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Nucleation of CuGa Phases on the MgO(100) Surface Gerald Geudtner and Karl Jug* Hannover, Theoretische Chemie der Universität Hannover Received October 1st, 2002. Abstract. MSINDO calculations are presented for the coadsorption of Cu and Ga atoms as clusters and islands on the MgO(100) sur- face. The surface is simulated by a (8 8 3) Mg 96 O 96 cyclic cluster. The relative number of Cu and Ga atoms was varied in order to understand the influence of copper rich and gallium rich phases. It was found that the copper atoms have a dominating in- Keimbildung von CuGa-Phasen auf der MgO(100)-Oberfläche Inhaltsübersicht. Es werden MSINDO-Rechnungen für die Coad- sorption von Cu- und Ga-Atomen als Cluster und Inseln auf der MgO(100)-Oberfläche präsentiert. Die Oberfläche wird durch ei- nen zyclischen 8 8 3-Mg 96 O 96 -Cluster simuliert. Die relative Anzahl von Cu- und Ga-Atomen wurde variiert, um die Bildung von Kupfer- bzw. Gallium-reichen Phasen zu verstehen. Dabei 1 Introduction The deposition of copper on an MgO(100) surface is an ideal model system for studying the interface between met- als and the surface of an ionic crystal and the growth mechanism. Therefore many experimental [19] and theor- etical [1014] studies were performed on this system. In previous work [15] we studied the growth of pure copper clusters and layers on the MgO (100) surface. Our present aim was the investigation of the effect of other metal atoms on the copper clusters and therefore on the reactivity of such clusters. As the other metal atom gallium was chosen because such intermetallic compounds can be conveniently synthesized via chemical transport [16]. It was known from experiment that a few percent gallium inside the copper bulk, where copper atoms are substituted at their lattice po- sitions, does not change the copper lattice [17]. As a com- plementary study we also investigated adsorbed pure gal- lium clusters and gallium clusters with one gallium atom substituted by a copper atom. 2 Method The calculations were performed with the semiempirical SCF-MO method MSINDO [1821]. It had been demon- * Prof. Dr. K. Jug Theoretische Chemie der Universität Am Kleinen Felde 30 D-30167 Hannover E-mail: [email protected] Z. Anorg. Allg. Chem. 2003, 629, 17311736 DOI: 10.1002/zaac.200300121 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 1731 fluence on the structural arrangement in mixed phases. The adsorp- tion sites of Cu and Ga atoms are preferably O atoms, but in mixed phases these sites are usually occupied by Cu atoms. Keywords: MSINDO Calculations, MgO(100) surface, CuGa, Ad- sorption wurde gefunden, dass den Kupferatomen ein dominierender Ein- fluß auf die strukturelle Anordnung in gemischten Phasen zu- kommt. Die Adsorption von Cu und Ga erfolgt auf bevorzugte Plätze, nämlich an O-Atome der Oberfläche, wohingegen in ge- mischten Phasen diese Lagen üblicherweise durch Cu-Atome be- setzt werden. strated that this method is capable of providing reliable re- sults of small metal clusters on a surface of an ionic crystal [15]. For the bulk and surface simulation the cyclic cluster model (CCM) [22] was used which allows to generate per- iodic boundary conditions for a finite cluster. With the CCM we were able to avoid border effects which would arise in a free cluster. Another advantage of this model is that adsorbed atoms are not periodically repeated so that no ‘self interaction’ of an adsorbed atom occurs as is usu- ally the case in the standard periodic methods which are based on units cells. The surface was modelled by an Mg 96 O 96 of (8 8 3) shape. The MgO distance of this cluster was optimized. The resulting value of 2.112 A ˚ is in good agreement with the experimental value of 2.105 A ˚ [23]. For the adsorbed metal clusters different starting geo- metries were assumed and fully optimized in cartesian coor- dinates. In this procedure the MgO distance was kept fixed. Examination of the eigenvalues of the Hessian proved that the optimized structures represent equilibrium structures. 3 Structures and Adsorption Energies 3.1 Cu n Ga clusters The structure of the adsorbed CuGa cluster of the surface is shown in Figure 1a. Both atoms are located above O atoms of the surface. The adsorption energy E ads for Cu n- Ga m clusters is defined as E ads E tot (Mg 96 O 96 Cu n Ga m ) E tot (Mg 96 O 96 ) n E tot (Cu) mE tot (Ga).

Nucleation of CuGa Phases on the MgO(100) Surface

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Page 1: Nucleation of CuGa Phases on the MgO(100) Surface

Nucleation of CuGa Phases on the MgO(100) Surface

Gerald Geudtner and Karl Jug*

Hannover, Theoretische Chemie der Universität Hannover

Received October 1st, 2002.

Abstract. MSINDO calculations are presented for the coadsorptionof Cu and Ga atoms as clusters and islands on the MgO(100) sur-face. The surface is simulated by a (8 � 8 � 3) Mg96O96 cycliccluster. The relative number of Cu and Ga atoms was varied inorder to understand the influence of copper rich and gallium richphases. It was found that the copper atoms have a dominating in-

Keimbildung von CuGa-Phasen auf der MgO(100)-Oberfläche

Inhaltsübersicht. Es werden MSINDO-Rechnungen für die Coad-sorption von Cu- und Ga-Atomen als Cluster und Inseln auf derMgO(100)-Oberfläche präsentiert. Die Oberfläche wird durch ei-nen zyclischen 8 � 8 � 3-Mg96O96-Cluster simuliert. Die relativeAnzahl von Cu- und Ga-Atomen wurde variiert, um die Bildungvon Kupfer- bzw. Gallium-reichen Phasen zu verstehen. Dabei

1 Introduction

The deposition of copper on an MgO(100) surface is anideal model system for studying the interface between met-als and the surface of an ionic crystal and the growthmechanism. Therefore many experimental [1�9] and theor-etical [10�14] studies were performed on this system. Inprevious work [15] we studied the growth of pure copperclusters and layers on the MgO (100) surface. Our presentaim was the investigation of the effect of other metal atomson the copper clusters and therefore on the reactivity ofsuch clusters. As the other metal atom gallium was chosenbecause such intermetallic compounds can be convenientlysynthesized via chemical transport [16]. It was known fromexperiment that a few percent gallium inside the copperbulk, where copper atoms are substituted at their lattice po-sitions, does not change the copper lattice [17]. As a com-plementary study we also investigated adsorbed pure gal-lium clusters and gallium clusters with one gallium atomsubstituted by a copper atom.

2 Method

The calculations were performed with the semiempiricalSCF-MO method MSINDO [18�21]. It had been demon-

* Prof. Dr. K. JugTheoretische Chemie der UniversitätAm Kleinen Felde 30D-30167 HannoverE-mail: [email protected]

Z. Anorg. Allg. Chem. 2003, 629, 1731�1736 DOI: 10.1002/zaac.200300121 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 1731

fluence on the structural arrangement in mixed phases. The adsorp-tion sites of Cu and Ga atoms are preferably O atoms, but in mixedphases these sites are usually occupied by Cu atoms.

Keywords: MSINDO Calculations, MgO(100) surface, CuGa, Ad-sorption

wurde gefunden, dass den Kupferatomen ein dominierender Ein-fluß auf die strukturelle Anordnung in gemischten Phasen zu-kommt. Die Adsorption von Cu und Ga erfolgt auf bevorzugtePlätze, nämlich an O-Atome der Oberfläche, wohingegen in ge-mischten Phasen diese Lagen üblicherweise durch Cu-Atome be-setzt werden.

strated that this method is capable of providing reliable re-sults of small metal clusters on a surface of an ionic crystal[15]. For the bulk and surface simulation the cyclic clustermodel (CCM) [22] was used which allows to generate per-iodic boundary conditions for a finite cluster. With theCCM we were able to avoid border effects which wouldarise in a free cluster. Another advantage of this model isthat adsorbed atoms are not periodically repeated so thatno ‘self interaction’ of an adsorbed atom occurs as is usu-ally the case in the standard periodic methods which arebased on units cells. The surface was modelled by anMg96O96 of (8 � 8 � 3) shape. The MgO distance of thiscluster was optimized. The resulting value of 2.112 A is ingood agreement with the experimental value of 2.105 A[23]. For the adsorbed metal clusters different starting geo-metries were assumed and fully optimized in cartesian coor-dinates. In this procedure the MgO distance was kept fixed.Examination of the eigenvalues of the Hessian proved thatthe optimized structures represent equilibrium structures.

3 Structures and Adsorption Energies

3.1 CunGa clusters

The structure of the adsorbed CuGa cluster of the surfaceis shown in Figure 1a. Both atoms are located above Oatoms of the surface. The adsorption energy Eads for Cun-

Gam clusters is defined as

Eads � Etot(Mg96O96�CunGam) � Etot(Mg96O96)

� n Etot(Cu) � m Etot(Ga).

Page 2: Nucleation of CuGa Phases on the MgO(100) Surface

G. Geudtner, K. Jug

Figure 1 Stucture of adsorbed copper�gallium clusters CuGa (a), Cu2Ga (b), Cu3Ga (c), Cu4Ga (d), Cu5Ga (e); MgO support as cycliccluster Mg96O96

This means that the reference is the cyclic Mg96O96 clus-ter and the free atoms of the adsorbed cluster. The calcu-lated value for the adsorption energy is �92.2 kcal/mol.

The structure of the Cu2Ga cluster, shown in Figure 1b,is similar to the structure of the adsorbed Cu3 cluster [15].Two atoms are located above an O atom of the surface andthe third atom has a position above an Mg atom. In thisstructure there are two possible sites for the Ga atom, oneon top of an O atom and one on top of an Mg atom. Thefirst position has an adsorption energy of �116 kcal/mol,the second is less stable by 1.2 kcal/mol.

The same situation occurs for the Cu3Ga cluster whosestructure is shown in Fig. 1c. Again, the structure is similarto that of an adsorbed Cu4 cluster [15]. In this structurethere are also two different possibilities for the position ofthe Ga atom. The structure with the Ga positioned on topof an O atom of the surface has an adsorption energy of�257.2 kcal/mol. The other site with the Ga atom on topof an Mg atom is 4.8 kcal/mol less stable.

As can be seen from Fig. 1d the structure of the adsorbedCu4Ga cluster is a square pyramid. This is different fromthe adsorbed Cu5 cluster which has a planar structure [15].In the present structure with an adsorption energy of�300.8 kcal/mol the position of the Ga atom is above an

2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim zaac.wiley-vch.de Z. Anorg. Allg. Chem. 2003, 629, 1731�17361732

Mg atom of the surface. The most stable structure, wherethe position of the Ga atom is above an O atom, is also asquare pyramid, but it is 59 kcal/mol less stable than forthe Mg site.

Figure 1e shows the structure of the adsorbed Cu5Gacluster which is again similar to that of the absorbed Cu6

cluster. This structure can be described by adding a Cuatom to the adsorbed Cu4Ga cluster above an Mg atom ofthe surface. Again we found a stable structure with the Gaatom positioned above an O atom. This site is 57 kcal/molless stable than for the corresponding Mg site which has anadsorption energy of �451.2 kcal/mol.

3.2 Cu35Ga and Cu34Ga2 islands

We also investigated the influence of a Ga atom on thestructure of an Cu36 island on an MgO surface. For thispurpose we substituted a Cu atom in the middle of the Cu36

island by a Ga atom. In the first case we substituted oneCu atom at a position above an Mg atom and then in thesecond case one Cu atom at a position above an O atom.The structure with the Ga atom on top of an Mg atom wasmore stable by �7 kcal/mol and is shown in Figure 2a. Wealso substituted one Cu atom at the border of the Cu36

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Nucleation of CuGa Phases on the MgO(100) Surface

Figure 2 Stucture of adsorbed copper�gallium islands Cu35Ga (a), Cu34Ga2 (b); Ga atom in black, MgO support as cyclic cluster Mg96O96

Table 1 Relative energy Erel (in kcal/mol) for Cu34Ga2 islands ona cyclic Mg96O96 cluster (see text for notation)

Mg0�Mg1 O0�O1 Mg0�O1 Mg0�Mg2 O0�O2 Mg0�O2

Erel 18.5 29.2 33.5 0.0 28.9 26.4

island, but theses structures are by over 10 kcal/mol lessstable than the structures with the substitution in themiddle of the island.

In a further step we substituted an additional Cu atomof the island by a Ga atom. Here the positions and thedistance between the two Ga atoms were varied. The rela-tive energies for different combinations are summarized inTable 1. The abreviation Mg0�O1 means that one Ga atomis located above an Mg atom and the second Ga atom at aposition above an O atom which is a nearest neighbor tothis Mg atom. Mg0�Mg2 means that one Ga atom is at aposition above an Mg atom and the second Ga atom at aposition of an Mg atom which is a second nearest neighborto the first Mg atom. The most stable Mg0�Mg2 structureis shown in Fig. 2b.

3.3 Gan cluster

The structure of the adsorbed Ga2 cluster is shown in Fig.3a. It is the same as for the Cu2 cluster. The adsorptionenergy per atom Eads is definied as

Eads �1

n(Etot(Mg96O96�Gan) � Etot(Mg96O96) � n Etot(Ga))

The calculated value is �40.7 kcal/mol.

Z. Anorg. Allg. Chem. 2003, 629, 1731�1736 zaac.wiley-vch.de 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 1733

For the adsorbed Ga3 cluster all three atoms have posi-tions on top of O atoms of the surface. This structure isshown in Fig. 3b. It has an adsorption energy of �48.7kcal/mol. Such an arrangement was not found in the casesof the Cu3 or Cu2Ga cluster. In those cases one atom hada position on top of an Mg atom.

Also in the case of an adsorbed Ga4 cluster all Ga atomshave positions on top of an O atoms of the surface. Thecorresponding structure is shown in Fig. 3c. This squareform has an adsorption energy of �53.8 kcal/mol.

The trend that all Ga atoms prefer a position above Oatoms of the surface was also found for the adsorbed Ga5

cluster which is shown in Fig. 3d. This structure has anadsorption energy of �55.8 kcal/mol. A square pyramidstructure was not stable.

For the adsorbed Ga6 cluster there is not only one struc-ture which is most stable, but two. The adsorption energyof �55.3 kcal/mol is the same for both structures. One isshown in Fig. 3e and the other one in Fig. 3f. Both struc-tures can be generated by adding one Ga atom to the Ga5

cluster.

3.4 GanCu cluster

The structure of the adsorbed Ga2Cu cluster cluster whichis shown in Fig. 4a is comparable to that of the Cu2Gacluster. Two atoms with a position above an O atom of thesurface and third atom with a position more or less abovean Mg atom. There are two possibilities now for the posi-tion of the Cu atom. The most stable one is the positionabove the Mg atom with an Eads value of �168.3 kcal/mol.The other position for the Cu atom over the O atom is lessstable by about 8 kcal/mol.

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G. Geudtner, K. Jug

Figure 3 Stucture of adsorbed gallium clusters Ga2 (a), Ga3 (b), Ga4 (c), Ga5 (d), Ga6 (e), Ga6 (f); MgO support as cyclic cluster Mg96O96

Fig. 4b shows the structure for the absorbed Ga3Cu clus-ter. All four atoms have positions above O atoms of thesurface. Of these the Cu atom has the greatest displacementfrom the position exactly on top of an O atom. This struc-ture with an adsorption energy of �239.8 kcal/mol can begenerated by substituting one Ga atom of the Ga4 structureby a Cu atom or by simply adding one Cu atom to theadsorbed Ga3 cluster. Other structures are less stable by atleast 24 kcal/mol.

The most stable structure, which was found for an ad-sorbed Ga4Cu cluster (Fig. 4c) can be generated by addingone Ga atom to the adsorbed Ga3Cu cluster at a positionabove an Mg atom which is adjacent to both the Cu atomand a Ga atom. This structure has an adsorption energy of�304.4 kcal/mol. Adding the Ga atom adjacent to two Gaatoms leads to a structure which is less stable by 9 kcal/mol. A structure similar to the adsorbed Ga5 cluster, butwhere one Ga atom is substituted by a Cu atom, is 6 kcal/mol less stable than the most stable structure. A pyramidalstructure with the Cu atom on top is less stable by 9 kcal/mol. One with a Ga atom on top and the Cu atom insidethe square basis of the pyramid was not stable.

The most stable structure on an adsorbed Ga5Cu cluster(Fig. 4d) is derived from the Ga6 form (Fig. 3e) where oneof the corner Cu atoms is substituted by a Ga atom. This

2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim zaac.wiley-vch.de Z. Anorg. Allg. Chem. 2003, 629, 1731�17361734

structure has an adsorption energy of �361.9 kcal/mol. Asecond structure which is only 1 kcal/mol less stable isshown in Fig. 4e. This structure can be described as asquare pyramid with a Cu atom on top to which one Gaatom is added. A similar structure which has one Ga atomon top was not found. Another structure which looks simi-lar to that of Fig. 4d but with the Cu atom not as a corneratom of this structure is less stable by 2 kcal/mol.

4 Discussion

The effect of a Ga atom on the structure of an adsorbedCun�1Ga cluster is small compared with that of an ad-sorbed Cun cluster. A difference in structure is found onlyfor the Cu4Ga cluster. Whereas the Cu5 cluster has a planarstructure, the Cu4Ga shows a pyramidal structure. Onequestion is where the preferred position of the Ga atom isin an adsorbed CunGa cluster. In the case of the CuGacluster, the Cu2Ga cluster and the Cu3Ga cluster the Gaatom is at a position above an O atom of the surface. Toexplain this, one has to look at the bond strength ofCu�Cu, Cu�Ga, Cu�O and Ga�O. We calculated thebinding energy for the Cu2 molecule to �50.3 kcal/mol andfor the CuGa molecule to �56.2 kcal/mol. The adsorptionenergy for a single Cu atom above an O atom of the surface

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Nucleation of CuGa Phases on the MgO(100) Surface

Figure 4 Stucture of adsorbed gallium�copper clusters Ga2Cu (a), Ga3Cu (b), Ga4Cu (c), Ga5Cu (d), Ga5Cu (e); MgO support as cycliccluster Mg96O96

was �27.6 kcal/mol. The corresponding value for a singleGa atom was �23.1 kcal/mol. This means that the systemshould be most stable by maximizing the number of Cu�Oand Cu�Ga interactions and minimizing the number ofGa�O and Cu�Cu interactions. Therefore the structuralprinciple can be derived that the most favorable arrange-ment is one where a Ga atom at a position above an Mgatom of the surface has as many Cu atoms as possible asneighbors. The structure of the adsorbed Cu4Ga cluster fol-lows the rule of the maximization of the Cu�Ga interac-tions. However, the structure of the absorbed Cu2Ga clusterdoes not follow this rule. There must be other factors whichinfluence the structure. One is the bond length. The calcu-lated Cu�Cu distance in the Cu2 molecule is 2.18 A andthe calculated Cu�Ga length for the CuGa molecule is 2.41A. The smallest distance between two O atoms of the MgOsurface is about 3 A. Cu atoms at positions above O atomsof the surface would extremely lengthen the Cu�Cu bond.The resulting loss in binding energy cannot be compensatedby the energy gain from the Cu�O binding. In the case ofone Cu atom and one Ga atom above two neighboring Oatoms of the surface the lengthening of the Cu�Ga bondis less, which results in a smaller loss in the Cu�Ga binding

Z. Anorg. Allg. Chem. 2003, 629, 1731�1736 zaac.wiley-vch.de 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 1735

energy which then can be compensated by the Ga�O bind-ing.

The trend that the positions above an Mg atom of thesurface is the preferred position for the Ga atom is retainedin the larger Cu islands. The stronger Cu�O bond leads tothe preferred position for a Cu atom over an O atom anddeprives the Ga atom of this site. For the number ofCu�Ga bonds both possibilities are equivalent. The last isnot valid for the case where two Ga atoms are part of theisland. In this case, there is the possibility of a Ga�Gabond. We calculated the binding energy for a Ga2 moleculeto �43.3 kcal/mol, which is smaller than the CuGa bindingenergy of �56.2 kcal/mol in the CuGa molecule. Thereforethe formation of Cu�Ga bonds has preference over the for-mation of Ga�Ga bonds which leads to a spatial separ-ation of the two Ga atoms.

In the case of the adsorbed Gan cluster each Ga atomhas a position above an O atom of the surface. This is incontrast to the adsorbed Cun cluster [15]. An explanationfor this can also be found by comparing again bond lengths.The calculated Ga�Ga distance in the Ga2 molecule is 2.64A which is even longer than the Cu�Ga distance. Thereforethe energy arguments, Cu�Ga versus Ga�Ga bond

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G. Geudtner, K. Jug

Figure 5 Adsorption energies Eads (kcal/mol) in dependence ofcluster size n

strength, given in the discussion of the CunGa cluster areeven more valid in this case. An additional question is whyno pyramidal structures where found. The Ga solid consistsof Ga2 units. So Ga does not tend to build up such a met-allic environment as Cu does. Furthermore the possibilityof forming Ga�Ga bonds of adsorbed Ga atoms is reducedby the Ga�O bond. This leads to the conclusion that thegain of energy for a Ga atom by binding to an O atom islarger than by binding to four already adsorbed Ga atoms.The lesser role of the Ga�Ga bond in the formation of theclusters can also be deduced from Fig. 5. The increase ofthe adsorption energy is almost linear with the number ofatoms. From the structures in Fig. 3 one would expect alarger step from Ga3 to Ga4 than from Ga4 to Ga5, becauseone could think that in the first case two new Ga�Gabonds are formed but in the second case only one.

The loss of binding energy because of bond lengtheningis also the explanation for the stucture of the adsorbedGa2Cu cluster where the two Ga atoms bind to the O atomsof the surface even though the Cu�O interaction isstronger. In comparison to the structure of the adsorbedGa5 cluster one would expect for the Ga4Cu cluster a struc-ture in which all four Ga atoms bind to O atoms. As canbe seen from for the adsorbed Ga3Cu cluster in Fig. 4b theinteraction of the Cu atom with the Ga atoms leads to alarge displacement of the Cu atom relative to a positionexactly on top of an O atom of the surface. This displace-ment would lengthen the bond of the Cu atom to an ad-ditional Ga atom above an O atom. For an adsorbedGa5Cu cluster there are two different structures within anenergy range of 1 kcal/mol. With the number of adsorbed

2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim zaac.wiley-vch.de Z. Anorg. Allg. Chem. 2003, 629, 1731�17361736

atoms the number of generated bonds increases. For thisreason it is difficult to give a simple explanation for thesestructures. Nevertheless one can conclude that a conversionof these structures from one to the other would be difficultbecause such a rearrangement would require a migration ofthe Cu atom over a distance of about 4.5 A together witha migration of a Ga atom. But in a thermodynamic con-trolled environment like the one during a chemical trans-port reaction the most stable structure should be produced.Acknowledgement. This work was partly supported by DeutscheForschungsgemeinschaft. The structures were drawn with the pro-gram SCHAKAL. We thank Prof. M. Binnewies and his coworkersfor discussions on this topic.

References

[1] J.-W. He, P. J. Møller, Surf. Sci. 1986, 178, 934.[2] T. Conard, J. M. Vohs, P. A. Thiry, R. Caudano, Interface

Anal. 1990, 16, 446.[3] T. Conard, J. Ghijsen, J. M. Vohs, P. A. Thiry, R. Caudano,

R. L. Johnson, Surf. Sci. 1992, 265, 31.[4] J. B. Zhou, H. C. Lu, T. Gustafsson, E. Garfunkel, Surf. Sci.

1993, 293, L887.[5] M.-C. Wu, W. S. Oh, D. W. Goodmann, Surf. Sci. 1995, 330,

61.[6] J. B. Zhou, T. Gustafsson, Surf. Sci. 1997, 375, 221.[7] I. Alstrup, P. J. Møller, Appl. Surf. Sci. 1988, 33/34, 143.[8] J. T. Ranney, D. E. Starr, J. E. Musgrove, D. J. Bald, C. T.

Campbell, Faraday Discuss. 1999, 114, 195.[9] G. Eilers, K. Mukasa, Jpn. J. App. Phys. 2000, 39, 3780.

[10] G. Pacchioni, N. Rösch, J. Chem. Phys. 1996, 104, 7329.[11] V. Musolino, A. Selloni, R. Car, Surf. Sci. 1998, 402�404, 413.[12] M.-H. Schaffner, F. Patthey, W.-D. Schneider, L. G. M. Pet-

tersson, Surf. Sci. 1998, 402�404, 450.[13] V. Musolino, A. Selloni, R. Car, J. Chem. Phys. 1998, 108,

5044.[14] A. V. Matveev, K. M. Neyman, G. Pacchioni, Chem. Phys.

Lett. 1999, 299, 603.[15] G. Geudtner, K. Jug, A. M. Köster, Surf. Sci. 2000, 467, 98.[16] T. Plaggenborg, M. Binnewies, Z. Anorg. Allg. Chem. 2000,

626, 1478.[17] W. B. Pearson, A Handbook of Lattice Spacing and Structures

of Metals and Alloys, Vol. 2, Pergamon Press, 1967.[18] B. Ahlswede, K. Jug, J. Comput. Chem. 1999, 20, 563.[19] B. Ahlswede, K. Jug, J. Comput. Chem. 1999, 20, 572.[20] T. Bredow, G. Geudtner, K. Jug, J. Comput. Chem. 1999, 22,

861.[21] K. Jug, G. Geudtner, T. Homann, J. Comput. Chem. 2000,

21, 974.[22] T. Bredow, G. Geudtner, K. Jug, J. Comput. Chem. 2001, 22,

89.[23] D. Lide, Handbook of Chemistry and Physics; 72th ed., CRC

Press:Boca Raton 1991�1992.