Incoherent Ag islands growth on Ni(100)

Author’s Accepted Manuscript Incoherent Ag islands growth on Ni(100) J.B. Marie, I. Braems, A. Bellec, C. Chacon, J. Creuze, Y. Girard, S. Gueddani, J. Lagoute, V. Repain, S. Rousset www.elsevier.com

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S0039-6028(16)30354-5 http://dx.doi.org/10.1016/j.susc.2016.10.004 SUSC20946

To appear in: Surface Science Received date: 28 July 2016 Revised date: 30 September 2016 Accepted date: 16 October 2016 Cite this article as: J.B. Marie, I. Braems, A. Bellec, C. Chacon, J. Creuze, Y. Girard, S. Gueddani, J. Lagoute, V. Repain and S. Rousset, Incoherent Ag islands growth on Ni(100), Surface Science, http://dx.doi.org/10.1016/j.susc.2016.10.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Incoherent Ag islands growth on Ni(100) J. B. Mariea , I. Braemsb , A. Belleca , C. Chacona , J. Creuzec , Y. Girarda,∗, S. Gueddania , J. Lagoutea , V. Repaina , S. Rousseta a Laboratoire

Mat´ eriaux et Ph´ enom` enes Quantiques, Universit´ e Paris Diderot-Paris 7 and CNRS, UMR 7162, 75205 Paris Cedex, France b Institut des Mat´ eriaux Jean Rouxel (IMN), Universit´ e de Nantes, CNRS, 2 rue de la Houssini` ere, BP 32229, 44322 Nantes cedex 3, France c ICMMO/SP2M, Universit´ e Paris Sud UMR8182, 15 rue Georges Cl´ emenceau, F-91405 Orsay, France

Abstract Growth of two-dimensional superstructure and island morphologies of silver atoms evaporated on a nickel (100) surface are studied by scanning tunneling microscopy. Near-equilibrium islands form at moderate annealing temperature (lower than 500 K) and present two kinds of morphologies. While they share a common monolayer c(2×8) superstructure, two distinct populations of islands coexist: rounded islands grown on the surface and spindle-shaped islands grown inside the Ni surface. The latter present a clear saturation of their density with increasing coverage. These shapes are mostly dominated by boundary energies as confirmed by a simple two-dimensional Wulff model whose parameters are derived using molecular statics simulations. Further annealing to 700 K leads to long Ag strips decorating the Ni step edges. Keywords: Immiscible elements, Scanning tunneling microscopy, Submonolayer growth, Morphology, Molecular statics simulations

1. Introduction

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The formation of Ag films on Ni is interesting because Ag and Ni are immiscible in the solid state and thus present impressive catalytic [1] and plasmonic properties [2] due to their peculiar interface which confines electrons in two dimensions. From a more fundamental surface physics point of view, this bimetallic system belongs to the class of incoherent hetero-epitaxial materials [3, 4, 5]. The growth of Ag ultra-thin films on Ni(100) was studied by Auger Electrons Spectroscopy (AES) [6], STM [7], TOF-SARS [8], inelastic scattering of electrons [9] and photo-emission of adsorbed CO molecules [10]. All these studies agree on the quasi-hexagonal symmetry of the Ag c(8×2) superstructure, ∗ Corresponding

author Email address: [email protected] (Y. Girard)

Preprint submitted to Journal of LATEX Templates

October 18, 2016

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and the properties of this system are often compared to those of the c(10×2) superstructure of Ag on Cu(100) which is far much more studied [11, 12]. However, there are some intriguing differences. Briefly, below 13 % of coverage, Ag atoms form a surface alloy within the Cu plane (non-randomly distributed, but without long range order). With an increasing coverage, this alloy coexists with patches of embedded islands and at full monolayer (ML), all those patches cover the surface [11]. Ag/Ni(100) presents also embedded elongated Ag islands in the Ni surface (noted IN islands), but together with a second family of isotropic islands on the substrate (noted ON islands). This unexpected result is very similar to the bi-stability of nanoscale Ag islands on Si-In surface [13] which has been interpreted in the framework of anisotropic surface stress differences [14]. In this paper we show that this bi-stability can also be obtained by surface alloying. In the main part of this paper, we present STM results obtained on Ag submonolayer grown on a Ni(100) surface at various annealing temperatures. Our results are interpreted in the context of surface alloy formation at high temperature. Then, by comparison with the Ag/Ni(111) system, doubts concerning the possible silver bilayer formation are settled. Finally, concerning the understanding of the rounded and spindle-shaped islands [15, 16], we use a 2D-Wulff analysis to compare our measurements with Molecular Statics simulations (MS) in order to extract boundary formation energies of these two kinds of islands, i.e., almost isotropic step free energy for rounded islands on the surface (ON islands) and anisotropic inter-step free energy for spindle-shaped islands IN the surface (IN islands) (see Fig.2 for a clear view of those two families). 2. Experimental procedure We use a nickel single crystal from the Surface Preparation Laboratory (disk of 10 mm diameter and 3 mm height), with one side polished which presents a (100) surface orientation (better than 0.1 deg). After repeated cycles of argon ions sputtering and short annealing (around 700 K) in ultra-high vacuum condition (residual pressure better than 5.10−10 mbar), the sample quality and cleanness are checked by Low Energy Electron Diffraction (LEED) and AES. All STM images are recorded in-situ at room temperature (RT'300 K) with an Omicron Variable-Temperature-STM. Tunneling currents were set at 1 nA and voltage bias at 1 V. The Ni(100) sample shows typically 100 to 500 nm wide terraces, separated by step edges of monoatomic height (1.75 ˚ A). Ag is evaporated from a Mo crucible in an e-beam evaporator at a rate of about 0.1 ML/min on the sample kept at room temperature. The Ag atom flux and the absolute coverage were calibrated by measuring the surface coverage for different times of Ag evaporation and renormalization by the c(2×8) unit cell area. After deposition, samples were annealed thanks to a pyrolytic boron nitride furnace.

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Figure 1: Room temperature STM images of various Ag deposition times on Ni(100). a) 0.2 ML as deposited. b), c) and d): 0.2 ML, 0.5 ML and 0.8 ML after annealing at 490 K. Two populations of Ni islands appear at two different heights with respect to the Ni substrate: spindle-shaped (resp. rounded) at 1.2 ˚ A (resp. 3.2 ˚ A). Note that a typical profile is depicted in Fig. 4a. Those pictures were processed by the WSXM software [17].

3. Scanning Tunneling Microscopy Results

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3.1. Silver island morphologies versus coverage In order to study the surface morphology evolution as a function of Ag coverage, we evaporated increasing amounts of silver atoms at RT then annealed each sample at 490 K during five minutes. Fig. 1 presents large scale RT STM images for three different coverages. In Fig. 1a, as deposited 0.2 ML Ag is under the form of irregular islands surrounded by many small apparent defects on the Ni surface. Once annealed at 490 K, cf. Fig. 1b, the island morphology is smoother and two different populations coexist: rounded islands which have an apparent height of 3.2 ˚ A with respect to the Ni first surface plane and elongated islands which exhibit a spindle shape and have an apparent height around 1.2 ˚ A (these values were measured at 1 V, see Fig. 4). By increasing the coverage, both island type densities increase, all islands progressively coalesce and finally occupy the whole surface while keeping two distinct apparent heights (see Fig. 1c and d). As already known, all islands present a c(8×2) superstructure which 3

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appears along the two orthogonal orientations corresponding to the underlying Ni high-symmetry directions, [011] and [0¯11]. Moreover, spindle-shaped islands are also elongated along these two particular orientations and atomic resolution images (cf. Fig. 3c) show that the long axis of each island is the same as the incoherently packed Ag direction. A model for these islands will be discussed in the second part of this paper. In order to follow the relative coverage of each island population and their density as a function of the evaporation time, we plot those quantities in Fig. 2a and b. Below a coverage θ = 0.45 ± 0.05 Ag ML, the relative coverage of each population evolves equally with the deposition time. Above this coverage, the two populations evolve differently. While the ON island coverage continues to increase linearly, the IN island one saturates around θc = 0.2 Ag ML. This value corresponds to the maxima of both densities with a ratio of one ON island for three IN islands. We can notice that during the first stage, the aspect ratio length/width of the spindle-shaped IN islands is constant (cf. Fig. 2c) and that the length and the width evolve slowly as a function of θ. We conclude that all islands are in local equilibrium and there is a size selection which is known to be due to the interplay between interface, boundaries and elastic energies. This point will be discussed in part 4. Now, the question is why does the IN island coverage saturate ? After 0.45 ML, the two island densities decrease because of coalescence during growth. But, while the ON island mean size increases with the deposit, the IN island one evolves only because of the ripening and not by aggregation of more deposited material. It means that above θc there are no more Ag atoms inserting in the Ni plane and the IN island ripening is due to the induced stress by the overlayer. We can interpret this saying that an underlying Ag atom substitution process within the topmost Ni(100) surface plane takes place during the annealing procedure. Their minimal density is certainly around θc , but while cooling the system to RT, the Ni and Ag atoms of the top surface plane, and what we must actually call a surface alloy (quasi-liquid at high temperature), agglomerate under the form of IN islands (with a maximum of 20% surface coverage). The other atoms diffuse on the surface in order to rejoin ON islands. This interpretation is very similar to the results of Monte Carlo simulations obtained for the Ag on Cu(100) system [18]. Despite the fact that we never succeed to observe isolated Ag atoms within the Ni surface (the small aggregates observed in Fig. 1a could be a signature of atomic alloying) we confirm again that these two systems are very similar and form surface alloys at high temperature. So, following Sprunger et al. [11], the saturation in the present Ag-Ni system is due to a transition between the tensile stress of the clean Ni surface, which is relieved by the incorporation of the larger-size Ag atoms, and a compressive stress, which develops above 20% of Ag concentration within the surface. The main difference is the coexistence of the two IN and ON populations, what is not experimentally observed for Ag on Cu. So we investigated the IN and ON island evolution after high temperature annealing.

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Figure 2: a) Relative and total coverages (% of the surface) of islands as a function of deposition time, IN island coverage saturates around 20 % . b) Island densities as a function of the total Ag coverage, the two maxima occur for 0.45 ± 0.05 Ag ML. c) Length (L), width (l) and (nearly constant before coalescence) aspect ratio (L/l)∼ 3.5 of IN islands as a function of the total Ag coverage. All lines are guides to the eye. d) Definition of IN (spindle-shaped) and ON (rounded) islands.

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3.2. Annealing temperature dependence of island morphologies The previous measurements were performed for increasing coverages at a fixed annealing temperature of 490 K. In order to follow the ripening process induced by annealing, we present results obtained at a fixed coverage, 0.2 ML, 5

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but with increasing annealing temperatures. It is worth noting that in the limit of accuracy of our STM measurements, the coverage is found to remain constant whatever the annealing temperature. The ripening is evidenced in Fig. 3 and preserves the aspect ratios of the island shapes, except after the highest annealing (at 690 K) where islands disappeared and all silver atoms are located along the Ni steps, see Fig. 3d. We deduce that the coexistence of the two island populations is a near-equilibrium situation. Note that there is no Ag bilayer (read also part 3.3), so we can suppose that during annealing, IN and ON atoms globally migrated in opposite directions towards step edges acting as attractive traps for islands (a sketch of this interpretation is reported in Fig. 4): IN atoms coming from the upper terrace of the step edge and ON atoms from the lower terrace. This phenomenon is rather well known and related to Ehrlich Schwoebel barriers [19]. This simple scenario supposes that there is no interlayer atomic transport between IN and ON islands, which is supported by the absence of Ag bilayer. Of course, we cannot exclude any place-exchange mechanism between Ni and Ag atoms.

Figure 3: STM images of 0.2 Ag ML on Ni(100) after few minutes annealing at increasing temperatures: (a) 490 K, (b) 590 K and (d) 690 K. Notice the two simultaneous Ostwald ripening processes for IN and ON islands and the final Ni steps decoration by silver strips. (c): atomic resolution STM image (7×7 nm2 ) of the c(2×8) superstructure observed anywhere within the silver ON and IN islands.

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Figure 4: (a): a sketch of Ag on Ni(100) monolayer height islands. Black (resp. blue) arrows indicate that IN (resp. ON) islands collapse at the step edges coming from the upper (resp. lower) terraces (see also Fig. 3d). (b): STM measurements of ON and IN islands apparent heights as a function of bias voltage (error bars are smaller than the dot size).

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3.3. Comparison with Ag/Ni(111) Despite the fact that Ni(100) and Ni(111) have not the same surface symmetry, submonolayer Ag deposition on those two surfaces conducts to nearly the same hexagonal Ag(111) relaxed plane [20, 21]. This is due to the low coupling between Ni and Ag electronic states and has already been seen in case of similar materials. Nevertheless, there was a controversy about the Ag growth mode on Ni(111), under which an Ag bilayer would be [22] or would not be [23] a thermodynamical stable state. Of course this rises the question of comparisons between different experimental set-ups or modus operandi (calibration of atom deposition, temperature accuracy, annealing and cooling times, cleanness of the vacuum chambers, surface contamination, impurity segregation, etc...). However, the main argument concerning the controversy was about the two kinds of island height measurements. In order to settle out that point we performed height measurements of Ag islands on Ni(100) as a function of bias voltage. Right part of Fig. 4 shows that indeed, a variation of height of 1 ˚ A is observed for a ± 1 V bias variation. So depending of the STM bias, different island heights could be measured. What is effectively observed for Ag on Ni(111): C. Chambon et al. mentioned a height of 1 ˚ A for a bias of 1 V [22] while K. At-Mansour et al. [23] mentioned 0.69 ˚ A for −1 V. Here we point that surface alloy for Ag on Ni(111) was briefly mentioned [21] but is in fact the major result. At 300 K, for submonolayer Ag depositions, after annealing below 525 K, IN triangular islands are observed. We conjuncture that (i) these monolayer height islands result from embedded silver atoms condensing within the Ni(111) surface; (ii) their coverage saturates above a critical value and (iii) these surface alloys are unstable against island formation above a critical value which is temperaturedependent. Coming back to our island height measurements as a function of the bias voltage (Fig. 4b), it is worth noting that the two curves are nearly exactly superposable. So, the local density of states above an island is exactly the 7

same whatever the kind of island, ON or IN. This point could be interesting in order to study the confinement of electron in two dimensions similarly to other systems such as Ag/Si(111)-(77)[24] or Ag on NiAl(110) [25]. 4. Molecular Statics Simulations and spindle-shaped islands 160

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Here we discuss the elongated shape of IN islands. Based on a 3D theoretical model (the Wulff construction) transposed in 2D, it is known that the island shape can be derived from total free energy minimization for a fixed total island area. The inverse Wulff construction [26, 27] allows to obtain the ratio between the free energies of different step edges perpendicular to each other, for our twofold symmetry islands. In certain cases, shape transitions as a function of size [13] or temperature [28] have been analyzed. In the following, we use a simple model to extract this ratio for IN islands. Then, we compare this result with MS simulations performed for IN and ON islands. 4.1. Ratio of boundary formation energies The Ni(100) surface presents a 4-fold symmetry and the Ag layer a nearly exact 3-fold symmetry. So, there are two minimal energy orientations for a superstructure: c(2×8) and c(8×2). Moreover, each individual Ag island (IN or ON) presents experimentally only one domain, so we expect an island shape with a 2-fold symmetry. Consequently, the basic equations extracted from a 2D model of the Wulff construction [28, 29, 30, 31] are the following: β(θ) = β0 (1 +  cos(2θ)) dβ . sin θ x = β(θ). cos θ − dθ dβ y = β(θ). sin θ + . cos θ dθ

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(1) (2) (3)

In Eq. 1, β(θ) is the boundary energy, θ is the angle between the boundary direction and a dense atomic Ni(100) direction (say [011] direction) and  defines the degree of step energy anisotropy. Eqs. 2 and 3 are the Cartesian coordinates of a point M belonging to the island border. Note that the island center is supposed to be the Wulff point [27], i.e. parallel step edges do not differ both in structure and in formation energy. From the aspect ratio of the elongated islands reported in Fig. 2c we can extract . Effectively, L/l = (1 + )/(1 − ) = β(θ = 0)/β(θ = π/2) ' 3.5. We find  = exp ∼ 0.6, i.e. a very large step energy anisotropy: β(θ = 0) − β(θ = π/2) ' 1.2 β0 . This explains the sharp corners of these spindle-shaped islands. Concerning ON islands, their nearly rounded shape implicates a quasi-isotropic step energy and exp ∼ 0. 4.2. Comparison with MS simulations and discussion The preceding result is based on a model which supposed that the ad hoc Eq. 1 incorporates effects of surface stress, misfit strain induced by the lattice

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mismatch, elastic relaxations etc... As mentioned in reference [30], this result is a good approximation in cases when the equilibrium shape is size independent, what is effectively observed in Fig. 2c and Fig. 3a, for islands bigger than 10 nm (after our annealing process we never observed smaller islands). It is worth noting that this crude model is certainly wrong for very small islands, as discussed for Cu/Ni(100) [32], if substrates exhibit an important surface stress anisotropy [33]. Moreover, exact theoretical expression for the step free energy of an arbitrarily oriented step edge is not yet available [34], this obviously applies even more to hetero-steps of islands on surface. However, we can try to understand the value of  ∼ 0.6 by means of MS. Here we calculate the step and inter-step free energies, more precisely: i) the boundary energy for an Ag strip on the surface and ii) the boundary energy between an Ag strip within the surface and the surrounding Ni atoms. Methods We calculated these energies by means of MS, using interatomic potentials derived from the second-moment approximation (SMA) of the tight-binding scheme [35]. These potentials were quite successful in the calculation of equilibrium configurations of bulk [35], surfaces [12, 18, 20, 21, 36, 37, 38, 39, 40], grain boundaries [40, 41] and nanoparticles [42, 43] for both pure metals and binary alloys. The sets of parameters used in the simulations are the same than those used for the study of Ag/Ni(111), with which bulk properties for pure metals (cohesive energies, lattice parameters and elastic properties) and for the Ni-Ag alloy (mixing enthalpies and very low solubility limits) are well reproduced [20, 43]. All the present results are obtained after relaxation by MS using the fast inertial relaxation engine (FIRE) method [44], which is an improvement of the algorithm of quenched molecular dynamics that minimizes the potential energy at T = 0 K. To briefly summarize the principles, the relaxation procedure consists in integrating the equation of motion for each atom of the simulation box, dvi (t) , (4) Fi (t) = mi dt where vi (t) is the velocity at time t of atom i of mass mi and Fi (t) is the force acting on this atom at this time, calculated using the Verlet algorithm [45]. Then, the atom trajectories are adjusted by proposing two types of velocity changes: (i) cancellation of vi when the product Fi (t).vi (t) is negative (equivalent to the classical quenched molecular dynamics procedure [46]) and (ii) additional acceleration, γ, in the ‘steeper’ directions than the direction at time t if Fi (t).vi (t) > 0. This procedure is obtained by a simple linear combination between the global velocity (3N dimensional) and the forces via v = (1 − αv )v + αv |v| ||F F|| , where αv = γ∆t and ∆t is the trajectory integration step, these two parameters being dynamically treated during the optimization procedure [43]. The force is calculated with the SMA potentials described above. 9

In practice, it is not possible to reach exactly T = 0 K. Therefore, the simulations are stopped when T < 1.10−6 K, which ensures a precision on the total energy of the system better than 10−4 eV. 235

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Results Firstly, we verified that a relaxed c(2×8) structure was energetically favourable (against every other c(2×N) structure, N =1, 2,..., 15) and presented an atomic rumpling similar to our STM results (0.14˚ A vs 0.12˚ A). Then, we calculate four boundary energies, i.e. boundaries parallel to the [011] and [0¯11] directions for IN and ON islands. A boundary energy is equal to the cost in energy to create a boundary in

Figure 5: Schematic view of 2D Ag strips on a surface of 4-fold symmetry. Periodic conditions are applied in the two directions, so, strips are infinite along the [0¯ 11] direction. Red: Ag atoms presenting a nearly 3-fold symmetry, i.e. a c(8×2) superstructure oriented along the [011] direction (initial strip of length 2n). Blue: Ni atoms. (up) An Ag strip of width 2n (down) has been cut in two equal strips of width n separated from each other by a distance d/2.

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an island. MS simulations enable us to calculate the energy differences between various relaxed atomic configurations. So, we calculate on one side, for example ON along the [0¯ 11] direction (see Fig. 5), the energy E2n of an infinite Ag strip [0¯ 11] of width 2n oriented along this direction, and, on the other side, the energy EnON of two infinite Ag strips of width n parallel to the same direction. The [0¯ 11] difference between the energies of those two configurations is equal to the cost in energy to separate a strip in two equal parts. Similar energies are defined for the other direction. Then, the energy difference of those two configurations is equal to four times the boundary energy in the [0¯11] direction. More precisely, we considered a Ni slab with periodic conditions along those two previous directions and perpendicularly limited by two (100) faces. The thickness of this slab has been turned in order that the two surfaces do not interact. It requires more than 60 000 atoms (at least 40 Ni planes) in order to 10

Islands ON Islands IN

β(π/2) 381 83

β(0) 438 484

β(0)/β(π/2) 1.1 5.8

L/l (exp) 1 3.5

calc 0.05 0.71

Table 1: Boundary formation energies, (meV/nm), parallel to the [011] and [0¯ 11] substrate directions, for ON and IN islands. Their ratios; the experimental aspect ratios deduced from STM images, see Fig. 2; and the calculated degree of anisotropy.

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recover bulk Ni conditions at the center. Note also that Ag strips of width n must be enough spaced out so Ag atoms at the center of a strip have the same energy as an atom inside an infinite c(8×2) plane (i.e. the two sides of a strip do not interact). Similarly, the distance d/2 separating two strips of width n should be larger than a cut-off distance in order to neglect interaction between strips. Moreover, we were careful to translate the initial Ag strips along the two directions in order to find the lowest energy configurations.Similar calculations were performed for IN islands. Thus: β(0) = (E2n[0¯11] − En[0¯11] )/4lb[0¯11] β(π/2) = (E2n[011] − En[011] )/4lb[011]

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(5) (6)

where lb is the length of one boundary (boundary energies are given in unit of energy per unit length, (meV/nm)). The factor four comes from the fact that when we cut the strip on one face, we create two boundaries on that side and two other boundaries on the opposite side. So, we calculated one boundary formation energy for the two dense directions of the substrate, and for the two island populations: β ON (0), β IN (0), β ON (π/2) and β IN (π/2). The results are reported in Table 1. We can observe that the two boundary formation energies for the ON islands are nearly equal, so rounded islands are expected, which is effectively observed experimentally. With respect to IN islands, the boundary formation energy parallel to the [0¯ 11] direction is almost six times greater than the other direction. This large anisotropy (calc = 0.71) has to be compared to our STM results (exp = 0.6). So, we used those MS results in Eqs. 2-3 and calculated island shapes. Fig. 6 presents a side-by-side comparison of these shapes (comparing different island sizes does not change this conclusion). There are two complementary reasons for this 15% difference between the calculated and the measured anisotropies. (i) A careful examination of Fig.3, shows that IN islands are slightly truncated, which reduces the aspect ratio compared to sharp islands. This indicates that islands are in a near-equilibrium configuration and an analysis of their shape fluctuations could give a better estimation of their anisotropy [47]. (ii) MS simulations conduct to a boundary energy value β IN (0) which is certainly over-estimated. Indeed, forcing a hexagonal structure in a square one induced more modifications of the interface than what can be relaxed by MS simulations. Equilibrium Monte Carlo simulations that allow both atomic relaxations and optimization of the repartition of the chemical species could 11

Figure 6: Contours of IN (white) and ON (black) islands obtained from Eqs. 2 and 3 with calc equal to 0.71 and 0.05 respectively.

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be useful to obtain perfectly relaxed configurations and so could give rise to a lower ratio. Nevertheless, and in the limit of our crude analysis, we can report MS results in Eq.1, and obtain the orientation dependence of the step energy for ON islands and the inter-step formation energy for IN islands (meV/nm): β ON (θ) = 410(1 + 0.05 cos(2θ)) and β IN (θ) = 284(1 + 0.71 cos(2θ)). 5. Conclusions

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In conclusion, the growth and structure of Ag on Ni(100) for submonolayer coverages after annealing at various temperatures was investigated with STM. After annealing above 600 K, Ag forms a pseudo-hexagonal c(2×8) overlayer structure covering the surface and decorating Ni steps. However, at slightly lower temperatures, silver form simultaneously two kinds of islands: rounded islands ON the surface and spindle-shaped islands IN the surface. The coverage of IN islands saturates around 20% and is certainly limited by the surfaceinduced strain. For lower coverages, the size-independent shapes of ON and IN islands are interpreted by using a simple two-dimensional Wulff model that only involves the boundary energies. Their semi-empirical ratios are found to equal respectively ∼ 1 (nearly-isotropic) and 3.5 (highly anisotropic). Then, those ratios were compared with results based on Molecular Statics Simulations (respectively 1.1 and 5.8). Despite this discrepancy, Wulff shapes obtained with these values fit nearly exactly our experimental observations, in the limit of both the experimental resolution and the simplicity of the model. 12

6. Acknowledgments 310

This work has been supported by the Region ˆIle-de-France in the framework of DIM des atomes froids aux nanosciences. Authors are grateful to Dr. G. Pr´evot and F. Berthier for helpful discussions. References

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