 2001
Abstract Low-energy electron diffraction (LEED) I–V has been utilized to determine the surface structure of Cu(2 1 0). The surface structure is found to exhibit multilayer relaxation following the trend þ ( is contraction and þ is expansion in the interlayer spacing). The magnitude of interplanar relaxation is found to be damped, where jDd12 j > jDd23 j > jDd34 j, etc. This kind of behavior is quite different from that observed on Al(2 1 0) [Phys. Rev. B 38 (1988) 7913], where the magnitude of interplanar relaxation in the third interlayer is larger than that in the second interlayer (i.e., jDd23 j < jDd34 j). The difference of damped multilayer relaxation behavior of Cu(2 1 0) and Al(2 1 0) could be related to a charge density oscillation perpendicular to the surface. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Copper; Low energy electron diffraction (LEED); Surface relaxation and reconstruction
The study of surface relaxations has fascinated scientists for decades. As a bulk material is separated into two halves exposing two pristine surfaces, the electrons near the surface will respond to a new environment, readjusting to lower their kinetic energy and to screen out the presence of the surface. Atoms near a surface will move to new equilibrium positions because of the forces created by the redistributed electrons at the surface. Atomic planes in the surface region will shift inward or outward perpendicular to the surface (interlayer-relaxation), and lateral or parallel to the surface (in-plane relaxation), with or without
*
Corresponding author. Address: Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN 37996-1200, USA. Fax: +1-865-576-8135. E-mail address: [email protected] (Ismail).
preserving the bulk symmetry parallel to the surface. The most commonly observed phenomenon for an open surface is the interplanar relaxation of a damped behavior following the trend þ þ or þ, where and þ are contraction and expansion in the interlayer spacing, respectively. The magnitude of interplanar relaxation is usually damped, where jDd12 j > jDd23 j > jDd34 j, etc. However, the interplanar relaxations are not uniformly damped into the bulk for several cases: Al(2 1 0), Fe(2 1 0), Al(3 3 1) (see Ref. [1]), and Pd(2 1 0) [2]. For Al(2 1 0) [1], the magnitude of relaxation in the third interlayer spacing ðDd34 =d0 ¼ þ9:0ð3:0Þ%Þ is significantly larger than that in the second interlayer ðDd23 =d0 ¼ 1:0ð3:0ÞÞ, where d0 is the bulk interlayer spacing in the [2 1 0] direction. While in the case of Pd(2 1 0) [2], the magnitude of relaxation in the second interlayer spacing ðDd23 =d0 ¼ þ7ð5Þ%Þ is larger than that in the
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first interlayer spacing ðDd12 =d0 ¼ 3:0ð6:0ÞÞ. However, this behavior was not observed in the case of Pt(2 1 0) [3] even though the stacking sequence of Pt(2 1 0) is the same as that of Al(2 1 0) and Pd(2 1 0). The challenge has been to identify the contributions to interplanar relaxation from different sources. Finnis–Heine’s model [4] using Smoluchowski’s concept of charge spreading and smoothing, is widely accepted to explain the first interlayer relaxation for an open surface. Feibelman has discussed the effect of bond-energy, bondorder on surface relaxation [5]. Landman et al. correlated stacking sequence of the lattice to interplanar relaxation in metal surfaces by using an electrostatic model [6]. They found that there is, in general, a simple correlation between stacking sequences of the crystal and the oscillatory relaxation, where the effect of allowing more than one or two layers to relax is significant. Subsequently, Jiang et al. [7] and Adams et al. [1] used even simpler versions of the electrostatic interaction to reach the same qualitative conclusion. In contrast, Cho et al. [8] and Staikov and Rahman [9] showed that for simple metals, Friedel oscillations perpendicular to the surface with wave vector k ¼ 2=2kF (where kF is a Fermi wave vector) of the charge density caused by the redistribution of the electrons to screen the presence of the surface would also contribute to drive multilayer relaxation. A very recent study showed that surface states contribute to drive the oscillatory interplanar relaxation and thermal expansion on Mg(1 0 1 0) [10]. The question is what is the mechanism that drives a larger magnitude of relaxation in the third interlayer than in the second interlayer at a metal surface as has been observed on Al(2 1 0) [1] or larger magnitude of relaxation in the second interlayer spacing than that in the first interlayer on Pd(2 1 0) [2]. While this behavior was not observed on Pt(2 1 0) [3]. In an attempt to answer the question posed, we have utilized low-energy electron diffraction (LEED) I–V analysis to study the surface structure of Cu(2 1 0). The interlayer spacing for Cu(2 1 0) is ) allowing one to observe the short (i.e., 0:8079 A relaxation in deeper layers. We found that the trend of the magnitude of interlayer relaxation for
Cu(2 1 0) is uniformly damped into the bulk, i.e., jDd12 j > jDd23 j > jDd34 j, etc. This behavior is similar to that of Pt(2 1 0) [3], which is different than that for the cases of Al(2 1 0) [1] and Pd(2 1 0) [2]. A simple argument based on a charge density perpendicular to the surface could explain this behavior. The clean surface of Cu(2 1 0) was prepared by cycles of Ne-ion bombardment with a 10 lA sputtering current and subsequent anneals at 700 K. The cleanliness of the sample was monitored by Auger-electron spectroscopy. A (1 1) LEED pattern was observed which indicated that there is no reconstruction on the Cu(2 1 0) surface. Intensities of the diffracted beams as a function of incident electron energy were measured with the sample held at 130 K. A video LEED system was used to record the intensities (I–V ) with 0.5 eV increments at normal incidence. Normal incidence was determined by adjusting the position of the sample until I–V curves of symmetrically equivalent beams were almost identical. All available equivalent beams were averaged and normalized by incident electron beam current. Finally, nine inequivalent beams [(2,0), (3,0), (2,0), (3,0), (1,1), (2,1), (0,2), (1,2) and (2,2)] with the total energy range of DE ¼ 2550 eV were acquired. The analysis of the LEED I–V spectra was carried out using standard multiple scattering algorithms combined with automated tensor-LEED (TLEED) programs of Barbieri and Van Hove [11]. A full dynamical calculation for the initial reference structure was performed by using the Beeby matrix inversion scheme where multiple scattering within a layer was treated exactly and renormalized forward scattering for stacking layers was employed [12–14]. Because the interlayer spacing is short, a large composite layer consisting of ten atomic planes was employed for full dynamical calculations in order to avoid divergence in the calculations. Below this composite layer is the bulk termination of Cu(2 1 0). Thirteen atomic phase shifts for Cu were employed in our calculations, which were derived from the muffin–tin potential approximation with a muffin–tin radius of 2.39 a.u. Electron attenuation was described by an optical potential; the real part (Vor ) was constant and optimized during the search, while the
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Ismail et al. / Surface Science 504 (2002) L201–L207
imaginary part (Voi ) was modeled by Voi ¼ Vi fE= 1=3 ð200=27:21 þ Vor Þg where E is the incident electron energy (eV) and Vi is a constant optimized during the search. The temperature effect was included through the multiplication of atomic scattering matrix with a Debye Waller factor, where the Debye temperature was converted into isotropic mean-square displacements hu2 i1 , hu2 i2 , and hu2 ib for the first two top surface layers and the bulk, respectively. The method of TLEED approximation was used for the structural determination [15–17]. Calculated intensities (I–V ) were compared to the experimental data by using the Pendry’s R-factor (RP ) [18], and the error-bar calculated as defined by Pendry [18]. Fig. 1 shows the ball-model atomic arrangement of fcc(2 1 0), where ~ a1 and ~ a2 are the vectors of the surface unit cell. Vector~ s connects a layer to the successive layer parallel to the surface. Thus, the normal component of vector ~ s is the interlayer spacing (d0 ) perpendicular to the surface, and its
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parallel component along the [1 2 0] direction is defined as the interlayer registry ~ r. For Cu, the [19]; then lattice constant at T ¼ 130 K is 3.6132 A the bulk values of interlayer spacing (d0 ) and in reterlayer registry ðr0 Þ are 0.8079 and 1:6158 A spectively. We define the interplanar relaxation as Ddij ¼ ðdij d0 Þ=d0 and the registry relaxation as Drij ¼ ðrij r0 Þ=r0 , where dij is the interlayer spacing between the ith and jth atomic planes, rij is the interlayer registry between the ith and jth atomic planes. The values of optimized model parameters are listed in Table 1. Comparison of experimental and best fit spectra for all inequivalent beams are shown in Fig. 2, where the agreement is excellent, reflecting the total RP -factor (RP ¼ 0:15). The interlayer relaxation with respect to the bulk values (Ddij ) for the Cu(2 1 0) surface at a temperature of T ¼ 130 K are found to be: Dd12 ¼ 11:12ð2:0Þ%, Dd23 ¼ 5:68ð2:3Þ%, Dd34 ¼ þ3:83ð2:5Þ%, Dd45 ¼ þ0:06ð3:0Þ%, Dd56 ¼ 0:66ð3:5Þ%. We also found a small registry relaxation (Drij ) for Cu(2 1 0) (see Table 1), which is similar to other fcc(2 1 0). Table 1 Geometric parameters extracted from best fit to LEED I–V data of Cu(2 1 0) at T ¼ 130 K
Fig. 1. Top view and side view of hard-sphere model of Cu(2 1 0).
Interlayer relaxations Dd12 ð%Þ Dd23 ð%Þ Dd34 ð%Þ Dd45 ð%Þ Dd56 ð%Þ
11:12ð2:0Þ 5:68ð2:3Þ þ3:83ð2:5Þ þ0:06ð3:0Þ 0:66ð3:5Þ
Registry relaxations Dr12 ð%Þ Dr23 ð%Þ Dr34 ð%Þ Dr45 ð%Þ Dr56 ð%Þ
1:83ð3:0Þ 2:51ð3:2Þ þ1:68ð3:5Þ 0:48ð3:7Þ þ0:06ð4:0Þ
Bulk parameters ) d0 (A ) r0 (A
0.8079 1.6158
Non-structural parameters ) hui1 (A ) hui2 (A ) huibulk (A Vi Vor (eV)
0.134 0.096 0.086 4.0 5.99
RP
0.15
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Fig. 2. Comparison of measured (––) and calculated best fit I–V spectra ( ) for Cu(2 1 0) at temperature T ¼ 130 K.
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Now lets compare the surface relaxation for Cu(2 1 0) to other fcc(2 1 0): Al(2 1 0), Pt(2 1 0), and Pd(2 1 0). The interlayer spacing in the bulk of all for Al, 0.81 A for these systems is short: 0.90 A Cu, 0.88 A for Pt, and 0.87 A for Pd. The behavior of multilayer relaxation for Cu(2 1 0) is þ, where the first interlayer spacing is contracted (), the second interlayer spacing is contracted (), the third interlayer spacing is expanded (þ). The trend of relaxation ( þ) is the same as observed on Al(2 1 0) [1] and Pt(2 1 0) [3], but different with Pd(2 1 0) [2], where the trend of relaxation ( þ þ), see Table 2. The interplanar relaxations are uniformly damped into the bulk for Cu(2 1 0), (i.e., jDd12 j > jDd23 j > jDd34 j). This behavior is similar to the case of Pt(2 1 0) but significantly different from what has been observed on Al(2 1 0) [1] and Pd(2 1 0) [2]. For Al(2 1 0), the magnitude of the interlayer relaxation in the third interlayer spacing ðDd34 =d0 ¼ þ9:0ð3:0Þ%Þ is larger than that of in the second interlayer ðDd23 =d0 ¼ 1:0ð3:0Þ%Þ. While for Pd(2 1 0), the magnitude of the interlayer relaxation in the second interlayer spacing ðDd23 = d0 ¼ þ7:0ð5:0Þ%Þ is larger than that of in the first interlayer ðDd12 =d0 ¼ 3:0ð6:0Þ%Þ. Clearly, even though the stacking sequence of lattice for these four systems is the same (i.e., fcc(2 1 0)), the behavior of the surface relaxation is not always the same! In an attempt to understand the behavior of damped surface relaxation on fcc(2 1 0), we will use a charge density oscillation perpendicular to the surface, motivated by recent studies showing that Table 2 Previous structural studies of the fcc(2 1 0) surfaces Al(2 1 0) [1]
Pt(2 1 0) [3]
Pd(2 1 0) [2]
Interlayer relaxations Dd12 ð%Þ 16:0ð2:0Þ 1:0ð3:0Þ Dd23 ð%Þ Dd34 ð%Þ þ9:0ð3:0Þ Dd45 ð%Þ 4:0ð4:0Þ Dd56 ð%Þ 1:0ð5:0Þ
23:0ð4:0Þ 12:0ð5:0Þ þ4:0ð7:0Þ 3:0ð7:0Þ
3ð6Þ þ7ð5Þ þ3ð5Þ 1ð5Þ
Registry relaxations 0:00ð3:0Þ Dr12 ð%Þ 3:00ð3:0Þ Dr2 3 ð%Þ Dr3 4 ð%Þ þ2:00ð3:0Þ Dr45 ð%Þ 2:00ð4:0Þ 1:00ð5:0Þ Dr56 ð%Þ
þ1:14ð4:0Þ 1:71ð4:6Þ 4:56ð5:7Þ 0:57ð5:7Þ
2ð7Þ 1ð5Þ
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the Friedel oscillations contribute to drive multilayer relaxations [8,9]. The charge density oscillation for a simple model (one dimensional) is given by [20]: ! Dq cosð2qzÞ sinð2qzÞ / ð1Þ q0 ð2qzÞ2 ð2qzÞ3 where Dq ¼ q q0 , q is electron density, q0 is the mean electron density, q is a wave vector. The position of top surface (i.e., between vacuum and crystal) is not given in Eq. (1). Therefore, in this study the position of surface is assumed at a certain position for a certain system. Since the behavior of damped relaxation for Cu(2 1 0) is similar to Pt(2 1 0), and Al(2 1 0) is similar to Pd(2 1 0), we will compare only the charge density oscillation of Cu(2 1 0) to that of Al(2 1 0). Fig. 3a shows a schematic plot of one dimensional charge density oscillation perpendicular to the surface for 1 . Thick solid lines and Cu(2 1 0), where q ¼ 1:5 A numbers (1, 2,. . .) indicate the atomic layers. In Fig. 3a we can see that the depletion of electrons in the first layer is dominant, causing the first layer to be positively charged (þ). In the second layer, the accumulation of electrons is dominant, making the second layer to be negatively charged (). Similarly, we have that the third layer is positively charged (þ), the fourth layer is positively charged (þ), and the fifth layer is negatively charged (). The signs of the net charges for the five top layers are þ þ þ . Because the net charge in the first layer is positive, while it is negative in the second layer, there will be attractive forces between the first (F1 ) and second (F2 ) layers (see the arrows in Fig. 3a). Similarly, the net charges in the third and fourth layers are positive, while it is negative in the second and fifth layers, there will be repulsive forces between the third (F3 ) and fourth (F4 ) layers, attractive forces between the second (F2 ) and third (F3 ) layers, and the fourth (F4 ) and fifth (F5 ) layers (see the arrows in Fig. 3a). As a result the interlayer spacing d12 is contracted, d23 is contracted, d34 is expanded, etc. Similar to the case of Al(2 1 0) as shown in Fig. 3b, 1, we have a contraction in the where q ¼ 1:6 A interlayer spacing of d12 and d23 , expansion in d34 , etc.
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In summary, we have presented a study of the surface structure on Cu(2 1 0). The magnitude of interplanar relaxations for Cu(2 1 0) is uniformly damped into the bulk, (i.e., jDd12 j > jDd23 j > jDd34 j, etc.), which is similar to those observed on Pt(2 1 0) but different than what has been observed on Al(2 1 0) and Pd(2 1 0). This shows that even though the stacking sequence of lattice for these systems is the same (i.e., fcc(2 1 0)), the behavior of damped relaxation is not always the same. This behavior could be related to charge density oscillations perpendicular to the surface.
Acknowledgements We are grateful to Barbieri and Van Hove for LEED codes, A.P. Baddorf and Zhenyu Zhang for useful discussions, and G.W. Ownby for preparation of the sample. This work was supported by Oak Ridge National Laboratory, managed by UTBattelle, LLC, for the US Department of Energy under contract DE-AC05-00OR22725. Fig. 3. A schematic plot of charge density oscillation perpendicular to the surface for (a) Cu(2 1 0) and (b) Al(2 1 0). Thick solid lines and the numbers (1, 2, 3, etc.) indicate the atomic layers.
The magnitude of contraction or expansion in the interlayer spacing depends on the magnitude of the force on the atomic planes, where the force itself is related to the amount of net charges. If the net forces from every pair of atomic planes, first and second planes (F1 þ F2 ), second and third planes (F2 þ F3 ), third and fourth planes (F3 þ F4 ), etc., are uniformly damped into the bulk, then the magnitude of the interplanar relaxations is uniformly damped into the bulk. This is what happen in general cases, such as Cu(2 1 0). But for Al(2 1 0), the arrangement of charges such that the net forces from the second and third atomic planes (F2 þ F3 ) is smaller than those from the third and fourth planes (F3 þ F4 ), leading the magnitude of interlayer relaxation in the second interlayer to be smaller than that in the third interlayer spacing.
References [1] D.L. Adams, V. Jensen, X.F. Sun, J.H. Vollesen, Phys. Rev. B 38 (1988) 7913. [2] D. Kolthoff, H. Pfn€ ur, A.G. Fedorus, V. Koval, A.G. Naumovets, Surf. Sci. 439 (1999) 224. [3] X.-G. Zhang et al., Phys. Rev. Lett. 67 (1991) 1298. [4] M.W. Finnis, V. Heine, J. Phys. F 4 (1974) L37. [5] P.J. Feibelman, Phys. Rev. B 46 (1992) 2532. [6] U. Landman, R.N. Hill, M. Mostoller, Phys. Rev. B 21 (1980) 448. [7] P. Jiang, P.M. Marcus, F. Jona, Solid State Commun. 59 (1986) 275. [8] J.-H. Cho, Ismail, Z. Zhang, E.W. Plummer, Phys. Rev. B 59 (1999) 1677. [9] P. Staikov, T.S. Rahman, Phys. Rev. B 60 (1999) 15613. [10] Ismail, S.-J. Tang, P.T. Sprunger, E.V. Chulkov, V.M. Silkin, E.W. Plummer, unpublished. [11] Barbieri, Van Hove, private communications. [12] J.B. Pendry, Low Energy Electron Diffraction, Academic Press, London, 1974. [13] M.A.V. Hove, S.Y. Tong, Surface Crystallography by LEED, Springer, Berlin, 1979. [14] M.A.V. Hove, W.H. Weinberg, C.M. Chan, Low Energy Electron Diffraction, Springer, Berlin, 1986.
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Ismail et al. / Surface Science 504 (2002) L201–L207 [15] P.J. Rous et al., Phys. Rev. Lett. 57 (1986) 2951. [16] P.J. Rous, J.B. Pendry, Surf. Sci. 219 (1989) 355. [17] P.J. Rous, M.A.V. Hove, G.A. Somorjai, Surf. Sci. 226 (1990) 15. [18] J.B. Pendry, J. Phys. C 13 (1980) 937. [19] Y.S. Touloukian, R.K. Kirby, R.E. Taylor, P.D. Desai, in: International Tables for X-Ray Crystallography, vol. III, The Kynoch Press, Birmingham, England, 1962;
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Thermal Expansion: Metallic Elements and Alloys, Thermophysical Properties Research Center at Perdue University, Thermophysical Properties of Matter, vol. 12, IFI/ Plenum, New York, 1970; Metallic Elements and Alloys, Thermophysical Properties Research Center at Perdue University, Thermophysical Properties of Matter, vol. 12, IFI/Plenum, New York, 1970. [20] A.W. Overhauser, Phys. Rev. B 33 (1986) 1468.
Surface Science Letters
Multilayer relaxation of the Cu(2 1 0) surface Ismail a
a,b,* ,
S. Chandravakar b, D.M. Zehner
b
Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN 37996-1200, USA b Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6057, USA Received 10 September 2001; accepted for publication 21 December 2001
Abstract Low-energy electron diffraction (LEED) I–V has been utilized to determine the surface structure of Cu(2 1 0). The surface structure is found to exhibit multilayer relaxation following the trend þ ( is contraction and þ is expansion in the interlayer spacing). The magnitude of interplanar relaxation is found to be damped, where jDd12 j > jDd23 j > jDd34 j, etc. This kind of behavior is quite different from that observed on Al(2 1 0) [Phys. Rev. B 38 (1988) 7913], where the magnitude of interplanar relaxation in the third interlayer is larger than that in the second interlayer (i.e., jDd23 j < jDd34 j). The difference of damped multilayer relaxation behavior of Cu(2 1 0) and Al(2 1 0) could be related to a charge density oscillation perpendicular to the surface. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Copper; Low energy electron diffraction (LEED); Surface relaxation and reconstruction
The study of surface relaxations has fascinated scientists for decades. As a bulk material is separated into two halves exposing two pristine surfaces, the electrons near the surface will respond to a new environment, readjusting to lower their kinetic energy and to screen out the presence of the surface. Atoms near a surface will move to new equilibrium positions because of the forces created by the redistributed electrons at the surface. Atomic planes in the surface region will shift inward or outward perpendicular to the surface (interlayer-relaxation), and lateral or parallel to the surface (in-plane relaxation), with or without
*
Corresponding author. Address: Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN 37996-1200, USA. Fax: +1-865-576-8135. E-mail address: [email protected] (Ismail).
preserving the bulk symmetry parallel to the surface. The most commonly observed phenomenon for an open surface is the interplanar relaxation of a damped behavior following the trend þ þ or þ, where and þ are contraction and expansion in the interlayer spacing, respectively. The magnitude of interplanar relaxation is usually damped, where jDd12 j > jDd23 j > jDd34 j, etc. However, the interplanar relaxations are not uniformly damped into the bulk for several cases: Al(2 1 0), Fe(2 1 0), Al(3 3 1) (see Ref. [1]), and Pd(2 1 0) [2]. For Al(2 1 0) [1], the magnitude of relaxation in the third interlayer spacing ðDd34 =d0 ¼ þ9:0ð3:0Þ%Þ is significantly larger than that in the second interlayer ðDd23 =d0 ¼ 1:0ð3:0ÞÞ, where d0 is the bulk interlayer spacing in the [2 1 0] direction. While in the case of Pd(2 1 0) [2], the magnitude of relaxation in the second interlayer spacing ðDd23 =d0 ¼ þ7ð5Þ%Þ is larger than that in the
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first interlayer spacing ðDd12 =d0 ¼ 3:0ð6:0ÞÞ. However, this behavior was not observed in the case of Pt(2 1 0) [3] even though the stacking sequence of Pt(2 1 0) is the same as that of Al(2 1 0) and Pd(2 1 0). The challenge has been to identify the contributions to interplanar relaxation from different sources. Finnis–Heine’s model [4] using Smoluchowski’s concept of charge spreading and smoothing, is widely accepted to explain the first interlayer relaxation for an open surface. Feibelman has discussed the effect of bond-energy, bondorder on surface relaxation [5]. Landman et al. correlated stacking sequence of the lattice to interplanar relaxation in metal surfaces by using an electrostatic model [6]. They found that there is, in general, a simple correlation between stacking sequences of the crystal and the oscillatory relaxation, where the effect of allowing more than one or two layers to relax is significant. Subsequently, Jiang et al. [7] and Adams et al. [1] used even simpler versions of the electrostatic interaction to reach the same qualitative conclusion. In contrast, Cho et al. [8] and Staikov and Rahman [9] showed that for simple metals, Friedel oscillations perpendicular to the surface with wave vector k ¼ 2=2kF (where kF is a Fermi wave vector) of the charge density caused by the redistribution of the electrons to screen the presence of the surface would also contribute to drive multilayer relaxation. A very recent study showed that surface states contribute to drive the oscillatory interplanar relaxation and thermal expansion on Mg(1 0 1 0) [10]. The question is what is the mechanism that drives a larger magnitude of relaxation in the third interlayer than in the second interlayer at a metal surface as has been observed on Al(2 1 0) [1] or larger magnitude of relaxation in the second interlayer spacing than that in the first interlayer on Pd(2 1 0) [2]. While this behavior was not observed on Pt(2 1 0) [3]. In an attempt to answer the question posed, we have utilized low-energy electron diffraction (LEED) I–V analysis to study the surface structure of Cu(2 1 0). The interlayer spacing for Cu(2 1 0) is ) allowing one to observe the short (i.e., 0:8079 A relaxation in deeper layers. We found that the trend of the magnitude of interlayer relaxation for
Cu(2 1 0) is uniformly damped into the bulk, i.e., jDd12 j > jDd23 j > jDd34 j, etc. This behavior is similar to that of Pt(2 1 0) [3], which is different than that for the cases of Al(2 1 0) [1] and Pd(2 1 0) [2]. A simple argument based on a charge density perpendicular to the surface could explain this behavior. The clean surface of Cu(2 1 0) was prepared by cycles of Ne-ion bombardment with a 10 lA sputtering current and subsequent anneals at 700 K. The cleanliness of the sample was monitored by Auger-electron spectroscopy. A (1 1) LEED pattern was observed which indicated that there is no reconstruction on the Cu(2 1 0) surface. Intensities of the diffracted beams as a function of incident electron energy were measured with the sample held at 130 K. A video LEED system was used to record the intensities (I–V ) with 0.5 eV increments at normal incidence. Normal incidence was determined by adjusting the position of the sample until I–V curves of symmetrically equivalent beams were almost identical. All available equivalent beams were averaged and normalized by incident electron beam current. Finally, nine inequivalent beams [(2,0), (3,0), (2,0), (3,0), (1,1), (2,1), (0,2), (1,2) and (2,2)] with the total energy range of DE ¼ 2550 eV were acquired. The analysis of the LEED I–V spectra was carried out using standard multiple scattering algorithms combined with automated tensor-LEED (TLEED) programs of Barbieri and Van Hove [11]. A full dynamical calculation for the initial reference structure was performed by using the Beeby matrix inversion scheme where multiple scattering within a layer was treated exactly and renormalized forward scattering for stacking layers was employed [12–14]. Because the interlayer spacing is short, a large composite layer consisting of ten atomic planes was employed for full dynamical calculations in order to avoid divergence in the calculations. Below this composite layer is the bulk termination of Cu(2 1 0). Thirteen atomic phase shifts for Cu were employed in our calculations, which were derived from the muffin–tin potential approximation with a muffin–tin radius of 2.39 a.u. Electron attenuation was described by an optical potential; the real part (Vor ) was constant and optimized during the search, while the
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imaginary part (Voi ) was modeled by Voi ¼ Vi fE= 1=3 ð200=27:21 þ Vor Þg where E is the incident electron energy (eV) and Vi is a constant optimized during the search. The temperature effect was included through the multiplication of atomic scattering matrix with a Debye Waller factor, where the Debye temperature was converted into isotropic mean-square displacements hu2 i1 , hu2 i2 , and hu2 ib for the first two top surface layers and the bulk, respectively. The method of TLEED approximation was used for the structural determination [15–17]. Calculated intensities (I–V ) were compared to the experimental data by using the Pendry’s R-factor (RP ) [18], and the error-bar calculated as defined by Pendry [18]. Fig. 1 shows the ball-model atomic arrangement of fcc(2 1 0), where ~ a1 and ~ a2 are the vectors of the surface unit cell. Vector~ s connects a layer to the successive layer parallel to the surface. Thus, the normal component of vector ~ s is the interlayer spacing (d0 ) perpendicular to the surface, and its
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parallel component along the [1 2 0] direction is defined as the interlayer registry ~ r. For Cu, the [19]; then lattice constant at T ¼ 130 K is 3.6132 A the bulk values of interlayer spacing (d0 ) and in reterlayer registry ðr0 Þ are 0.8079 and 1:6158 A spectively. We define the interplanar relaxation as Ddij ¼ ðdij d0 Þ=d0 and the registry relaxation as Drij ¼ ðrij r0 Þ=r0 , where dij is the interlayer spacing between the ith and jth atomic planes, rij is the interlayer registry between the ith and jth atomic planes. The values of optimized model parameters are listed in Table 1. Comparison of experimental and best fit spectra for all inequivalent beams are shown in Fig. 2, where the agreement is excellent, reflecting the total RP -factor (RP ¼ 0:15). The interlayer relaxation with respect to the bulk values (Ddij ) for the Cu(2 1 0) surface at a temperature of T ¼ 130 K are found to be: Dd12 ¼ 11:12ð2:0Þ%, Dd23 ¼ 5:68ð2:3Þ%, Dd34 ¼ þ3:83ð2:5Þ%, Dd45 ¼ þ0:06ð3:0Þ%, Dd56 ¼ 0:66ð3:5Þ%. We also found a small registry relaxation (Drij ) for Cu(2 1 0) (see Table 1), which is similar to other fcc(2 1 0). Table 1 Geometric parameters extracted from best fit to LEED I–V data of Cu(2 1 0) at T ¼ 130 K
Fig. 1. Top view and side view of hard-sphere model of Cu(2 1 0).
Interlayer relaxations Dd12 ð%Þ Dd23 ð%Þ Dd34 ð%Þ Dd45 ð%Þ Dd56 ð%Þ
11:12ð2:0Þ 5:68ð2:3Þ þ3:83ð2:5Þ þ0:06ð3:0Þ 0:66ð3:5Þ
Registry relaxations Dr12 ð%Þ Dr23 ð%Þ Dr34 ð%Þ Dr45 ð%Þ Dr56 ð%Þ
1:83ð3:0Þ 2:51ð3:2Þ þ1:68ð3:5Þ 0:48ð3:7Þ þ0:06ð4:0Þ
Bulk parameters ) d0 (A ) r0 (A
0.8079 1.6158
Non-structural parameters ) hui1 (A ) hui2 (A ) huibulk (A Vi Vor (eV)
0.134 0.096 0.086 4.0 5.99
RP
0.15
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Fig. 2. Comparison of measured (––) and calculated best fit I–V spectra ( ) for Cu(2 1 0) at temperature T ¼ 130 K.
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Now lets compare the surface relaxation for Cu(2 1 0) to other fcc(2 1 0): Al(2 1 0), Pt(2 1 0), and Pd(2 1 0). The interlayer spacing in the bulk of all for Al, 0.81 A for these systems is short: 0.90 A Cu, 0.88 A for Pt, and 0.87 A for Pd. The behavior of multilayer relaxation for Cu(2 1 0) is þ, where the first interlayer spacing is contracted (), the second interlayer spacing is contracted (), the third interlayer spacing is expanded (þ). The trend of relaxation ( þ) is the same as observed on Al(2 1 0) [1] and Pt(2 1 0) [3], but different with Pd(2 1 0) [2], where the trend of relaxation ( þ þ), see Table 2. The interplanar relaxations are uniformly damped into the bulk for Cu(2 1 0), (i.e., jDd12 j > jDd23 j > jDd34 j). This behavior is similar to the case of Pt(2 1 0) but significantly different from what has been observed on Al(2 1 0) [1] and Pd(2 1 0) [2]. For Al(2 1 0), the magnitude of the interlayer relaxation in the third interlayer spacing ðDd34 =d0 ¼ þ9:0ð3:0Þ%Þ is larger than that of in the second interlayer ðDd23 =d0 ¼ 1:0ð3:0Þ%Þ. While for Pd(2 1 0), the magnitude of the interlayer relaxation in the second interlayer spacing ðDd23 = d0 ¼ þ7:0ð5:0Þ%Þ is larger than that of in the first interlayer ðDd12 =d0 ¼ 3:0ð6:0Þ%Þ. Clearly, even though the stacking sequence of lattice for these four systems is the same (i.e., fcc(2 1 0)), the behavior of the surface relaxation is not always the same! In an attempt to understand the behavior of damped surface relaxation on fcc(2 1 0), we will use a charge density oscillation perpendicular to the surface, motivated by recent studies showing that Table 2 Previous structural studies of the fcc(2 1 0) surfaces Al(2 1 0) [1]
Pt(2 1 0) [3]
Pd(2 1 0) [2]
Interlayer relaxations Dd12 ð%Þ 16:0ð2:0Þ 1:0ð3:0Þ Dd23 ð%Þ Dd34 ð%Þ þ9:0ð3:0Þ Dd45 ð%Þ 4:0ð4:0Þ Dd56 ð%Þ 1:0ð5:0Þ
23:0ð4:0Þ 12:0ð5:0Þ þ4:0ð7:0Þ 3:0ð7:0Þ
3ð6Þ þ7ð5Þ þ3ð5Þ 1ð5Þ
Registry relaxations 0:00ð3:0Þ Dr12 ð%Þ 3:00ð3:0Þ Dr2 3 ð%Þ Dr3 4 ð%Þ þ2:00ð3:0Þ Dr45 ð%Þ 2:00ð4:0Þ 1:00ð5:0Þ Dr56 ð%Þ
þ1:14ð4:0Þ 1:71ð4:6Þ 4:56ð5:7Þ 0:57ð5:7Þ
2ð7Þ 1ð5Þ
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the Friedel oscillations contribute to drive multilayer relaxations [8,9]. The charge density oscillation for a simple model (one dimensional) is given by [20]: ! Dq cosð2qzÞ sinð2qzÞ / ð1Þ q0 ð2qzÞ2 ð2qzÞ3 where Dq ¼ q q0 , q is electron density, q0 is the mean electron density, q is a wave vector. The position of top surface (i.e., between vacuum and crystal) is not given in Eq. (1). Therefore, in this study the position of surface is assumed at a certain position for a certain system. Since the behavior of damped relaxation for Cu(2 1 0) is similar to Pt(2 1 0), and Al(2 1 0) is similar to Pd(2 1 0), we will compare only the charge density oscillation of Cu(2 1 0) to that of Al(2 1 0). Fig. 3a shows a schematic plot of one dimensional charge density oscillation perpendicular to the surface for 1 . Thick solid lines and Cu(2 1 0), where q ¼ 1:5 A numbers (1, 2,. . .) indicate the atomic layers. In Fig. 3a we can see that the depletion of electrons in the first layer is dominant, causing the first layer to be positively charged (þ). In the second layer, the accumulation of electrons is dominant, making the second layer to be negatively charged (). Similarly, we have that the third layer is positively charged (þ), the fourth layer is positively charged (þ), and the fifth layer is negatively charged (). The signs of the net charges for the five top layers are þ þ þ . Because the net charge in the first layer is positive, while it is negative in the second layer, there will be attractive forces between the first (F1 ) and second (F2 ) layers (see the arrows in Fig. 3a). Similarly, the net charges in the third and fourth layers are positive, while it is negative in the second and fifth layers, there will be repulsive forces between the third (F3 ) and fourth (F4 ) layers, attractive forces between the second (F2 ) and third (F3 ) layers, and the fourth (F4 ) and fifth (F5 ) layers (see the arrows in Fig. 3a). As a result the interlayer spacing d12 is contracted, d23 is contracted, d34 is expanded, etc. Similar to the case of Al(2 1 0) as shown in Fig. 3b, 1, we have a contraction in the where q ¼ 1:6 A interlayer spacing of d12 and d23 , expansion in d34 , etc.
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In summary, we have presented a study of the surface structure on Cu(2 1 0). The magnitude of interplanar relaxations for Cu(2 1 0) is uniformly damped into the bulk, (i.e., jDd12 j > jDd23 j > jDd34 j, etc.), which is similar to those observed on Pt(2 1 0) but different than what has been observed on Al(2 1 0) and Pd(2 1 0). This shows that even though the stacking sequence of lattice for these systems is the same (i.e., fcc(2 1 0)), the behavior of damped relaxation is not always the same. This behavior could be related to charge density oscillations perpendicular to the surface.
Acknowledgements We are grateful to Barbieri and Van Hove for LEED codes, A.P. Baddorf and Zhenyu Zhang for useful discussions, and G.W. Ownby for preparation of the sample. This work was supported by Oak Ridge National Laboratory, managed by UTBattelle, LLC, for the US Department of Energy under contract DE-AC05-00OR22725. Fig. 3. A schematic plot of charge density oscillation perpendicular to the surface for (a) Cu(2 1 0) and (b) Al(2 1 0). Thick solid lines and the numbers (1, 2, 3, etc.) indicate the atomic layers.
The magnitude of contraction or expansion in the interlayer spacing depends on the magnitude of the force on the atomic planes, where the force itself is related to the amount of net charges. If the net forces from every pair of atomic planes, first and second planes (F1 þ F2 ), second and third planes (F2 þ F3 ), third and fourth planes (F3 þ F4 ), etc., are uniformly damped into the bulk, then the magnitude of the interplanar relaxations is uniformly damped into the bulk. This is what happen in general cases, such as Cu(2 1 0). But for Al(2 1 0), the arrangement of charges such that the net forces from the second and third atomic planes (F2 þ F3 ) is smaller than those from the third and fourth planes (F3 þ F4 ), leading the magnitude of interlayer relaxation in the second interlayer to be smaller than that in the third interlayer spacing.
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