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PHYSICAL REVIEW B 15 OCTOBER 2000-IVOLUME 62, NUMBER 15

Low-energy-deposited Au clusters investigated by high-resolution electron microscopyand molecular dynamics simulations

B. Pauwels* and G. Van TendelooElektronenmicroscopie voor Materiaalonderzoek, Universiteit Antwerpen (RUCA), Groenenborgerlaan 171, B-2020 Antwerpen, B

W. Bouwen,† L. Theil Kuhn,‡ and P. LievensLaboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, Celestijnenlaan 200 D, B-3001 Leuven, B

H. Lei and M. HouPhysique des Solides Irradie´s CP234, Universite´ Libre de Bruxelles, Boulevard du Triomphe, B-1050 Bruxelles, Belgium

~Received 4 May 2000!

We investigated the cluster-surface interaction of Au clusters deposited on MgO cubes and on amorphouscarbon, and its influence on the morphology of the Au cluster. Au clusters, produced in a laser vaporizationsource, are deposited with low energy on carbon-coated microscope grids on which MgO cubes are firstdeposited as substrates. Clusters on the amorphous carbon as well as clusters on the MgO cubes are studied byhigh-resolution electron microscopy~HREM!. The clusters have different morphologies for the two differentsurfaces, and a dilation of the Au lattice is also measured for the clusters deposited on the crystalline surfaceof MgO to perfectly accommodate the MgO lattice. Classical molecular dynamics~MD! is applied to modelthis behavior. Good agreement is found between experimental cross-section HREM images and theoreticalimages simulated with the multislice technique using the model calculated by MD.

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I. INTRODUCTION

A cluster deposited on a surface constitutes a systemspecific properties determined by the morphology andmaterial of the cluster, and the interaction between the cter and the surface. It is of fundamental importance to stthe evolution of the properties with the size of a deposicluster, e.g., the morphology and, closely related to it,electron density of states determining its physical and checal properties. For instance, fivefold symmetry is an examof a morphology uniquely related to clusters. Deposited clters are also suited as well-controlled building blocksconstructing nanostructures.1,2 In particular, deposited metaclusters have proven to have potential for a wide rangetechnological applications, e.g. catalysts,3 optoelectronics,nanocircuits, magnetic devices, metal-ceramic sensors,chanically high-strength granular materials, coatings, etc4

Various methods have been applied to study the morpogy of single deposited metal clusters on surfaces, e.g., sning probe techniques@ultrahigh vacuum scanning tunnelinmicroscopy~UHV-STM!5 and scanning tunneling spectrocopy ~STS!6#, field-ion microscopy ~FIM!,7 transmissionelectron microscopy~TEM!,8 and, in particular, high-resolution electron microscopy~HREM!; pioneering workwas presented in Refs. 9–11, more recent work incluRefs. 12–19. At present, the atomic resolution achievawith UHV-STM is limited to the facets of the cluster’s tolayers, and FIM only provides information on the positionthe vertex atoms at the cluster facets, whereas HREM madetailed studies of the cluster morphology possible.

The investigation of the morphology of deposited clustcan be divided into two major groups: clusters nucleateda substrate by atom deposition, and clusters fabricatedcluster source and subsequently deposited on a subs

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Clusters fabricated by nucleation on a surface are formeddiffusion and aggregation of adatoms during interaction wthe substrate. The preformed clusters differ substantifrom those because they have achieved their morpholog‘‘free’’ objects. Inevitably, the preformed clusters interawith the substrate after deposition, and depending on hstrong this interaction is, the morphology of the preformclusters and the substrate can change. Depending on thnetic energy of the preformed cluster several depositiongimes exist: soft-landing (Ekin,0.1 eV/atom!, low-energycluster beam deposition~LECBD! (Ekin,1.0 eV/atom!, andenergetic cluster impact~ECI! (Ekin.10 eV/atom!.20,21 Inboth the soft-landing and LECBD regimes the impact eneis low enough to prevent deformation of the substrate, athe single cluster keeps its identity, whereas in the ECIgime the substrate is damaged and the cluster is compledeformed, losing its identity. Soft-landing and LECBD rgimes can be used for growing nanostructured materia1,2

and ECI is suited for fabricating thin films.20 In this paper,we shall be discussing the morphology of preformed meclusters deposited by LECBD.

The structural properties of deposited metal clusters wintensively studied by theoreticians, among the most powful tools are molecular dynamics~MD! simulations. For ashort review see, for instance, Ref. 22. From a fundamepoint of view quantum-mechanical MD is the most correbut it can only be performed for a limited cluster size. Fclusters consisting of elements with many electrons theper limit is approximately 50 atoms. For simulating largclusters containing many electrons classical MD has toapplied.

In Ref. 23 the authors used quantum-mechanical MDsimulate the ‘‘magic’’ Na8 cluster when it was either deposited on an insulating NaCl~001! surface or on a metallic

10 383 ©2000 The American Physical Society

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FIG. 1. An overview of the laser vaporization cluster source, mass analyzer, and cluster deposition setup.

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Na~110! surface, or brought into contact with another N8cluster in vacuum. They observed that the Na8 cluster on theNaCl~001! surface remained very stable, and almost didchange its geometric and electronic structure, but onNa~110! surface it immediately collapsed and formed an eitaxial layer. The interaction between two Na8 clusterscaused them to lose their identity, and form a Na16 clusterwith a completely different geometric and electronic struture. These MD simulations show how determining tcluster-surface interaction is for the morphology of the dposited cluster, even when the preformed cluster is phcally and chemically very stable.

Recently, classical MD simulations of a fcc Cu440 clusterdeposited at room temperature by LECBD on a fcc Au~111!surface was presented.24 The evolution of the cluster ansurface morphology after the impact was simulated, showthat the substrate is compressed for a short time but mtains its fcc structure, whereas the cluster exhibits strrelaxation effects depending on the impact energy. Forlowest impact energy (Ekin,0.25 eV/atom! the cluster ad-justs epitaxially to the substrate, and evolves facets. Thfacets become modified with increasing impact energy,the epitaxy is maintained untilEkin51 eV/atom. For impactenergiesE kin.1 eV/atom the Cu cluster wets the Au suface, the cluster morphology is disordered, and there10% mixing of the Au and Cu atoms. The epitaxy causinternal stress in the Cu cluster which is mostly accommdated by the first interfacial layer. Since the interfacial relaation is closely related to the balance between the coheenergies, these simulated morphologies are specific forsystem of a Cu440 cluster on a Au~111! surface, but theyillustrate the strong influence of the impact energy eventhe narrow range 0.25–1 eV/atom of LECBD on the resuing cluster morphology.

Here we present a combination of HREM studies ofmorphology of well-characterized preformed Au clustersmultaneously deposited by LECBD on two fundamentadifferent types of substrates—amorphous carbon and sicrystalline MgO—and classical MD simulations of the oserved systems. Substrates of single-crystalline MgO cuon amorphous carbon were chosen to be able to simuneously study the differences in morphology of clusters sject to strong and weak interactions with the substrate. Mis characterized and described in the literature,25 and it servesas an internal microscope reference for measuring absolattice parameters of the clusters. Au clusters consistingfew up to several thousand atoms are produced by a lvaporization cluster source.26 Depositing clusters of the

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noble metal Au prevented contamination. Furthermore,clusters are very well characterized both experimentallytheoretically providing the necessary information for tHREM image analysis and the MD simulations. First, tHREM images were analyzed by standard image analsimulations, showing that these were insufficient in descing the morphology of all of the cluster layers. Second,cluster morphology obtained from the HREM image analywas used as the initial configuration for the MD simulationThird, the resulting configuration of the MD simulation waused for the HREM image analysis, and a perfect mabetween the experimentally observed and the simulated mphologies was obtained. By combining these complementechniques we have been able to study the evolution oflattice parameters of Au clusters on MgO throughoutcluster layers from the interface to the top showing relaation, contraction, and dilation.

The paper is structured as follows: In Sec. II the expemental techniques are described; in Sec. II A the sampreparation is presented, and in Sec. II B the HREM tenique including image analysis is explained. Section III cotains an overview of the MD simulations, Sec. IV a discusion of the results, and Sec. V conclusions.

II. EXPERIMENTS

A. Cluster deposition

The Au clusters are fabricated in a laser vaporization clter source. Figure 1 shows an overview of the apparatuwas described in detail in Ref. 26. A pulsed laser ablamaterial from a target. The supersaturated metal vaporformed is cooled by a He gas pulse and expansion whcauses condensation of the vapor into clusters. A beamclusters is setup by several stages of differential pumpThe free-flying clusters are analyzed by time-of-flight maspectrometry, Fig. 2 shows the size distribution. The prsures in the cluster source and in the time-of-flight mspectrometer chamber are 1027 and 1029 hPa, respectively.During cluster production these pressures rise to typic1024 and 1027 hPa, respectively, due to the He gas.

Characteristic for this type of cluster source is that tmetal vapor is quenched producing a cold beam of cluswith a temperature lower than 300 K, and the kinetic eneof a cluster is about 0.5 eV/atom. Thus the clusters canused for low-energy cluster beam deposition.1,20,27The clus-ters are not formed in equilibrium, and they therefore do

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PRB 62 10 385LOW-ENERGY-DEPOSITED Au CLUSTERS . . .

exhibit magic numbers in the mass spectrum. However,transferring energy to the clusters by photon absorption~de-livered by the laser ‘‘ionization laser’’ in Fig. 1! they canachieve equilibrium shapes, and the stability as functionnumber of atoms per cluster can be studied.28 In the experi-ments presented here the Au clusters are deposited aspared directly from the frozen metal vapor.

Figure 2 shows the size distribution of the cationic frAu clusters as measured by reflection time-of-flight~RTOF!mass spectrometry. The RTOF technique measures the adance as function of number of atoms in the clusters. Assing the clusters to be spherical and using the Wigner-Sradius for Au ~1.59 Å!,29 this has been converted to abudance as function of diameter. A large number of small clters is present in the beam, but the major part of materiaconcentrated in the larger clusters having an average deter of approximately 1.9 nm. However, due to decreasefficiency of the detector for the heaviest clusters, this sdistribution has an upper cutoff, such that clusters larger tobserved with the mass spectrometer may be present inbeam.

For the sample preparation MgO cubes on amorphousbon film are used as substrates for the Au clusters. Mg grare heated in air with a Bunsen burner. When they starburn, a white smoke is produced. The smoke contains Msingle crystals which are collected on a carbon-coatedgrid by holding the grid in the smoke. The crystals haalways the shape of a cube, and their size is dependent otemperature at which the grains are heated. The numbecubes is dependent on the time the grid is held in the smIn the experiments described here, mostly cubes with sizethe order of 300 nm are used because they can easiloriented along a zone axis. The MgO single crystals havesame structure as rock salt~NaCl!, and, because of their sizethey can be considered bulk materials with a known lattparameter of 4.20 Å .25

A substrate of amorphous carbon with MgO cubesplaced in the cluster beam in the second chamber~see Fig.1!, and Au clusters of all produced charge states are deited on the surface by LECBD, minimizing the interactiobetween the clusters and the substrate during impact.

FIG. 2. Size distribution of ionic free Au clusters as observedtime-of-flight mass spectrometry, without correction for the dcrease of the detector efficiency for the heaviest clusters. Thisdistribution thus can have an upper cutoff. The diameter was calated assuming the clusters to be spherical.

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substrate is constantly kept at room temperature, andclusters are deposited at very low density so they are isolfrom each other at the substrate. After deposition the samis transferred to the transmission electron microscope. Bthe Au clusters deposited on the MgO cubes and onamorphous carbon are studied by HREM.

B. High-resolution electron microscopy

HREM images are taken with a JEOL 4000 EX micrscope, which has a point resolution of 1.7 Å. Other paraeters of the microscope which are needed to performsimulations of HREM images are the spherical aberratconstantCs51.0 mm, the defocal spreadD f 58.0 nm, and asemiconvergence anglea50.55 mrad. Because of the eptaxial relation between the Au clusters and the MgO, itpossible to orient the MgO cubes along a zone axis atmagnification, and then both the lattices of the clustersthe MgO substrate can be imaged together. For clustersposited on amorphous carbon, the orientation of the clusis random, and one has to search for a cluster which hazone axis along the incident electron beam. The high restion observations are carried out at a low electron-beamradiation density~17 pA/cm2) in order to avoid structurareorientations caused by the electron beam. Most of the tthe clusters are stable under the beam; only a few timstructural reorientations are observed before the clusterbilizes.

To obtain a size distribution for the Au clusters on amophous carbon, image analysis is done using the Kontron400 Version 1.2 image processing software. Because ofamorphous background, which shows many features, idifficult to separate the clusters from the background angreat deal of image processing is needed. The followsteps are performed. An image, as shown in Fig. 3~a!, isscanned with a resolution of 300 dpi and 256~eight-bit! graylevels. Taking into account the enlargement of the micscope, this means that 1 pixel is 0.87 Å. First a shad

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FIG. 3. ~a! Overview of clusters deposited on amorphous cbon. The deposition time for this sample was 1.5 min.~b!–~d! Someexamples of HREM images of Au clusters deposited on amorphcarbon:~b! shows a cubo octahedron viewed in a@011# direction;~c! and ~d! show two images of decahedral particles which consof five tetrahedra along a@011# zone axis.

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correction is applied. The original image is smoothed witlow pass filter of size 49 (737 pixels, repeated 20 times! toproduce a reference for the actual shading correction. Wapplying this correction a more or less evenly illuminatimage is obtained. Then the image is further enhancedapplying a low pass filter of size 9 (333 pixels!, followedby a contrast enhancement. To perform the image segmetion, a binary image is created using an arbitrary thresholgray level 100. Hereby image objects with an area less t30 pixels~or an equivalent diameter of 5.4 Å! are removedbecause it is not possible to distinguish clusters from featuin the amorphous carbon for these sizes. This binary imagused as a mask to measure the objects in the original imThe area, the equivalent diameter, and the coordinates ocenter of gravity for each object are produced in pixels. Tenlargement of the microscope is known, and the data carecalculated in nm. All this image processing is done aumated, but it is always necessary to verify the results by ebecause sometimes features in the amorphous carbon crecognized by the program as a cluster. It also happensthe software does not find a small cluster which is visuathere.

To evaluate lattice distances in the clusters, theDALI pro-gram~Digital Analysis of Lattice Images! is used.30 The gen-eral procedure to measure the distances is as follows: bemeasuring, a Wiener filter is applied on the experimenimages to reduce the noise level. First the positions of mmum intensity are searched. Afterward, to yield a morecurate estimate of the peak positions, a parabolic functiofitted in a region close to the estimated maximum intensitFitting with a parabolic function can be done becauseintensity profile of a spot is nearly sinusoidal.

The MgO cubes on which the Au clusters are deposcan be considered as bulk material with a known latticerameter~4.20 Å!. The lattice distances in the Au clusters ameasured relative to the lattice distances of MgO, andpossible to study small local variations of the lattice in tclusters. This cannot be done for clusters deposited onamorphous carbon of the microscope grid, because the eenlargement of the microscope is dependent on the objeclens current and other microscope parameters, and dislightly from image to image.

All simulations of HREM images are done with theEMS

program,31 running on a DEC Alpha XP 1000 WorkstationThe Au cluster and the substrate are placed in a squarepercell of 6 nm inx and y directions perpendicular to thzone axis, which is taken as thez direction. The supercell istaken large enough to avoid influences of the supercell bders on the image. To obtain the right contrast of the sstrate, some extra MgO layers are added. First the elecwave function of the model is calculated with a multislidynamic calculation.32 The sampling in thex andy directionsis always 1024 pixels in each direction, which gives a presion of 5.8631022 Å between two neighboring points. Ththickness of the slices in thez direction is 1.5 or 1.0 Å.Afterward the influence of the microscope on the image fmation process is added. Using the electron wave funcand the microscope parameters of the JEOL 4000 EX miscope, the HREM images are simulated.32

In this contribution a selection of the HREM imagespresented. Many more images, both from clusters on am

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phous carbon and from clusters deposited on the MgO cuwere obtained. Figure 3 shows some images of clustersposited on amorphous carbon. An overview is shown in F3~a!; most of the clusters are not oriented. Only somethem have a simple zone axis along the incident electbeam. Figure 3~b! shows a cubo octahedron along the@011#direction. Decahedral clusters viewed along the@011# zoneaxis are shown in Figs. 3~c! and 3~d!. The fivefold symmetryis clearly seen. Also icosahedral clusters and twinned sttures are often observed in Au clusters deposited on amphous carbon.

To study the morphology and small lattice dilationsclusters deposited on MgO, projection of the clusters perpdicular to the Au/MgO interface~cross-section! is necessary.Two different orientations are imaged in cross-section vie^011& and^001&. Figure 4~a! shows a Au cluster of 2.2 nm inheight ~distance from the interface to the top of the clust!and 3.0 nm in width deposited on a MgO cube oriented alothe @011# zone axis. Other cross-section images of clustare shown in Figs. 4~b! and 4~c!: ~b! shows a cluster in the@011# orientation, while the cluster shown in~c! is a clusterwith the same morphology but in the@001# orientation. Thecorresponding profiles of the clusters with an indexationthe crystallographic directions and faces are shown in F4~d!, 4~e!, and 4~f!, respectively. The morphology of thcluster shown in Fig. 4~a! is different than the morphology othe other two clusters of Fig. 4. Figure 4~a! is a truncatedoctahedral cluster, while Figs. 4~b! and 4~c! are truncatedhalf octahedral clusters. This will be discussed in more dein Sec. IV. In the^011& orientation HREM images are alsmade of clusters in a top view, parallel to the interface~seeFig. 5!.

III. MOLECULAR-DYNAMICS MODEL

In order to understand the internal relaxation inducedthe substrate, the atomic configuration in a Au clusterobserved by HREM after deposition is modeled by meansclassical MD. Therefore, an accurate knowledge ofatomic positions at the substrate surface is necessary, wis only available in the case of MgO. This is the reason w

FIG. 4. Au clusters deposited on MgO:~a! HREM image of atruncated octahedral cluster in a^011& zone axis orientation.~b!Half octahedral cluster in a011& orientation.~c! Half octahedralcluster in a 001& orientation.~d!–~f! Profiles of the clusters shownin ~a!–~c!, respectively, with an indexation of the crystallographdirections and the faces.

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PRB 62 10 387LOW-ENERGY-DEPOSITED Au CLUSTERS . . .

the present modeling is restricted to the case of a Au clusas deposited on MgO and observed at room temperature

Several ingredients are necessary to achieve a MD meling. One first needs initial conditions. These are providby HREM, from which clear information is deduced abothe cluster morphology~see Sec. IV! and also about theatomic row positions projected onto the@100# and @110# di-

FIG. 5. Image of a MgO cube along the^011& zone axis. Twoprofiles of octahedral clusters on the surface are visible. Profilwhich is often seen in plan view images, is from a truncated ohedral particle; profile 2 could be from an ideal octahedron. Hoever such a perfect octahedral cluster is never seen in a csection HREM image. Also in top view images, it is observed oa few times.

FIG. 6. Initial configuration of Au786/MgO(100). The layernumber is given in the first column, and the number of atomseach layerl in the second column.

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rections parallel to the interface. Figure 6 shows suchmodel where the Au cluster morphology is identical to thof the selected cluster@Fig. 4~a!#. Despite the equilibriumlattice mismatch, HREM shows evidence for accommodatat the interface, with most of the distortion absorbed bycluster. Therefore, in our initial conditions, the interfacial Aatoms are displaced to match exactly the MgO geometrlattice, and the nearest-neighbor distance in the Au intecial layer is 2.97 Å.

One then needs a cohesion model for Au. Those sgested in the literature are numerous, though most genebased either on the embedded-atom model33 or on thesecond-moment approximation of the tight binding mode34

We selected the latter, according to which the configuratenergy of the Au system, projected on an atomi, is written as

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The summations in Eq.~1! represent the contributions of aother atoms in the system.r i j is the distance between thatomsi andj, andV(r i j ) is a repulsive pair potential betweethese atoms.F(r i j ) describes the sum of squares of hoppiintegrals between atomic sitesi andj. The potential functionsare constructed as a series of cubic splines, and their ranlimited just beyond the third neighbor distance.35

The third ingredient is a tool, which allows one to shothe influence of the MgO substrate on the atomic relaxatin the cluster, as can be identified by HREM. We are uaware of reasonable models for the interaction between gmagnesium, and oxygen at the Au/MgO interface. Therefoand in view of characterizing the effect of interfacial forcon the internal cluster relaxation, the interaction betweenterfacial Au atoms and the MgO substrate is modeled bsimple effective harmonic potential. A harmonic force is thadded to each interfacial Au atom, that can be written as

Fh,i5k~r i2r0,i !, ~3!

wherek is a force constant to be adjusted.r i andr0,i are theinstantaneous and epitaxial position vectors of atomi, re-spectively. One problem is to select a realistic force consk. In order to find a reasonable range ofk values, we firstdetermined the effective atomic force constant of bulk crtalline Au. It is deduced in the harmonic approximation frothe experimental value of the bulk modulus askbulk53.843102 J/m2. At the Au/MgO interface,k is taken as aparameter which magnitude is lower thankbulk . Values be-tweenk50 andk52.03102 J/m2 are considered. The cask50 corresponds to a free cluster with the same morphol~see Fig. 6!. A comparison withk.0 will help us to under-stand the influence of the substrate on the internal straithe cluster.

In the present simulation, the equation of motion ofatom i can be written as

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a is the inverse coupling time to the thermal bath at teperatureTe , and it is taken to be equal to 1 ps for convnience.Ti is the instantaneous temperature of atomi andmiis its mass.e is a small constant introduced in order to avodivergence when the instantaneous velocity tends to zershould be noted that the velocity-dependent term in Eq.~4!represents the contribution of an external force on the stem. Consequently, the total angular momentum of the cter may not be preserved.

When the force constant in Eq.~3! is zero, the cluster isfree, and cluster rotation is possible. Therefore, in this cathe Newton equations of motion are used rather than Eq~4!to avoid angular momentum resulting from external forcThermalization is then achieved by means of a velocityscaling procedure.

Starting with the initial configuration shown in Fig. 6, ththermal evolution of the Au cluster is followed during 20ps. The integration time step is 2 fs, and the temperaturthe thermal bath isTe5300 K. The equilibrium is achievedwhen there are nothing but statistical temporal variationsthe mean kinetic and configuration energies of the systempractice, it takes about 10 ps to reach thermal equilibriuStarting somewhat later, the instantaneous nearest-neigdistances are recorded and accumulated to evaluatemean values. The mean atomic positions are evaluatewell. In addition, HREM images from the model configurtion can be simulated and compared to the real imageswill be discussed below.

FIG. 7. Size distribution of 694 Au clusters obtained fromsample with a deposition time of 1.5 min. The Gaussian functfitted to the data is also shown.

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IV. DISCUSSION

The relations between the cluster structure, morpholoand size distribution in the beam and on the substrate areobvious. Since the clusters are produced out of equilibriuno intensity enhancement relates to magic numbers andto particularly frequent morphologies. Classical MD predicmetallic clusters of the order of 100 atoms and more to hbinding energies only little dependent on their morphology36

Quantum-mechanical tight binding models37 provide similarestimates. This suggests the possible coexistence of seisomers which morphology, once deposited, may be signcantly influenced by the substrate. Temperature, in cerconditions, may activate overall rearrangements.38 On graph-ite surfaces, every bonding state is occupied, so that a laing metallic cluster only interacts with it via van der Waaforces after impact. These are weak enough that clustersfuse as a whole at room temperature,1 and aggregate. In contrast, the interaction with a silica surface is estimated tomuch more significant.39

Significant cluster-surface interactions may also bepected for amorphous carbon surfaces characterized by savailable for bonds. These bonds are directional, but notrelated between neighbors and might influence the clustructure. Whatever the nature of the interaction is, the inaction energy is sufficient to prevent cluster diffusion, andallow characterization by atomic scale observation teniques. Hence, even when the substrate surface is strucless ~i.e., amorphous!, an influence on the cluster structuand morphology cannot be excluded. Significant questiremain. In what follows, however, the Au cluster state afdeposition on amorphous carbon and on crystalline Mwill be characterized. These substrates differ from each oby their surface state since MgO microcrystals are pnouncedly ionic, and they display well-defined~100! sur-faces.

A. Cluster size distributions on amorphous carbon and MgO

Figure 7 shows the size distribution of 694 Au clustersan amorphous carbon surface. This size distribution istained by TEM from a sample, such as shown in Fig. 3~a!,with a deposition of Au clusters for 1.5 min. A Gaussia

n FIG. 8. Graph which shows the cluster morphology in functiof the width ~distance in^011& view! and the height~distanceinterface-top! of the clusters.

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PRB 62 10 389LOW-ENERGY-DEPOSITED Au CLUSTERS . . .

FIG. 9. ~a! HREM image of a deposited cluster along the^011& zone axis. The same cluster is also shown in Fig. 4~a!. ~b! Graph showingthe averagedd220 lattice spacing in the different layers through the cluster and the substrate. The dashed lines represent the bulk M~1.485 Å! and Aud220 value~1.442 Å!, and are shown for comparison. Layer 1 is the top layer of the cluster, and the Au/MgO interfbetween layers 11 and 12. Looking at the image in~a!, one could conclude that the interface Au/MgO is around layer 9, because thalready some contrast of the substrate. This is due to a step in the MgO behind the cluster which is not in focus.

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function is fitted to these data. The average cluster sizem)and the geometrical standard deviation (s) are determined as1.59 and 0.74 nm, respectively. The average cluster sizestandard deviation for a log-normal fit are 1.71 and 0.77 nrespectively, andx2, which is a measure of the ‘‘goodnessfit,’’ was only slightly smaller. Also a size distribution o514 Au clusters obtained from a sample of which the desition time was doubled, is fitted by a Gaussian and a lnormal distribution. In this case, a Gaussian function witmean cluster diameter of 1.90 nm and a standard deviatio0.82 nm, gave a better fit than a log-normal function withmean diameter of 2.03 nm and a standard deviation of 0nm. The mean diameters obtained from these TEM samare in good agreement with the diameter of the larger clusin the free cluster beam measured in the reflection timeflight mass spectrometer. The conclusion is that afterclusters are deposited, they do not significantly coalescelarger clusters.

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A classification is made of all cross-section HREM images of Au clusters deposited on MgO in the two differemorphologies~see Fig. 8!. It is clearly seen that the largeclusters with an average height of 1.9260.24 nm and anaverage width of 2.2760.40 nm are truncated octahedrwhile the smaller clusters~average height 0.9460.22 nm andaverage width 1.4260.30 nm! are truncated half-octahedra

Comparing the graph of Fig. 8 with the size distributioof Fig. 7, it is seen that the average height and width ofclusters deposited on MgO are of the same size as the aage cluster sizes found for the clusters on amorphous carThe interaction between a Au cluster and the MgO surfaclarger than the interaction of a Au cluster with the amophous carbon. For clusters deposited on amorphous cathere is no coalescence, so it can be expected that thelescence between clusters deposited on the MgO cubealso limited. This is also supported by the fact that clustlarger than 3 nm are not observed. If there is coalesce

.

FIG. 10. ~a! Cluster of six layers high on the MgO substrate.~b! Graph showing the averagedd200 distances of the different Au layersThe dashed lines represent the bulk MgO~2.10 Å! and Aud200 lattice distance~2.04 Å! and are shown for comparison.

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between two or more small clusters then also clusters lathan 3 nm should be present. Also, when clusters coaleinto larger ones, planar defects~such as, e.g., stacking faulor twins! should form in the larger clusters. This is not oserved for the Au clusters deposited on MgO.

B. Cluster morphology and lattice distortions on MgO

The morphology of the deposited clusters is determinby projection of the clusters perpendicular to the Au/Mginterface~cross-section! in two different orientations:011&and ^001&. Also, clusters imaged in top view helped to dtermine the morphology. The profile of the cluster of F4~a! is limited to four^112& directions and two011& direc-tions; the latter two parallel to the interface and asymmecally truncating the cluster. An ideal octahedral cluster in@011# orientation is limited to four112& directions. By trun-cating at the top and the interface with$001% planes, twoextra^011& directions appear to limit the cluster profile@seeFig. 4~d!#. Figures 4~b! and 4~c! show two clusters whichhave both the same morphology, in cross-section view; tare smaller than the cluster shown in Fig. 4~a!. From thesecross-sections it is deduced that the clusters are hoctahedral shaped; the truncation at the interface has dpeared.

Figure 4~b! shows a cluster in the@011# orientation. Theprofile of the particle is limited to two112& directions andtwo ^011& directions. Viewed along the001& zone axis@Fig.4~c!#, these smaller clusters are limited to two^011& direc-tions and four 001& directions: two 001& directions are par-allel to the interface; the other two, which arise from ttruncation at the side corners, are perpendicular to the inface. In a^011& zone axis it is not possible to observe trucations at the side corners of octahedral clusters. Thereone has to observe the clusters in a^001& orientation. Suchimages show that also the side corners of the clusterstruncated. Projection of a cluster as shown in Fig. 4~a! in the@101# or @110# direction, two directions along which a toview image is obtained, should show a hexagonal proThis is indeed often observed in HREM images~see Fig. 5!.

The same morphologies for supported Au clusters areserved by several other authors,14,17 but in these cases thclusters were fabricated by evaporation of Au atoms, whwere directly deposited on the MgO cubes. With our prodtion technique, the Au clusters are first formed in the clussource, and then deposited by LECBD on the MgO.

All deposited clusters show the same epitaxial relati(001)MgO//(001)Au and @100#MgO//@100#Au . This epitaxialrelation was also observed by several other authors,14,16,17

and considered as the most stable one. This epitaxial ortation is a result of the interaction between the cluster andMgO surface. Other epitaxies, as observed in Ref. 14, arefound in the present study.

The slowing down of metallic clusters in the LECBD rgime on a metallic surface is studied in detail in Refs. 24 a40 experimentally and by means of atomic scale modelNo obvious relation is found between the free-flying clusmorphology—not known in the present case—and its mphology after deposition. Within the first few picosecondsthe impact, the cluster is heavily destroyed. The subststructure and the electron-phonon coupling govern its la

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evolution. Modeling predicts no significant substrate daage, nor any sizable impact-induced interfacial mixing.

Here, by HREM, we studied small local dilations ancontractions of the lattice of the deposited Au clustersMgO. Because the clusters are in epitaxy with the MgO sstrate, and because this substrate can be considered as amaterial with a known lattice parameter, both the cluster athe substrate lattices can be imaged, and the distances iAu clusters can be measured relative to the MgO distanFigure 9~b! shows the variation of the~220! lattice distancesfor the Au cluster and the MgO substrate in the@011# orien-tation of Fig. 9~a!. Layer 1 is the top layer of the clustewhich consists of 11 layers. Looking at Fig. 9~a!, one can saythat there is another layer above layer 1. However, becauis difficult to determine the edge between the cluster andvacuum~or to determine the first Au layer! due to edge ef-fects, and because filtering the image introduces some eperiodicity outside the cluster, we have neglected this lay

FIG. 11. Equidistances and interlayer spacing, layer by layethe cluster, starting from the top layer of the cluster. l refers tolayer number.~a! d220 equidistance.~b! d200 equidistance.~c! dl ,l 11

interlayer spacing. The results are shown at 300 K for fourk values.The dashed lines represent the bulk Au values at 300 K, asdicted by MD, and are shown for comparison. The arrows showposition of the fulcrum layer.

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PRB 62 10 391LOW-ENERGY-DEPOSITED Au CLUSTERS . . .

FIG. 12. ~a! Simulated HREM image. The model used as input for the simulations is obtained with MD using a force consk52.03102 J/m2. ~b! Comparison between the measured~220! distances of the experimental image of Fig. 9 and the simulated image in~a!.

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All layers with n.11 belong to the MgO substrate. Thisalso seen on the graph were all layers withn.11 are, withinthe errors, equal to 1.485 Å. The~220! distances in the Aulayers close to the interface decrease from 1.47260.013 Å~in layer 11! to 1.45160.010 Å ~in layer 9!. For layersabove (n,9) the ~220! lattice distance for bulk Au~1.442Å! is reached, except for the two topmost layers. In thlayers the lattice dilates by 1.4%. This is an imaging effecthe microscope, as will be discussed below.

The same behavior is also observed for clusters in a@001#orientation. Figure 10 shows a cluster of six layers highposited on MgO, and a graph of thed200 distances in thecluster and the substrate. The interface is between layeand 7. From the graph it can be concluded that laye(2.08160.033 Å! adapts itself partially to the MgO substrate. For the other layers (n,6) thed200 value for bulk Au~2.04 Å! is reached. Again the top two layers of the clusare dilated by 3% due to imaging artifacts in the microscoSuch values of dilation are also observed in other studiedeposited clusters.15

To crosscheck the results derived from the HREM iages, image simulations were made. A model of a Au cluwith bulk lattice parameters on a MgO substrate was usFrom these simulations it is confirmed that the image aalso the changes in lattice distances at the surface aredependent on defocus. For several defocus values a contion of the top layer was found; only a few values of defocshowed that the top layer could also be dilating. When msuring thed220 lattice distances on the simulated imagewhich show dilations in the top layer, these dilations aclearly visible, but no change in the~220! distances are seenear the Au/MgO interface. It is therefore concluded thatobserved dilations near the Au/MgO interface are not micscope imaging effects but real changes in structure.

C. Comparison between experiments and MD

To obtain a better structure model as starting point forimage simulations, a classical molecular-dynamics simution is used, with the previous model as starting point. Tmeand220 and d200 equidistances parallel to the substrasurface are estimated layer by layer in the cluster, as wethe spacing between these layers. The spacing betweenl and layerl 11 is noted asdl ,l 11. The results are shown in

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Fig. 11 for four force-constant values. For the discussionis useful to section the cluster into two areas at the eiglayer, represented by an arrow in Fig. 11. This was seeFig. 6 to be the intersection between the$111% facets of thecluster. In the area close to the substrate, the results fk.0 contrast with the free cluster, for whichk50. In thelatter case,d220, d200, andd11,12 contract, as is typical for afree surface, while the same quantities expand for thek.0values considered. This is the direct consequence ofMgO surface, whose lattice parameter is larger than bulkshown as a dashed horizontal line in Fig. 11. It is remarkathat the same three parameters in the eighth layer are ipendent ofk, and hence, within statistical uncertainties, hathe same values as in the free cluster. The deformation inlayer due to the Au/MgO interaction is thus weak in comparison with that in the other layers.

The situation is just the opposite for the series of layfurther away from the substrate, that is, for layer numbsmaller than 8.d220 and d200 are close to the bulk value athe free cluster is concerned, while it is systematicasmaller whenk.0. At the topmost layer, which containonly 16 atoms, relaxation is pronounced, and the lattice issmallest for all the four cases. The convergence of the resin the facets intersection~layer 8!, obtained with constraintsof different strengths, shows that its stiffness is rather pnounced. As a consequence, it acts as the fulcrum of a lethe increase of the equidistance on the one side, subseqto the constraint imposed by the substrate, is balancedtheir decrease on the other side. The lever effect withfacet intersection as a fulcrum is systematically found tocrease with the magnitude of the force constant@Figs. 11~a!and 11~b!#, which confirms the present interpretation. Trelation between the lever effect and the interlayer spacinFig. 11~c! is less obvious, although it can be emphasizIndeed, the effect of the substrate is to induce a pure shethe cluster. If one considers that a shear deformation ocat a constant volume, the increase of the equidistance parto the substrate surface must be balanced by a decreaselattice spacing normal to this surface, and vice versa. Thiexactly what is seen by comparing Fig. 11~c! with Figs.11~a! and 11~b!. An examination of the numerical values olayer spacings and equidistances show this conservatiobe quantitative.

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With the model obtained using ak value of2.03102 J/m2, HREM images were simulated following thsame procedure as before. The simulated image ofmodel is shown in Fig. 12, together with a graph of tmeasuredd220 distances in the Au cluster and the substraBecause the outer layer of the cluster is delocalized tooutside, we do not take this layer into account when meaing thed220 distances. These distances are calculated inmiddle part of the cluster. Figure 12~b! shows thed220 dis-tances of both the experimental and simulated images.obvious that both the interface between Au and MgO andlattice dilations in the cluster match very well. Only the twtop layers have ad220 distance, which is much smaller thawould be expected from the experimental image.

Another remarkable feature in both the experimentalage as well as in the simulated one is the delocalizationthe whole outer layer of the particle. In Fig. 13, circles reresent individual lattice spacings between two neighborbright dots in one layer for the experimental cluster imaThe two squares are the two lattice spacings near the surIt is seen that they are always larger than the other distanThe same behavior is also seen on the simulated image

V. SUMMARY AND CONCLUSIONS

Au clusters were produced by a laser vaporization souand were deposited with low kinetic energy onto amorphcarbon and single crystalline MgO surfaces. The individclusters were examined by high-resolution electron micrcopy. Different structures and morphologies were founddifferent surfaces—cubo-octahedral, decahedral, and ichedral clusters, as well as twinned structures on amorph

FIG. 13. Graph of the separate lattice distances measured idifferent layers of the Au cluster shown in Fig. 9. The circles reresent lattice distances in the middle of the cluster, and the squrepresent the two outermost distances in every layer.

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carbon—while fcc truncated octahedral and truncated hoctahedral shapes were found on MgO. From a comparbetween size distributions for the beam of free clustersfor the deposited clusters, it could be deduced that therlittle or no cluster coagulation taking place on either surfaThis was anticipated by the localizing behavior of the dagling bonds of the surface atoms in the case of amorphcarbon, and by the lattice matching condition in the caseMgO.

For cluster deposition on MgO, its well-known lattice prameter serves as an internal calibration of the HREMages, allowing a detailed investigation of dilations and cotractions of the fcc lattice within the nanoparticle. Thcluster structure was also simulated by classical molecdynamics, including an effective harmonic force that dscribes the binding of the interfacial Au atoms to the sustrate atoms. In the case of an 11-layer truncated octaheparticle, good agreement between experiment and mosimulation was found. Here the result of a MD simulatiousing a force constant of about half the Au bulk modulusa harmonic approximation was used as input for a HREimage simulation. Detailed investigations of equidistancparallel to the substrate and the spacings between the lain this particle revealed a shear deformation of the cluslattice induced by the substrate. The lattice dilation duethe epitaxial matching of Au on MgO in the layers closethe substrate goes along with lattice contractions for theper layers. Thus the layer corresponding to the facets insection can be seen to act as the fulcrum of a lever.

The present observations demonstrated that nanoclupreformed in the gas phase can be deposited with LECBDvarious substrates, without a measurable influence of tkinetic energy on the resulting structure or shape. Moreportant are cluster-surface interactions as shown by theserved differences in cluster morphology for the differesubstrates that were used. This is corroborated by thethat structures similar to the structures of nanoparticgrown from the gas phase are observed in the present stWith the availability of binary cluster sources, readily prducing binary clusters with compositions that are not avable as bulk alloys, several research opportunities openFurther research will therefore include structural investigtions of nanoalloys deposited on different substrates.

ACKNOWLEDGMENTS

B.P. and P.L. are grateful to the Fund for Scientific Rsearch - Flanders~Belgium! for financial support. L.T.K. isgrateful for grants from the Danish Research Council~SNFand STVF!. This research was part of the InteruniversPoles of Attraction Program—Belgian State, Prime Minter’s Office—Federal Office for Scientific, Technical anCultural Affairs ~IUAP!.

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.

*Corresponding author. Email: bapauw@ruca.ua.ac.be†Present address: Atlas Copco Airpower, Boomsesteenweg 9B-2610, Wilrijk, Belgium.

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