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Multilayer relaxation of Pd{3 2 0} surface by quantitative LEED revisited
Surface Science 566–568 (2004) 24–28 www.elsevier.com/locate/susc
Multilayer relaxation of Pd{3 2 0} surface by quantitative LEED revisited K. Pussi *, M. Hirsim€ aki, M. Valden, M. Lindroos Institute of Physics, Tampere University of Technology, P.O. Box 692, 33101 Tampere, Finland Available online 2 June 2004
Abstract The multilayer relaxation of the stepped Pd{3 2 0} surface has been reanalyzed by quantitative low energy electron diffraction using two different programs, CHANGE and Symmetrized Automated Tensor LEED. Relaxations with are )0.05 ± 0.03, )0.14 ± 0.03, +0.09 ± 0.03, )0.07 ± 0.03, +0.07 ± 0.03 and respect to the bulk value of 0.539 A for the first six interlayer spacings, respectively (negative sign corresponds to contraction). The relax+0.03 ± 0.03 A ation sequence () ) + ) + +) is thus in agreement with the theoretical prediction. The relaxations are damped in a nonuniform manner. The Pendry R-factor for the favored structure is 0.26. 2004 Elsevier B.V. All rights reserved. Keywords: Low energy electron diffraction (LEED); High index single crystal surfaces; Palladium; Surface relaxation and reconstruction
1. Introduction Structural properties of stepped metal surfaces have been the subject of many theoretical and experimental studies because of the significant role they play in many technologically important phenomena such as catalysis and thin film growth [1]. Steps on the surface cause local rearrangement of the surface electronic structure. This modifies the force fields between the selvage atoms and leads to structural relaxations. The force between layers is attractive or repulsive depending on the signs of the net charges for each atomic layer. An
*
Corresponding author. Tel.: +358-3-3115-2681; fax: +3583-3115-2600. E-mail address: [email protected].fi (K. Pussi).
attractive/repulsive force between two layers leads to a contraction/expansion of the interlayer spacing. The magnitude of relaxation is related to the magnitude of the force between atomic layers. Damping of relaxations perpendicular to the surface is a consequence of the damping of the forces of each pair of layers and it is usually considered to be uniform i.e. jdz12 j > jdz23 j > jdz34 j . . . [2]. Multilayer relaxation of stepped fcc metal surfaces particularly the close packed cubic (fcc) surfaces of type f11ð2n þ 1Þg, n ¼ 1; 2; 3; . . . , have been studied extensively by theoretical methods [3– 6]. These studies suggest that the relaxations of atomic layers form a periodic sequence. The length of this period is equal to the number of atoms forming the terrace (n þ 1). The first n interlayer spacings experience contraction and the (n þ 1)st interlayer spacing is expanded (e.g. for fcc{1 1 5}
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.05.017
K. Pussi et al. / Surface Science 566–568 (2004) 24–28
the sequence is () ) + )). For the fcc surfaces of type fðn þ 1Þn0g; n ¼ 1; 2; 3; . . . , a clear prediction for the relaxation sequence or its periodicity is lacking in the theoretical studies [1,7–10]. However, comparison of the theoretical and the quantitative LEED analyses available gives a relatively good picture of what kind of relaxations could be expected for these type of surfaces. For fcc{2 1 0} (n ¼ 1) and fcc{3 2 0} (n ¼ 2) surfaces, both theoretical and some quantitative LEED results are available [1,2,7–13]. In the case of fcc{2 1 0}, most of the studies agree that the relaxation of the first few layers follows the () ) + )) sequence [2,8–12]. In the dynamical LEED analysis of Hirsim€ aki et al. [14] the multilayer relaxation of the Pd{3 2 0} surface has been studied. Relaxations of )0.08 ± 0.05, )0.05 ± 0.05, were found )0.03 ± 0.05, +0.08 ± 0.05 and +0.03 A for the first five interlayer spacings, respectively. These relaxations form a sequence of () ) ) + +). In the quantitative LEED analysis of Tian et al. [13] a relaxation sequence of () ) +) was found for the Cu{3 2 0}. Recent studies of Durukano~ glu and Rahman [1] and Makkonen et al. [7] present results from embedded atom method (EAM) and ab initio calculations. These studies suggests a relaxation sequences of () ) + ) + ) )) and () ) + )+ ) ) +) for the Cu{3 2 0} and Pd{3 2 0} surfaces, respectively. These new results together with the moderate level of agreement (RP ¼ 0:35) in our previous analysis [14] hint that reanalysis of this system is needed. This paper presents a combined CHANGE [15,16] and Symmetrized Automated Tensor LEED (SATLEED) [17] study of the multilayer relaxation of the Pd{3 2 0} surface. The results presented correct the results of our previous analysis with CHANGE [14], which was restricted by the fact that the search was guided by human effort. The use of the automatic search routines of SATLEED made it possible to probe a larger parameter space. It turned out that our previous result was a local minimum. In this paper we also discuss the relaxation sequence and the damping of relaxations on Pd{3 2 0} surface. In the following paragraphs the computational procedures are explained and the results of this analysis are presented. After that, comparisons to the similar
25
theoretical and quantitative LEED analyses will be made.
2. Analysis The LEED calculations were done using the same experimental data set as used in the CHANGE study of Hirsim€aki et al. [14]. (For the experimental details see the reference [14].) The use of SATLEED for the high index surface calculations demands some special procedures in the input file preparation. This method has been explained in the recent paper by Pussi et al. [18]. The structural parameters varied included the first six interlayer spacings normal to the {3 2 0} surface, lateral relaxations of the step atoms and the angle of incidence with respect to the {3 2 0} surface. The nonstructural parameters were kept fixed at the beginning of the analysis apart from the real part of the inner potential which was allowed to vary in order to achieve an optimal agreement between the theory and the experiment. The theory–experiment agreement was tested using the Pendry R-factor [19] and the errorbars quoted are calculated using the Pendry RR-method [19]. The thermal vibrations were modeled using a layer dependent Debye temperature. Phase shifts up to lmax ¼ 10 were used to describe scattering properties of palladium. The phase shifts needed for the SATLEED input were calculated using the Barbieri/Van Hove Phase Shift Package [20]. The calculations were first performed for normal incidence with both programs. Since the SATLEED program is capable of testing a large number of trial structures fast, it was used to speed up the search for the optimum structure. Because SATLEED can only be used for normal incidence, CHANGE was used to refine the structure. After the perpendicular relaxations were optimized, lateral displacements were introduced to the step region. The lateral relaxations did not further improve the agreement. At the end of the analysis the angle of incidence was varied with respect to the {3 2 0} surface. Angles of incidence of 0, ±1 and ±2 were tested. Similarly to the earlier study +1 yielded the best result. The nonstructural
26
K. Pussi et al. / Surface Science 566–568 (2004) 24–28
parameters were optimized to VI ¼ 4 eV, HD ðSurfaceÞ ¼ 280 K and HD ðBulkÞ ¼ 280 K.
Table 1 The interlayer spacings and the Pendry R-factor for Pd{3 2 0} from the two independent analyses [This work] Value (A) [14] Parameter Value (A)
3. Results and discussion The Pd{3 2 0} (3(1 1 0) · (1 0 0)) surface consists of three-atom-row-wide terraces that are separated by single atom height steps. Fig. 1 shows the top and side views of the surface. For the fcc{3 2 0} the step profile involves the top five atom layers. All of the step atoms are under-coordinated with respect to the bulk atoms. The coordination numbers for the first four step atoms are 6, 7, 9 and 11, respectively (see Fig. 1(b) for the atom numbering). The fifth atom is the last step atom (coordination of 11) and the bulk begins with the sixth atom. Since the fifth atom is the last step atom and thus bonded to the first bulk layer it must adjust its position in order to smooth out the charge density of the surface region. Ab initio calculations of the Pd{3 2 0} predict that the largest relaxation is to be seen in the bond between the least under-coordi-
dz12 dz23 dz34 dz45 dz56 dz67
)0.05 ± 0.03 )0.14 ± 0.03 +0.09 ± 0.03 )0.07 ± 0.03 +0.07 ± 0.03 +0.03 ± 0.03
)0.08 ± 0.05 )0.05 ± 0.05 )0.03 ± 0.05 +0.08 ± 0.05 +0.03 ±0.00
Pendry Rfactor [19]
0.26
0.35
The results from this analysis are shown with the bold font.
nated step atom and its nearest neighbor bulk atom [7]. The relaxations perpendicular to the surface found for the first six interlayer spacings are listed in Table 1. Fig. 1(c) shows a detailed side view of the favored surface structure. The figure illustrates that the relaxations tend to smooth out the step profile. The relatively large outward relaxation of the fifth layer agrees with the theoretical prediction
[110]
-0.05 Å -0.14 Å
[001]
+0.09 Å
-0.07 Å +0.07 Å +0.03 Å dzBulk=0.539 Å
Terrace2
Terrace1 (a)
(c)
1 6
(b)
[320]
2 4
3 5
7
8
[110]
[110]
Fig. 1. (a) Top view and (b) side view (along the dotted line) of the Pd{3 2 0} surface. The crystallographic directions are indicated by arrows. The p(1 · 1) unit cell is shown with a dashed line. In the side view the atoms forming the different atomic layers are numbered. (c) Detailed side view of the surface. The interlayer spacings are exaggerated for clarity. The direction of relaxation on each layer is shown with an arrow. The magnitude of relaxation is related to the thickness of the arrow. Numbers on the right show the change in the interlayer spacing with respect to the bulk value (the bottom number shows the value of the bulk interlayer spacing). (For a colour version of the figure see the online paper.)
K. Pussi et al. / Surface Science 566–568 (2004) 24–28
[7] although the biggest relaxation in this study was found for the third layer. This third layer relaxation leads to a large contraction of the second interlayer spacing ()26%) and also to a relatively large expansion of the third interlayer spacing. These displacements of the third and the fifth atom layers lead to noticeable relaxations of the interlayer spacings that are not uniformly damped. In Fig. 2 the theory–experiment agreement is shown. The overall level of agreement is very good. All of the main peaks are produced by the theory and the relative intensities agree very well.
Experiment Theory Theor y
(11)
(11) (12)
Intensity [arbitary units]
(12) (13)
(13) (10)
(21) (03)
(23) (02)
(14) (22)
(03) (01)
(02) 0
100 200 Energy [eV]
300 0
100 200 Energy [eV]
300
Fig. 2. The theory–experiment agreement. The solid line corresponds to the experiment and the dashed line to the theory. The total energy range is 2100 eV.
27
The damping of the relaxations on four different fcc{2 1 0} surfaces (Al, Pt, Cu and Pd) is compared in the study of Ismael et al. [2]. They note that Pt and Cu exhibit uniform damping, but for Al and Pd nonuniform damping is observed. If similar comparison is done with the fcc{3 1 1} surfaces (Ni, Cu, Rh, Al and Pb) [21–25] the damping is uniform for all of the surfaces. In the case of fcc{3 2 0} uniform damping was observed for Cu by quantitative LEED [13]. The EAM study of the same surface expands the analysis to the deeper layers and shows that the relaxations are not in fact uniformly damped, because of a large relaxation of the fifth layer [1]. Our results and the ab initio calculations [7] for the Pd{3 2 0} show nonuniform damping behavior. Table 2 compares the damping effects observed on the stepped fcc surfaces studied using quantitative LEED analysis. These observations suggest that when the interlayer spacing gets smaller the damping of relaxations depends both on the crystallographic face and on the chemical identity of the surface. Comparison of the results from this analysis and from the earlier study [14] is done in the Table 1. Because our earlier analysis was trapped in a local minimum the new and old results do not meet inside the errorbars of either analysis. The most noticeable difference between the two structures can be seen in the relaxations of the third and the fourth interlayer spacings. In the analysis of Hirsim€aki et al. [14] a contraction of the third interlayer spacing is followed by an expansion of the fourth interlayer spacing. Contrary to that in this analysis, the third interlayer spacing is expanded and the fourth contracted.
Table 2 Damping of the relaxations of the interlayer spacings compared in the light of quantitative LEED analyses Surface Chemical element dzBulk (A) Damping Reference fcc{3 1 1} fcc{2 1 0} fcc{3 2 0}
Ni, Cu, Rh, Al and Pb Pt and Cu Al and Pd Cu Pd
1.063–1.485 0.641–0.906 0.501–0.539
Uniform Uniform Nonuniform Uniform Nonuniform
[21–25] [2,10] [11,12] [13]a [This work]
In the EAM analysis [1] nonuniform behavior was found because of the large relaxation of the fifth interlayer spacing. a The quantitative LEED analysis of Tian et al. [13] studied only the top three interlayer spacings.
28
K. Pussi et al. / Surface Science 566–568 (2004) 24–28
4. Conclusions In this paper the results from the quantitative LEED analysis of Pd{3 2 0} have been presented. The relaxation sequence of () ) + ) + +) agrees well with the theoretical prediction for Pd{3 2 0} [7] and is similar to the results found for the Cu{3 2 0} [1,13]. The damping of the relaxations is found to be nonuniform. The level of agreement is improved from the earlier study (RP ¼ 0:35) [14] leading to Pendry R-factor of 0.26 for the favored structure.
Acknowledgement K. Pussi would like to thank the National Graduate School in Material Physics (NGSMP) for financial support.
References [1] S. Durukano~ glu, T.S. Rahman, Phys. Rev. B 67 (2003) 205406. [2] Ismael, S. Chandravakar, D.M. Zehner, Surf. Sci. 504 (2002) L201. [3] B. Loisel, D. Gorse, V. Pontikis, J. Lapujoulade, Surf. Sci. 221 (1989) 365. [4] A. Gravil, S. Holloway, Phys. Rev. B 53 (1996) 11128. [5] S. Durukano~ glu, A. Kara, T.S. Rahman, Phys. Rev. B 55 (1987) 13894.
[6] C. Weis, S.P. Lewsi, E.J. Miele, A.M. Rappe, Phys. Rev. B 57 (1998) 10062. [7] T. Makkonen, P. Salo, M. Alatalo, Phys. Rev. B 67 (2003) 165415. [8] R.N. Barnett, U. Landman, C.L. Cleveland, Phys. Rev. Lett. 51 (1983) 1359. [9] P. Jiang, P.M. Marcus, F. Jona, Solid State Commun. 59 (1986) 275. [10] X.-G. Zhang et al., Phys. Rev. Lett. 67 (10) (1991) 1298. [11] D.L. Adams, V. Jensen, X.F. Sun, J.H. Vollesen, Phys. Rev. B 38 (12) (1988) 7913. [12] D. Kolthoff, H. Pfn€ ur, A.G. Fedorus, V. Koval, A.G. Naumovets, Surf. Sci. 439 (1999) 224. [13] Y. Tian, J. Quinn, K.-W. Lin, F. Jona, Phys. Rew. B 61 (7) (2000) 4904. [14] M. Hirsim€aki, T. Pitk€anen, M. Valden, M. Lindroos, C.J. Barnes, Surf. Sci. 454–456 (2000) 6. [15] D.W. Jepsen, Phys. Rev. B 22 (1980) 814. [16] D.W. Jepsen, Phys. Rev. B 22 (1980) 5701. [17] M.A. Van Hove, W. Moritz, H. Over, P.J. Rous, A. Wander, A. Barbieri, N. Materer, U. Starke, G.A. Somorjai, Surf. Sci. Rep. 19 (1993) 191. [18] K. Pussi, M. Caragiu, M. Lindroos, R.D. Diehl, Surf. Sci. 544 (2003) 35. [19] J.B. Pendry, J. Phys. C 13 (1980) 937. [20] A. Barbieri, M.A. Van Hove, private communication. [21] D.L. Adams, W.T. Moore, K.A.R. Mitchell, Surf. Sci. 149 (2–3) (1985) 407. [22] R.W. Streater, W.T. Moore, P.R. Watson, D.C. Frost, K.A.R. Mitchell, Surf. Sci. 72 (1978) 744. [23] S. Liepold, N. Elbel, M. Michl, W. Nichtl-Pecher, K. Heinz, K. M€ uller, Surf. Sci. 240 (1–3) (1990) 81. [24] J.R. Noonan, H.L. Davis, W. Erley, Surf. Sci. 152–153 (1985) 142. [25] Y.S. Li, F. Jona, P.M. Marcus, Phys. Rev. B 44 (15) (1991) 8267.
Multilayer relaxation of Pd{3 2 0} surface by quantitative LEED revisited K. Pussi *, M. Hirsim€ aki, M. Valden, M. Lindroos Institute of Physics, Tampere University of Technology, P.O. Box 692, 33101 Tampere, Finland Available online 2 June 2004
Abstract The multilayer relaxation of the stepped Pd{3 2 0} surface has been reanalyzed by quantitative low energy electron diffraction using two different programs, CHANGE and Symmetrized Automated Tensor LEED. Relaxations with are )0.05 ± 0.03, )0.14 ± 0.03, +0.09 ± 0.03, )0.07 ± 0.03, +0.07 ± 0.03 and respect to the bulk value of 0.539 A for the first six interlayer spacings, respectively (negative sign corresponds to contraction). The relax+0.03 ± 0.03 A ation sequence () ) + ) + +) is thus in agreement with the theoretical prediction. The relaxations are damped in a nonuniform manner. The Pendry R-factor for the favored structure is 0.26. 2004 Elsevier B.V. All rights reserved. Keywords: Low energy electron diffraction (LEED); High index single crystal surfaces; Palladium; Surface relaxation and reconstruction
1. Introduction Structural properties of stepped metal surfaces have been the subject of many theoretical and experimental studies because of the significant role they play in many technologically important phenomena such as catalysis and thin film growth [1]. Steps on the surface cause local rearrangement of the surface electronic structure. This modifies the force fields between the selvage atoms and leads to structural relaxations. The force between layers is attractive or repulsive depending on the signs of the net charges for each atomic layer. An
*
Corresponding author. Tel.: +358-3-3115-2681; fax: +3583-3115-2600. E-mail address: [email protected].fi (K. Pussi).
attractive/repulsive force between two layers leads to a contraction/expansion of the interlayer spacing. The magnitude of relaxation is related to the magnitude of the force between atomic layers. Damping of relaxations perpendicular to the surface is a consequence of the damping of the forces of each pair of layers and it is usually considered to be uniform i.e. jdz12 j > jdz23 j > jdz34 j . . . [2]. Multilayer relaxation of stepped fcc metal surfaces particularly the close packed cubic (fcc) surfaces of type f11ð2n þ 1Þg, n ¼ 1; 2; 3; . . . , have been studied extensively by theoretical methods [3– 6]. These studies suggest that the relaxations of atomic layers form a periodic sequence. The length of this period is equal to the number of atoms forming the terrace (n þ 1). The first n interlayer spacings experience contraction and the (n þ 1)st interlayer spacing is expanded (e.g. for fcc{1 1 5}
0039-6028/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2004.05.017
K. Pussi et al. / Surface Science 566–568 (2004) 24–28
the sequence is () ) + )). For the fcc surfaces of type fðn þ 1Þn0g; n ¼ 1; 2; 3; . . . , a clear prediction for the relaxation sequence or its periodicity is lacking in the theoretical studies [1,7–10]. However, comparison of the theoretical and the quantitative LEED analyses available gives a relatively good picture of what kind of relaxations could be expected for these type of surfaces. For fcc{2 1 0} (n ¼ 1) and fcc{3 2 0} (n ¼ 2) surfaces, both theoretical and some quantitative LEED results are available [1,2,7–13]. In the case of fcc{2 1 0}, most of the studies agree that the relaxation of the first few layers follows the () ) + )) sequence [2,8–12]. In the dynamical LEED analysis of Hirsim€ aki et al. [14] the multilayer relaxation of the Pd{3 2 0} surface has been studied. Relaxations of )0.08 ± 0.05, )0.05 ± 0.05, were found )0.03 ± 0.05, +0.08 ± 0.05 and +0.03 A for the first five interlayer spacings, respectively. These relaxations form a sequence of () ) ) + +). In the quantitative LEED analysis of Tian et al. [13] a relaxation sequence of () ) +) was found for the Cu{3 2 0}. Recent studies of Durukano~ glu and Rahman [1] and Makkonen et al. [7] present results from embedded atom method (EAM) and ab initio calculations. These studies suggests a relaxation sequences of () ) + ) + ) )) and () ) + )+ ) ) +) for the Cu{3 2 0} and Pd{3 2 0} surfaces, respectively. These new results together with the moderate level of agreement (RP ¼ 0:35) in our previous analysis [14] hint that reanalysis of this system is needed. This paper presents a combined CHANGE [15,16] and Symmetrized Automated Tensor LEED (SATLEED) [17] study of the multilayer relaxation of the Pd{3 2 0} surface. The results presented correct the results of our previous analysis with CHANGE [14], which was restricted by the fact that the search was guided by human effort. The use of the automatic search routines of SATLEED made it possible to probe a larger parameter space. It turned out that our previous result was a local minimum. In this paper we also discuss the relaxation sequence and the damping of relaxations on Pd{3 2 0} surface. In the following paragraphs the computational procedures are explained and the results of this analysis are presented. After that, comparisons to the similar
25
theoretical and quantitative LEED analyses will be made.
2. Analysis The LEED calculations were done using the same experimental data set as used in the CHANGE study of Hirsim€aki et al. [14]. (For the experimental details see the reference [14].) The use of SATLEED for the high index surface calculations demands some special procedures in the input file preparation. This method has been explained in the recent paper by Pussi et al. [18]. The structural parameters varied included the first six interlayer spacings normal to the {3 2 0} surface, lateral relaxations of the step atoms and the angle of incidence with respect to the {3 2 0} surface. The nonstructural parameters were kept fixed at the beginning of the analysis apart from the real part of the inner potential which was allowed to vary in order to achieve an optimal agreement between the theory and the experiment. The theory–experiment agreement was tested using the Pendry R-factor [19] and the errorbars quoted are calculated using the Pendry RR-method [19]. The thermal vibrations were modeled using a layer dependent Debye temperature. Phase shifts up to lmax ¼ 10 were used to describe scattering properties of palladium. The phase shifts needed for the SATLEED input were calculated using the Barbieri/Van Hove Phase Shift Package [20]. The calculations were first performed for normal incidence with both programs. Since the SATLEED program is capable of testing a large number of trial structures fast, it was used to speed up the search for the optimum structure. Because SATLEED can only be used for normal incidence, CHANGE was used to refine the structure. After the perpendicular relaxations were optimized, lateral displacements were introduced to the step region. The lateral relaxations did not further improve the agreement. At the end of the analysis the angle of incidence was varied with respect to the {3 2 0} surface. Angles of incidence of 0, ±1 and ±2 were tested. Similarly to the earlier study +1 yielded the best result. The nonstructural
26
K. Pussi et al. / Surface Science 566–568 (2004) 24–28
parameters were optimized to VI ¼ 4 eV, HD ðSurfaceÞ ¼ 280 K and HD ðBulkÞ ¼ 280 K.
Table 1 The interlayer spacings and the Pendry R-factor for Pd{3 2 0} from the two independent analyses [This work] Value (A) [14] Parameter Value (A)
3. Results and discussion The Pd{3 2 0} (3(1 1 0) · (1 0 0)) surface consists of three-atom-row-wide terraces that are separated by single atom height steps. Fig. 1 shows the top and side views of the surface. For the fcc{3 2 0} the step profile involves the top five atom layers. All of the step atoms are under-coordinated with respect to the bulk atoms. The coordination numbers for the first four step atoms are 6, 7, 9 and 11, respectively (see Fig. 1(b) for the atom numbering). The fifth atom is the last step atom (coordination of 11) and the bulk begins with the sixth atom. Since the fifth atom is the last step atom and thus bonded to the first bulk layer it must adjust its position in order to smooth out the charge density of the surface region. Ab initio calculations of the Pd{3 2 0} predict that the largest relaxation is to be seen in the bond between the least under-coordi-
dz12 dz23 dz34 dz45 dz56 dz67
)0.05 ± 0.03 )0.14 ± 0.03 +0.09 ± 0.03 )0.07 ± 0.03 +0.07 ± 0.03 +0.03 ± 0.03
)0.08 ± 0.05 )0.05 ± 0.05 )0.03 ± 0.05 +0.08 ± 0.05 +0.03 ±0.00
Pendry Rfactor [19]
0.26
0.35
The results from this analysis are shown with the bold font.
nated step atom and its nearest neighbor bulk atom [7]. The relaxations perpendicular to the surface found for the first six interlayer spacings are listed in Table 1. Fig. 1(c) shows a detailed side view of the favored surface structure. The figure illustrates that the relaxations tend to smooth out the step profile. The relatively large outward relaxation of the fifth layer agrees with the theoretical prediction
[110]
-0.05 Å -0.14 Å
[001]
+0.09 Å
-0.07 Å +0.07 Å +0.03 Å dzBulk=0.539 Å
Terrace2
Terrace1 (a)
(c)
1 6
(b)
[320]
2 4
3 5
7
8
[110]
[110]
Fig. 1. (a) Top view and (b) side view (along the dotted line) of the Pd{3 2 0} surface. The crystallographic directions are indicated by arrows. The p(1 · 1) unit cell is shown with a dashed line. In the side view the atoms forming the different atomic layers are numbered. (c) Detailed side view of the surface. The interlayer spacings are exaggerated for clarity. The direction of relaxation on each layer is shown with an arrow. The magnitude of relaxation is related to the thickness of the arrow. Numbers on the right show the change in the interlayer spacing with respect to the bulk value (the bottom number shows the value of the bulk interlayer spacing). (For a colour version of the figure see the online paper.)
K. Pussi et al. / Surface Science 566–568 (2004) 24–28
[7] although the biggest relaxation in this study was found for the third layer. This third layer relaxation leads to a large contraction of the second interlayer spacing ()26%) and also to a relatively large expansion of the third interlayer spacing. These displacements of the third and the fifth atom layers lead to noticeable relaxations of the interlayer spacings that are not uniformly damped. In Fig. 2 the theory–experiment agreement is shown. The overall level of agreement is very good. All of the main peaks are produced by the theory and the relative intensities agree very well.
Experiment Theory Theor y
(11)
(11) (12)
Intensity [arbitary units]
(12) (13)
(13) (10)
(21) (03)
(23) (02)
(14) (22)
(03) (01)
(02) 0
100 200 Energy [eV]
300 0
100 200 Energy [eV]
300
Fig. 2. The theory–experiment agreement. The solid line corresponds to the experiment and the dashed line to the theory. The total energy range is 2100 eV.
27
The damping of the relaxations on four different fcc{2 1 0} surfaces (Al, Pt, Cu and Pd) is compared in the study of Ismael et al. [2]. They note that Pt and Cu exhibit uniform damping, but for Al and Pd nonuniform damping is observed. If similar comparison is done with the fcc{3 1 1} surfaces (Ni, Cu, Rh, Al and Pb) [21–25] the damping is uniform for all of the surfaces. In the case of fcc{3 2 0} uniform damping was observed for Cu by quantitative LEED [13]. The EAM study of the same surface expands the analysis to the deeper layers and shows that the relaxations are not in fact uniformly damped, because of a large relaxation of the fifth layer [1]. Our results and the ab initio calculations [7] for the Pd{3 2 0} show nonuniform damping behavior. Table 2 compares the damping effects observed on the stepped fcc surfaces studied using quantitative LEED analysis. These observations suggest that when the interlayer spacing gets smaller the damping of relaxations depends both on the crystallographic face and on the chemical identity of the surface. Comparison of the results from this analysis and from the earlier study [14] is done in the Table 1. Because our earlier analysis was trapped in a local minimum the new and old results do not meet inside the errorbars of either analysis. The most noticeable difference between the two structures can be seen in the relaxations of the third and the fourth interlayer spacings. In the analysis of Hirsim€aki et al. [14] a contraction of the third interlayer spacing is followed by an expansion of the fourth interlayer spacing. Contrary to that in this analysis, the third interlayer spacing is expanded and the fourth contracted.
Table 2 Damping of the relaxations of the interlayer spacings compared in the light of quantitative LEED analyses Surface Chemical element dzBulk (A) Damping Reference fcc{3 1 1} fcc{2 1 0} fcc{3 2 0}
Ni, Cu, Rh, Al and Pb Pt and Cu Al and Pd Cu Pd
1.063–1.485 0.641–0.906 0.501–0.539
Uniform Uniform Nonuniform Uniform Nonuniform
[21–25] [2,10] [11,12] [13]a [This work]
In the EAM analysis [1] nonuniform behavior was found because of the large relaxation of the fifth interlayer spacing. a The quantitative LEED analysis of Tian et al. [13] studied only the top three interlayer spacings.
28
K. Pussi et al. / Surface Science 566–568 (2004) 24–28
4. Conclusions In this paper the results from the quantitative LEED analysis of Pd{3 2 0} have been presented. The relaxation sequence of () ) + ) + +) agrees well with the theoretical prediction for Pd{3 2 0} [7] and is similar to the results found for the Cu{3 2 0} [1,13]. The damping of the relaxations is found to be nonuniform. The level of agreement is improved from the earlier study (RP ¼ 0:35) [14] leading to Pendry R-factor of 0.26 for the favored structure.
Acknowledgement K. Pussi would like to thank the National Graduate School in Material Physics (NGSMP) for financial support.
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