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Dynamics of gold clusters on amorphous carbon films induced by annealing in a transmission electron microscope
Surface Science 600 (2006) 632–640 www.elsevier.com/locate/susc
Dynamics of gold clusters on amorphous carbon films induced by annealing in a transmission electron microscope Matthias Wanner a, Ralph Werner
b,1
, Dagmar Gerthsen
a,*
a
b
Laboratorium fu¨r Elektronenmikroskopie, Universita¨t Karlsruhe, D-76128 Karlsruhe, Germany Institut fu¨r Theorie der Kondensierten Materie, Universita¨t Karlsruhe, D-76128 Karlsruhe, Germany Received 26 April 2005; accepted for publication 26 October 2005 Available online 9 December 2005
Abstract The change of the size distribution of Au clusters induced by annealing was studied in situ by transmission electron microscopy. Starting from statistically distributed Au clusters on a thin amorphous carbon film, ‘‘islands’’ are formed within a few months storage at room temperature, which consist of Au clusters with sizes <4 nm embedded in a thin Au film. These islands cover originally areas with sizes around 25 · 70 nm2. If the temperature is increased in the transmission electron microscope two different processes can be clearly distinguished that lead to the coarsening of the cluster size distribution: cluster coalescence and (contactless) Ostwald ripening. The degree and rate of the coarsening are found to depend on the underlying surface (Au film or amorphous carbon) and the exposure to the highflux high-energy electron beam, which can be estimated to lead to high-temperature excursions in a cluster on a 1012 s time scale. The experimental findings are confirmed by Monte-Carlo simulations using the many-body Gupta potentials in order to calculate the Au/Au interaction. Moreover, the results of MC simulations suggest an electron-beam induced formation of a ‘‘quasi-two-dimensional gas’’ of small highly mobile Au species on the Au film, which promotes Ostwald ripening. 2005 Elsevier B.V. All rights reserved. Keywords: Au clusters; Au film; Ostwald ripening; Transmission electron microscopy; Monte-Carlo simulations
1. Introduction Investigations concerning the stability of arrays of nanoparticles deposited on a substrate are of considerable interest with regard to potential applications in catalysis, nanoelectronics or nanooptics [1]. In technical applications the temporal behaviour of the particle size distribution and the interaction of particles with a substrate needs to be well understood because it strongly affects the functional properties of the particles, in some cases irreversibly [2–4]. In particular at elevated temperatures, a strong effect on the particle sizes must be expected. It is therefore highly relevant to study the effects of heating on nanoparticle arrays. *
Corresponding author. Tel.: +49 721 608 3200; fax: +49 721 608 3721. E-mail address: [email protected] (D. Gerthsen). 1 Present address: d-fine GmbH, Opernplatz 2, D-60313 Frankfurt, Germany. 0039-6028/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.10.056
Ostwald ripening is a well-known phenomenon, which has been studied thoroughly in bulk alloy systems as one decisive process during the precipitation of a new phase [5]. The phenomenon is based on the Gibbs–Thomson effect according to which small precipitates have a higher ‘‘vapour pressure’’ than larger precipitates [6]. This causes a net flow of material from small to larger precipitates leading to the coarsening of the particle size distribution. Ostwald ripening has been also shown to occur for ensembles of nanoparticles focusing particularly on model systems like two-dimensional Ag islands on Ag(1 1 1) substrates [7]. Applying transmission electron microscopy (TEM) the dynamic behaviour of nanoparticles can be imaged conveniently with high spatial resolution. Clearly, the influence of the high-flux high-energy electron beam has to be considered if TEM experiments are performed [8,9]. TEM studies have revealed the existence of a quasimolten [10]
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state in which small Au particles change the shape and structure on a time scale of minutes or a few hours. The energy to initiate this unstable state is provided by the highflux electron beam, by which the interaction of the particle with the substrate is reduced [11]. Recently, we have carried out transmission electron microscopy (TEM) experiments regarding the temporal behaviour of statistically distributed Au clusters with a diameter d < 4 nm deposited on amorphous carbon (a-C) films by laser ablation [12]. Experimentally, after a four months storage at room temperature it was observed that Au clusters embedded in a thin Au film with a typical area of 25 · 70 nm2 are formed, which modify significantly the initial statistical particle distribution found immediately after the deposition. We will further denote the film with the embedded clusters as ‘‘islands’’. In Fig. 1a, a TEM image of Au clusters supported on an a-C film one day after
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the deposition is shown. Fig. 1b displays an island consisting of a continuous Au film (region with darker contrast compared to a-C film) with embedded Au clusters, which is formed after the sample was stored about four months at room temperature in a sealed container in air. A detailed analysis in combination with Monte-Carlo (MC) simulations revealed that the embedding Au film results most likely from diffusion and agglomeration processes of very small Au species, which stem from the cluster source operating without mass selection [12]. In a first annealing experiment we observed coarsening phenomena when annealing the aforementioned Au films [12]. Fig. 1c illustrates how after 2 h of annealing at 373 K (i) the amount of Au forming the film is diminished (ii) the mean size of the particles is increased and (iii) the shape of the particles has become irregular. In this study, we report detailed annealing experiments of the given Au island system investigated by TEM. The influence of the electron beam on the dynamics of the Au adsorbate system is shown and contrasted to the temperature effects. MC simulations are performed to obtain a microscopic understanding of the observed phenomena. 2. Experimental techniques and theory 2.1. Experimental techniques
Fig. 1. TEM images of Au clusters deposited on an amorphous carbon substrate by laser ablation (3000 shots): (a) sample one day after its preparation, (b) sample about 100 d after its preparation and (c) sample about 100 d after its preparation and additional in situ annealing at 373 K for 2 h under exclusion of electron beam exposure.
The primary samples were prepared depositing Au clusters on commercial a-C films, which were produced by evaporation in a carbon arc by Arizona Carbon Foil Co., Inc. and distributed by Plano GmbH as type S160. These films are mounted on 200 mesh Cu grids. The thickness of the films is given by the manufacturer as 10–12.5 nm, its density is about 2.0 g/cm3. The Au clusters were collected from the primary beam of a laser vaporization cluster source, which has been described elsewhere [13]. In brief, the laser vaporization cluster source is a variant of the Smalley–deHeer-type [14] setup optimized by Heiz [15] for high yield. The source is equipped with a rotating Au disc target with a diameter of 50 mm, which is sealed with a teflon gasket against the source block. A pulsed laser (Neodym-YAG, Continuum, 532 nm, 30 Hz repetition rate) is focused through a nozzle onto the target. A pulsed valve (General Valve, 5 bar backing pressure of He), which is synchronized with the laser, quenches the vaporized atoms into clusters, which expand through the nozzle and a skimmer into an oil diffusion pumped vacuum chamber. Au clusters (and atoms) are deposited—however, without further mass selection—onto a TEM grid placed in the primary beam in a distance of about 40 cm from the nozzle. TEM was carried out with a Philips CM200 FEG/ST electron microscope operated at an energy of 200 keV. Typical current densities are in the order of 100 A/cm2. A Gatan 652 Double Tilt Heating Holder operated by a Gatan 901 SmartSet Hot Stage Controller was used to perform the in situ annealing experiments.
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2.2. Monte-Carlo (MC) simulations In order to simulate the dynamic behaviour of the given system we performed calculations using the canonical MC method. A standard Metropolis algorithm is employed [16– 18] with an update after each random displacement of an Au atom within the interval [0, dmax] in all spatial dimensions. dmax is set to yield an MC acceptance rate of 50– 60%. The pffiffiffiffi resulting temperature dependence is roughly d max / T . The boundary conditions are imposed by a hard wall cube with linear dimension Lx, Ly and Lz. The Au–Au interaction is modelled via the many-body Gupta potential [19] (GP): N X N N sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X 2 X X V ðfrij gÞ ¼ Aepðrij =r0 1Þ n e2qðrij =r0 1Þ i
j6¼i
i
j6¼1
ð1Þ The distances rij = jri rjj are measured in units of the ˚ . The indices first neighbour distance r0(Au) = 2.885 A i, j 2 {1, . . . , N} label the Au atoms at positions ri and rj, respectively. The parameterisation for Au as found in the literature [20], i.e. A = 0.2061 eV, n = 1.790 eV, p = 10.229 and q = 4.036, has been determined to match the bulk elastic constants and the surface contraction. The Au/a-C substrate interaction is modelled by two-particle interactions in the form of generalized Lennard-Jones 6–12 and 3–6 potentials. More precisely, the Au/a-C substrate potentials are averaged using approximate relative surface areas as weights and fitted to a modified Lennard-Jones potential ! 297 34:5 V LJ;mean ¼ V LJ;0 ð2Þ ðz=r0 1:2Þ12 ðz=r0 1:2Þ6
ing as shown in Fig. 1c for a sample, which was annealed for 2 h at 373 K. No further coarsening into larger clusters is observed if the period of annealing is prolonged. Therefore, we conclude that the system tends to develop to a metastable configuration, which depends on the maximum temperature it has been exposed to. 3.1. MC simulations of the cluster coalescence process To confirm this conclusion we performed MC simulations using the previously described platform. In order to model the situation of annealing we set the thermal energy to kBT = 0.0321 eV (T = 373 K). Due to the size limitations of the method, the calculations may only refer to a small section of such an Au island. Our simulations are based on a configuration consisting of two isolated Au clusters containing 55 and 147 atoms with 148 Au atoms dispersed randomly on an a-C substrate (top row of Fig. 2, 0 k MC steps). The left-hand side column of Fig. 2 shows the structure from above (x/y-projection) for an increasing number of MC steps, the right-hand side
where VLJ,0 is the binding energy and r0 = r0(Au). The details of their derivation, their application for the description of the Au–C interaction in our system as well as the approximation of the a-C structure are in detail outlined elsewhere [12]. Runs at the atomic level have been performed for up to 107 updates per atom for up to 590 atoms. Runs were stopped when a metastable configuration is obtained that does not evolve anymore on a reasonably accessible time scale. Depending on the size of the system metastable configurations are attained after a few minutes (N = 55) or a couple of days (Au double layer formation with embedded clusters with N = 590). Runs were performed up to three weeks to assure that the lifetime of the metastable configuration is at least an order of magnitude larger than its formation time. 3. Results and discussion Islands in all eight samples kept at room temperature even for more than a year look as the one displayed in Fig. 1b. Altering the structure of the islands requires heat-
Fig. 2. Time evolution of a system of one Au147, one Au55 cluster and 148 Au atoms placed randomly on the a-C substrate (not displayed). The Au/ a-C interaction energy is kept at 0.3 eV [12]. After 2060 k MC steps the thermal energy is increased from 0.0321 eV to 0.0642 eV. The two columns of images show orthogonal perspectives of the calculated model.
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column displays a side view (x/z-projection). All atoms are Au atoms while the C atoms are not plotted for clarity. Atoms located closer to the eye are shown in a brighter grey shade than the others. The formation of a crystalline Au layer can be observed in Fig. 2 as the number of MC steps increases, which agrees with previous MC simulations at room temperature [12]. Fig. 2 gives in addition a representative example for the calculations of the cluster coalescence process in an Au island at 373 K. The small Au55 cluster draws near the larger Au147 species until the two touch within about 40 k MC steps. At 190 k MC steps the calculation shows that the clusters coalesce. The fcc restructuring of the originally icosahedral multiply twinned clusters completed at 190 k MC steps (Fig. 2) is obviously induced by the fcc structure of the Au film. No further appreciable changes are observed if the calculation is continued beyond 190 k MC steps. Even a more than tenfold larger number of MC steps (cf. panel for 2060 k MC steps in Fig. 2) does not result in configurations that deviate significantly from the situation at 190 k MC steps, i.e. a metastable configuration is attained. This metastable configuration agrees with the one observed experimentally in the sense that no complete fusion to a spherical structure with minimal cohesive energy in observed. Note that most of the experimentally observed particles displayed in Fig. 1c do not show an ideal spherical shape. However, if the thermal energy is increased, e.g. by a factor of two (kBT = 0.0642 eV, T = 745 K), a fraction of the so far performed MC steps is sufficient to progress the cluster fusion significantly (Fig. 2, bottom row). Therefore, experimental images and MC simulations are consistent with the conclusion that the system tends to fall in temperature-dependent metastable configurations. 3.2. Time-dependent monitoring of the annealing process In order to study the details of the coarsening process we performed experiments monitoring continuously the systems evolution from metastable configurations. To this end a sample kept under ambient conditions for about four months after its preparation and exhibiting the typical Au island formation (Fig. 1b) is heated in situ from 361 K to 387 K in steps of 2 K. The sample is kept at each temperature for 2 min. The effect of this annealing on a small island was observed by TEM recording continuously images after each step of annealing. The images were used to generate a short video sequence. Four of these images recorded at 361 K, 369 K, 377 K and 387 K are displayed in Fig. 3a– d, respectively. The most eminent consequence of the heating process is the decrease of the particle number, whereas the averaged particle size increases. The latter is measured by the projected area covered by the individual particles divided by their number. Both quantities are shown in Fig. 5a by the squares (particle number N) and circles (averaged projected particle area A) as a function of the temperature. Note that the scaling of the axis applies to A and N.
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Concerning the embedding Au film one observes an outward fluctuation of the film at its boundaries. Small clusters near the film boundary appear to partially follow this movement. For instance the particle marked ‘‘A’’ in Fig. 3a–d is found to move as if it would be ‘‘flushed away’’ by the expanding film. The motion of the Au film and the particle A is easily seen in the video sequence while it is difficult to recognize in Fig. 3. However, the increase of the distance between particle A and the group of particles D marked by arrows in Fig. 3a and d serves as an indicator of the system dynamics. In this process the particle A is never observed to cross the border of the film as if the surface tension of a viscous liquid would keep it inside. This effect can be understood in terms of the binding energy of the particle to the Au film and is consistent with the observations in previous simulations [12]. The particle number continuously decreases while the remaining clusters increase in size. In some cases this process can be observed to result from approaching and fusing particles as opposed to a classical Ostwald ripening process by which (surface) diffusion leads to gradual size changes of the clusters. In some cases this process is preceded by remarkable extents of deformation of the participating particles, whereby the deformations are typically directed towards the particle with which it is going to fuse. These deformations are frequently accompanied by particle movement in the same direction. 3.3. Influence of the Au film on the cluster dynamics It can be observed that some particles suddenly start to shrink without noticeable contact to others, which is expected for ‘‘classical’’ Ostwald ripening. This is likely to correlate with the observation that some larger particles grow without any cognisable fusion processes for reasons of mass conservation. All the phenomena described can be observed, for instance, by considering the particles in selection ‘‘B’’ and the large particle (‘‘C’’) in Fig. 3. Up to 379 K the particles inside selection ‘‘B’’ fuse caused by purposive particle movement and deformation processes. However, at 379 K this large, fused particle starts to shrink and vanishes completely at 385 K (Fig. 3c and d). In this range of temperature one observes simultaneously an enormous growth of the lone large particle in ‘‘C’’, which now may be regarded as the center of a typical depletion zone [21,22]. Since in addition the three particles located outside the visible area of the Au film (‘‘D’’) obviously do not move, grow or shrink at all, we conclude that there is a close correlation between the observed extent of the particles’ growth, shrinking or movement and the presence of the Au film. In order to get a more detailed idea about the effect of the presence of the Au film on the dynamic behaviour of the adsorbed clusters we performed a second experiment under the impact of gradual heating. However, in contrast to the experiment described above, the sample observed
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Fig. 3. TEM images displaying the situation of an Au island before, during and after an annealing experiment with gradual heating: an original sample at (a) 361 K, (b) 369 K, (c) 377 K and (d) 387 K.
here was preheated for 4 h at 373 K without exposing it to the electron beam. As discussed above (cf. Section 1) this preheating leads to a dissolution of the Au film and thus yields a sample that allows to study the dynamics of the Au clusters in the absence of the film for comparison. Fig. 4 displays the first and the last micrograph taken while heating the sample from 365 K to 706 K at a continuous rate of 2 K/min. Again a short video sequence of one TEM image per about four minutes allows to observe more details in the course of annealing. As found in the annealing experiment described above, here the small clusters vanish and large ones grow at their expense, too. However, significant differences concerning these two experiments are found. Fig. 5b displays the decrease of the particle number and the increase of the averaged projected particle area with increasing temperature for the second annealing experiment. A comparison with Fig. 5a results in the following findings: (i) To achieve a comparable reduction of the particle number the experiment with the preheated sample has to be performed at much higher temperature, and (ii) it processes less uniformly.
The experimental data displayed in Fig. 5a can be roughly approximated by the best-fit straight lines s1 (N = 2.767 Æ T/K + 1083.299) and s2 (A/nm2 = 0.455 Æ T/K 159.865), whereas the data displayed in Fig. 5b is approximated by s3 (N = 0.105 Æ T/K + 104.961) and s4 (A/nm2 = 0.115 Æ T/K 33.568). N is the particle number in the observed area, whereas A is the projected average particle area and is approximated by N 1 X A¼ ai bi p; ð3Þ N i¼1 where a and b are the long and the short axes of the respective roughly ellipsoidal area. The inconsistency of the coarsening process for the preheated sample is reflected in the behaviour of N and A displayed in Fig. 5b. During the annealing of the preheated sample at least four sections seem to be distinguishable: the first section (up to 450 K) is dominated by the coalescence of small particles. In the second section (up to 580 K) a merely low extent of dynamic behaviour is observed. The third section (up to 670 K) is characterized
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Fig. 4. TEM images displaying the situation of an Au island before and after an annealing experiment with gradual heating of a preheated sample (details see text). The images are recorded at (a) 365 K and (b) 706 K.
by the enormous growth of the three larger particles at the expense of smaller ones. In the last section these grown, larger particles fuse. In fact, there seems to be a direct correlation between the Au film thickness and the homogeneity of the dynamic processes of Au clusters deposited on it. The Au clusters studied by Berlinger [21] are located on a Au film with t = 10 nm, where coarsening processes occurred without significant application of energy. In the case of the annealing experiment displayed in Fig. 3 the Au film thickness initially ranges most probably around 4–8 monolayers [12] and furthermore it may be reduced during the annealing experiment due to outward fluctuation and mass transport towards larger particles. Therefore it seems to be reasonable that some of the particles are observed to participate in cluster dynamics, whereas others, whose extent of interaction with the system is reduced due to a local lack of embedding Au film, seem to remain unaffected, at least temporary. Since an embedding Au film is missing at least almost completely in the case of the annealing experiment reflected in Fig. 5b, here, the dynamic processes occur intermittently. Obviously, the a-C surface inhibits the homogeneous development of the dynamic processes due to high-energy barriers. 3.4. Au film mediated Ostwald ripening induced by electronbeam energy transfer
Fig. 5. Particle number N and averaged particle area A as a function of the temperature observed during an annealing experiment (a) in an original island and (b) in a preheated island.
It has already been pointed out that in the annealing experiment, which was performed in the presence of a Au film, a significant number of events were observed, where larger particles grew at the expense of smaller ones without direct contact of the involved particles. On the other hand, such contactless events occur only very rarely in the case of the second annealing experiment in the absence of the Au film, although it is performed up to a much higher temperature. This is another argument to conclude that the Au film supports mass transport phenomena significantly.
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At the same time, all samples that were annealed without TEM monitoring as represented by Fig. 1c generally show a much larger number of clusters than samples that were annealed under the repeated influence of the electron beam as shown in Fig. 3d. In our system ‘‘classical’’ Ostwald ripening is only observed in the presence of an embedding film, heating and electron-beam exposure, which contrasts to the observations described for other systems [7,21]. This discrepancy might be caused, as already mentioned, by the lack of homogeneity of our very thin Au film, which is possibly induced by the poorly defined a-C surface, and by the absence of UHV conditions inside the microscope. Heating of the sample might result in the vaporisation of surface contaminating adsorbates, which therefore will facilitate the migration of Au atoms across this surface. Particle movement and deformation under electronbeam exposure are phenomena, which are studied in detail for about two decades [8–11]. The experimental findings are explained by the concept of quasimelting [11] as well as by calculations concerning electron-beam induced short-time temperature excursions. The latter can readily be understood by the production of Auger electrons and a subsequent local heating of the sample as suggested by Williams [9]. Following these calculations one has to expect a local temperature increase up to about 2100, which results in a particle temperature of 2473 K. The excess energy dissipates on time scales in the order of a few picoseconds. Due to the short duration of this state, no substantial extent of evaporation can be observed, although surface tension effects may increase the vapor pressure of small Au clusters up to 10 Torr at such temperatures [9]. In order to obtain a microscopic understanding of the physical consequences of such a local energy surplus, we simulated the atomic motion in an originally icosahedral Au309 cluster embedded in a thin Au film at 2473 K. The results of this simulation are displayed in Fig. 6. The top
Fig. 6. Time evolution of a system of an icosahedral Au309 cluster and 160 Au atoms placed randomly on the a-C substrate. The Au/a-C interaction is kept at 0.3 eV [12]. The top row shows images from the MC simulation at 373 K (kBT = 0.0321 eV), images in the center and the bottom row are calculated for 2473 K (kBT = 0.2131 eV).
row of images shows the system at 373 K (kBT = 0.0321 eV), which corresponds to the process of annealing without electron-beam exposure. Restructuring and an increase of the film thickness occurs but no release of Au atoms or small molecules from the cluster could be observed during the whole period of 41 k MC steps. The images in the middle and bottom row of Fig. 6 refer to the electron-beam induced maximum local temperature after 1, 5, 6 and 7 k MC steps. Since the mean atomic displacement during one MC step corresponds roughly to the mean atomic displacement due to lattice vibrations, the time constant of a MC step can be estimated to be 1013 s the simulation length covers the estimated dissipation time of the local energy increase. The image recorded after 6 k MC steps shows a fully released Au2 molecule recorded in its largest distance from the cluster. While such ‘‘gaseous’’ monomer and dimer fluctuations occur with a fairly high rate, the energy fluctuations are insufficient to completely dissociate these species at the given temperature [18]. On the other hand, the fluctuations allow atoms to migrate and recondense somewhere else after some time thus overcoming even large local energy barriers. The simulations of the local temperature fluctuations due to electron-beam energy transfer suggest that Au diffusion is strongly enhanced during TEM imaging consistent with the experimental observation. Note that all clusters displayed in the video sequences, which grow larger than 8 nm in diameter, do exhibit a significant loss of their dynamic behaviour. They do not move anymore and seem to be resistant towards shrinking. In fact, Smith et al. [8], who investigated the electron-beam induced dynamic behaviour of small Au clusters by HRTEM, found that structural rearrangements indicating the presence of a quasimolten state were rare for crystals larger than 8 nm. This finding may explain, why the cluster formed in selection ‘‘B’’ in Fig. 3 suddenly starts to shrink again: its maximum diameter of about 6.5 nm at 379 K is obviously not enough to leave the quasimolten state. It must be stressed at this point once again that the electron beam does not induce any noticeable Au mass transport at room temperature. Thermal activation is required for the observed phenomena, because the total sample energy density due to electron-beam energy transfer is small. To be specific, the simulation of the short-time temperature excursion is only suitable to illustrate that the excess energy induced by the Auger process can lead to an enhanced mobility of the surface atoms. In the region of the energy transfer the system is not in thermal equilibrium and as a consequence a microcanonical simulation of a system sufficiently large to allow for the proper description of the dissipation of the excess energy would be required for a full quantitative reproduction of the experiment. While such an extensive investigation is beyond the scope of the present work the fact that the enhancement of the Ostwald ripening process is not observed at room temperature shows the importance of the kinetic initial condition of the Auger process. At the temperature of the experimental observa-
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tion of the enhanced Ostwald ripening of T 400 K the Au clusters of the sample are close to their melting temperature [8,11]. The higher mobility of the surface atoms near the melting temperature obviously is a necessary condition for the observed effect. Therefore, in order to explain the observed phenomenon of contactless combined cluster growing/shrinking, which depends on the presence of a Au film as well as on electron-beam exposure, we propose the presence of a ‘‘quasitwo-dimensional gas’’ of Au atoms and small Au molecules. Such a ‘‘gas’’ could easily enhance Ostwald ripening via surface diffusion over larger distances without direct contact of the interacting clusters on an observable time scale. Note that the presence of such a ‘‘gas’’ could also explain the previously mentioned finding of the electronbeam induced boundary fluctuation of the Au film. Small Au molecules or Au atoms, which randomly cross the edge of the Au film recondense nearby on the defective a-C surface. The cohesive energy yields a restoring force. Since there should emerge more migrating Au species from the inner of the film than from its edge, in fact one may expect an expansion of the film. 4. Summary In this work we describe the effects of annealing of previously described Au ‘‘islands’’ [12], which are observed in situ in a transmission electron microscope. The islands consist of Au clusters embedded in a thin Au film, which are observed about 100 days after the deposition of non-size-selected Au clusters by laser ablation technique on a-C substrates. To model the experimental findings we performed MC simulations using Gupta-potentials, which describe the Au/Au interaction, whereas the Au/a-C interaction is obtained via DFT approach. If the temperature is increased in the transmission electron microscope, coarsening of the particles size distribution occurs by (a) cluster coalescence and (b) contact-less Ostwald ripening. The extent and rate of cluster coarsening, which depend on the temperature, surface and electron-beam exposure can be summarized in the following way: • The coarsening of the Au clusters was assessed by the average projected area of the clusters. It increases if the temperature is raised. The cluster size distributions are found to settle into metastable configurations if the temperature remains constant. • Islands (Au clusters on an Au film), which are annealed under continuous electron-beam exposure (monitoring by the TEM) show pronounced cluster coalescence and contact-less shrinking and growth even over large cluster distances, which is typical for classical Ostwald ripening. • Annealing of islands at 373 K without electron-beam exposure for about 4 h results in the dissolution of the Au film in which the clusters are embedded. If the clusters without underlying Au film are annealed up to 706 K further coarsening occurs. However, Ostwald ripening is
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strongly impeded as compared to cluster coalescence, which can be explained by the strong interaction of small diffusing Au species with the structurally irregular a-C surface. • Due to energy transfer from the high-energy electrons to the clusters high-temperature excursions on a 1012 s time scale must be taken into account. The results of Monte-Carlo simulations suggest the formation of a ‘‘quasi-two-dimensional gas’’ of small Au species, which are highly mobile only on a Au film. This will lead to the promotion of Ostwald ripening as a consequence of electron-beam exposure. • The influence of the electron beam in TEM studies of particle coarsening processes as a function of temperature can be minimized by the following procedure. During the in situ annealing the sample is only exposed to the electron beam to take snapshots in time intervals, which are adequate for the time scale of the coarsening process.
Acknowledgements We thank S.-S. Jester and M. M. Kappes (Institute for Physical Chemistry, University of Karlsruhe, Germany) for the sample preparation, outlining the preparation process, and fruitful discussions. The work was supported by the Center for Functional Nanostructures of the Deutsche Forschungsgemeinschaft. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.susc.2005. 10.056. References [1] G. Schmid, D.V. Talapin, E.V. Shevchenko, Nanoparticles (2004) 251, and references therein. [2] D.L. Peng, T.J. Konno, K. Wakoh, T. Hiara, K. Sumiyama, Appl. Phys. Lett. 78 (2001) 1535. [3] J. Du, S. Wang, J.N. Zhou, J.W. Harrell, J.A. Barnard, J. Magn. Magn. Mater. 219 (2000) 78. [4] N. Sandhyarani, T. Pradeep, J. Mater. Chem. 10 (2000) 981. [5] P.G. Shewman, Transformations in Metals, McGraw-Hill, New York, 1969. [6] I.M. Lifshitz, V.V. Slyozow, J. Phys. Chem. Solids 19 (1961) 35. [7] K. Morgenstern, G. Rosenfeld, G. Comsa, Phys. Rev. Lett. 289 (1996) 2113. [8] D.J. Smith, A.K. Petford-Long, L.R. Wallenberg, J.-O. Bovin, Science 233 (1986) 872. [9] P. Williams, Appl. Phys. Lett. 50 (1987) 1760. [10] P.M. Ajayan, L.D. Marks, Phys. Rev. Lett. 60 (1988) 585. [11] P.M. Ajayan, L.D. Marks, Phys. Rev. Lett. 63 (1989) 279. [12] R. Werner, M. Wanner, G. Schneider, D. Gerthsen, Phys. Rev. B 72 (2005) 045426. [13] (a) P. Weis, O. Welz, E. Vollmer, M.M. Kappes, J. Chem. Phys. 120 (2004) 677; (b) P. Weis, S. Gilb, P. Gerhardt, M.M. Kappes, Int. J. Mass Spec. 216 (2002) 59.
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Dynamics of gold clusters on amorphous carbon films induced by annealing in a transmission electron microscope Matthias Wanner a, Ralph Werner
b,1
, Dagmar Gerthsen
a,*
a
b
Laboratorium fu¨r Elektronenmikroskopie, Universita¨t Karlsruhe, D-76128 Karlsruhe, Germany Institut fu¨r Theorie der Kondensierten Materie, Universita¨t Karlsruhe, D-76128 Karlsruhe, Germany Received 26 April 2005; accepted for publication 26 October 2005 Available online 9 December 2005
Abstract The change of the size distribution of Au clusters induced by annealing was studied in situ by transmission electron microscopy. Starting from statistically distributed Au clusters on a thin amorphous carbon film, ‘‘islands’’ are formed within a few months storage at room temperature, which consist of Au clusters with sizes <4 nm embedded in a thin Au film. These islands cover originally areas with sizes around 25 · 70 nm2. If the temperature is increased in the transmission electron microscope two different processes can be clearly distinguished that lead to the coarsening of the cluster size distribution: cluster coalescence and (contactless) Ostwald ripening. The degree and rate of the coarsening are found to depend on the underlying surface (Au film or amorphous carbon) and the exposure to the highflux high-energy electron beam, which can be estimated to lead to high-temperature excursions in a cluster on a 1012 s time scale. The experimental findings are confirmed by Monte-Carlo simulations using the many-body Gupta potentials in order to calculate the Au/Au interaction. Moreover, the results of MC simulations suggest an electron-beam induced formation of a ‘‘quasi-two-dimensional gas’’ of small highly mobile Au species on the Au film, which promotes Ostwald ripening. 2005 Elsevier B.V. All rights reserved. Keywords: Au clusters; Au film; Ostwald ripening; Transmission electron microscopy; Monte-Carlo simulations
1. Introduction Investigations concerning the stability of arrays of nanoparticles deposited on a substrate are of considerable interest with regard to potential applications in catalysis, nanoelectronics or nanooptics [1]. In technical applications the temporal behaviour of the particle size distribution and the interaction of particles with a substrate needs to be well understood because it strongly affects the functional properties of the particles, in some cases irreversibly [2–4]. In particular at elevated temperatures, a strong effect on the particle sizes must be expected. It is therefore highly relevant to study the effects of heating on nanoparticle arrays. *
Corresponding author. Tel.: +49 721 608 3200; fax: +49 721 608 3721. E-mail address: [email protected] (D. Gerthsen). 1 Present address: d-fine GmbH, Opernplatz 2, D-60313 Frankfurt, Germany. 0039-6028/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2005.10.056
Ostwald ripening is a well-known phenomenon, which has been studied thoroughly in bulk alloy systems as one decisive process during the precipitation of a new phase [5]. The phenomenon is based on the Gibbs–Thomson effect according to which small precipitates have a higher ‘‘vapour pressure’’ than larger precipitates [6]. This causes a net flow of material from small to larger precipitates leading to the coarsening of the particle size distribution. Ostwald ripening has been also shown to occur for ensembles of nanoparticles focusing particularly on model systems like two-dimensional Ag islands on Ag(1 1 1) substrates [7]. Applying transmission electron microscopy (TEM) the dynamic behaviour of nanoparticles can be imaged conveniently with high spatial resolution. Clearly, the influence of the high-flux high-energy electron beam has to be considered if TEM experiments are performed [8,9]. TEM studies have revealed the existence of a quasimolten [10]
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state in which small Au particles change the shape and structure on a time scale of minutes or a few hours. The energy to initiate this unstable state is provided by the highflux electron beam, by which the interaction of the particle with the substrate is reduced [11]. Recently, we have carried out transmission electron microscopy (TEM) experiments regarding the temporal behaviour of statistically distributed Au clusters with a diameter d < 4 nm deposited on amorphous carbon (a-C) films by laser ablation [12]. Experimentally, after a four months storage at room temperature it was observed that Au clusters embedded in a thin Au film with a typical area of 25 · 70 nm2 are formed, which modify significantly the initial statistical particle distribution found immediately after the deposition. We will further denote the film with the embedded clusters as ‘‘islands’’. In Fig. 1a, a TEM image of Au clusters supported on an a-C film one day after
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the deposition is shown. Fig. 1b displays an island consisting of a continuous Au film (region with darker contrast compared to a-C film) with embedded Au clusters, which is formed after the sample was stored about four months at room temperature in a sealed container in air. A detailed analysis in combination with Monte-Carlo (MC) simulations revealed that the embedding Au film results most likely from diffusion and agglomeration processes of very small Au species, which stem from the cluster source operating without mass selection [12]. In a first annealing experiment we observed coarsening phenomena when annealing the aforementioned Au films [12]. Fig. 1c illustrates how after 2 h of annealing at 373 K (i) the amount of Au forming the film is diminished (ii) the mean size of the particles is increased and (iii) the shape of the particles has become irregular. In this study, we report detailed annealing experiments of the given Au island system investigated by TEM. The influence of the electron beam on the dynamics of the Au adsorbate system is shown and contrasted to the temperature effects. MC simulations are performed to obtain a microscopic understanding of the observed phenomena. 2. Experimental techniques and theory 2.1. Experimental techniques
Fig. 1. TEM images of Au clusters deposited on an amorphous carbon substrate by laser ablation (3000 shots): (a) sample one day after its preparation, (b) sample about 100 d after its preparation and (c) sample about 100 d after its preparation and additional in situ annealing at 373 K for 2 h under exclusion of electron beam exposure.
The primary samples were prepared depositing Au clusters on commercial a-C films, which were produced by evaporation in a carbon arc by Arizona Carbon Foil Co., Inc. and distributed by Plano GmbH as type S160. These films are mounted on 200 mesh Cu grids. The thickness of the films is given by the manufacturer as 10–12.5 nm, its density is about 2.0 g/cm3. The Au clusters were collected from the primary beam of a laser vaporization cluster source, which has been described elsewhere [13]. In brief, the laser vaporization cluster source is a variant of the Smalley–deHeer-type [14] setup optimized by Heiz [15] for high yield. The source is equipped with a rotating Au disc target with a diameter of 50 mm, which is sealed with a teflon gasket against the source block. A pulsed laser (Neodym-YAG, Continuum, 532 nm, 30 Hz repetition rate) is focused through a nozzle onto the target. A pulsed valve (General Valve, 5 bar backing pressure of He), which is synchronized with the laser, quenches the vaporized atoms into clusters, which expand through the nozzle and a skimmer into an oil diffusion pumped vacuum chamber. Au clusters (and atoms) are deposited—however, without further mass selection—onto a TEM grid placed in the primary beam in a distance of about 40 cm from the nozzle. TEM was carried out with a Philips CM200 FEG/ST electron microscope operated at an energy of 200 keV. Typical current densities are in the order of 100 A/cm2. A Gatan 652 Double Tilt Heating Holder operated by a Gatan 901 SmartSet Hot Stage Controller was used to perform the in situ annealing experiments.
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2.2. Monte-Carlo (MC) simulations In order to simulate the dynamic behaviour of the given system we performed calculations using the canonical MC method. A standard Metropolis algorithm is employed [16– 18] with an update after each random displacement of an Au atom within the interval [0, dmax] in all spatial dimensions. dmax is set to yield an MC acceptance rate of 50– 60%. The pffiffiffiffi resulting temperature dependence is roughly d max / T . The boundary conditions are imposed by a hard wall cube with linear dimension Lx, Ly and Lz. The Au–Au interaction is modelled via the many-body Gupta potential [19] (GP): N X N N sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X 2 X X V ðfrij gÞ ¼ Aepðrij =r0 1Þ n e2qðrij =r0 1Þ i
j6¼i
i
j6¼1
ð1Þ The distances rij = jri rjj are measured in units of the ˚ . The indices first neighbour distance r0(Au) = 2.885 A i, j 2 {1, . . . , N} label the Au atoms at positions ri and rj, respectively. The parameterisation for Au as found in the literature [20], i.e. A = 0.2061 eV, n = 1.790 eV, p = 10.229 and q = 4.036, has been determined to match the bulk elastic constants and the surface contraction. The Au/a-C substrate interaction is modelled by two-particle interactions in the form of generalized Lennard-Jones 6–12 and 3–6 potentials. More precisely, the Au/a-C substrate potentials are averaged using approximate relative surface areas as weights and fitted to a modified Lennard-Jones potential ! 297 34:5 V LJ;mean ¼ V LJ;0 ð2Þ ðz=r0 1:2Þ12 ðz=r0 1:2Þ6
ing as shown in Fig. 1c for a sample, which was annealed for 2 h at 373 K. No further coarsening into larger clusters is observed if the period of annealing is prolonged. Therefore, we conclude that the system tends to develop to a metastable configuration, which depends on the maximum temperature it has been exposed to. 3.1. MC simulations of the cluster coalescence process To confirm this conclusion we performed MC simulations using the previously described platform. In order to model the situation of annealing we set the thermal energy to kBT = 0.0321 eV (T = 373 K). Due to the size limitations of the method, the calculations may only refer to a small section of such an Au island. Our simulations are based on a configuration consisting of two isolated Au clusters containing 55 and 147 atoms with 148 Au atoms dispersed randomly on an a-C substrate (top row of Fig. 2, 0 k MC steps). The left-hand side column of Fig. 2 shows the structure from above (x/y-projection) for an increasing number of MC steps, the right-hand side
where VLJ,0 is the binding energy and r0 = r0(Au). The details of their derivation, their application for the description of the Au–C interaction in our system as well as the approximation of the a-C structure are in detail outlined elsewhere [12]. Runs at the atomic level have been performed for up to 107 updates per atom for up to 590 atoms. Runs were stopped when a metastable configuration is obtained that does not evolve anymore on a reasonably accessible time scale. Depending on the size of the system metastable configurations are attained after a few minutes (N = 55) or a couple of days (Au double layer formation with embedded clusters with N = 590). Runs were performed up to three weeks to assure that the lifetime of the metastable configuration is at least an order of magnitude larger than its formation time. 3. Results and discussion Islands in all eight samples kept at room temperature even for more than a year look as the one displayed in Fig. 1b. Altering the structure of the islands requires heat-
Fig. 2. Time evolution of a system of one Au147, one Au55 cluster and 148 Au atoms placed randomly on the a-C substrate (not displayed). The Au/ a-C interaction energy is kept at 0.3 eV [12]. After 2060 k MC steps the thermal energy is increased from 0.0321 eV to 0.0642 eV. The two columns of images show orthogonal perspectives of the calculated model.
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column displays a side view (x/z-projection). All atoms are Au atoms while the C atoms are not plotted for clarity. Atoms located closer to the eye are shown in a brighter grey shade than the others. The formation of a crystalline Au layer can be observed in Fig. 2 as the number of MC steps increases, which agrees with previous MC simulations at room temperature [12]. Fig. 2 gives in addition a representative example for the calculations of the cluster coalescence process in an Au island at 373 K. The small Au55 cluster draws near the larger Au147 species until the two touch within about 40 k MC steps. At 190 k MC steps the calculation shows that the clusters coalesce. The fcc restructuring of the originally icosahedral multiply twinned clusters completed at 190 k MC steps (Fig. 2) is obviously induced by the fcc structure of the Au film. No further appreciable changes are observed if the calculation is continued beyond 190 k MC steps. Even a more than tenfold larger number of MC steps (cf. panel for 2060 k MC steps in Fig. 2) does not result in configurations that deviate significantly from the situation at 190 k MC steps, i.e. a metastable configuration is attained. This metastable configuration agrees with the one observed experimentally in the sense that no complete fusion to a spherical structure with minimal cohesive energy in observed. Note that most of the experimentally observed particles displayed in Fig. 1c do not show an ideal spherical shape. However, if the thermal energy is increased, e.g. by a factor of two (kBT = 0.0642 eV, T = 745 K), a fraction of the so far performed MC steps is sufficient to progress the cluster fusion significantly (Fig. 2, bottom row). Therefore, experimental images and MC simulations are consistent with the conclusion that the system tends to fall in temperature-dependent metastable configurations. 3.2. Time-dependent monitoring of the annealing process In order to study the details of the coarsening process we performed experiments monitoring continuously the systems evolution from metastable configurations. To this end a sample kept under ambient conditions for about four months after its preparation and exhibiting the typical Au island formation (Fig. 1b) is heated in situ from 361 K to 387 K in steps of 2 K. The sample is kept at each temperature for 2 min. The effect of this annealing on a small island was observed by TEM recording continuously images after each step of annealing. The images were used to generate a short video sequence. Four of these images recorded at 361 K, 369 K, 377 K and 387 K are displayed in Fig. 3a– d, respectively. The most eminent consequence of the heating process is the decrease of the particle number, whereas the averaged particle size increases. The latter is measured by the projected area covered by the individual particles divided by their number. Both quantities are shown in Fig. 5a by the squares (particle number N) and circles (averaged projected particle area A) as a function of the temperature. Note that the scaling of the axis applies to A and N.
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Concerning the embedding Au film one observes an outward fluctuation of the film at its boundaries. Small clusters near the film boundary appear to partially follow this movement. For instance the particle marked ‘‘A’’ in Fig. 3a–d is found to move as if it would be ‘‘flushed away’’ by the expanding film. The motion of the Au film and the particle A is easily seen in the video sequence while it is difficult to recognize in Fig. 3. However, the increase of the distance between particle A and the group of particles D marked by arrows in Fig. 3a and d serves as an indicator of the system dynamics. In this process the particle A is never observed to cross the border of the film as if the surface tension of a viscous liquid would keep it inside. This effect can be understood in terms of the binding energy of the particle to the Au film and is consistent with the observations in previous simulations [12]. The particle number continuously decreases while the remaining clusters increase in size. In some cases this process can be observed to result from approaching and fusing particles as opposed to a classical Ostwald ripening process by which (surface) diffusion leads to gradual size changes of the clusters. In some cases this process is preceded by remarkable extents of deformation of the participating particles, whereby the deformations are typically directed towards the particle with which it is going to fuse. These deformations are frequently accompanied by particle movement in the same direction. 3.3. Influence of the Au film on the cluster dynamics It can be observed that some particles suddenly start to shrink without noticeable contact to others, which is expected for ‘‘classical’’ Ostwald ripening. This is likely to correlate with the observation that some larger particles grow without any cognisable fusion processes for reasons of mass conservation. All the phenomena described can be observed, for instance, by considering the particles in selection ‘‘B’’ and the large particle (‘‘C’’) in Fig. 3. Up to 379 K the particles inside selection ‘‘B’’ fuse caused by purposive particle movement and deformation processes. However, at 379 K this large, fused particle starts to shrink and vanishes completely at 385 K (Fig. 3c and d). In this range of temperature one observes simultaneously an enormous growth of the lone large particle in ‘‘C’’, which now may be regarded as the center of a typical depletion zone [21,22]. Since in addition the three particles located outside the visible area of the Au film (‘‘D’’) obviously do not move, grow or shrink at all, we conclude that there is a close correlation between the observed extent of the particles’ growth, shrinking or movement and the presence of the Au film. In order to get a more detailed idea about the effect of the presence of the Au film on the dynamic behaviour of the adsorbed clusters we performed a second experiment under the impact of gradual heating. However, in contrast to the experiment described above, the sample observed
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Fig. 3. TEM images displaying the situation of an Au island before, during and after an annealing experiment with gradual heating: an original sample at (a) 361 K, (b) 369 K, (c) 377 K and (d) 387 K.
here was preheated for 4 h at 373 K without exposing it to the electron beam. As discussed above (cf. Section 1) this preheating leads to a dissolution of the Au film and thus yields a sample that allows to study the dynamics of the Au clusters in the absence of the film for comparison. Fig. 4 displays the first and the last micrograph taken while heating the sample from 365 K to 706 K at a continuous rate of 2 K/min. Again a short video sequence of one TEM image per about four minutes allows to observe more details in the course of annealing. As found in the annealing experiment described above, here the small clusters vanish and large ones grow at their expense, too. However, significant differences concerning these two experiments are found. Fig. 5b displays the decrease of the particle number and the increase of the averaged projected particle area with increasing temperature for the second annealing experiment. A comparison with Fig. 5a results in the following findings: (i) To achieve a comparable reduction of the particle number the experiment with the preheated sample has to be performed at much higher temperature, and (ii) it processes less uniformly.
The experimental data displayed in Fig. 5a can be roughly approximated by the best-fit straight lines s1 (N = 2.767 Æ T/K + 1083.299) and s2 (A/nm2 = 0.455 Æ T/K 159.865), whereas the data displayed in Fig. 5b is approximated by s3 (N = 0.105 Æ T/K + 104.961) and s4 (A/nm2 = 0.115 Æ T/K 33.568). N is the particle number in the observed area, whereas A is the projected average particle area and is approximated by N 1 X A¼ ai bi p; ð3Þ N i¼1 where a and b are the long and the short axes of the respective roughly ellipsoidal area. The inconsistency of the coarsening process for the preheated sample is reflected in the behaviour of N and A displayed in Fig. 5b. During the annealing of the preheated sample at least four sections seem to be distinguishable: the first section (up to 450 K) is dominated by the coalescence of small particles. In the second section (up to 580 K) a merely low extent of dynamic behaviour is observed. The third section (up to 670 K) is characterized
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Fig. 4. TEM images displaying the situation of an Au island before and after an annealing experiment with gradual heating of a preheated sample (details see text). The images are recorded at (a) 365 K and (b) 706 K.
by the enormous growth of the three larger particles at the expense of smaller ones. In the last section these grown, larger particles fuse. In fact, there seems to be a direct correlation between the Au film thickness and the homogeneity of the dynamic processes of Au clusters deposited on it. The Au clusters studied by Berlinger [21] are located on a Au film with t = 10 nm, where coarsening processes occurred without significant application of energy. In the case of the annealing experiment displayed in Fig. 3 the Au film thickness initially ranges most probably around 4–8 monolayers [12] and furthermore it may be reduced during the annealing experiment due to outward fluctuation and mass transport towards larger particles. Therefore it seems to be reasonable that some of the particles are observed to participate in cluster dynamics, whereas others, whose extent of interaction with the system is reduced due to a local lack of embedding Au film, seem to remain unaffected, at least temporary. Since an embedding Au film is missing at least almost completely in the case of the annealing experiment reflected in Fig. 5b, here, the dynamic processes occur intermittently. Obviously, the a-C surface inhibits the homogeneous development of the dynamic processes due to high-energy barriers. 3.4. Au film mediated Ostwald ripening induced by electronbeam energy transfer
Fig. 5. Particle number N and averaged particle area A as a function of the temperature observed during an annealing experiment (a) in an original island and (b) in a preheated island.
It has already been pointed out that in the annealing experiment, which was performed in the presence of a Au film, a significant number of events were observed, where larger particles grew at the expense of smaller ones without direct contact of the involved particles. On the other hand, such contactless events occur only very rarely in the case of the second annealing experiment in the absence of the Au film, although it is performed up to a much higher temperature. This is another argument to conclude that the Au film supports mass transport phenomena significantly.
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At the same time, all samples that were annealed without TEM monitoring as represented by Fig. 1c generally show a much larger number of clusters than samples that were annealed under the repeated influence of the electron beam as shown in Fig. 3d. In our system ‘‘classical’’ Ostwald ripening is only observed in the presence of an embedding film, heating and electron-beam exposure, which contrasts to the observations described for other systems [7,21]. This discrepancy might be caused, as already mentioned, by the lack of homogeneity of our very thin Au film, which is possibly induced by the poorly defined a-C surface, and by the absence of UHV conditions inside the microscope. Heating of the sample might result in the vaporisation of surface contaminating adsorbates, which therefore will facilitate the migration of Au atoms across this surface. Particle movement and deformation under electronbeam exposure are phenomena, which are studied in detail for about two decades [8–11]. The experimental findings are explained by the concept of quasimelting [11] as well as by calculations concerning electron-beam induced short-time temperature excursions. The latter can readily be understood by the production of Auger electrons and a subsequent local heating of the sample as suggested by Williams [9]. Following these calculations one has to expect a local temperature increase up to about 2100, which results in a particle temperature of 2473 K. The excess energy dissipates on time scales in the order of a few picoseconds. Due to the short duration of this state, no substantial extent of evaporation can be observed, although surface tension effects may increase the vapor pressure of small Au clusters up to 10 Torr at such temperatures [9]. In order to obtain a microscopic understanding of the physical consequences of such a local energy surplus, we simulated the atomic motion in an originally icosahedral Au309 cluster embedded in a thin Au film at 2473 K. The results of this simulation are displayed in Fig. 6. The top
Fig. 6. Time evolution of a system of an icosahedral Au309 cluster and 160 Au atoms placed randomly on the a-C substrate. The Au/a-C interaction is kept at 0.3 eV [12]. The top row shows images from the MC simulation at 373 K (kBT = 0.0321 eV), images in the center and the bottom row are calculated for 2473 K (kBT = 0.2131 eV).
row of images shows the system at 373 K (kBT = 0.0321 eV), which corresponds to the process of annealing without electron-beam exposure. Restructuring and an increase of the film thickness occurs but no release of Au atoms or small molecules from the cluster could be observed during the whole period of 41 k MC steps. The images in the middle and bottom row of Fig. 6 refer to the electron-beam induced maximum local temperature after 1, 5, 6 and 7 k MC steps. Since the mean atomic displacement during one MC step corresponds roughly to the mean atomic displacement due to lattice vibrations, the time constant of a MC step can be estimated to be 1013 s the simulation length covers the estimated dissipation time of the local energy increase. The image recorded after 6 k MC steps shows a fully released Au2 molecule recorded in its largest distance from the cluster. While such ‘‘gaseous’’ monomer and dimer fluctuations occur with a fairly high rate, the energy fluctuations are insufficient to completely dissociate these species at the given temperature [18]. On the other hand, the fluctuations allow atoms to migrate and recondense somewhere else after some time thus overcoming even large local energy barriers. The simulations of the local temperature fluctuations due to electron-beam energy transfer suggest that Au diffusion is strongly enhanced during TEM imaging consistent with the experimental observation. Note that all clusters displayed in the video sequences, which grow larger than 8 nm in diameter, do exhibit a significant loss of their dynamic behaviour. They do not move anymore and seem to be resistant towards shrinking. In fact, Smith et al. [8], who investigated the electron-beam induced dynamic behaviour of small Au clusters by HRTEM, found that structural rearrangements indicating the presence of a quasimolten state were rare for crystals larger than 8 nm. This finding may explain, why the cluster formed in selection ‘‘B’’ in Fig. 3 suddenly starts to shrink again: its maximum diameter of about 6.5 nm at 379 K is obviously not enough to leave the quasimolten state. It must be stressed at this point once again that the electron beam does not induce any noticeable Au mass transport at room temperature. Thermal activation is required for the observed phenomena, because the total sample energy density due to electron-beam energy transfer is small. To be specific, the simulation of the short-time temperature excursion is only suitable to illustrate that the excess energy induced by the Auger process can lead to an enhanced mobility of the surface atoms. In the region of the energy transfer the system is not in thermal equilibrium and as a consequence a microcanonical simulation of a system sufficiently large to allow for the proper description of the dissipation of the excess energy would be required for a full quantitative reproduction of the experiment. While such an extensive investigation is beyond the scope of the present work the fact that the enhancement of the Ostwald ripening process is not observed at room temperature shows the importance of the kinetic initial condition of the Auger process. At the temperature of the experimental observa-
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tion of the enhanced Ostwald ripening of T 400 K the Au clusters of the sample are close to their melting temperature [8,11]. The higher mobility of the surface atoms near the melting temperature obviously is a necessary condition for the observed effect. Therefore, in order to explain the observed phenomenon of contactless combined cluster growing/shrinking, which depends on the presence of a Au film as well as on electron-beam exposure, we propose the presence of a ‘‘quasitwo-dimensional gas’’ of Au atoms and small Au molecules. Such a ‘‘gas’’ could easily enhance Ostwald ripening via surface diffusion over larger distances without direct contact of the interacting clusters on an observable time scale. Note that the presence of such a ‘‘gas’’ could also explain the previously mentioned finding of the electronbeam induced boundary fluctuation of the Au film. Small Au molecules or Au atoms, which randomly cross the edge of the Au film recondense nearby on the defective a-C surface. The cohesive energy yields a restoring force. Since there should emerge more migrating Au species from the inner of the film than from its edge, in fact one may expect an expansion of the film. 4. Summary In this work we describe the effects of annealing of previously described Au ‘‘islands’’ [12], which are observed in situ in a transmission electron microscope. The islands consist of Au clusters embedded in a thin Au film, which are observed about 100 days after the deposition of non-size-selected Au clusters by laser ablation technique on a-C substrates. To model the experimental findings we performed MC simulations using Gupta-potentials, which describe the Au/Au interaction, whereas the Au/a-C interaction is obtained via DFT approach. If the temperature is increased in the transmission electron microscope, coarsening of the particles size distribution occurs by (a) cluster coalescence and (b) contact-less Ostwald ripening. The extent and rate of cluster coarsening, which depend on the temperature, surface and electron-beam exposure can be summarized in the following way: • The coarsening of the Au clusters was assessed by the average projected area of the clusters. It increases if the temperature is raised. The cluster size distributions are found to settle into metastable configurations if the temperature remains constant. • Islands (Au clusters on an Au film), which are annealed under continuous electron-beam exposure (monitoring by the TEM) show pronounced cluster coalescence and contact-less shrinking and growth even over large cluster distances, which is typical for classical Ostwald ripening. • Annealing of islands at 373 K without electron-beam exposure for about 4 h results in the dissolution of the Au film in which the clusters are embedded. If the clusters without underlying Au film are annealed up to 706 K further coarsening occurs. However, Ostwald ripening is
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strongly impeded as compared to cluster coalescence, which can be explained by the strong interaction of small diffusing Au species with the structurally irregular a-C surface. • Due to energy transfer from the high-energy electrons to the clusters high-temperature excursions on a 1012 s time scale must be taken into account. The results of Monte-Carlo simulations suggest the formation of a ‘‘quasi-two-dimensional gas’’ of small Au species, which are highly mobile only on a Au film. This will lead to the promotion of Ostwald ripening as a consequence of electron-beam exposure. • The influence of the electron beam in TEM studies of particle coarsening processes as a function of temperature can be minimized by the following procedure. During the in situ annealing the sample is only exposed to the electron beam to take snapshots in time intervals, which are adequate for the time scale of the coarsening process.
Acknowledgements We thank S.-S. Jester and M. M. Kappes (Institute for Physical Chemistry, University of Karlsruhe, Germany) for the sample preparation, outlining the preparation process, and fruitful discussions. The work was supported by the Center for Functional Nanostructures of the Deutsche Forschungsgemeinschaft. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.susc.2005. 10.056. References [1] G. Schmid, D.V. Talapin, E.V. Shevchenko, Nanoparticles (2004) 251, and references therein. [2] D.L. Peng, T.J. Konno, K. Wakoh, T. Hiara, K. Sumiyama, Appl. Phys. Lett. 78 (2001) 1535. [3] J. Du, S. Wang, J.N. Zhou, J.W. Harrell, J.A. Barnard, J. Magn. Magn. Mater. 219 (2000) 78. [4] N. Sandhyarani, T. Pradeep, J. Mater. Chem. 10 (2000) 981. [5] P.G. Shewman, Transformations in Metals, McGraw-Hill, New York, 1969. [6] I.M. Lifshitz, V.V. Slyozow, J. Phys. Chem. Solids 19 (1961) 35. [7] K. Morgenstern, G. Rosenfeld, G. Comsa, Phys. Rev. Lett. 289 (1996) 2113. [8] D.J. Smith, A.K. Petford-Long, L.R. Wallenberg, J.-O. Bovin, Science 233 (1986) 872. [9] P. Williams, Appl. Phys. Lett. 50 (1987) 1760. [10] P.M. Ajayan, L.D. Marks, Phys. Rev. Lett. 60 (1988) 585. [11] P.M. Ajayan, L.D. Marks, Phys. Rev. Lett. 63 (1989) 279. [12] R. Werner, M. Wanner, G. Schneider, D. Gerthsen, Phys. Rev. B 72 (2005) 045426. [13] (a) P. Weis, O. Welz, E. Vollmer, M.M. Kappes, J. Chem. Phys. 120 (2004) 677; (b) P. Weis, S. Gilb, P. Gerhardt, M.M. Kappes, Int. J. Mass Spec. 216 (2002) 59.
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