Quantitative Measurement of the Surface Self-Diffusion on Au

Letter pubs.acs.org/NanoLett

Quantitative Measurement of the Surface Self-Diffusion on Au Nanoparticles by Aberration-Corrected Transmission Electron Microscopy A. Surrey,†,‡ D. Pohl,†,‡ L. Schultz,†,‡ and B. Rellinghaus*,† †

IFW Dresden, Institute for Metallic Materials, P.O. Box 270116, D-01171 Dresden, Germany TU Dresden, Institut für Festkörperphysik, D-01062 Dresden, Germany

‡

S Supporting Information *

ABSTRACT: We present a method that allows for a quantitative measurement of the surface self-diffusion on nanostructures, such as nanoparticles, at the atomic scale using aberration-corrected high-resolution transmission electron microscopy (HRTEM). The diffusion coefficient can be estimated by measuring the fluctuation of the atom column occupation at the surface of Au nanoparticles, which is directly observable in temporal sequences of HRTEM images. Both a Au icosahedron and a truncated Au octahedron are investigated, and their diffusion coefficients are found to be in the same order of magnitude, D = 10−17 to 10−16 cm2/s. It is to be assumed that the measured surface diffusion is affected by the imaging electron beam. This assumption is supported by the observed instability of a (5 × 1) surface reconstruction on a {100} Au facet. KEYWORDS: Surface diffusion, aberration-corrected HRTEM, nanoparticles, gold, diffusion coefficient, surface reconstruction

I

beam. In a HRTEM investigation of Pt nanoparticles on an amorphous carbon substrate diffusion of single atoms, dimers, and small clusters due to beam heating was also reported recently.20 However, all of these studies describe the surface diffusion qualitatively, and a quantitative description is still lacking. Along with the ongoing process of developing aberration-corrected HRTEM from a mere imaging technique to a quantitative measurement tool, we introduce a method to estimate the surface self-diffusion coefficient for structures on the nanoscale, for example, nanoparticles or nanoelectrodes, in the present Letter. Hereto, we first describe our experimental observations of the atomic motion at the surfaces of Au nanoparticles in detail. It will be shown that the majority of the observed motion is due to the diffusion of Au atoms at steps and edges of the particle surface. Accordingly, the diffusion coefficient for the tracer diffusion of (nonisolated) Au adatoms is then determined quantitatively utilizing a methodology that will be introduced in this Letter. Finally, the obtained diffusion coefficient will be critically compared to the results of other experimental and theoretical studies. In a first set of experiments we have investigated Au icosahedra on amorphous carbon support provided by a commercially available sample (“S132” from Agar Scientific Ltd.) using a FEI Titan3 80−300 microscope equipped with an

n (scanning) transmission electron microscopy, (S)TEM, the electron beam provides detailed information about the structure of the specimen but simultaneously can cause temporary or permanent, desired or unwanted changes in the surface or bulk structure of a specimen.1 Here the effect of the electron beam can be manifold. For example, effects such as specimen degradation,2 radiolysis,3 contamination,4 or amorphization5 as well as knock-on damage resulting in atomic displacements or sputtering6 and beam-induced heating of the sample1 are well-known. In (S)TEM studies on nanoparticles, either the electron beam-induced or heat-induced coalescence of adjacent particles, also referred to as sintering, was reported repeatedly.7−14 The predominant mechanism of the mass transport during this process is believed to be the surface diffusion,15,16 since the sintering neck grows relatively fast within seconds and already at relatively low temperatures around room temperature. In the present study we confirm the observations of the electron beam-induced coalescence with parallel illumination (see Figure 1). To fully understand the influence of the electron beam on the process, a quantification of the underlying atom diffusion is mandatory. In recent studies it was shown that the diffusion of a few atoms on a Au surface can be directly observed in the aberration-corrected highresolution transmission electron microscope (HRTEM)17 and that the electron beam can be utilized to sculpt Au nanoelectrodes through electron-beam-induced surface and grain boundary diffusion.18 Further, a recent STEM study provided clear evidence of an enhanced migration of Au adatoms on Au nanoparticles19 induced by the focused electron © XXXX American Chemical Society

Received: June 18, 2012 Revised: November 1, 2012

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dx.doi.org/10.1021/nl302280x | Nano Lett. XXXX, XXX, XXX−XXX

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Figure 2. HRTEM images of the surface of an icosahedral Au nanoparticle (cf. upper particle in Figure 1). Red lines are guides to the eye. (a) N = 5 step columns are indicated by green arrows. (b) Image of the same nanoparticle acquired 4 s after the acquisition of the image in a. f = 6 significant contrast changes are indicated by blue arrows. Figure 1. Temporal sequence of HRTEM images showing the coalescence of an icosahedral (upper) and a single crystalline (lower) Au nanoparticle under the influence of the electron beam. (a) Both nanoparticles are separated. (b) Initial formation of a sintering neck. (c and d) Growth of the neck diameter and recrystallization.

multiple atomic steps which play a crucial role in diffusion processes.21 Isolated atom columns on an otherwise flat facet such as the column labeled “3” in Figure 2b are scarcely observed, and a clear exception in the here reported experiments. Most significant contrast changes occur at the atomic step edges. Due to the noisy contrast background originating from the amorphous carbon substrate and residual aberrations, the signal-to-noise ratio of the contrast at some surface column positions is very small, which sometimes hampers a clear determination of the occupational state. Hence, some evaluations may be erroneous; for example, the column which is labeled with a blue “5” for the occurrence of a significant contrast change in Figure 2b is interpreted to be empty, but in fact it could still be occupied. Furthermore, C atoms may interact with Au and subsequently form a (partial) C−Au interface that certainly affects the surface diffusion. In another set of experiments we prepared predominantly single crystalline Au nanoparticles with truncated octahedral shapes by inert gas condensation through DC magnetron sputtering in argon. To stabilize the octahedral over the icosahedral morphology we added small amounts of oxygen (3,75 vol. %) to the argon sputter gas22 (a detailed description will be published elsewhere23). The Au particles were directly deposited on a holey carbon grid to overcome the problem of the noisy contrast background of the amorphous carbon substrate. Figure 3 shows the HRTEM image of a single crystalline Au nanoparticle residing right at the edge of the amorphous carbon support. The applied current density is ≈ 7.2 × 106 electrons nm−2 s−1 = 115 A cm−2. In contrast to the icosahedral Au particle on the continuous amorphous carbon film the surfaces of the truncated Au octahedron appear much

image CS-corrector at an acceleration voltage of 300 kV. Figure 2 shows close-ups of two consecutively acquired HRTEM images of the surface of the upper icosahedral Au particle from Figure 1. The applied current density is ≈ 2.5 × 106 electrons nm−2 s−1 = 40 A cm−2. The time delay between the acquisitions of the two images is 4 s, and the exposure time is texp = 0.5 s. During a temporal sequence of HRTEM images, the motion of atoms at the two well-resolved {111} facets of the icosahedral nanoparticle is directly observable. In Figure 2a, contrasts which are originally observed at the atom column positions labeled with the green numbers “1”, “3”, “4”, and “5” vanish in the subsequent image (displayed in Figure 2b). Here, new contrasts arise at the positions labeled with the blue numbers “1” and “3” where no contrast had priorly been observed. Hereafter these scenarios are called “significant” contrast changes and represent events where either an occupied column is emptied or an unoccupied column is populated. Since in a HRTEM image atoms are indistinguishable and since not only single atoms but rather the projections of atom columns occupied by a varying number of atoms are visible, the quantification of the observed surface diffusion is not trivial, and the trajectories of individual atoms cannot be identified. With a temporal sequence of HRTEM images, only jumps lateral to the imaging electron beam can be revealed because jumps parallel to the electron beam do not result in significant contrast changes due to the projected imaging. The surface of the icosahedral nanoparticle does not exhibit flat facets but rather is characterized by B


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Figure 4. Graph showing the fitted intensities of the column marked by the red circle in Figure 3 for all 22 images of the temporal sequence. The threshold is defined by the intensity of the vacuum in the close proximity to the particle. This allows to clearly discriminate between empty and occupied columns.

Figure 3. HRTEM image of a single crystalline Au nanoparticle with truncated octahedral morphology. The shown particle is attached to the edge of the amorphous carbon support. The major part of the particle extends into vacuum and can thus be imaged substrate-free. The area marked with the dashed red rectangle is displayed in Figure 5. The intensities of the column marked by the dashed red circle are analyzed for all 22 images of the sequence in Figure 4.

considered a potential origin for the experimental finding that both {100} and {111} facets were almost equally populated by Au adatoms as observed in a STEM study on Au nanoparticles.19 In our present study, this reconstruction seems to be unstable as can be seen from the fact that the top layer changes dynamically between the {111} and the {100} configuration (compare first and 20th HRTEM images to the other images of the temporal sequence in Figure 5). This instability can be either caused by the energetic impact of the electron beam or by the small size of the facet where both configurations may be energetically equivalent. During the extensive and detailed study of the surfaces of a large number of likewise prepared Au nanoparticles with diameters in the range 5 nm ≤ dP ≤ 10 nm, such a surface reconstruction was, however, never observed.23 Unlike in these experiments where single-shot HRTEM images were acquired at minimum exposure times and electron doses, in the present study the applied dose is significantly larger due to the necessity of continuous image acquisition. It is thus to be assumed that not only the surface reconstruction, but also the observed diffusion is affected by the impact of the imaging electron beam. Since in our experiments HRTEM contrast changes due to the motion of individual atoms are determined, this atomic motion is quantified utilizing the intrinsic or tracer diffusion coefficient D as defined in the review article of Gomer:26

smoother without any atomic steps and only at the low coordinated corners labeled “A”, “B”, and “C” empty columns, and significant contrast changes are observed in the temporal HRTEM image sequence. The single crystalline nanoparticle exhibits both {111} and {100} facets due to the morphology of a truncated octahedron. In the left part of Figure 3, where the particle is still in contact with the substrate, the tremendous impact due to the contrast background of the amorphous carbon on the intensity becomes apparent. In contrast, the right part of the particle extends into the hole of the support film and is thus imaged substrate-free in vacuum. As a consequence, here the contrast of the atom columns exhibits a higher signal-tonoise ratio compared to the previously analyzed icosahedron. This allows for a more quantitative intensity analysis and consequently for an unambigiuous determination of the surface column’s occupation. The temporal fluctuation in the occupation of these columns is analyzed for a sequence of 22 images at very stable imaging conditions. By measuring the greyscale of the vacuum in the close proximity to the particle, a threshold is defined which allows us to clearly discriminate between empty and occupied columns. Two-dimensional Gaussians are fitted to the intensity peaks of the columns. Then the fitted amplitudes are compared to the vacuum threshold. As an example, Figure 4 shows the fitted intensities of a particular column which is marked with a dashed red circle in Figure 3 at the corner labeled “B” for all 22 consecutively acquired images. The time delay between the acquisition of two images is on average 1.3 s and the exposure time is also texp = 0.5 s. On the (100) facet of the Au nanoparticle in Figure 3 (marked with a dashed red rectangle) the atom columns appear more diffuse than the inner columns, and there is one additional column at this facet as compared to what the rigid lattice would allow for. As a consequence, the facet is buckled. This finding is attributed to the occurrence of the well-known (5 × 1) reconstruction of Au 24,25 that describes the rearrangement of the (100) surface layer into a quasihexagonal {111} overlayer. This surface reconstruction was already

D = lim

τ→∞

1 2dnτ

n

∑ ⟨|(ri(τ) − ri(0)|2 ⟩

(1)

i=1

where n is the total number of adatoms, ⟨|(ri(τ) − ri(0)| ⟩ is the mean square displacement of the i-th adatom in the ddimensional motion, and τ is the observation time. In the ideal case of uncorrelated jumps D can also be expressed using the atomic jump frequency Γ and the mean jump length ⟨l2⟩:27 2

D=

⟨l 2⟩ Γ 2d

with

Γ = ν0exp(−Ea /kT )

(2)

where Ea is the activation energy and ν0 the so-called attempt frequency. In the simplest case only nearest neighbor jumps with the length a are allowed, that is, ⟨l2⟩ = a2. The preexponential factor D0 can be defined as D0 = (a2ν0/2d).26 C


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Figure 5. Consecutively acquired HRTEM images of the (100) facet of the Au nanoparticle displayed in Figure 3. The time delay between two images is 1.3 s. The unstable surface reconstruction creating a bulge of the (100) facet vanishes in the first and 20th image.

2 or 1 and depends on the direction of the electron beam (see Figure 6b). Then Γ takes the form

In the following we introduce a method to quantitatively estimate this diffusion coefficient by measuring the characteristic jump frequency of lateral jumps. For the diffusion of n adatoms the jump frequency Γ used in eq 2 is given by28,26 1 Γ= nτ

n

m Γ= nτ

m

∑ ∑ μij i=1 j=1

∑ μih = m nτk i=1

with

(3)

where μij are the number of jumps in the time τ. The subscript i labels the n adatoms, and the subscript j denotes the m different diffusion channels on a crystal surface. For example, there are m = 3 possible diffusion channels on a flat (111) surface of a fcc crystal and m = 2 channels on a flat (100) surface; see Figure 6a. The dimensionality d of the diffusion is determined by this

n

γl =

1 nτk

n

∑ μil = mγl i=1

n

∑ μil i=1

(4)

Here γl denotes the lateral jump frequency containing the number of all lateral jumps of the n adatoms in the time period τ. With this the diffusion coefficient D given by eq 2 can be rewritten to D=

a2 γ 2 l

(5)

From the fact that empty and occupied columns can be clearly distinguished, it can be assumed that the time resolution of the temporal HRTEM image sequences with τ ≈ 1 s is sufficient to observe single jump events (see discussion below). In principle this approach allows for the exact determination of D. However, in a TEM the lateral jump frequency can only be measured with some residual uncertainty, since here not only single atoms but rather the projection of atom columns occupied by a varying number of atoms are visible. Nonetheless, the number of adatoms, n, can be approximated by the number of columns, N, that provide a step at the surface. Atoms contained in such step edges are minimally coordinated and therefore contribute mainly to the diffusion (for schematic illustration see Figure 7). Further, in a temporal sequence of HRTEM images lateral jumps can only be unambiguously identified when “significant” contrast changes of individual columns occur in consecutive images. Small intensity changes (for example those from image numbers 5−9 displayed in Figure 4) that occur in columns remaining occupied and that are thus not considered “significant” are not further interpreted, since they cannot be unambiguously attributed to the motion of atoms but can rather be due to artifacts: The most important ones are instabilities of the defocus or height and tilt, which vary slightly within the observation time as the particle itself may move. From all consecutive images the number of the significant contrast changes, f, can be counted. Hence, γl can be approximated by the frequency

Figure 6. Schematic illustration of the possible diffusion channels on different surfaces of a fcc crystal. (a) There are m = 3 diffusion channels on the (111) surface. Possible hexagonal close-packed sites as accessible by isolated adatoms47 are neglected here because isolated adatoms diffusion is not observed here. On the (001) surface m = 2 diffusion channels exist. (b) The factor k is defined as the number of lateral diffusion channels relative to the electron beam. These channels shaded in green in part a cannot be distinguished in the projected HRTEM image.

number m, that is, d = m. If isotropic diffusion is assumed, the probabilities for the occurrence of a jump are equal among all channels, hence ∑mj=1μij = mμih, where the subscript h labels one arbitrary diffusion channel. In a TEM only the number of all lateral atom jumps μil along the channels l which are not parallel to the electron beam can be detected. To account for the existence of more than one channel that allow for lateral jumps and that cannot be distinguished in the projected HRTEM images we introduce the factor k defined as the number of all such lateral diffusion channels. In the examples of the (111) and (100) surfaces of a fcc crystal k is either equal to

γl* =

f Nτk

(6)

The approximate γl* may deviate from γl due to the following four reasons: (i) Figure 7 illustrates that both atoms at the top D


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of a truncated octahedron with 13 959 atoms which is characterized by the indexes (nl,ncut) = (29,10)30). However, the surface columns are believed to be only partially occupied, that is, with less than 10 atoms for both nanoparticles. Even if the uncertainties of the approximated quantities N and f do not always cancel out and if more than only the minimally coordinated atoms of a step column perform jumps, the lateral jump frequency γl* using N and f is a good approximation for the exact frequency γl with an uncertainty of one decade. In the following this method is employed to quantify the surface diffusion on Au nanoparticles from our experimentally obtained HRTEM image series. In the case of the Au icosahedral nanoparticle a temporal sequence of 19 images which are all acquired before the particle is getting in contact with the adjacent one is analyzed for changes in the configuration of the surface atoms. For these 19 images it can be assumed that the particle’s surface remains unaffected by the neighboring particle and that the diffusion exhibits a random walk-like behavior. Images acquired at a later stage are neglected for this analysis, since directed and anisotropic diffusion toward the to be formed sintering neck occur as soon as the particles are in contact. In every image the occupations of the individual surface atom columns are determined for the two well-resolved {111} facets (k = 2) in the lower left part of the icosahedron. These occupations are then compared to those of the preceding images. From this comparison the number of step columns, N, and the number of significant contrast changes, f, are obtained for every image resulting in 18 values for the lateral jump frequency γl*. In Figure 2 two example images of the temporal sequence are shown where both the step columns and the fluctuations with significant contrast changes are indicated by arrows. The analysis of all images yields a mean atomic jump frequency γl*̅ = 0.1 ± 0.01 Hz. Using eq 5 the diffusion coefficient for the surface self-diffusion on the Au nanoparticle can be estimated to be D1 = (4.5 ± 0.6) × 10−17 cm2/s. If long jumps with ⟨l2⟩ = 4a2 are assumed the diffusion coefficient is D2 = (1.8 ± 0.2)·10−16 cm2/s which serves as an upper limit of the estimation. The given errors represent the standard deviation of the mean value. Based on the more quantitative intensity analysis of 22 subsequent HRTEM images of the substrate-free octahedral Au nanoparticle, the numbers f and N are determined yielding a mean lateral jump frequency γ*l̅ = 0.07 ± 0.02 Hz and a diffusion coefficient which is in the range of D = 10−17 to 10−16 cm2/s. Here the factor k = 2 was used because (i) all observed atomic jumps occur at corner sites connecting {111} and {100} facets and (ii) the {100} facets are unstable with respect to a (5 × 1) surface reconstruction. The fact that the value of the lateral jump frequency agrees very well with the result of the icosahedral Au nanoparticle implies that the statistical errors due to the contrast background of the substrate largely cancel out. For obtaining better statistics and reducing the stated errors considerably more images would need to be analyzed which, however, is challenging because the particles move or rotate out of the zone axis due to the impact of the electron beam. If the nanoparticles are imaged at reduced electron doses to stabilize them, enhanced observation time will be gained. Surface self-diffusion on Au was already observed in experiments using atomic force and scanning tunneling microscopy (AFM and STM). Here the diffusion coefficient was deduced from the temporal evolution of artificially created hillocks or scratches on Au surfaces in the nanometer regime. Since (i) this method involves macroscopic concepts such as

Figure 7. Schematic drawing of a stepped (111) surface of a fcc crystal where one atomic layer (blue circles) is half covered by another layer (orange circles). (a) Plane view illustration along the [111] direction. In the microscope, diffusion will be observed if the electron beam comes from the top. The arrows are indicating possible jumps. Hexagonal close-packed sites as accessible by isolated adatoms47 are neglected here because isolated adatoms diffusion is not observed here. (b) The projection of the (111) surface as seen in the microscope.

and bottom of a column at a surface step can diffuse, because of their minimal coordination. As a consequence N may be underestimated by a factor of 2 compared to n. (ii) These two atoms can jump into the next empty column within the time period τ resulting in only one significant contrast change. Hence, f may be smaller than ν by a factor of 2 (which could in fact cancel the first factor). (iii) Furthermore both atoms can jump with the same probability in the opposite direction toward an already partially filled column, resulting in no significant contrast change at all. Hence, the measured frequency can be too small by again a factor of 2. (iv) In contrast, the lateral jump of an isolated adatom to an empty position would produce two significant contrast changes and thus result in a two times larger γl*. However, as isolated adatom diffusion is not observed in our experiments, this case is not of importance. The diffusion coefficient also depends strongly on the mean jump length ⟨l⟩ which could also be as large as twice the nearest neighbor distance a if long jumps are assumed,29 resulting in a four times larger diffusion coefficient. Although this simplified description of the diffusion problem is only a rough approximation, it should allow for the measurement of the order of magnitude of the diffusion coefficient as the above-mentioned uncertainties partially cancel out. From the size of the investigated Au icosahedron and the number of atom columns forming the {111} facets, the number of atoms within the surface columns can be estimated to be 14 in maximum (deduced from the comparison with the model of a perfect icosahedron with 8217 atoms consisting of 13 shells30). The maximum number of atoms within the columns at the corners “A”, “B”, and “C” of the truncated Au octahedron can likewise be determined to 10 atoms (deduced from a model E


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the minimization of the surface curvature and/or the surfacefree energy thereby ignoring any atomistic effects31 and (ii) the reported results vary over decades from D = 10−20 cm2/s to D = 10−14 cm2/s at room temperature,32−35 these studies merely provide a rough orientation for the comparison with the here observed atomic tracer diffusion on Au nanoparticles. Furthermore strain is known to influence the activation energies of surface diffusion processes,36−38 and the surfaces of nanoparticles are frequently strained. Despite all of these uncertainties, the diffusion coefficient determined by the method introduced in the present Letter matches the results of these AFM and STM studies. A more direct access to the tracer diffusion coefficient is provided by theoretical studies using methods such as density functional theory (DFT), molecular dynamics (MD), and Monte Carlo variational transition state theory (MCVTST). Here it is instructive to first consider the diffusion of isolated adatoms on flat surfaces. The activation energy for a single, isolated Au adatom on an infinitely large flat Au surface is calculated to be as low as 0.12 eV for (111) surfaces.39 At room temperature this results in an atomic jump frequency of some GHz or in other words in a mean residence time tres = 1/Γ < 1 ns, during which the atoms reside at a particular lattice site. As a consequence and irrespective of the probability for their occurrence, such jumps of isolated adatoms on (111) surfaces of Au nanoparticles would not be visible in the HRTEM images at exposure times texp = 0.5 s. In such a case, where tres ≪ texp, all surface columns would be temporarily occupied during the image acquisition. As a consequence, all surface columns should exhibit a finite though similar contrast, and diffusion would not be visible at all. From the fact that in the here described experiments empty and occupied atom columns at the surface of the nanoparticles are clearly distinguishable, it is thus concluded that the residence time of diffusing adatoms is in the order of or larger than the experimental exposure time. An example of atomic motion on a time scale shorter than the exposure time is the unstable surface reconstruction on the (100) facet of the octahedral nanoparticle (see Figure 5). Here the atoms rearrange within the time of the image acquisition which is visible in the diffuse contrast of the atom columns. In our present investigation the adatom motion is clearly dominated by the diffusion of atoms across atomic steps. Using MD simulations Ferrando and Tréglia have calculated a whole ensemble of activation energies of up to 0.67 eV at stepped Au(111) surfaces,40,41 which results in jump frequencies of only a few Hz at room temperature assuming a typical attempt frequency ν0 ≈ 1012 Hz.26,42−44 As a consequence such jumps can be observed in the electron microscope. Similar to the diffusion on (111) facets, the activation energy for the diffusion of isolated adatoms on (100) Au surfaces was calculated to be as low as 0.55 eV for exchange diffusion on a flat surface. The resulting jump frequencies are again to high to allow for an observation of such isolated adatom diffusion in HRTEM image sequences. However, for the migration of an atom leaving a step edge as illustrated in Figure 8 this activation energy is enhanced to 0.86 eV.43 At room temperature this translates to a jump frequency of only a few mHz, and consequently, this diffusion across step edges is well-observable in the TEM. We like to emphasize that the herein described scenario is in perfect agreement with our experimental observations. The order of magnitude of the measured mean atomic jump frequency Γ̅ ≈ mγl*̅ ≈ 0.1 Hz agrees very well with the calculated values of jumps at steps on (111) and (100)

Figure 8. Schematic drawing of a stepped (100) surface of a fcc crystal where one atomic layer (blue circles) is half covered by another layer (orange circles). (a) Plane view illustration along the [100] direction. In the microscope diffusion will be observed if the electron beam comes from the top. The arrow is indicating a possible jump with an activation energy of Ea = 0.86 eV.43 (b) The projection of the (100) surface as seen in the microscope.

surfaces at room temperature. The differences between the theoretical and experimental values are limited to one or 2 orders of magnitude. Such remaining discrepancies may be easily due to the heating of the specimen through the imaging electron beam. Unfortunately the local temperature of the imaged nanoparticles cannot be measured directly. However, we believe that massive heating does not occur in our experiments because the diffusion grows exponentially upon increasing the temperature and would soon be too fast for an observation in temporal HRTEM image sequences. Still, knockon damages can play a significant role in surface diffusion at an incident electron energy of 300 keV.45 Baletto and Ferrando have used MD simulations to calculate the surface diffusion on small gold clusters. They obtain relatively low activation energies in the range of 0.1 to 0.4 eV for various jump mechanisms.46 With an attempt frequency of ν0 ≈ 1012 Hz these energies translate to jump frequencies of 105 Hz or higher, which again renders such diffusion processes unobservable in the electron microscope. However the particle size used for their MD simulations (up to 1289 atoms) is much smaller than in our present experimental study (about 14 000 atoms), and surface diffusion and/or melting is known to be strongly size-dependent. This implies that the calculated low activation energies do not apply for our current experimental situation. In summary, a method is introduced that allows for the quantification of the surface self-diffusion on nanostructures using aberration-corrected HRTEM image sequences. As a first application of the proposed method, the diffusion coefficient of the surface self-diffusion on Au nanoparticles is estimated to be D = 10−17 to 10−16 cm2/s. In future HRTEM experiments under heating and cooling conditions it should thus not only be possible to determine activation energies and pre-exponential factors, but also to correlate the diffusion coefficient to the F


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(25) Fiorentini, V.; Methfessel, M.; Scheffler, M. Phys. Rev. Lett. 1993, 71, 1051−1054. (26) Gomer, R. Rep. Prog. Phys. 1990, 53, 917−1002. (27) Ala-Nissila, T.; Ferrando, R.; Ying, S. C. Adv. Phys. 2002, 51, 949−1078. (28) Tsong, T. T. Physica A 2005, 357, 250−281. (29) Antczak, G.; Ehrlich, G. Surf. Sci. Rep. 2007, 62, 39−61. (30) Baletto, F.; Ferrando, R. Rev. Mod. Phys. 2005, 77, 371−423. (31) Mullins, W. W. J. Appl. Phys. 1957, 28, 333−339. (32) Schneir, J.; Sonnenfeld, R.; Marti, O.; Hansma, P. K.; Demuth, J. E.; Hamers, R. J. J. Appl. Phys. 1988, 63, 717−721. (33) Sommerfeld, D. A.; Cambron, R. T.; Beebe, T. P. J. Phys. Chem. 1990, 94, 8926−8932. (34) Hagan, H. P.; Campbell, P. A.; Smith, K. W.; Turner, R. J.; Walmsley, D. G. Ultramicroscopy 1992, 42−44, 587−593. (35) Göbel, H.; von Blanckenhagen, P. Surf. Sci. 1995, 331−333, 885−890. (36) Brune, H.; Bromann, K.; Röder, H.; Kern, K.; Jacobsen, J.; Stoltze, P.; Jacobsen, K.; Norskov, J. Phys. Rev. B 1995, 52, R14380− R14383. (37) Ratsch, C.; Seitsonen, A. P.; Scheffler, M. Phys. Rev. B 1997, 55, 6750−6753. (38) Schindler, A. Theoretical aspects of growth on one and two dimensional strained crystal surfaces. Ph.D. thesis, Gerhard-MercatorUniversität Duisburg, Duisburg, Germany, 1999. (39) Agrawal, P. M.; Rice, B. M.; Thompson, D. L. Surf. Sci. 2002, 515, 21−35. (40) Ferrando, R.; Tréglia, G. Phys. Rev. B 1994, 50, 12104−12117. (41) Ferrando, R.; Tréglia, G. Surf. Sci. 1997, 377−379, 843−846. (42) Liu, C. L.; Cohen, J. M.; Adams, J. B.; Voter, A. F. Surf. Sci. 1991, 253, 334−344. (43) Pötting, K.; Schmickler, W.; Jacob, T. ChemPhysChem 2010, 11, 1395−1404. (44) Ferrando, R.; Tréglia, G. Phys. Rev. Lett. 1996, 76, 2109−2112. (45) Martin, A. V.; Ishizuka, K.; Kisielowski, C.; Allen, L. J. Phys. Rev. B 2006, 74, 172102. (46) Baletto, F.; Mottet, C.; Ferrando, R. Surf. Sci. 2000, 446, 31−45. (47) Ferrando, R.; Tréglia, G. Surf. Sci. 1995, 331−333 (Part B), 920−924.

applied electron energies and doses. As a consequence, this approach opens an experimental pathway to quantitatively study the interaction of the incident electron beam with the specimen through measurements of the impact of the electron irradiation on the diffusion coefficient. Metallic nanoparticles with their well-defined facets and their most appropriate thickness provide an ideal system for this kind of investigations. To better understand the observed surface reconstruction on the {100} facets, further experimental and theoretical research is needed.

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ASSOCIATED CONTENT

S Supporting Information *

Full temporal HRTEM image series of the interparticle coalescence (coalescence.avi), the close-up of the surface of the icosahedral Au particle (icosahedron.avi), and the substratefree truncated Au octahedron (octahedron.avi). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Quantitative Measurement of the Surface Self-Diffusion on Au

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