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High-temperature morphology of stepped gold surfaces
Surface Science 280 (1993) 335-348 Noah-Holland
High-temperature
morphology of stepped gold surfaces
G. Bilalbegovi6 a,b-l,F. Ercolessi a and E. Tosatti a*b ’ International School for Advanced Studies, Vii Beirut 4, I-34014 Trieste, Italy b international
Centre for Theoretical Physics, P.O. Box 584, I-34014 Trieste, Italy
Received 2 April 1992; accepted for publication IO September 1992
Molecular dynamics simulations with a classical many-body potential are used to study the high-temperature stability of stepped non-melting metal surfaces. We have studied in particular the A~(1111 vicinal surfaces in the (M+ l,M- 1,M) family and the A~(1001 vicinals in the (M,l,l) family. Some vicinal orientations close to the non-melting Au(ll1) surface become unstable close to the bulk melting temperature and facet into a mixture of crystalline (111) regions and localized surface-melted regions. On the contrary, we do not find high-temperature faceting for vicinals close to Au(1001, also a non-melting surface. These (100) vicinal surfaces gradually disorder with disappearance of individual steps well below the bulk melting temperature. We have also studied the high-temperature stability of ledges formed by pairs of monatomic steps of opposite sign on the A~(1111 surface. It is found that these ledges attract each other, so that several of them merge into one larger ledge, whose edge steps then act as a nucleation site for surface melting.
1. Int~u~tion An important aspect of phase transitions at surfaces, such as roughening [l-3] and surface melting [4-61, is their anisotropy, i.e. crystal face dependence. The existence of different roughening transitions associated with the disappearance of different facets of the same crystal at different temperatures is well known. On the contrary, the anisotropy of surface melting, as well as the interplay between roughening and surface melting although of great current interest - are considerably less understood. Since surface melting is just a specific type of wetting, this problem can be formulated as one of interrelation between roughening and wetting. Statistical mechanics studies [7-91 show that, even in the simplest models of wetting and roughening, different routes for the behavior of an interface are possible. The question of stability of surfaces is connected with the anisotropy of the surface free energy of crystals [l-3,10]. Unstable vicinal sur’ Present address: Ames Laboratory and Department of Chemistry, Iowa State University, Ames, IA 50011, USA.
faces facet and evolve into hill-and-valley structures. Sharp edges are then present on the equilibrium crystal shape. In early experimental investigations of the surface melting anisotropy for crystals, such as Cu and Au, it was found [11,12] that all faces of the hot crystal are covered with melt except for circular areas around (111) and (100) facets, which appear to remain crystalline and flat. Recent ion shadowing and blocking experiments [4,13], as well as scanning electron microscopy measurements [14-171, for Pb crystals also provide strong evidence of surface melting anisotropy. In particular, the open Pb(ll0) surface exhibits a very pronounced surface melting, whereas the closepacked Pb(lll) does not melt. A cylindrical Pb crystal [13] reveals the existence of surface melting for many orientations, except for a well-developed band around the (111) face and, possibly also a zone around (100). Heyraud et al. [14-161, as well as Pavlovska et al. [17], studied extensively the equilibrium shapes of lead crystals in the surface melting temperature region (some percent below T,), They found that the junction between the non-melting (111) facet and the
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rounded, surface melted part of the crystal becomes sharp N 20 K below the bulk melting point. Although a non-melting zone was found also around (loo), the existence of sharp edges cfose to these facets remained unsolved [14-171. Nozieres recently proposed some thermodynamics arguments which suggest that surface melting close to the non-melting face may be induced by the presence of steps on vicinal surfaces [18,191. A generalization of the Wulff construction to the temperatures near the bulk melting point was also presented [ZO]. Yang et al. studied thermal stabiIity of the stepped Pb(ll1) surface [21]. They found that near the bulk melting temperature surface steps appear to suddenly collapse, leaving behind a step-free, flat surface. A possible explanation could be fo~ation of melted drops, or steps collapse to form crystalline microfacets. We present here a molecular dynamics (MD) study of the high-temperature morphology for several stepped surfaces in particular those that are vicinals of the non-melting (111) and (100) faces of gold. In section 2 some details of the MD simulation method are given. Our results for the Au(ll1) vicinal surfaces (presented in section 3) indicate how (111) vicinals are unstable near the bulk melting temperature and facet into the flat (111) region and the surface-melted region. This high-temperature melting-related faceting has been presented and discussed recently by our group [22,23]. On the contrary, the (100) vicinals in the (M,l,l) family (section 51, as well as surfaces with monatomic steps of opposite sign on A~(1111 (section 41, do not facet but show a different type of the step instability at high temperatures. Possible reasons for the different behavior of these surfaces are discussed.
2. ~olecuiar
dynamics
simulation
many-body “glue” potential for Au [25]. This potential was constructed empirically, i.e. in order to reproduce some bulk gold properties and vacancy and surface formation energies. All parameters in the potential were fixed in a previous simulation for bulk gold [25]. The glue Hamiltonian for gold is now very well tested and gives good results for different surface properties and phase transitions, such as surface melting [26,27] and reconstruction [28-301. We use the same potential in the present simulation, in order to investigate the high-temperature behavior of some stepped gold surfaces. Since all parameters of the potential were fixed before [2.5], no arbitrary parameters enter the simulations presented here. We have performed MD simulations for several stepped configurations on Au(ll1) and Au(100). In our MD simulations for vicinal surfaces we use slabs contained by tilted MD boxes together with suitable periodic boundary conditions in two directions. Several bottom layers of the slab are kept fixed in order to mimic the infinite bulk crystal. We start from fully reconstructed surface configurations 128,301 at T = 0 K and then warm up, proceeding at each successive higher temperature from a well-equilibrated configuration at the lower temperature in steps of 100 K and 50 K. The bulk melting temperature CT, = 1355 K) is known from previous MD simulations [25]. The temperature of the system is controlled by resealing particle velocities. The lattice spacing of the samples was changed with temperature according to the expansion coefficient determined in an earlier bulk simulation 1251. Depending on the sample and on the temperature our systems have been equilibrated from at least lo4 up to lo6 MD time steps at each temperature. The time step used in our simulations is 7.14 X 10-r” s.
method
In order to be able to simulate correctly surface properties and phase transitions it is very important to have an accurate description of interatomic forces. It is well known that the pair potentials do not give a correct description of metal surfaces and that it is necessary to include many-body forces [24]. We have used here the
3. High-temperature vicinals
faceting of the Au(ll1)
The Au(1 II) surface reconstructs with an incommensurate, approximately (23 x 6) unit cell 131,321. Recentiy, the state of reconstruction on this surface was studied experimentally between
G. BilalbegociC et al. / High-temperature morphology of stepped gold surfaces
300 and 1250 K and it was found that reconstruction is still present at 0.94T, [32]. The glue potential is the only many-body potential for which the Au(l11) surface reconstruction was reported [30]. MD simulation study shows that, although contractive forces in the model are too large and give a smaller (11 X 6) reconstruction cell, many features of the Au(ll1) surface reconstruction found in experiments are also present for the glue potential [30]. For example, it yields the correct alternance of fee and hcp stacking.
337
Circular black areas around the Au(ll1) facet, indicating non-melting of the Au(ll1) surface and a complicated behavior of vicinais around it, were found in optical emissivity measurements on crystalline gold particles [12]. Non-melting of the Au(ll1) surface was also found in a MD simulation study [263. Sharp edges close to non-melting Pb(ll1) were recently discovered about twenty degrees below the bulk melting temperature [14171. We expect the existence of similar sharp edges on gold crystal shape close to Au(l11) in
(b) Fig. 1. Particle trajectories for the Au(534) vicinal of Au(ll1) at: (a) T = 0.37&,, (b) T = 0.99T,. Our trajectory plots refer to a time span of 10 ps, after an equilibration time up to several ns. Trajectories are observed along (112) and four (112) planes are overlapped in the pictures. The surface exhibits the high-temperature faceting.
the surface melting temperature region. Nozieres presented some thermodynamic arguments [18,19] which may explain the presence of these sharp edges. The competition between melted and non-melted surface free energies produces an unstable region in the orientation of crystal faces.
As is well known, a system eliminates unstable (i.e. non-convex) regions of its free energy by undergoing phase separation into neighboring stable phases 1331. Surface faceting is precisely such a phase separation process. The origin of surface faceting may be diverse including recon-
(b)
Fig. 2. Examples of fluctuations for the high-temperature faceting. The Au(534) surface is shown at T = O.YYT, after: (a) 2.9, Cc)3.6, Cd) 4.6, (e) 5.4, (f) 6.1, (g) 6.4 and (h) 7.1 ns.
1.8,(b)
G. BilalbegociC et al. / High-temperature morphology of stepped gold su$aces
struction [29,37-411, or the presence of adsorbates [42,43]. Our results for the Au(534) surface presented here show that surface faceting at high temperatures is induced in this case by surface melting anisotropy on the crystal shape. We analyse the high-temperature behavior of Au(ll1) vicinal surfaces of the (M + 1,M - 1,Ml family. They consist of the (111) terraces which are infinitely long along the (112) direction and M atoms wide along the (170) direction. It is important in building of MD boxes to consider the proper ABC stacking of the (111) layers in order to have a good match by periodic boundary conditions at the box boundaries. For this reason the number of steps and terraces for Au(ll1) vicinals must be a multiple of 3, the number of (111) sublattices. After some testing we decided to model the Au(ll1) vicinal surfaces using MD boxes with 6 steps and 6 terraces. Although we did in fact carry out MD simulations for a number of Au(ll1) vicinal surfaces, a particularly detailed study was conducted for the Au(534) vicinal and only these results will be shown here as rather typical for all (111) vicinal faces. The similar behavior of the Au(423) [22], as well as a related study for the Pb(ll1) vicinal faces [231 were presented elsewhere. A MD trajectory for the A~(5341 surface at low temperature is shown in fig. la. This face is misoriented by 11.5” with respect to the (111) plane, and the MD box consists of 1440 particles. The same surface at a higher temperature, very close to the melting point is shown in fig. lb. The steps have collapsed together to form surface liquid drops, which gives rise to the high-temperature faceting. The vicinal surface facets into crystalline, flat (111) terraces and surface-melted, droplet-like regions. The liquid drop in fig. lb is tilted by an angle m 14” relative to the flat face. Examples of fluctuations in fig. 2. show that dur-
Fig. 3. Top view for the A&34)
vicinal surface
339
ing our long simulation time (our sample has been equilibrated up to 7.5 ns) the system still fluctuates between different combinations of two phases. Such behavior is common for systems undergoing phase separation [33]. Fig. 3 illustrates the coexistence of “dry” and “wet” regions at the surface. A top view of an MD box (already shown as a side view in fig. 2b) demonstrates that the middle, “dry”, region gradually transforms into “wet” regions at both ends of the picture. For the same MD box, which represents our sample after 2.9 ns of equilibration, we show in fig. 4 that the disordered drop is liquid-like. From the density plot it is possible to see the absence of a layered crystalline density for the disordered region of the MD box. Particle trajectories, shown in figs. 1-3, are made after a long equilibration time ( _ ns), but correspond to a finite “resolution time” of * 10 ps. Since particles not only move during the equilibration time, but also in the 10 ps time intervals, sometimes the (111) oriented facets give the impression of a two-dimensional disordering. This is the consequence of diffusion of the particles along facets. Such diffusion is necessary for a change of surface morphology i.e. surface faceting. Impression of lateral disordering of (1111 facets (even for 10 ps) is increased by the overlaping of four (11% planes in figs. 1 and 2. Surface-melted regions in these figures show some residual crystalline structure. Such quasi-crystallinity, induced by the underlying crystalline periodic potential, also exists for surface-melted regions on flat surfaces [4-61. Differences in the particle diffusion between solid and liquid regions are not only in the intensity, but also in the fact that in liquid regions particles diffuse between different layers as well. The diffusion coefficient for all moving particles in the sample shown in fig. la, at 0.37T,, is 0.029 X lop6 cm2/s, while in fig. lb, i.e. after the high-temper-
at T = 0.99T,,
after 2.9 ns (see also fig. 2b).
340
G. Bilalbegocit
et al. / High-temperature
morphology of stepped gold surfaces
[22,23]. Since this contradicts to the “lever rule” for phase separation on crystal shapes, we suppose that the finite size of MD boxes and in-plane periodic boundary conditions may have a substantial influence on facet sizes and orientations. These effects are difficult to analyse in a quantitative way since, as shown in fig. 2, the non-wetting angles are snapshot values and fluctuations are present even after 7 ns. MD boxes also have a different number of particles which gives rise to a different kinetics in phase separation on simulated vicinal surfaces. It is interesting to discuss the time and the length scale for the high-temperature faceting in “real” experiments. The size of our MD boxes is already rather close to the experimental samples. For example, the MD box shown in fig. lb, with an xy area of - 725 A2 and a slab thickness along the z direction of - 47 A, exhibits faceting after - 1 ns. MD simulation gives the real time system evolution and we expect that experimental samples will behave in a similar way. Since surface faceting can be viewed as a phase separation process, due to the non-lin-
ature faceting at 0.99T,, the same total diffusion coefficient increases up to 2.022 X lop6 cm*/s. Although it is rather difficult to define layers for the complicated, irregular, MD boxes, our estimate for the maximum diffusion coefficient for the whole top layer in fig. lb is 0.242 x 10e3 cm*/s for the surface diffusion and 0.165 x lop3 cm*/s for the volume diffusion in this layer. The maximum values of the diffusion coefficients for individual particles in the melted region (shown in fig. lb) are up to 6 x lop3 cm2/s. Results of our simulations for the high-temperature faceting of Au(ll1) and Pb(ll1) vicinals (see also refs. [22,23]) are, from the quantitative point of view, biased by the finite size and the shape of MD boxes. We expect that the edge effects and the step interactions play a significant role. In particular, we have performed test-simulations for same (111) vicinal surfaces, using MD boxes with 3 and 6 steps, and have noticed a tendency towards different orientations of liquid drops. We also noticed that liquid drops are less tilted for (111) vicinals which are misoriented by smaller angles
.OB -
0
‘IIII’Intt’tl -5
I 0
5
10
15
20
z (8)
Fig. 4. The density plot for the liquid drop shown in fig. 2b.
I,
I
I! 25
I_
G. BilalbegociCet al. / High-temperaturemorphologyof steppedgold surfaces
ear character and the size dependence for phase separation, the complete answer to the question of the time-length scale should be the subject of future studies. Relatively few crystal shape experimental studies are available for Au [12,34-361. Optical measurements on spherical gold particles show only
. . . . . . . . . . ...*.... l
. . . . . . . ..-
.......
..r........
. . . . . . . ..*...............
... ...... . ... .....
,........,L,......
(0)
the existence of non-melting orientations around Au(lll), close to the bulk melting point 1121. Equilibrium crystal shape experiments for gold were done at lower temperatures (1273 K in refs. [34,351 and 1303 K in ref. 1361). These experiments show the existence of reconstruction related sharp edges and instabilities (see also ref. Ill). Heyraud and Metois found that gold shape at T = 1273 K [34,35] is closer to a sphere than the shape in the Winterbottom-Gjostein experiment at T = 1303 K [36]. This is in contradiction with the expectation that, due to a roughening transition [l-3], crystal shapes become more rounded at higher temperatures. That might be the sign of surface melting-induced anisotropies at higher temperatures. Obviously, close to the bulk melting point, surface melting should make a pronounced influence on equilibrium crystal shapes, as already was found in experiments on Pb [14-171. On the basis of our results we expect similar results for Au. The detailed investigation of equilibrium crystal shape of gold at high temperatures and of interplay between surface reconstruction and surface melting induced sharp edges will hopefully be the subject of future experiments.
4. Behavior of unlike Au(ll1) surface
Fig. 5. MD trajectories showing a slab with unlike steps on Au(ll1) after 0.07 ns at: (a) T = 0.22, (b) 0.73, (c) 0.81 and (d) 0.99 X 7”. Note the attraction of the steps and the absence of faceting.
341
steps and ledges on the
Yang et al. performed the high-resolution LEED study of the stepped Pb(ll1) surface [21]. They found that at 20 K below the bulk melting point steps collapse and the surface “appears to be extremely flat”. We propose that the observed thermal step collapsing is due to the high-temperature faceting. The stepped surface in ref. [21] was characterized by an average terrace width. Different stepped configurations may give the same average terrace width. Steps of the same and the opposite sign are possible on real stepped surfaces. These steps may be induced by miscuts and different types of defects and inhomogeneities during surface preparation. Motivated by the experiment of ref. 1211we decided to check the high-temperature stability of steps of opposite sign.
342
G. Bilalbegoric’
et al. / High-temperature morphology of stepped gold surfaces
In this MD simulation the slab consists of 12 (111) layers and a total of 828 particles. We have 72 particles per layer, except for the topmost layer of the slab, which is made of three monatomic, 3 atoms wide ledges. Our MD box at T = 0.22T, is shown in fig. 5a. Clearly, this configuration is more “stepped” than most real surfaces found in experiments. It was chosen in order to be close to the Au{4231 vicinal, where a previous MD study showed a very pronounced high-temperature faceting /22]. On the contrary, we find here that the stepped surface in fig. Sa does not facet, but exhibits a different type of high-temperature instability. Particles in the top layer of rhe configuration shown in fig. 5a perform a collective motion on the surface, i.e. the whole step diffuses with a small exchange of particles with the underlying Au(3 11) substrate. A similar motion of single columns of gold atoms added on the Au(lll) surface was observed by high-resolution electron microscopy [44]. In our simulation steps appear to attract each other and the two ledges merge into a larger one as shown in fig. 5b. At higher temperatures the third ledge joins them (fig. 519 While the ff at Au(ll1) surface shows overheating, i.e. it melts N 100 K above the bulk melting point for our potential [.X1, local meIting and droplet formation does start at the edges of the large ledge below the bulk melting point (fig. 5d). In conclusion, the results presented in this section show that, although the steps attract each other, the stepped Au(Ill) surface with monatomic steps of the opposite sign does not exhibit the high-temperature faceting.
5. High-temperature vicinals
(100) faces we have also performed
MD simulations for the Au(100) vicinal surfaces. The Au(100) surface reconstructs at low temperatures into an incommensurate hexagonal
(0)
(b)
behavior of the Au(100)
In experimental studies of crystals at high temperatures it was found that some orientations around (100) faces do not exhibit surface melting 11l-1 71. The existence of sharp edges, indicating the presence of high-temperature faceting for (100) vicinals, is not conclusive. Prompted by the unexplained high-temperature behavior around
Fig. 6. Particle trajectories for the AuCJ I,l,l)vicinal of Au(,lOO) at: (a) 7’= 0.3, (b) 0.66 and Cc) 0.73 x T,,. This surface gradually disorders with temperature.
after 0.36 ns
first-layer structure sitting on top of square bulk lattice. Recent X-ray diffraction studies I45 461 have shown that domains of distorted slightly rotated hexagonal reconstructed phase exist between 300 and 970 K. This phase undergoes a tranSitiOn at 970 K into an unrotated distorted hexagonal phase which then disorders at 1170 K. MD simulation for the Au(100) surface reconstruction showed that the optimal structure for our potential at T = 0 K is 34 x 5, and all (M x 5) 28 SMS 40, give a very small difference in the’ surface energy [281.We are interested here in the high-temperature properties of the Au(l00) surface smce these properties determine the high-
343
temperature morphology of the Au(100) vicinals. Recently, a MD simulation study of the high-temperature disordering of the Au(l#) surface was performed [471.It was found that the top layers disorder, but the A~(1001 surface does not melt. The Au(100) vicinal surfaces were also studied re=ntjy LXW,411 and it was found that reconstruction induces the presence of favored par& ularly stable vicinals. MD simulation s&y (with the “glue” potential) for the T = 0 structure and the energetics of gold vicinals has shown that on these “magic” vicinal surfaces, terraces contain an integer number of reconstruction celts [29J It was found that the particularly stable AU(&)
‘(b) Fig. 7. The Au(l~l,l)
viciml WfaCe
at T= C?.99T, after: (a) 0.34
(d) (h) 0.71, (c) 1.07 and (d) 1.43
high-temperature faceting.
nS. The surface does not exhibit the
344
G. Bilalbqoci6
et al. / H’ hK temDeratm
vicinals are: (ll,l,l), (511) and (311). This result agrees with JXED 1391 and scanning tunneling microscoPY [411 studies of the Au(100) vicinals and periodic profiles. Non-magic vicinal surfaces facet into a suitable combination of magic vicinals and of flat (100). Th’ 1s reconstruction-induced faceting takes place at much lower temperatures
Fk
8. Particle
Wakxtoriesfor Liquid-k
the A~(91 I) vjcinaf of A”( 100) after 0.36 diffusion at high-temperatures
morpholoRv of stepped gold surfa,-esy
than the faceting of the Au(ll1) vicinals de_ scribed in section 3. Recently, reconstruction in_ duced faceting for the (111) vicinajs was studied at T- O.ST, 1401. It was found that while some Au(ll1) vicinak are unstable and facet vicinals of unreconstructed Pb(l11) remain stabie under the same conditions. Therefore the Au(lll) vici_
Cd)
is located mainly in the two topmost layers, ns at: (a) I-‘= 0.81, (b) 0.92, (c) 0.95 and (d) 0.‘)~ x T,,
G. Bilalbegocic’ et al. / High-temperature morphology of stepped gold surfaces
(b) Fig. 9. Snapshot of the MD slab for the Au(29,1,1) vicinal of Au(100). A side view of two MD boxes is shown at: (a) T = 0 (ideal sample) and (b) T = O.l5T,,, after 1.43 ns. This unstable vicinal surface exhibits reconstruction induced faceting at very low temperatures.
nals show reconstruction-induced faceting as well as a high-temperature faceting. It is important to find out whether the Au(100) vicinals (which show the reconstruction induced faceting) also exhibit the high-temperature faceting. We simulate here the Au(100) vicinal surfaces in the (M,l,l) family 04 odd). They consist of the (100) terraces, infinitely long along the (001) direction and 04 + 1)/2 atoms wide along the (011) direction. Due to the two-sublattice structure of the Au(100) surface the number of steps and terraces in periodically replicated MD boxes which represent the A~(1001 vicinals must be a multiple of 2. We choose here MD boxes with 2 steps and 2 terraces. MD trajectories for the magic Au(ll,l,l) vicinal surface are shown in figs. 6 and 7. This vicinal is misoriented by 6.7” from the (100) plane and the MD box consists of 752 particles. Fig. 7 shows that the high-temperature morphology of this surface does not change much with MD simulation time. Local melting fluctuations appear to take place, which make the two outermost layers very liquid-like close to T,. We have also studied the Au(911) vicinal misoriented
34.5
by 8” from the (100) plane, with 628 particles (shown in fig. 8) and the Au(29,lJ) vicinal misoriented by 2.7”, with 1884 particles (shown in figs. 9 and 10. The results for the Au(29,1,1) vicinal confirm the MD study for the T = 0 surface energetics of the Au(100) vicinals [291. This non-magic vicinal is unstable and, if prepared as an ideal sample at T = 0 (fig. 9a), facets immediately (i.e. after a very short simulation time) even at a low temperature (fig. 9b). We expect that the process of reconstruction induced faceting in our MD simulation at these low temperatures is not complete due to the limited diffusion. By contrast, the two other Au(100) vicinals we have studied, namely Au(ll,l,l) and Au(910, are stable at low temperature, i.e. do not undergo reconstruction induced faceting. They eventually disorder with temperature, as shown by figs. 6-8,
(0)
(b)
(cl Fig. 10. Particle trajectories for the Au(29,1,1) vicinal after 1.43 ns, at: (a) T = 0.81, (b) 0.95 and (c) 0.99~ T,,. The surface undergoes reconstruction induced faceting at low temperatures (see fig. 9) and then the two topmost layers disorder at high temperatures.
346
G. LGlaibegocic’et al. / Hogs-temperature rnorp~~l~~ of stepped gold surfaces
and steps disappear (but do not collapse) around T = 0.6T,. At higher temperatures the surfaces deconstruct and several top layers become compietely disordered. These surfaces do not exhibit proper surface melting close to the bulk melting point, in accordance with our results for the high-temperature properties of the Au(100) surface [47]. The density plot for the top of the Am91 1) vicinal surface shown in fig. 11 illustrates the fact that the layered structure is present up to the bulk melting point. The results for the high-temperature morphology of the Au(100) vicinals in the (M,l,l) family CM odd) show that these vicinals do not exhibit the high-temperature faceting. We are not definitely able to rule out the presence of sharp edges on the crystal shape close to Au(lOO~ in the surface melting temperature region, since there remains a possibility of high-temperature faceting for some other vicinal families not studied here. However, we feel this is an unlikely possibility. The reason is that lack of faceting for our (100)
vicinal surfaces appears to be tied to the hightemperature disordering of the two uppermost layers of the flat (100) surface, a phenomenon which does not occur on the stable reconstructed (111). If this is true, then non-faceting at high temperatures is a property of (100) and will be true for all vicinals. As a counterexample, we can however recall the behavior of Sic11 1) vicinal surfaces. In experimental studies of the reconstruction induced faceting for the Sit1 11) vicinals it was found that some of them are unstable due to the (7 x 7) --+(1 X 1) reconstruction on terraces and facet into the reconstructed flat (111) regions and regions with a high step density 137,381. Still, one Si(lll) vicinal family is found not to facet under the same conditions, but to exhibit a tripling of the step height at the (1 x 1) + (7 x 7) transition 2481.Thus the reconstruction induced faceting for the Sit1 11) vicinals is strongly dependent on the interaction between the terrace reconstruction and the step orientation. Whether such dependence also exists for the high-temper-
Fig. 11. The density plot for the A491 1) vicinal shown in fig. Xd
G. Bilalbegocic? et al. / High-temperature morphology of stepped gold surfaces
ature faceting, i.e. the study of the high-temperature morphology for other (100) and (111) vicinal families, must therefore be left for future work.
6. Conclusions We have shown by direct MD simulation that near the bulk melting temperature some Au(ll1) vicinal surfaces should be unstable and facet into flat (111) surface regions and tilted surface melted drops where surface diffusion is of a liquid type. This high-temperature faceting is induced by the surface melting anisotropy, i.e. the presence of both melting and non-melting faces on the crystal shape in the vicinity of unstable vicinal surfaces. On the contrary, vicinal surfaces of the (M,l,l) family (M odd), close to Au(100) do not facet near the bulk melting point. There steps disappear without collapsing well below the bulk melting temperature. High-temperature faceting is also absent for unlike monatomic steps on the Au(ll1) surface. We expect a similar high-temperature morphology for stepped surfaces of other fee metals.
References
[ll M. Wortis, in: Chemistry and Physics of Solid Surfaces, Vol. 7, Eds. R. Vanselow and R. Howe (Springer, Berlin, 1988) p. 367. Bl H. van Beijeren and I. Nolden, in: Structure and Dynamics of Surfaces II, Eds. W. Schommers and P. Blanckenhagen (Springer, Berlin, 1987) p. 259. [31 R.K.P. Zia, in: Progress in Statistical Mechanics, Ed. C.K. Hu (World Scientific, Singapore, 1988) p. 303. 141 J.F. van der Veen, B. Pluis and A.W. Denier van der Gon, in: Chemistry and Physics of Solid Surfaces, Vol. 7, Eds. R. Vanselow and R. Howe (Springer, Berlin, 1988) p. 455. [51 J.G. Dash, in: Proceedings of the Solvay Conference on Surface Science, Ed. F.W. de Wette (Springer, New York, 1988) p. 142. [61E. Tosatti, in: The Structure of Surfaces II, Eds. J.F. van der Veen and M.A. van Hove (Springer, Berlin, 1988) p. 535. [71 R. Pandit, M. Schick and M. Wortis, Phys. Rev. B 26 (1982) 5112. Is1 A.C. Levi and E. Tosatti, Surf. Sci. 178 (1986) 425.
347
[9] G. Bilalbegovic, V. Privman and N.M. Svrakic, J. Phys. A 22 (1989) L833. [lo] C. Herring, Phys. Rev. 82 (1951) 87. [ll] K.D. Stock and E. Menzel, J. Cryst. Growth 43 (1978) 135. [12] K.D. Stock and B. Grosser, J. Cryst. Growth 50 (1980) 485. [13] B. Pluis, A.W. Denier van der Gon, J.W.M. Frenken and J.F. van der Veen, Phys. Rev. Lett. 59 (1987) 2678. [14] J.C. Heyraud, J.J. Metois and J.M. Bermond, J. Cryst. Growth 98 (1989) 355. [15] J.J. Metois and J.C. Heyraud, Ultramicroscopy 31 (1989) [16] ::. Mttois and J.C. Heyraud, J. Phys. (Paris) 50 (1989) 3175. [17] A. Pavlovska, K. Faulien and E. Bauer, Surf. Sci. 221 (1989) 233. [18] P. Nozieres, J. Phys. (Paris) 50 (1989) 2541. [19] P. Nozieres, Shape and Growth of Crystals, Proceedings of the 1989 Beg-Rohu School (Cambridge University Press, Cambridge, 1991). [20] H. Liiwen, Surf. Sci. 234 (1990) 315. [21] H.N. Yang, T.M. Lu and G.C. Wang, Phys. Rev. Lett. 62 (1989) 2148. [22] G. Bilalbegovic, F. Ercolessi and E. Tosatti, Surf. Sci. Len. 258 (1991) L676. [23] G. Bilalbegovic, F. Ercolessi and E. Tosatti, Europhys. Lett. 17 (1992) 333. [24] R.M. Nieminen, M.J. Puska and M.J. Manninen, Eds., Many-Atom Interactions in Solids (Springer, Berlin, 1990). 1251 F. Ercolessi, M. Parrinello and E. Tosatti, Phil. Mag. A 58 (1988) 213. 1261 P. Carnevali, F. Ercolessi and E. Tosatti, Phys. Rev. B 36 (1987) 6701. [27] F. Ercolessi, S. Iarlori, 0. Tomagnini, E. Tosatti and X.J. Chen, Surf. Sci. 251/252 (1991) 645. [28] F. Ercolessi, E. Tosatti and M. Parrinello, Phys. Rev. Lett. 57 (1986) 719. [29] A. Bartolini, F. Ercolessi and E. Tosatti, Phys. Rev. Lett. 63 (1989) 872. [30] A. Bartolini, F. Ercolessi and E. Tosatti, in: The Structure of Surfaces II, Eds. J.F. van der Veen and M.A. Van Hove (Springer, Berlin, 1988) p. 132. [31] J.V. Barth, H. Brune, G. Ertl and R.J. Behm, Phys. Rev. B 42 (1990) 9307, and references therein. [32] A.R. Sandy, S.G.J. Mochrie, D.M. Zehner, K.G. Huang and D. Gibbs, Phys. Rev. B 43 (1991) 4667, and references therein. 1331J.D. Gunton, M. San Miguel and P. Sahni, in: Phase Transitions and Critical Phenomena, Vol. 8, Eds. C. Domb and J.L. Lebowitz (Academic Press, London, 1983) p. 267. 1341J.C. Heyraud and J.J. Metois, J. Cryst. Growth 50 (1980) 571. 1351J.C. Heyraud and J.J. Metois, Acta Metal]. 28 (1980) 1789.
348 [36] W.L. Winterbottom,
[37] f38] [39] [40] [41] [42]
in: Surfaces and Interfaces I, Eds. J.J. Burke, W.L. Reed and V. Weiss (Syracuse University Press, New York, 1967) p. 133. R.J. Phaneuf and E.D. Williams, Phys. Rev. Lett. 58 (1987) 2563. R.J. Phaneuf, E.D. Williams and N.C. Bartett, Phys. Rev. B 38 (1988) 1984. M. Sotto and J.C. Boulliard, Surf. Sci. 214 (1989) 97. G. Bilalbegovi& F. Ercolessi and E. Tosatti, Europhys. Lett. 18 (1992) 163. H.P. Bonzel, U. Breuer, B. Voigtlander and E. Zeldov, Surf. Sci. 272 (1992) 10. M. Flytzani-Stephanopoulos and L.D. Schmidt, Prog. Surf. Sci. 9 (1979) 83.
1431 M. Drechsler, Surf. Sci. 286 (1992) 1. [44] J.O. Malm and J.O. Bovin, Surf. Sci. 200 (1988) 67. 1451 S.G.J. Mochrie, D.M. Zehner, B.M. Ocko and D. Gibbs, Phys. Rev. Lett. 64 (1990) 2925. [46] B.M. Ocko, D. Gibbs, K.G. Huang, D.M. Zehner and S.G.J. Mochrie, Phys. Rev. B 44 (1991) 6429, and references therein. 147) G. Bilalbegovi& F. Ercolessi and E. Tosatti, to be published. [48] R.J. Phaneuf and E.D. Williams, Phys. Rev. B 41 (1990) 2991.
High-temperature
morphology of stepped gold surfaces
G. Bilalbegovi6 a,b-l,F. Ercolessi a and E. Tosatti a*b ’ International School for Advanced Studies, Vii Beirut 4, I-34014 Trieste, Italy b international
Centre for Theoretical Physics, P.O. Box 584, I-34014 Trieste, Italy
Received 2 April 1992; accepted for publication IO September 1992
Molecular dynamics simulations with a classical many-body potential are used to study the high-temperature stability of stepped non-melting metal surfaces. We have studied in particular the A~(1111 vicinal surfaces in the (M+ l,M- 1,M) family and the A~(1001 vicinals in the (M,l,l) family. Some vicinal orientations close to the non-melting Au(ll1) surface become unstable close to the bulk melting temperature and facet into a mixture of crystalline (111) regions and localized surface-melted regions. On the contrary, we do not find high-temperature faceting for vicinals close to Au(1001, also a non-melting surface. These (100) vicinal surfaces gradually disorder with disappearance of individual steps well below the bulk melting temperature. We have also studied the high-temperature stability of ledges formed by pairs of monatomic steps of opposite sign on the A~(1111 surface. It is found that these ledges attract each other, so that several of them merge into one larger ledge, whose edge steps then act as a nucleation site for surface melting.
1. Int~u~tion An important aspect of phase transitions at surfaces, such as roughening [l-3] and surface melting [4-61, is their anisotropy, i.e. crystal face dependence. The existence of different roughening transitions associated with the disappearance of different facets of the same crystal at different temperatures is well known. On the contrary, the anisotropy of surface melting, as well as the interplay between roughening and surface melting although of great current interest - are considerably less understood. Since surface melting is just a specific type of wetting, this problem can be formulated as one of interrelation between roughening and wetting. Statistical mechanics studies [7-91 show that, even in the simplest models of wetting and roughening, different routes for the behavior of an interface are possible. The question of stability of surfaces is connected with the anisotropy of the surface free energy of crystals [l-3,10]. Unstable vicinal sur’ Present address: Ames Laboratory and Department of Chemistry, Iowa State University, Ames, IA 50011, USA.
faces facet and evolve into hill-and-valley structures. Sharp edges are then present on the equilibrium crystal shape. In early experimental investigations of the surface melting anisotropy for crystals, such as Cu and Au, it was found [11,12] that all faces of the hot crystal are covered with melt except for circular areas around (111) and (100) facets, which appear to remain crystalline and flat. Recent ion shadowing and blocking experiments [4,13], as well as scanning electron microscopy measurements [14-171, for Pb crystals also provide strong evidence of surface melting anisotropy. In particular, the open Pb(ll0) surface exhibits a very pronounced surface melting, whereas the closepacked Pb(lll) does not melt. A cylindrical Pb crystal [13] reveals the existence of surface melting for many orientations, except for a well-developed band around the (111) face and, possibly also a zone around (100). Heyraud et al. [14-161, as well as Pavlovska et al. [17], studied extensively the equilibrium shapes of lead crystals in the surface melting temperature region (some percent below T,), They found that the junction between the non-melting (111) facet and the
0039~602&/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
rounded, surface melted part of the crystal becomes sharp N 20 K below the bulk melting point. Although a non-melting zone was found also around (loo), the existence of sharp edges cfose to these facets remained unsolved [14-171. Nozieres recently proposed some thermodynamics arguments which suggest that surface melting close to the non-melting face may be induced by the presence of steps on vicinal surfaces [18,191. A generalization of the Wulff construction to the temperatures near the bulk melting point was also presented [ZO]. Yang et al. studied thermal stabiIity of the stepped Pb(ll1) surface [21]. They found that near the bulk melting temperature surface steps appear to suddenly collapse, leaving behind a step-free, flat surface. A possible explanation could be fo~ation of melted drops, or steps collapse to form crystalline microfacets. We present here a molecular dynamics (MD) study of the high-temperature morphology for several stepped surfaces in particular those that are vicinals of the non-melting (111) and (100) faces of gold. In section 2 some details of the MD simulation method are given. Our results for the Au(ll1) vicinal surfaces (presented in section 3) indicate how (111) vicinals are unstable near the bulk melting temperature and facet into the flat (111) region and the surface-melted region. This high-temperature melting-related faceting has been presented and discussed recently by our group [22,23]. On the contrary, the (100) vicinals in the (M,l,l) family (section 51, as well as surfaces with monatomic steps of opposite sign on A~(1111 (section 41, do not facet but show a different type of the step instability at high temperatures. Possible reasons for the different behavior of these surfaces are discussed.
2. ~olecuiar
dynamics
simulation
many-body “glue” potential for Au [25]. This potential was constructed empirically, i.e. in order to reproduce some bulk gold properties and vacancy and surface formation energies. All parameters in the potential were fixed in a previous simulation for bulk gold [25]. The glue Hamiltonian for gold is now very well tested and gives good results for different surface properties and phase transitions, such as surface melting [26,27] and reconstruction [28-301. We use the same potential in the present simulation, in order to investigate the high-temperature behavior of some stepped gold surfaces. Since all parameters of the potential were fixed before [2.5], no arbitrary parameters enter the simulations presented here. We have performed MD simulations for several stepped configurations on Au(ll1) and Au(100). In our MD simulations for vicinal surfaces we use slabs contained by tilted MD boxes together with suitable periodic boundary conditions in two directions. Several bottom layers of the slab are kept fixed in order to mimic the infinite bulk crystal. We start from fully reconstructed surface configurations 128,301 at T = 0 K and then warm up, proceeding at each successive higher temperature from a well-equilibrated configuration at the lower temperature in steps of 100 K and 50 K. The bulk melting temperature CT, = 1355 K) is known from previous MD simulations [25]. The temperature of the system is controlled by resealing particle velocities. The lattice spacing of the samples was changed with temperature according to the expansion coefficient determined in an earlier bulk simulation 1251. Depending on the sample and on the temperature our systems have been equilibrated from at least lo4 up to lo6 MD time steps at each temperature. The time step used in our simulations is 7.14 X 10-r” s.
method
In order to be able to simulate correctly surface properties and phase transitions it is very important to have an accurate description of interatomic forces. It is well known that the pair potentials do not give a correct description of metal surfaces and that it is necessary to include many-body forces [24]. We have used here the
3. High-temperature vicinals
faceting of the Au(ll1)
The Au(1 II) surface reconstructs with an incommensurate, approximately (23 x 6) unit cell 131,321. Recentiy, the state of reconstruction on this surface was studied experimentally between
G. BilalbegociC et al. / High-temperature morphology of stepped gold surfaces
300 and 1250 K and it was found that reconstruction is still present at 0.94T, [32]. The glue potential is the only many-body potential for which the Au(l11) surface reconstruction was reported [30]. MD simulation study shows that, although contractive forces in the model are too large and give a smaller (11 X 6) reconstruction cell, many features of the Au(ll1) surface reconstruction found in experiments are also present for the glue potential [30]. For example, it yields the correct alternance of fee and hcp stacking.
337
Circular black areas around the Au(ll1) facet, indicating non-melting of the Au(ll1) surface and a complicated behavior of vicinais around it, were found in optical emissivity measurements on crystalline gold particles [12]. Non-melting of the Au(ll1) surface was also found in a MD simulation study [263. Sharp edges close to non-melting Pb(ll1) were recently discovered about twenty degrees below the bulk melting temperature [14171. We expect the existence of similar sharp edges on gold crystal shape close to Au(l11) in
(b) Fig. 1. Particle trajectories for the Au(534) vicinal of Au(ll1) at: (a) T = 0.37&,, (b) T = 0.99T,. Our trajectory plots refer to a time span of 10 ps, after an equilibration time up to several ns. Trajectories are observed along (112) and four (112) planes are overlapped in the pictures. The surface exhibits the high-temperature faceting.
the surface melting temperature region. Nozieres presented some thermodynamic arguments [18,19] which may explain the presence of these sharp edges. The competition between melted and non-melted surface free energies produces an unstable region in the orientation of crystal faces.
As is well known, a system eliminates unstable (i.e. non-convex) regions of its free energy by undergoing phase separation into neighboring stable phases 1331. Surface faceting is precisely such a phase separation process. The origin of surface faceting may be diverse including recon-
(b)
Fig. 2. Examples of fluctuations for the high-temperature faceting. The Au(534) surface is shown at T = O.YYT, after: (a) 2.9, Cc)3.6, Cd) 4.6, (e) 5.4, (f) 6.1, (g) 6.4 and (h) 7.1 ns.
1.8,(b)
G. BilalbegociC et al. / High-temperature morphology of stepped gold su$aces
struction [29,37-411, or the presence of adsorbates [42,43]. Our results for the Au(534) surface presented here show that surface faceting at high temperatures is induced in this case by surface melting anisotropy on the crystal shape. We analyse the high-temperature behavior of Au(ll1) vicinal surfaces of the (M + 1,M - 1,Ml family. They consist of the (111) terraces which are infinitely long along the (112) direction and M atoms wide along the (170) direction. It is important in building of MD boxes to consider the proper ABC stacking of the (111) layers in order to have a good match by periodic boundary conditions at the box boundaries. For this reason the number of steps and terraces for Au(ll1) vicinals must be a multiple of 3, the number of (111) sublattices. After some testing we decided to model the Au(ll1) vicinal surfaces using MD boxes with 6 steps and 6 terraces. Although we did in fact carry out MD simulations for a number of Au(ll1) vicinal surfaces, a particularly detailed study was conducted for the Au(534) vicinal and only these results will be shown here as rather typical for all (111) vicinal faces. The similar behavior of the Au(423) [22], as well as a related study for the Pb(ll1) vicinal faces [231 were presented elsewhere. A MD trajectory for the A~(5341 surface at low temperature is shown in fig. la. This face is misoriented by 11.5” with respect to the (111) plane, and the MD box consists of 1440 particles. The same surface at a higher temperature, very close to the melting point is shown in fig. lb. The steps have collapsed together to form surface liquid drops, which gives rise to the high-temperature faceting. The vicinal surface facets into crystalline, flat (111) terraces and surface-melted, droplet-like regions. The liquid drop in fig. lb is tilted by an angle m 14” relative to the flat face. Examples of fluctuations in fig. 2. show that dur-
Fig. 3. Top view for the A&34)
vicinal surface
339
ing our long simulation time (our sample has been equilibrated up to 7.5 ns) the system still fluctuates between different combinations of two phases. Such behavior is common for systems undergoing phase separation [33]. Fig. 3 illustrates the coexistence of “dry” and “wet” regions at the surface. A top view of an MD box (already shown as a side view in fig. 2b) demonstrates that the middle, “dry”, region gradually transforms into “wet” regions at both ends of the picture. For the same MD box, which represents our sample after 2.9 ns of equilibration, we show in fig. 4 that the disordered drop is liquid-like. From the density plot it is possible to see the absence of a layered crystalline density for the disordered region of the MD box. Particle trajectories, shown in figs. 1-3, are made after a long equilibration time ( _ ns), but correspond to a finite “resolution time” of * 10 ps. Since particles not only move during the equilibration time, but also in the 10 ps time intervals, sometimes the (111) oriented facets give the impression of a two-dimensional disordering. This is the consequence of diffusion of the particles along facets. Such diffusion is necessary for a change of surface morphology i.e. surface faceting. Impression of lateral disordering of (1111 facets (even for 10 ps) is increased by the overlaping of four (11% planes in figs. 1 and 2. Surface-melted regions in these figures show some residual crystalline structure. Such quasi-crystallinity, induced by the underlying crystalline periodic potential, also exists for surface-melted regions on flat surfaces [4-61. Differences in the particle diffusion between solid and liquid regions are not only in the intensity, but also in the fact that in liquid regions particles diffuse between different layers as well. The diffusion coefficient for all moving particles in the sample shown in fig. la, at 0.37T,, is 0.029 X lop6 cm2/s, while in fig. lb, i.e. after the high-temper-
at T = 0.99T,,
after 2.9 ns (see also fig. 2b).
340
G. Bilalbegocit
et al. / High-temperature
morphology of stepped gold surfaces
[22,23]. Since this contradicts to the “lever rule” for phase separation on crystal shapes, we suppose that the finite size of MD boxes and in-plane periodic boundary conditions may have a substantial influence on facet sizes and orientations. These effects are difficult to analyse in a quantitative way since, as shown in fig. 2, the non-wetting angles are snapshot values and fluctuations are present even after 7 ns. MD boxes also have a different number of particles which gives rise to a different kinetics in phase separation on simulated vicinal surfaces. It is interesting to discuss the time and the length scale for the high-temperature faceting in “real” experiments. The size of our MD boxes is already rather close to the experimental samples. For example, the MD box shown in fig. lb, with an xy area of - 725 A2 and a slab thickness along the z direction of - 47 A, exhibits faceting after - 1 ns. MD simulation gives the real time system evolution and we expect that experimental samples will behave in a similar way. Since surface faceting can be viewed as a phase separation process, due to the non-lin-
ature faceting at 0.99T,, the same total diffusion coefficient increases up to 2.022 X lop6 cm*/s. Although it is rather difficult to define layers for the complicated, irregular, MD boxes, our estimate for the maximum diffusion coefficient for the whole top layer in fig. lb is 0.242 x 10e3 cm*/s for the surface diffusion and 0.165 x lop3 cm*/s for the volume diffusion in this layer. The maximum values of the diffusion coefficients for individual particles in the melted region (shown in fig. lb) are up to 6 x lop3 cm2/s. Results of our simulations for the high-temperature faceting of Au(ll1) and Pb(ll1) vicinals (see also refs. [22,23]) are, from the quantitative point of view, biased by the finite size and the shape of MD boxes. We expect that the edge effects and the step interactions play a significant role. In particular, we have performed test-simulations for same (111) vicinal surfaces, using MD boxes with 3 and 6 steps, and have noticed a tendency towards different orientations of liquid drops. We also noticed that liquid drops are less tilted for (111) vicinals which are misoriented by smaller angles
.OB -
0
‘IIII’Intt’tl -5
I 0
5
10
15
20
z (8)
Fig. 4. The density plot for the liquid drop shown in fig. 2b.
I,
I
I! 25
I_
G. BilalbegociCet al. / High-temperaturemorphologyof steppedgold surfaces
ear character and the size dependence for phase separation, the complete answer to the question of the time-length scale should be the subject of future studies. Relatively few crystal shape experimental studies are available for Au [12,34-361. Optical measurements on spherical gold particles show only
. . . . . . . . . . ...*.... l
. . . . . . . ..-
.......
..r........
. . . . . . . ..*...............
... ...... . ... .....
,........,L,......
(0)
the existence of non-melting orientations around Au(lll), close to the bulk melting point 1121. Equilibrium crystal shape experiments for gold were done at lower temperatures (1273 K in refs. [34,351 and 1303 K in ref. 1361). These experiments show the existence of reconstruction related sharp edges and instabilities (see also ref. Ill). Heyraud and Metois found that gold shape at T = 1273 K [34,35] is closer to a sphere than the shape in the Winterbottom-Gjostein experiment at T = 1303 K [36]. This is in contradiction with the expectation that, due to a roughening transition [l-3], crystal shapes become more rounded at higher temperatures. That might be the sign of surface melting-induced anisotropies at higher temperatures. Obviously, close to the bulk melting point, surface melting should make a pronounced influence on equilibrium crystal shapes, as already was found in experiments on Pb [14-171. On the basis of our results we expect similar results for Au. The detailed investigation of equilibrium crystal shape of gold at high temperatures and of interplay between surface reconstruction and surface melting induced sharp edges will hopefully be the subject of future experiments.
4. Behavior of unlike Au(ll1) surface
Fig. 5. MD trajectories showing a slab with unlike steps on Au(ll1) after 0.07 ns at: (a) T = 0.22, (b) 0.73, (c) 0.81 and (d) 0.99 X 7”. Note the attraction of the steps and the absence of faceting.
341
steps and ledges on the
Yang et al. performed the high-resolution LEED study of the stepped Pb(ll1) surface [21]. They found that at 20 K below the bulk melting point steps collapse and the surface “appears to be extremely flat”. We propose that the observed thermal step collapsing is due to the high-temperature faceting. The stepped surface in ref. [21] was characterized by an average terrace width. Different stepped configurations may give the same average terrace width. Steps of the same and the opposite sign are possible on real stepped surfaces. These steps may be induced by miscuts and different types of defects and inhomogeneities during surface preparation. Motivated by the experiment of ref. 1211we decided to check the high-temperature stability of steps of opposite sign.
342
G. Bilalbegoric’
et al. / High-temperature morphology of stepped gold surfaces
In this MD simulation the slab consists of 12 (111) layers and a total of 828 particles. We have 72 particles per layer, except for the topmost layer of the slab, which is made of three monatomic, 3 atoms wide ledges. Our MD box at T = 0.22T, is shown in fig. 5a. Clearly, this configuration is more “stepped” than most real surfaces found in experiments. It was chosen in order to be close to the Au{4231 vicinal, where a previous MD study showed a very pronounced high-temperature faceting /22]. On the contrary, we find here that the stepped surface in fig. Sa does not facet, but exhibits a different type of high-temperature instability. Particles in the top layer of rhe configuration shown in fig. 5a perform a collective motion on the surface, i.e. the whole step diffuses with a small exchange of particles with the underlying Au(3 11) substrate. A similar motion of single columns of gold atoms added on the Au(lll) surface was observed by high-resolution electron microscopy [44]. In our simulation steps appear to attract each other and the two ledges merge into a larger one as shown in fig. 5b. At higher temperatures the third ledge joins them (fig. 519 While the ff at Au(ll1) surface shows overheating, i.e. it melts N 100 K above the bulk melting point for our potential [.X1, local meIting and droplet formation does start at the edges of the large ledge below the bulk melting point (fig. 5d). In conclusion, the results presented in this section show that, although the steps attract each other, the stepped Au(Ill) surface with monatomic steps of the opposite sign does not exhibit the high-temperature faceting.
5. High-temperature vicinals
(100) faces we have also performed
MD simulations for the Au(100) vicinal surfaces. The Au(100) surface reconstructs at low temperatures into an incommensurate hexagonal
(0)
(b)
behavior of the Au(100)
In experimental studies of crystals at high temperatures it was found that some orientations around (100) faces do not exhibit surface melting 11l-1 71. The existence of sharp edges, indicating the presence of high-temperature faceting for (100) vicinals, is not conclusive. Prompted by the unexplained high-temperature behavior around
Fig. 6. Particle trajectories for the AuCJ I,l,l)vicinal of Au(,lOO) at: (a) 7’= 0.3, (b) 0.66 and Cc) 0.73 x T,,. This surface gradually disorders with temperature.
after 0.36 ns
first-layer structure sitting on top of square bulk lattice. Recent X-ray diffraction studies I45 461 have shown that domains of distorted slightly rotated hexagonal reconstructed phase exist between 300 and 970 K. This phase undergoes a tranSitiOn at 970 K into an unrotated distorted hexagonal phase which then disorders at 1170 K. MD simulation for the Au(100) surface reconstruction showed that the optimal structure for our potential at T = 0 K is 34 x 5, and all (M x 5) 28 SMS 40, give a very small difference in the’ surface energy [281.We are interested here in the high-temperature properties of the Au(l00) surface smce these properties determine the high-
343
temperature morphology of the Au(100) vicinals. Recently, a MD simulation study of the high-temperature disordering of the Au(l#) surface was performed [471.It was found that the top layers disorder, but the A~(1001 surface does not melt. The Au(100) vicinal surfaces were also studied re=ntjy LXW,411 and it was found that reconstruction induces the presence of favored par& ularly stable vicinals. MD simulation s&y (with the “glue” potential) for the T = 0 structure and the energetics of gold vicinals has shown that on these “magic” vicinal surfaces, terraces contain an integer number of reconstruction celts [29J It was found that the particularly stable AU(&)
‘(b) Fig. 7. The Au(l~l,l)
viciml WfaCe
at T= C?.99T, after: (a) 0.34
(d) (h) 0.71, (c) 1.07 and (d) 1.43
high-temperature faceting.
nS. The surface does not exhibit the
344
G. Bilalbqoci6
et al. / H’ hK temDeratm
vicinals are: (ll,l,l), (511) and (311). This result agrees with JXED 1391 and scanning tunneling microscoPY [411 studies of the Au(100) vicinals and periodic profiles. Non-magic vicinal surfaces facet into a suitable combination of magic vicinals and of flat (100). Th’ 1s reconstruction-induced faceting takes place at much lower temperatures
Fk
8. Particle
Wakxtoriesfor Liquid-k
the A~(91 I) vjcinaf of A”( 100) after 0.36 diffusion at high-temperatures
morpholoRv of stepped gold surfa,-esy
than the faceting of the Au(ll1) vicinals de_ scribed in section 3. Recently, reconstruction in_ duced faceting for the (111) vicinajs was studied at T- O.ST, 1401. It was found that while some Au(ll1) vicinak are unstable and facet vicinals of unreconstructed Pb(l11) remain stabie under the same conditions. Therefore the Au(lll) vici_
Cd)
is located mainly in the two topmost layers, ns at: (a) I-‘= 0.81, (b) 0.92, (c) 0.95 and (d) 0.‘)~ x T,,
G. Bilalbegocic’ et al. / High-temperature morphology of stepped gold surfaces
(b) Fig. 9. Snapshot of the MD slab for the Au(29,1,1) vicinal of Au(100). A side view of two MD boxes is shown at: (a) T = 0 (ideal sample) and (b) T = O.l5T,,, after 1.43 ns. This unstable vicinal surface exhibits reconstruction induced faceting at very low temperatures.
nals show reconstruction-induced faceting as well as a high-temperature faceting. It is important to find out whether the Au(100) vicinals (which show the reconstruction induced faceting) also exhibit the high-temperature faceting. We simulate here the Au(100) vicinal surfaces in the (M,l,l) family 04 odd). They consist of the (100) terraces, infinitely long along the (001) direction and 04 + 1)/2 atoms wide along the (011) direction. Due to the two-sublattice structure of the Au(100) surface the number of steps and terraces in periodically replicated MD boxes which represent the A~(1001 vicinals must be a multiple of 2. We choose here MD boxes with 2 steps and 2 terraces. MD trajectories for the magic Au(ll,l,l) vicinal surface are shown in figs. 6 and 7. This vicinal is misoriented by 6.7” from the (100) plane and the MD box consists of 752 particles. Fig. 7 shows that the high-temperature morphology of this surface does not change much with MD simulation time. Local melting fluctuations appear to take place, which make the two outermost layers very liquid-like close to T,. We have also studied the Au(911) vicinal misoriented
34.5
by 8” from the (100) plane, with 628 particles (shown in fig. 8) and the Au(29,lJ) vicinal misoriented by 2.7”, with 1884 particles (shown in figs. 9 and 10. The results for the Au(29,1,1) vicinal confirm the MD study for the T = 0 surface energetics of the Au(100) vicinals [291. This non-magic vicinal is unstable and, if prepared as an ideal sample at T = 0 (fig. 9a), facets immediately (i.e. after a very short simulation time) even at a low temperature (fig. 9b). We expect that the process of reconstruction induced faceting in our MD simulation at these low temperatures is not complete due to the limited diffusion. By contrast, the two other Au(100) vicinals we have studied, namely Au(ll,l,l) and Au(910, are stable at low temperature, i.e. do not undergo reconstruction induced faceting. They eventually disorder with temperature, as shown by figs. 6-8,
(0)
(b)
(cl Fig. 10. Particle trajectories for the Au(29,1,1) vicinal after 1.43 ns, at: (a) T = 0.81, (b) 0.95 and (c) 0.99~ T,,. The surface undergoes reconstruction induced faceting at low temperatures (see fig. 9) and then the two topmost layers disorder at high temperatures.
346
G. LGlaibegocic’et al. / Hogs-temperature rnorp~~l~~ of stepped gold surfaces
and steps disappear (but do not collapse) around T = 0.6T,. At higher temperatures the surfaces deconstruct and several top layers become compietely disordered. These surfaces do not exhibit proper surface melting close to the bulk melting point, in accordance with our results for the high-temperature properties of the Au(100) surface [47]. The density plot for the top of the Am91 1) vicinal surface shown in fig. 11 illustrates the fact that the layered structure is present up to the bulk melting point. The results for the high-temperature morphology of the Au(100) vicinals in the (M,l,l) family CM odd) show that these vicinals do not exhibit the high-temperature faceting. We are not definitely able to rule out the presence of sharp edges on the crystal shape close to Au(lOO~ in the surface melting temperature region, since there remains a possibility of high-temperature faceting for some other vicinal families not studied here. However, we feel this is an unlikely possibility. The reason is that lack of faceting for our (100)
vicinal surfaces appears to be tied to the hightemperature disordering of the two uppermost layers of the flat (100) surface, a phenomenon which does not occur on the stable reconstructed (111). If this is true, then non-faceting at high temperatures is a property of (100) and will be true for all vicinals. As a counterexample, we can however recall the behavior of Sic11 1) vicinal surfaces. In experimental studies of the reconstruction induced faceting for the Sit1 11) vicinals it was found that some of them are unstable due to the (7 x 7) --+(1 X 1) reconstruction on terraces and facet into the reconstructed flat (111) regions and regions with a high step density 137,381. Still, one Si(lll) vicinal family is found not to facet under the same conditions, but to exhibit a tripling of the step height at the (1 x 1) + (7 x 7) transition 2481.Thus the reconstruction induced faceting for the Sit1 11) vicinals is strongly dependent on the interaction between the terrace reconstruction and the step orientation. Whether such dependence also exists for the high-temper-
Fig. 11. The density plot for the A491 1) vicinal shown in fig. Xd
G. Bilalbegocic? et al. / High-temperature morphology of stepped gold surfaces
ature faceting, i.e. the study of the high-temperature morphology for other (100) and (111) vicinal families, must therefore be left for future work.
6. Conclusions We have shown by direct MD simulation that near the bulk melting temperature some Au(ll1) vicinal surfaces should be unstable and facet into flat (111) surface regions and tilted surface melted drops where surface diffusion is of a liquid type. This high-temperature faceting is induced by the surface melting anisotropy, i.e. the presence of both melting and non-melting faces on the crystal shape in the vicinity of unstable vicinal surfaces. On the contrary, vicinal surfaces of the (M,l,l) family (M odd), close to Au(100) do not facet near the bulk melting point. There steps disappear without collapsing well below the bulk melting temperature. High-temperature faceting is also absent for unlike monatomic steps on the Au(ll1) surface. We expect a similar high-temperature morphology for stepped surfaces of other fee metals.
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