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Molecular dynamics study of the ordered Cu3Au
Surface Science 488 (2001) 269±276
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Molecular dynamics study of the ordered Cu3Au II. Vibrational and structural properties of Cu and Au adatoms on the low indexed surfaces Ch.E. Lekka, N.I. Papanicolaou, G.A. Evangelakis * Department of Physics, Solid State Division, University of Ioannina, P.O. Box 1186, GR-45110 Ioannina, Greece Received 6 July 2000; accepted for publication 11 May 2001
Abstract Using an eective potential model in analogy to the tight-binding scheme to the second-moment approximation, we investigated the vibrational properties of the Cu and Au adatoms on the low index ordered Cu3 Au surfaces. We found that the presence of adatoms alters the surface phonon modes and introduces new ones situated mainly at high frequencies. This result indicates that the coupling between adatoms and surface atoms is stronger than between surface atoms. Moreover, we found that both adatoms on the (1 1 1) faces are unstable, segregating already at room temperature. On the (0 0 1) surface the vibrational amplitudes of both adatoms depend linearly on temperature up to Ts 500 K, exhibiting anomalous increase above this temperature. Concerning the (1 1 0) surface, the mean-squaredisplacements and the relaxed interlayer positions of the adatoms present strong anharmonic behaviour, the eect being more pronounced above Ts , accompanied by segregation and spontaneous creation of adatoms. Therefore, Ts appears as a characteristic temperature, above which phenomena stimulated by the presence of adatoms set up acting as precursors of the order±disorder transition which happens around Tr 663 K for the bulk system. These ®ndings are compatible with available experimental and theoretical data and with results referring to Au deposition on the low indexed Cu faces. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Molecular dynamics; Surface energy; Surface relaxation and reconstruction; Surface waves; Phonons; Alloys; Adatoms
1. Introduction The important role of the presence of adatoms on surfaces has been demonstrated in the cases of homo-epitaxial growth, heterogeneous catalysis segregation phenomena and surface alloying. Indeed, from thermal desorption spectroscopy (TDS)
* Corresponding author. Tel.: +30-6519-8590; fax: +30-65145631. E-mail address: [email protected] (G.A. Evangelakis).
and high-resolution-electron-energy-loss-spectroscopy (HREELS) studies of Pt on Cu(1 1 1) [1] and a core-level photo-emission-spectroscopy study of Cu on Pt[1 1 1] [2], it is found that above 500 K, Pt and Cu atoms diuse into the bulk resulting in surface segregation and bulk alloying. Furthermore, from calculations using the embedded atom method (EAM) [3] and molecular dynamics (MD) simulations [4,5] it was found that the deposited Au atoms on Cu(0 0 1) exchange their positions with surface atoms. In addition, the presence of adatoms on surfaces modi®es drastically most of the
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surface dynamical properties, e.g., the large anisotropic thermal vibrational amplitudes that were found from X-ray studies on gallium adatoms on the Si(1 1 1) surface [6]. However, the work done on properties of adatoms on alloy surfaces is rather limited. In this study we focus on the vibrational properties of Cu and Au adatoms on the low indexed Cu3 Au surfaces. Our results are counterpoised with the clean Cu3 Au surface cases [7] and with the cases of pure Cu surface [4,5,7] in presence of Cu [8] and Au [4,5] adatoms. The potential model [9] we used and the technical details are the same with a previous paper [7]. Since the spontaneous creation of Cu or Au adatoms on these faces is rather scarce, we put one of each kind on each surface of the slab, corresponding to an adatom concentration of the order of 1%. 2. Results and discussion 2.1. Geometrical and energetic considerations The behaviour of Cu and Au adatoms and the structure of the substrate are closely related. On the (0 0 1) surface, the Cu or Au adatom occupies the fourfold position, while on the (1 1 0) and (1 1 1) faces there are two distinct adatom positions. The Au adatom on the (1 1 0) surface occupies the in-channel adatom position. Surprisingly, the Cu adatom on the same face rests between two Cu surface atoms in the [0 0 1] direction, pushing one Cu surface atom towards the channel (Fig. 1). We observe that these Cu atoms are slightly lifted and that the positions of the neighbouring surface atoms are also distorted, while a third layer Au atom (patterned atom) is raised. In this ®gure the numbers are used to label the ®rst, second and third layer atoms, while shadowed and white particles stand for Au and Cu atoms, respectively. The dark particle represents the Cu adatom. This con®guration is referred to the literature as ``dump-bell con®guration'', it has been found in simulations of dierent metals as intermediate metastable position in the exchange diusion process [10,11] and experimentally in the Ag(1 1 0) case when an ad-
11 11 3 3 3 3 5 5 5 5
2 2 22 4 4 4 4
1 11 1 3 33 3 5 5 5 5
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2
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22 3 3
22
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Fig. 1. Cu adatom relaxed position on the Cu3 Au(1 1 0) surface. Filled and opened circles stand for the Au and Cu surface atoms, respectively. The numbers denote the atomic layers, while dark particle stands for the adatom.
atom is displaced by the STM tip [12]. It has to be pointed out that in our case this con®guration is found to be an equilibrium adatom position. This important dierence in the equilibrium positions of Cu and Au adatoms could be related to their dierent ionic radii and to the rippling eect. The latter can be understood taking into account the electronic structure of the alloy, that is a common d-band material, in which the Au bands are concentrated in the bottom of the d-band, while the Cu bands are gathered at the top of the d-band [13]. This spatial compression on the 5d shells of Au, that is likely due to the sp electrons compressing to a smaller atomic volume [14], can be released by an outwards and inwards displacement of the Au and Cu surface atoms, respectively, resulting in a rippled surface [15]. On this open surface the Au and Cu adatoms just follow the behaviour of the surface atoms. On the (1 1 1) surface, each of the hcp and fcc adatom positions originated from the structure of this face, split in two distinct sites referring to a Au rich and pure Cu triangle. The energetically favoured position of the Cu adatom is on the pure Cu hcp triangle, while the Au adatom relaxes in the Au rich fcc triangle. Summarising, the adatoms relax closer to the (1 1 0) face than on the (0 0 1) and (1 1 1) faces. The picture we presented above refers to zero temperature calculations. At ®nite temperatures the situation changes substantially, especially for
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the (1 1 1) surface. Both Cu and Au adatoms on this face are unstable at room temperature and above. In addition, the Cu adatom enters into the surface already at 200 K, while the Au adatom, appears more stable at this temperature. At room temperature, it becomes also quickly unstable and by pushing a Cu surface atom into the bulk it is also accommodated on the surface. In both cases the Cu surface atom initiates a concerted diusion process of the bulk Cu atoms. These results could explain the strong diuse scattering from shortrange-order ¯uctuations in the region 100±600 below the surface, found close to the bulk orA der±disorder transition by X-ray scattering [16]. In the same study it was found that the eect is much weaker closer to the surface, indicating that the (1 1 1) face exhibits anomalous behaviour below the surface and that this behaviour is stimulated by the adatom deposition. 2.2. Adatom phonon density of states Since both adatoms on the (1 1 1) surface are unstable at room temperature and above, we calculated the phonon DOSs of the Au and Cu adatoms on the (0 0 1) and (1 1 0) (Figs. 2±5). In the same ®gures, we give also the phonon DOSs of the Au and Cu surface atoms (dashed lines) of the (0 0 1) and (1 1 0) clean surface layers [7]. We observe that the morphology of the adatom DOSs is substantially dierent from those of the clean surfaces [7], while the structural dierences between the two faces are clearly re¯ected in the case of Cu adatom DOSs (Figs. 3 and 5). The Au adatom on the (0 0 1) face introduces a new mode at 0.85 THz, along the [1 0 0] in-plane direction (Fig. 2(a)). In the same ®gure we also give (in the inset) the main crystallographic directions for the (0 0 1) face. In presence of an adatom, the surface exhibits an anisotropic character that can be easily seen in the phonon DOSs in the inplane directions ([1 0 0] and [1 1 0]) (Fig. 2(a) and (b)). Moreover, two new modes are found at 3.80 THz and at 4.60 THz along the [1 1 0] in-plane and normal to the surface direction, respectively (Fig. 2(b) and (c)). These modes are in higher frequencies than the Au surface atoms. The Au surface mode around 1.5 THz appears at lower frequency
Fig. 2. Phonon DOS of the Au adatom (Ð) on the (0 0 1) surface at 300 K along with the DOS of the Au surface atoms (- - -): (a) along the [1 0 0] in-plane direction, (b) along the [1 1 0] in-plane direction and (c) normal to the surface direction. In the inset of (a), we show the main crystallographic directions of the surface. Filled and open circles stand for Au and Cu surface atoms, while the black particle represents the adatom.
(Fig. 2(a)±(c)). Summarising, it comes out that the Au adatom is more tightly bound than the Au surface atoms in the normal to the surface direction while the opposite is true along the [1 0 0] inplane direction.
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Fig. 3. Phonon DOS of the Cu adatom (Ð) on the (0 0 1) surface at 300 K along with the DOS of the Cu surface atoms (- - -): (a) along the [1 0 0] in-plane direction, (b) along the [1 1 0] in-plane direction and (c) normal to the surface direction.
The Cu adatom, along the [1 0 0] in-plane direction of the (0 0 1) surface, alters the high frequency Cu surface atoms modes and presents a new phonon mode around 1.4 THz (Fig. 3(a)). Along the [1 1 0] in-plane and normal to the surface direction there are no new phonon modes introduced by the Cu adatom (Fig. 3(b) and (c)). In addition, the surface phonon mode, along the [1 1 0] in-plane direction, around 5.9 THz is not recovered, while the other Cu surface modes are retained in the Cu adatom DOS (Fig. 3(b) and (c)).
Fig. 4. Phonon DOS of the Au adatom (Ð) on the (1 1 0) surface at 300 K along with the DOS of the Au surface atoms (- - -): (a) along the [1 1 0] in-plane direction, (b) along the [0 0 1] in-plane direction and (c) normal to the surface direction.
Summarising, the Cu adatom on the (0 0 1) face is less tightly bound than the Cu surface atoms along the in-plane direction, while in the normal to the surface directions it exhibits similar behaviour with the Cu surface atoms. The dierent vibrational behaviour of Cu and Au adatoms is related to their dierent masses and that in the in-plane direction the Cu adatom is more tightly bound with the surface than the Au adatom, while in the normal to the surface direction both adatoms have almost similar phonon DOS.
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Turning on the Cu adatom (Fig. 5(a)), we found a new phonon mode around 7 THz along the [1 1 0] in-plane direction, while we recognise the remaining Cu surface modes. In Fig. 5(b) we observe that there are three new phonon modes around 4.75, 5.60 and 7 THz along the [0 0 1] direction, while a new mode at 7 THz is found in the normal to the surface direction Fig. 5(c). The phonon mode around 7 THz suggests strong binding of the Cu adatom with surface, in agreement with the fact that it relaxes closer to the surface (Fig. 1). Concluding, as in the case of Au and Cu surface atoms [7], the Au adatoms introduce lower frequency modes than the Cu adatoms on both (0 0 1) and (1 1 0) faces. Furthermore, in the normal to the surface direction, the Au adatom is more tightly bound on the (0 0 1) surface than the Au adatom on the (1 1 0) face. Similarly, in the normal to the surface direction, the Cu adatom is more tightly bound with the surface atoms on the (1 1 0) than on the (0 0 1) face. This is compatible with the fact that the Cu adatom relaxes closer to the (1 1 0) surface than on the (0 0 1) face. 2.3. Mean-square-displacements
Fig. 5. Phonon DOS of the Cu adatom (Ð) on the (1 1 0) surface at 300 K along with the DOS of the Cu surface atoms (- - -): (a) along the [1 1 0] in-plane direction, (b) along the [0 0 1] in-plane direction and (c) normal to the surface direction.
The Au adatom on the (1 1 0) face exhibits a new phonon mode at 0.55 THz along the [1 1 0] in-plane direction (Fig. 4(a)). This is the lowest phonon mode introduced in the Cu3 Au system [7]. Along the [0 0 1] in-plane direction (Fig. 4(b)), the Au adatom introduces a new phonon mode around 3.30 THz, while along the in-plane direction the Au surface phonon modes are recovered. In the normal to the surface direction (Fig. 4(c)), there are no new modes introduced by the presence of Au adatom.
Since the adatoms on the closed packed surface are unstable, the mean-square-displacements in the normal to the surface direction of Cu and Au adatoms were calculated only for the (0 0 1) and (1 1 0) surfaces (Fig. 6). The vibrational amplitudes are larger for both adatoms on the (1 1 0) face, a result that can be easily understood by taking into account geometrical considerations. The MSDs of Cu adatom on both faces depend linearly on temperature up to Ts 500 K; above Ts , strong anharmonic behaviour is observed. Similar anharmonic behaviour in the MSDs of the (1 1 0) surface has been also found in dierent simulations [11,17]. In addition, above Ts , both adatoms exhibit vibrational amplitudes that are twice as large as those of the surface atoms [7]. It is interesting to note that up to 400 K the MSDs of the heavier adatom (Au) is smaller than the lighter Cu adatom on the (1 1 0) face, while above 400 K the opposite is true. This phenomenon is also observed for adatoms on the (0 0 1) face above 550 K.
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Fig. 6. Temperature dependence of the mean-square-displacements of Cu (®lled symbols) and Au (open symbols) adatoms. Circles and squares stand for the (0 0 1), (1 1 0) faces, respectively.
2.4. Relative interlayer relaxed positions From the calculated relative interlayer relaxed positions (RIRP) of both adatoms on the (0 0 1) and (1 1 0) surfaces, we found that the Cu adatom displays stronger contraction than the Au adatom (Fig. 7). This is compatible with the results of phonon SDs that indicated stronger coupling of
the Cu adatom with the surface in the perpendicular direction. The RIRP for the Cu adatom exhibit linear temperature dependence, whereas anharmonic behaviour is displayed for the Au adatom on the (1 1 0) surface, above Ts . At this high temperature region, both adatoms on the (1 1 0) face are relaxing closer to the surface, compared to those on the (0 0 1) surface. The Cu
Fig. 7. Temperature dependence of the RIRP of Cu (®lled symbols) and Au (open symbols) adatoms with respect to the bulk interlayer spacing. Circles and squares stand for the (0 0 1), (1 1 0) faces, respectively.
Ch.E. Lekka et al. / Surface Science 488 (2001) 269±276
adatom on the (1 1 0) face, already at room temperature, relaxes even beneath the half interlayer distance, while above Ts it can be considered as belonging to the surface layer. This phenomenon has to be related with the general changes found for this face above Ts . As mentioned in Ref. [7], some of the Au surface atoms segregate to relax ®nally in the pure Cu second layer, the surface atoms being displaced outwards. From low-energy diraction experiments on Cu3 Au (1 1 0) [18] it was found that the apparent activation energy of ordering has a value close to that of diusion in Cu3 Au. A diusive mechanism for island formation is therefore possible and it is consolidated by the results given in Ref. [7]. Concerning the adatoms on the (0 0 1) surface, we see that the Cu adatoms are more contracted than Au adatoms. Around Ts , the Au adatom exchanges positions with a surface Cu atom entering in the surface layer. This mechanism could be the beginning of disorder in (0 0 1) face, because it changes locally the order of the surface atoms. The existence of exchange mechanism for Au adatom was also observed in the case of the clean Cu(0 0 1) [4,5], while Cu exchange type diusion on this surface is not favoured [4,5,10,19]. Therefore, the gold adatom behaves dierently than the copper adatom both on pure Cu surface and on the alloy surface, re¯ecting its dierent bonding character.
3. Conclusions In this study we present results concerning the structural and vibrational properties of the Cu and Au adatoms on the ordered low-indexed Cu3 Au faces. We observed that the behaviour of Cu and Au adatoms depends on the substrate, with both adatoms being unstable on the closed packed face, relaxing ®nally on the site of a Cu surface atom that is forced in bulk diusion. For the (1 1 1) face this eect happens already at room temperature, while in the case of (1 0 0) it happens above Ts . In addition, this phenomenon was not observed in the case of adatoms on a clean Cu surface, indicating that in the Cu3 Au alloy surface the presence
275
of two kind surface atoms and the rippling eect [7], play an important role in the adatom's behaviour. The presence of both adatoms on the surfaces changes the morphology of the surface phonon density of states by introducing new vibrational modes or altering the existing ones. These new modes are situated in general at higher frequencies than the corresponding surface modes. An exception is coming from the Cu adatom on the (0 0 1) face, where the new modes are almost in the middle of the frequency range. The Cu adatom introduces high frequency modes, the highest one being around 7 THz for the (1 1 0) surface, while Au adatom is responsible for the lower vibrations; the lowest mode is found in the same face around 0.55 THz. Summarising, the vibrational modes of a mixed terminal layer are situated at lower frequencies compared to those of a pure Cu face. On the contrary, the location of the vibrational modes due to adatoms indicates that they are more tightly bound on a mixed terminal layer than on a pure Cu face. From the relaxed positions of the adatoms on the two other faces it came out that they are both contracted, the Cu adatom exhibiting more this eect. Exchange type diusion mechanisms occur above Ts on the (0 0 1) face resulting to the substitution of a Cu surface atom by the Au adatom. This mechanism could accelerate the order±disorder transition. On the (1 1 0) surface the Cu adatom relaxes very close to the surface layer, already at room temperature and it is almost assimilated in the surface layer when approaching Ts . Concerning the Au adatom, contraction is observed that becomes very important above Ts . This result is related with the general behaviour of this face that is characterised by segregation and spontaneous creation of adatoms [7]. In addition, this behaviour is associated with the MSDs of both adatoms that are characterised by strong anharmonicity above Ts . Therefore, Ts appears as a characteristic temperature, above which phenomena, that are also stimulated by the presence of adatoms, set up acting as precursors of the order±disorder transition. It would be of great interest to experimentally verify these new results by suitable methods such
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as ®eld ion microscopy, electron-energy-loss-spectroscopy or thermal helium beam scattering. Acknowledgements Stimulating discussions and constructive criticism of Prof. N.G. Alexandropoulos are gratefully acknowledged. References [1] U. Schoder, R. Linke, J.-H. Boo, K. Wandelt, Surf. Sci. 352 (1996) 211. [2] N.T. Barrett, R. Belchou, J. Thiele, Surf. Sci. 351 (1995) 776. [3] S.M. Foiles, Surf. Sci. 191 (1987) 329. [4] G.A. Evangelakis, G.C. Kallinteris, N.I. Papanicolaou, Surf. Sci. 394 (1997) 185. [5] N.I. Papanicolaou, G.A. Evangelakis, G.C. Kallinteris, in: Gonis et al. (Eds.), Properties of Complex Inorganic Solids, Plenum, New York, 1997, 151.
[6] R.E. Martinez, E. Fontes, J.A. Golovchenko, J.R. Patel, Phys. Rev. Lett. 69 (1992) 1061. [7] Ch.E. Lekka, N.I. Papanicolaou, G.A. Evangelakis, Surf. Sci. 479 (2001) 287. [8] G.C. Kallinteris, G.A. Evangelakis, N.I. Papanicolaou, Surf. Sci. 369 (1996) 185. [9] N.I. Papanicolaou, G.C. Kallinteris, G.A. Evangelakis, D.A. Papaconstantopoulos, M.J. Mehl, J. Phys.: Condens. Matter. 10 (1998) 10979. [10] C.L. Liu, J.M. Cohen, J.B. Adams, A.F. Voter, Surf. Sci. 253 (1991) 334. [11] R. Ferrando, Phys. Rev. Lett. 76 (1996) 4195. [12] J.J. Schulz, R. Koch, K.H. Rieder, Phys. Rev. Lett. 84 (2000) 4597. [13] B. Ginatempo, G.Y. Guo, W.M. Temmerman, J.B. Staunton, P.J. Durham, Phys. Rev. B 42 (1990) 2761. [14] V. Heine, L.D. Marks, Surf. Sci. 165 (1986) 65. [15] B. Gans, P.A. Knipp, D.D. Koleske, S.J. Sibener, Surf. Sci. 264 (1992) 81. [16] X.-M. Zhu, R. Feideuhans'l, H. Zabel, J. Als-Nielsen, R. Du, C.P. Flynn, F. Grey, Phys. Rev. B 37 (1988) 7157. [17] T.S. Rahman, Z.J. Tian, J. Electron Spectrosc. Rel. Phenom. 64/65 (1993) 651. [18] E.G. Mc Rae, R.A. Malic, Phys. Rev. B 42 (1990) 1509. [19] F. Montalenti, R. Ferrando, Phys. Rev. B 59 (1999) 5881.
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Molecular dynamics study of the ordered Cu3Au II. Vibrational and structural properties of Cu and Au adatoms on the low indexed surfaces Ch.E. Lekka, N.I. Papanicolaou, G.A. Evangelakis * Department of Physics, Solid State Division, University of Ioannina, P.O. Box 1186, GR-45110 Ioannina, Greece Received 6 July 2000; accepted for publication 11 May 2001
Abstract Using an eective potential model in analogy to the tight-binding scheme to the second-moment approximation, we investigated the vibrational properties of the Cu and Au adatoms on the low index ordered Cu3 Au surfaces. We found that the presence of adatoms alters the surface phonon modes and introduces new ones situated mainly at high frequencies. This result indicates that the coupling between adatoms and surface atoms is stronger than between surface atoms. Moreover, we found that both adatoms on the (1 1 1) faces are unstable, segregating already at room temperature. On the (0 0 1) surface the vibrational amplitudes of both adatoms depend linearly on temperature up to Ts 500 K, exhibiting anomalous increase above this temperature. Concerning the (1 1 0) surface, the mean-squaredisplacements and the relaxed interlayer positions of the adatoms present strong anharmonic behaviour, the eect being more pronounced above Ts , accompanied by segregation and spontaneous creation of adatoms. Therefore, Ts appears as a characteristic temperature, above which phenomena stimulated by the presence of adatoms set up acting as precursors of the order±disorder transition which happens around Tr 663 K for the bulk system. These ®ndings are compatible with available experimental and theoretical data and with results referring to Au deposition on the low indexed Cu faces. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Molecular dynamics; Surface energy; Surface relaxation and reconstruction; Surface waves; Phonons; Alloys; Adatoms
1. Introduction The important role of the presence of adatoms on surfaces has been demonstrated in the cases of homo-epitaxial growth, heterogeneous catalysis segregation phenomena and surface alloying. Indeed, from thermal desorption spectroscopy (TDS)
* Corresponding author. Tel.: +30-6519-8590; fax: +30-65145631. E-mail address: [email protected] (G.A. Evangelakis).
and high-resolution-electron-energy-loss-spectroscopy (HREELS) studies of Pt on Cu(1 1 1) [1] and a core-level photo-emission-spectroscopy study of Cu on Pt[1 1 1] [2], it is found that above 500 K, Pt and Cu atoms diuse into the bulk resulting in surface segregation and bulk alloying. Furthermore, from calculations using the embedded atom method (EAM) [3] and molecular dynamics (MD) simulations [4,5] it was found that the deposited Au atoms on Cu(0 0 1) exchange their positions with surface atoms. In addition, the presence of adatoms on surfaces modi®es drastically most of the
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surface dynamical properties, e.g., the large anisotropic thermal vibrational amplitudes that were found from X-ray studies on gallium adatoms on the Si(1 1 1) surface [6]. However, the work done on properties of adatoms on alloy surfaces is rather limited. In this study we focus on the vibrational properties of Cu and Au adatoms on the low indexed Cu3 Au surfaces. Our results are counterpoised with the clean Cu3 Au surface cases [7] and with the cases of pure Cu surface [4,5,7] in presence of Cu [8] and Au [4,5] adatoms. The potential model [9] we used and the technical details are the same with a previous paper [7]. Since the spontaneous creation of Cu or Au adatoms on these faces is rather scarce, we put one of each kind on each surface of the slab, corresponding to an adatom concentration of the order of 1%. 2. Results and discussion 2.1. Geometrical and energetic considerations The behaviour of Cu and Au adatoms and the structure of the substrate are closely related. On the (0 0 1) surface, the Cu or Au adatom occupies the fourfold position, while on the (1 1 0) and (1 1 1) faces there are two distinct adatom positions. The Au adatom on the (1 1 0) surface occupies the in-channel adatom position. Surprisingly, the Cu adatom on the same face rests between two Cu surface atoms in the [0 0 1] direction, pushing one Cu surface atom towards the channel (Fig. 1). We observe that these Cu atoms are slightly lifted and that the positions of the neighbouring surface atoms are also distorted, while a third layer Au atom (patterned atom) is raised. In this ®gure the numbers are used to label the ®rst, second and third layer atoms, while shadowed and white particles stand for Au and Cu atoms, respectively. The dark particle represents the Cu adatom. This con®guration is referred to the literature as ``dump-bell con®guration'', it has been found in simulations of dierent metals as intermediate metastable position in the exchange diusion process [10,11] and experimentally in the Ag(1 1 0) case when an ad-
11 11 3 3 3 3 5 5 5 5
2 2 22 4 4 4 4
1 11 1 3 33 3 5 5 5 5
11
0 2
2
11
22 3 3
22
2
2
3 34 4 4 4 4 4 55 4 4 5 5
Fig. 1. Cu adatom relaxed position on the Cu3 Au(1 1 0) surface. Filled and opened circles stand for the Au and Cu surface atoms, respectively. The numbers denote the atomic layers, while dark particle stands for the adatom.
atom is displaced by the STM tip [12]. It has to be pointed out that in our case this con®guration is found to be an equilibrium adatom position. This important dierence in the equilibrium positions of Cu and Au adatoms could be related to their dierent ionic radii and to the rippling eect. The latter can be understood taking into account the electronic structure of the alloy, that is a common d-band material, in which the Au bands are concentrated in the bottom of the d-band, while the Cu bands are gathered at the top of the d-band [13]. This spatial compression on the 5d shells of Au, that is likely due to the sp electrons compressing to a smaller atomic volume [14], can be released by an outwards and inwards displacement of the Au and Cu surface atoms, respectively, resulting in a rippled surface [15]. On this open surface the Au and Cu adatoms just follow the behaviour of the surface atoms. On the (1 1 1) surface, each of the hcp and fcc adatom positions originated from the structure of this face, split in two distinct sites referring to a Au rich and pure Cu triangle. The energetically favoured position of the Cu adatom is on the pure Cu hcp triangle, while the Au adatom relaxes in the Au rich fcc triangle. Summarising, the adatoms relax closer to the (1 1 0) face than on the (0 0 1) and (1 1 1) faces. The picture we presented above refers to zero temperature calculations. At ®nite temperatures the situation changes substantially, especially for
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the (1 1 1) surface. Both Cu and Au adatoms on this face are unstable at room temperature and above. In addition, the Cu adatom enters into the surface already at 200 K, while the Au adatom, appears more stable at this temperature. At room temperature, it becomes also quickly unstable and by pushing a Cu surface atom into the bulk it is also accommodated on the surface. In both cases the Cu surface atom initiates a concerted diusion process of the bulk Cu atoms. These results could explain the strong diuse scattering from shortrange-order ¯uctuations in the region 100±600 below the surface, found close to the bulk orA der±disorder transition by X-ray scattering [16]. In the same study it was found that the eect is much weaker closer to the surface, indicating that the (1 1 1) face exhibits anomalous behaviour below the surface and that this behaviour is stimulated by the adatom deposition. 2.2. Adatom phonon density of states Since both adatoms on the (1 1 1) surface are unstable at room temperature and above, we calculated the phonon DOSs of the Au and Cu adatoms on the (0 0 1) and (1 1 0) (Figs. 2±5). In the same ®gures, we give also the phonon DOSs of the Au and Cu surface atoms (dashed lines) of the (0 0 1) and (1 1 0) clean surface layers [7]. We observe that the morphology of the adatom DOSs is substantially dierent from those of the clean surfaces [7], while the structural dierences between the two faces are clearly re¯ected in the case of Cu adatom DOSs (Figs. 3 and 5). The Au adatom on the (0 0 1) face introduces a new mode at 0.85 THz, along the [1 0 0] in-plane direction (Fig. 2(a)). In the same ®gure we also give (in the inset) the main crystallographic directions for the (0 0 1) face. In presence of an adatom, the surface exhibits an anisotropic character that can be easily seen in the phonon DOSs in the inplane directions ([1 0 0] and [1 1 0]) (Fig. 2(a) and (b)). Moreover, two new modes are found at 3.80 THz and at 4.60 THz along the [1 1 0] in-plane and normal to the surface direction, respectively (Fig. 2(b) and (c)). These modes are in higher frequencies than the Au surface atoms. The Au surface mode around 1.5 THz appears at lower frequency
Fig. 2. Phonon DOS of the Au adatom (Ð) on the (0 0 1) surface at 300 K along with the DOS of the Au surface atoms (- - -): (a) along the [1 0 0] in-plane direction, (b) along the [1 1 0] in-plane direction and (c) normal to the surface direction. In the inset of (a), we show the main crystallographic directions of the surface. Filled and open circles stand for Au and Cu surface atoms, while the black particle represents the adatom.
(Fig. 2(a)±(c)). Summarising, it comes out that the Au adatom is more tightly bound than the Au surface atoms in the normal to the surface direction while the opposite is true along the [1 0 0] inplane direction.
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Fig. 3. Phonon DOS of the Cu adatom (Ð) on the (0 0 1) surface at 300 K along with the DOS of the Cu surface atoms (- - -): (a) along the [1 0 0] in-plane direction, (b) along the [1 1 0] in-plane direction and (c) normal to the surface direction.
The Cu adatom, along the [1 0 0] in-plane direction of the (0 0 1) surface, alters the high frequency Cu surface atoms modes and presents a new phonon mode around 1.4 THz (Fig. 3(a)). Along the [1 1 0] in-plane and normal to the surface direction there are no new phonon modes introduced by the Cu adatom (Fig. 3(b) and (c)). In addition, the surface phonon mode, along the [1 1 0] in-plane direction, around 5.9 THz is not recovered, while the other Cu surface modes are retained in the Cu adatom DOS (Fig. 3(b) and (c)).
Fig. 4. Phonon DOS of the Au adatom (Ð) on the (1 1 0) surface at 300 K along with the DOS of the Au surface atoms (- - -): (a) along the [1 1 0] in-plane direction, (b) along the [0 0 1] in-plane direction and (c) normal to the surface direction.
Summarising, the Cu adatom on the (0 0 1) face is less tightly bound than the Cu surface atoms along the in-plane direction, while in the normal to the surface directions it exhibits similar behaviour with the Cu surface atoms. The dierent vibrational behaviour of Cu and Au adatoms is related to their dierent masses and that in the in-plane direction the Cu adatom is more tightly bound with the surface than the Au adatom, while in the normal to the surface direction both adatoms have almost similar phonon DOS.
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Turning on the Cu adatom (Fig. 5(a)), we found a new phonon mode around 7 THz along the [1 1 0] in-plane direction, while we recognise the remaining Cu surface modes. In Fig. 5(b) we observe that there are three new phonon modes around 4.75, 5.60 and 7 THz along the [0 0 1] direction, while a new mode at 7 THz is found in the normal to the surface direction Fig. 5(c). The phonon mode around 7 THz suggests strong binding of the Cu adatom with surface, in agreement with the fact that it relaxes closer to the surface (Fig. 1). Concluding, as in the case of Au and Cu surface atoms [7], the Au adatoms introduce lower frequency modes than the Cu adatoms on both (0 0 1) and (1 1 0) faces. Furthermore, in the normal to the surface direction, the Au adatom is more tightly bound on the (0 0 1) surface than the Au adatom on the (1 1 0) face. Similarly, in the normal to the surface direction, the Cu adatom is more tightly bound with the surface atoms on the (1 1 0) than on the (0 0 1) face. This is compatible with the fact that the Cu adatom relaxes closer to the (1 1 0) surface than on the (0 0 1) face. 2.3. Mean-square-displacements
Fig. 5. Phonon DOS of the Cu adatom (Ð) on the (1 1 0) surface at 300 K along with the DOS of the Cu surface atoms (- - -): (a) along the [1 1 0] in-plane direction, (b) along the [0 0 1] in-plane direction and (c) normal to the surface direction.
The Au adatom on the (1 1 0) face exhibits a new phonon mode at 0.55 THz along the [1 1 0] in-plane direction (Fig. 4(a)). This is the lowest phonon mode introduced in the Cu3 Au system [7]. Along the [0 0 1] in-plane direction (Fig. 4(b)), the Au adatom introduces a new phonon mode around 3.30 THz, while along the in-plane direction the Au surface phonon modes are recovered. In the normal to the surface direction (Fig. 4(c)), there are no new modes introduced by the presence of Au adatom.
Since the adatoms on the closed packed surface are unstable, the mean-square-displacements in the normal to the surface direction of Cu and Au adatoms were calculated only for the (0 0 1) and (1 1 0) surfaces (Fig. 6). The vibrational amplitudes are larger for both adatoms on the (1 1 0) face, a result that can be easily understood by taking into account geometrical considerations. The MSDs of Cu adatom on both faces depend linearly on temperature up to Ts 500 K; above Ts , strong anharmonic behaviour is observed. Similar anharmonic behaviour in the MSDs of the (1 1 0) surface has been also found in dierent simulations [11,17]. In addition, above Ts , both adatoms exhibit vibrational amplitudes that are twice as large as those of the surface atoms [7]. It is interesting to note that up to 400 K the MSDs of the heavier adatom (Au) is smaller than the lighter Cu adatom on the (1 1 0) face, while above 400 K the opposite is true. This phenomenon is also observed for adatoms on the (0 0 1) face above 550 K.
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Fig. 6. Temperature dependence of the mean-square-displacements of Cu (®lled symbols) and Au (open symbols) adatoms. Circles and squares stand for the (0 0 1), (1 1 0) faces, respectively.
2.4. Relative interlayer relaxed positions From the calculated relative interlayer relaxed positions (RIRP) of both adatoms on the (0 0 1) and (1 1 0) surfaces, we found that the Cu adatom displays stronger contraction than the Au adatom (Fig. 7). This is compatible with the results of phonon SDs that indicated stronger coupling of
the Cu adatom with the surface in the perpendicular direction. The RIRP for the Cu adatom exhibit linear temperature dependence, whereas anharmonic behaviour is displayed for the Au adatom on the (1 1 0) surface, above Ts . At this high temperature region, both adatoms on the (1 1 0) face are relaxing closer to the surface, compared to those on the (0 0 1) surface. The Cu
Fig. 7. Temperature dependence of the RIRP of Cu (®lled symbols) and Au (open symbols) adatoms with respect to the bulk interlayer spacing. Circles and squares stand for the (0 0 1), (1 1 0) faces, respectively.
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adatom on the (1 1 0) face, already at room temperature, relaxes even beneath the half interlayer distance, while above Ts it can be considered as belonging to the surface layer. This phenomenon has to be related with the general changes found for this face above Ts . As mentioned in Ref. [7], some of the Au surface atoms segregate to relax ®nally in the pure Cu second layer, the surface atoms being displaced outwards. From low-energy diraction experiments on Cu3 Au (1 1 0) [18] it was found that the apparent activation energy of ordering has a value close to that of diusion in Cu3 Au. A diusive mechanism for island formation is therefore possible and it is consolidated by the results given in Ref. [7]. Concerning the adatoms on the (0 0 1) surface, we see that the Cu adatoms are more contracted than Au adatoms. Around Ts , the Au adatom exchanges positions with a surface Cu atom entering in the surface layer. This mechanism could be the beginning of disorder in (0 0 1) face, because it changes locally the order of the surface atoms. The existence of exchange mechanism for Au adatom was also observed in the case of the clean Cu(0 0 1) [4,5], while Cu exchange type diusion on this surface is not favoured [4,5,10,19]. Therefore, the gold adatom behaves dierently than the copper adatom both on pure Cu surface and on the alloy surface, re¯ecting its dierent bonding character.
3. Conclusions In this study we present results concerning the structural and vibrational properties of the Cu and Au adatoms on the ordered low-indexed Cu3 Au faces. We observed that the behaviour of Cu and Au adatoms depends on the substrate, with both adatoms being unstable on the closed packed face, relaxing ®nally on the site of a Cu surface atom that is forced in bulk diusion. For the (1 1 1) face this eect happens already at room temperature, while in the case of (1 0 0) it happens above Ts . In addition, this phenomenon was not observed in the case of adatoms on a clean Cu surface, indicating that in the Cu3 Au alloy surface the presence
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of two kind surface atoms and the rippling eect [7], play an important role in the adatom's behaviour. The presence of both adatoms on the surfaces changes the morphology of the surface phonon density of states by introducing new vibrational modes or altering the existing ones. These new modes are situated in general at higher frequencies than the corresponding surface modes. An exception is coming from the Cu adatom on the (0 0 1) face, where the new modes are almost in the middle of the frequency range. The Cu adatom introduces high frequency modes, the highest one being around 7 THz for the (1 1 0) surface, while Au adatom is responsible for the lower vibrations; the lowest mode is found in the same face around 0.55 THz. Summarising, the vibrational modes of a mixed terminal layer are situated at lower frequencies compared to those of a pure Cu face. On the contrary, the location of the vibrational modes due to adatoms indicates that they are more tightly bound on a mixed terminal layer than on a pure Cu face. From the relaxed positions of the adatoms on the two other faces it came out that they are both contracted, the Cu adatom exhibiting more this eect. Exchange type diusion mechanisms occur above Ts on the (0 0 1) face resulting to the substitution of a Cu surface atom by the Au adatom. This mechanism could accelerate the order±disorder transition. On the (1 1 0) surface the Cu adatom relaxes very close to the surface layer, already at room temperature and it is almost assimilated in the surface layer when approaching Ts . Concerning the Au adatom, contraction is observed that becomes very important above Ts . This result is related with the general behaviour of this face that is characterised by segregation and spontaneous creation of adatoms [7]. In addition, this behaviour is associated with the MSDs of both adatoms that are characterised by strong anharmonicity above Ts . Therefore, Ts appears as a characteristic temperature, above which phenomena, that are also stimulated by the presence of adatoms, set up acting as precursors of the order±disorder transition. It would be of great interest to experimentally verify these new results by suitable methods such
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as ®eld ion microscopy, electron-energy-loss-spectroscopy or thermal helium beam scattering. Acknowledgements Stimulating discussions and constructive criticism of Prof. N.G. Alexandropoulos are gratefully acknowledged. References [1] U. Schoder, R. Linke, J.-H. Boo, K. Wandelt, Surf. Sci. 352 (1996) 211. [2] N.T. Barrett, R. Belchou, J. Thiele, Surf. Sci. 351 (1995) 776. [3] S.M. Foiles, Surf. Sci. 191 (1987) 329. [4] G.A. Evangelakis, G.C. Kallinteris, N.I. Papanicolaou, Surf. Sci. 394 (1997) 185. [5] N.I. Papanicolaou, G.A. Evangelakis, G.C. Kallinteris, in: Gonis et al. (Eds.), Properties of Complex Inorganic Solids, Plenum, New York, 1997, 151.
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