Home

Search

Collections

Journals

About

Contact us

My IOPscience

Surface relaxation of Cu(5 1 1)

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 085002 (http://iopscience.iop.org/0953-8984/27/8/085002) View the table of contents for this issue, or go to the journal homepage for more

Download details: IP Address: 169.230.243.252 This content was downloaded on 21/02/2015 at 06:09

Please note that terms and conditions apply.

Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 085002 (4pp)

doi:10.1088/0953-8984/27/8/085002

Surface relaxation of Cu(5 1 1) K Pussi1 , M Caragiu2 , K J Hanna3 , W Moritz4 and R D Diehl3 1

Department of Mathematics and Physics, Lappeenranta University of Technology, PO Box 20 FIN-53851 Lappeenranta, Finland 2 Department of Physics, Ohio Northern University, Ada, OH 45810, USA 3 Department of Physics, Penn State University, University Park, PA 16802, USA 4 Department of Earth and Environmental Sciences, Crystallography Section, LMU, Theresienstrasse 41, D-80333 M¨unchen, Germany E-mail: [email protected] Received 2 October 2014, revised 10 December 2014 Accepted for publication 18 December 2014 Published 23 January 2015 Abstract

The multilayer relaxation of the stepped Cu(5 1 1) surface has been studied by quantitative low-energy electron diffraction and analyzed using the CLEED program package. Relaxations with respect to the bulk interlayer spacing of 0.6934 Å are −9.5%, −10.4%, +8.2% and −1.8% for the first four interlayer spacings, respectively (negative sign corresponds to contraction). The relaxation sequence (− − + −. . . ) is thus in agreement with the theoretical prediction. The deeper relaxations are damped in a non-uniform manner and the lateral relaxations are smaller than 2% of the lateral spacing. This result agrees well with theoretical studies of the same surface. The Pendry R-factor for the favored structure is 0.21. Keywords: LEED, vicinal surfaces, Cu, surface structure (Some figures may appear in colour only in the online journal)

between the rules and the experimental results. The surface of Cu(5 1 1) is one of these. There are only two experimental results cited for this surface structure, one from surface x-ray diffraction (SXRD) [5]. The other is an unpublished study using low-energy electron diffraction (LEED) [6] that was cited in the SXRD paper [5] as a result of a communication between the two experimental groups. That citation then propagated through all subsequent studies on this surface, which are all theoretical studies. We note for clarification that the experimental data used in the present analysis are those presented in the thesis [6] but the analysis in the thesis was not complete. The analysis presented here is entirely new. We have re-examined those unpublished LEED data. The new results are quite different from those cited earlier, and they also are quite different from the results of the SXRD study [5]. However, they offer much better agreement with many of the theoretical studies. In this paper, we present our analysis of the LEED data for Cu(5 1 1).

1. Introduction

The relaxations of the surface structures of stepped metal surfaces have been a subject of interest for many years for many reasons [1–3]. They represent an intermediate stage between low-index surfaces that have been the ‘ideal’ surface studied for many years in surface science and ‘real’ surfaces that are usually polycrystalline. The under-coordination of step atoms plays a major role in the modification of the physical properties of the surface, changing the electronic and vibrational properties and enhancing the chemical activity [2]. Many of these studies therefore are aimed at improving our understanding of how surfaces act as catalysts in chemical reactions at surfaces. Vicinal surfaces also offer opportunities to exert more control over self-assembled film growth. Stepped Cu surfaces in particular have received much attention, and have been the subject of many theoretical studies that can use a relatively well-understood elemental surface as a model for the structural and dynamical phenomena that occur at surface steps. Many different vicinal surfaces of Cu have been studied and several ‘rules’ have been developed to describe the expected relaxations of atoms, relative to their bulk positions, at the surfaces of vicinal surfaces [4]. These ‘rules’ have been compiled and reviewed in many of the recent publications on these surfaces, and in certain cases, poor agreement was found 0953-8984/15/085002+04$33.00

2. Experimental and computational procedures

The LEED intensity measurements were performed in a UHVchamber in Munich, with base pressure better than 2 × 10−10 mbar. Prior to mounting the sample into the chamber, the 1

© 2015 IOP Publishing Ltd Printed in the UK

J. Phys.: Condens. Matter 27 (2015) 085002

K Pussi et al

Figure 1. Schematic drawing of reciprocal lattice (left) and LEED pattern taken from Cu(5 1 1) at an incident beam energy of 150 eV. The beam-index scheme is shown on the drawing, and an equivalent lattice is superimposed on the LEED pattern. (The LEED pattern shown was acquired in the Penn State laboratory; the intensities shown in figure 2 were measured in Munich.)

(5 1 1) oriented Cu crystal was chemically polished in FeNO3 solution. The sample was prepared by Ar+ ion bombardment at 700–750 K for several hours until no S or C impurities could be detected in the AES spectrum. The crystal was subsequently cooled to 100 K by 3 K min−1 , after which a LEED pattern with sharp reflections was visible. The intensity data were obtained by recording the spot intensities from the fluorescent screen using a video-LEED system. The structure exhibits one mirror plane, therefore the alignment of the incident beam with respect to the mirror plane could be checked by measuring symmetrically equivalent beams. The polar angle was determined by rotation of the crystal around an axis normal to the incident beam and adjusting the normal incidence by measuring the position of the specular beam in both directions. This procedure does not allow the adjustment of the polar incidence angle very precisely. In the analysis therefore the polar angle has been taken as an additional adjustable parameter. The I (E) curves were corrected for primary current and background, symmetrically equivalent beams have been averaged. In total 12 symmetrically independent beams were measured at a temperature of 98 K by varying the electron energy in the range between 50 and 380 eV corresponding to a total energy range of 2300 eV. Figure 1 shows a LEED pattern taken with incident beam energy of 150 eV, and a schematic drawing of the LEED pattern that includes the indexing scheme for the diffraction beams. These patterns are aligned so that the mirror plane of the pattern, corresponding to a direction perpendicular to the surface steps, is vertical. The surface unit cell is oblique, as shown in the drawing, but the pattern is symmetric with respect to the mirror plane. Therefore, the beams having indices (1,1) and (−1,0), for instance, have equivalent intensities and were averaged in the analysis. The calculations were performed using the CLEED package [7]. Because of the small interlayer distance of

Table 1. Parameters deduced from the LEED analysis. Dimensions are in Å. The bulk interlayer spacing is 0.6934 and the bulk RMS vibration amplitude is 0.065 Å. The error on all interlayer spacings is ±0.02 Å, or about ±3%. The error on all vibration amplitudes is 0.02 Å.

Interlayer spacing and % relaxation RMS vibration amplitudes d12 d23 d34 d45 d56 d67

0.628 0.622 0.750 0.681 0.719 0.702

−9.5% −10.4% +8.2% −1.8% +3.7% +1.2%

0.11 0.10 0.09 0.08 0.07 0.07

0.69 Å, layer doubling could not be employed and the reflection matrix for the entire surface had to be calculated by using the combined space or ‘giant matrix inversion’ method. The surface was modeled by using a stack of 16 layers (≈10 Å). Increasing the stack size up to 24 layers (∼16 Å) did not lead to any significant changes in the calculated curves and structural results. The calculations included up to 9 phase shifts and the adjustable parameters included the x–y–z coordinates of the atoms in the top 4 layers, the z-coordinates of the 5th and 6th layers, and the vibration amplitudes of the atoms in each layer. Because it is very difficult to ascertain exact normal incidence in experiments on stepped surfaces, the angle of incidence was also an adjustable parameter. To test the agreement between the calculation and the experimental results, the Pendry RP and RR factors were used [8]. For the structure optimization and the determination of the angles of incidence, the downhill simplex method was used. LEED intensities were calculated for electron energies between 40 and 400 eV in steps of 5 eV. The damping parameter (imaginary part of the inner potential) was set to −5.0 eV. The root mean square (RMS) thermal displacements were initially set to 0.065 Å for all the copper atoms and at the end of the analysis they were optimized 2

J. Phys.: Condens. Matter 27 (2015) 085002

K Pussi et al

Figure 2. The intensity–energy curves for the best-fit structure. Individual beam R-factors are shown, the overall R-factor is 0.21.

Figure 3. (a) Top view of the Cu(5 1 1) surface. The first five atomic layers are numbered. (b) Side view of the Cu(5 1 1) surface.

layer-by-layer to produce the best fit. The scattering phase shifts for the copper atoms were calculated using the program package provided by Barbieri and Van Hove [9].

bulk). Figure 2 shows the agreement between the theory and experiment. Due to the loss of neighbors along the z direction for all surface atoms, and along the x direction for the step atoms, the vicinal surfaces are expected to relax in both vertical and lateral directions. The Cu(5 1 1) (3(1 0 0)×(1 1 1)) surface consists of three-atom-row-wide terraces of fcc(1 0 0) that are separated by single atom height steps of fcc(1 1 1). For the fcc(5 1 1) surface, the step profile involves the top three atom layers, i.e. the atoms in these layers are under-coordinated with respect to the bulk atoms. The coordination numbers for the first three step atoms are 7, 8 and 10 (see figure 3(a) for the atom numbering). The third atom is the last step atom and the bulk begins with the fourth atom (coordination 12). Since the third atom is the last step atom and thus bonded to the first bulk

3. Results and discussion

The structure was optimized as described, producing an ultimate R-factor of 0.21 and RR of 0.017. The optimized interlayer spacings are given in table 1. The incident angle was found to be 0.81◦ off normal—optimizing this improved the final R-factor from 0.25 to 0.21. The RMS displacements were optimized to 0.11 Å, 0.10 Å, 0.09 Å, 0.08 Å and 0.065 Å for the four top layers and the bulk atoms respectively. The lateral relaxations of the top four layers were within the error bars of the analysis (less than 2% of the Cu–Cu distance in 3

J. Phys.: Condens. Matter 27 (2015) 085002

K Pussi et al

Table 2. Measured and calculated surface relaxation in percent of the bulk interlayer spacing for Cu(5 1 1). The abbreviations are LEED (low-energy electron diffraction) SXRD (surface x-ray diffraction), TB (tight binding), EM (energy minimization) EAM (embedded atom method), GGA (generalized gradient method), LDA (local density approximation), FLAPW (fully linearized augmented plane waves), PPPW (pseudo-potential plane wave).

Experiment Method (year)

SXRD (1999)

d12 d23 d34 d45 d56 d67 d78 d89 d9−10 Ref

−15.4 +8.1 −1.1 −10.3 +5.4 −0.7 −6.9 +3.6 [5]

Theory TB (1989)

EM (1992)

EAM (1997)

GGA (2001)

LDA (2002)

GGA (2004)

GGA (2004)

LDA (2004)

FLAPW (2005)

PPPW (2010)

−9.5 −10.4 +8.2 −1.8 +3.7 +1.2

−8.0 −5.1 +7.0 −3.3 −3.1

−12.7 −10.3 +10.8 −6.3

−9.46 −7.87 +8.76 −4.19 −4.04 +3.44 −1.67 −1.14

−11.1 −16.4 +8.4 −4.6 +2.3 −1.5 0.2 0.8

−10.4 −13.6 +9.4 −3.8 +2.0 −0.3

[10]

[11]

[12]

[13]

−17.1 −13.8 +11.0 −7.4 +0.6 −0.8 −3.7 +0.7 −1.7 [15]

−13.4 −11.2 +7.3 −4.9 +1.9 −0.4 −2.4 +1.8 −1.0 [15]

−10.55 −9.81 +6.17 −4.3 +2.84 +1.33 −2.34 +1.67

This work

−9.3 −10.7 +7.2 −2.9 +1.1 +1.7 −1.5 +1.6 −0.5 [14]

−11.01 −14.13 +9.49 −4.85 +2.07 +0.51 −1.21 +1.47 −0.70 [17]

LEED

layer it must adjust its position in order to smooth out the charge density of the surface region. These considerations lead to the ‘rule’ for the relaxations of stepped surfaces [4]. This rule states that each interlayer spacing within this surface slab (defined by the layers having fewer nearest neighbors than the bulk) will contract, while the interlayer spacing between the slab and the bulk will expand. For Cu(5 1 1) surface, therefore, the prediction is a (−,−,+) relaxation sequence, as we have observed. Although the largest relaxations are seen for the top two interlayer spacings, there also exists a considerable relaxation between the last step atom and the first bulk atom (atoms 3 and 4 in figure 3(b)). A comparison of these results to earlier work is given in table 2. As the table shows, the surface relaxations of Cu(5 1 1) obtained from this LEED study agree relatively well with all of the earlier theoretical studies [4, 10–17]. In particular, it exhibits the (−,−,+,−) sequence of relaxations that all of theoretical studies predict (see table 2). The magnitudes of the relaxations, about 10% for the first two interlayer spacings and 8% for the third, are also in general agreement, although we note that the quantitative agreement appears to improve for the later studies. The lateral relaxations found in the theoretical studies, where cited, are generally small, 2% of the Cu–Cu distance in bulk at most, also in agreement with the LEED result. The SXRD study [5] on the other hand, exhibits a different (−,+,−,−) relaxation for the outermost layers. Unfortunately, we can offer no explanation for this discrepancy.

[4]

[16]

this surface [4, 10–17]. The lateral relaxation is minimal, and the damping of the relaxation for deeper layers is non-uniform, a result also observed in the theoretical studies. Acknowledgments

We gratefully acknowledge funding from the Academy of Finland projects #130818 and #263634, and CSC-IT Center for Science. References [1] Pratt S J, Jenkins S J and King D A 2005 Surf. Sci. 585 L159–65 [2] Vattuone L, Savio L and Rocca M 2008 Surf. Sci. Rep. 63 101–68 [3] Jenkins S J and Pratt S J 2007 Surf. Sci. Rep. 62 373–429 [4] Sun Y Y, Xu H, Feng Y P, Huan A C H and Wee A T S 2004 Phys. Rev. Lett. 93 136102 [5] Walko D A and Robinson I K 1999 Phys. Rev. B 59 15446–56 [6] Blome R 1992 LEED-Untersuchungen an der Cu(511) Oberfl¨ache Thesis University of Munich [7] CLEED Manual available from G Held ([email protected]) [8] Pendry J B 1980 J. Phys. C: Solid State 13 937 [9] Barbieri A and Van Hove M A 2012 private communication (www.icts.hkbu.edu.hk/vanhove/VanHove files/leed/ leedpack.html) [10] Loisel B, Gorse D, Pontikis V and Lapujoulade J 1989 Surf. Sci. 221 365–78 [11] Hammonds K D and Lynden-Bell R M 1992 Surf. Sci. 278 437–56 [12] Durukanoglu S, Kara A and Rahman T S 1997 Phys. Rev. B 55 13894–903 [13] Spisak D 2001 Surf. Sci. 489 151–60 [14] Heid R, Bohnen K P, Kara A and Rahman T S 2002 Phys. Rev. B 65 115405 [15] Yamaguchi M, Kaburaki H and Freeman A J 2004 Phys. Rev. B 69 045408 [16] Da Silva J L F, Schroeder K and Bl¨ugel S 2005 Phys. Rev. B 72 033405 [17] Shu Y, Zhang J-M, Wang G-H and Xu K-W 2010 Acta Phys. Sin. 59 4911–18

4. Conclusion

The results of the quantitative LEED analysis presented here clear up the long-standing mystery of the anomalous surface relaxation of Cu(5 1 1). Instead of being anomalous, this study shows that the surface behaves as expected, and obeys the ‘rules’ developed for surface relaxations on stepped surfaces. The relaxation sequence of the top layers (−,−,+,−) agrees well with the theoretical predictions, and is similar in magnitude to most of the earlier theoretical results found for

4

Surface relaxation of Cu(5 1 1).

The multilayer relaxation of the stepped Cu(5 1 1) surface has been studied by quantitative low-energy electron diffraction and analyzed using the CLE...
581KB Sizes 2 Downloads 6 Views