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Atomic surface diffusion on Pt nanoparticles quantified by high-resolution transmission electron microscopy S. Schneider a,b , A. Surrey a,b , D. Pohl a , L. Schultz a,b , B. Rellinghaus a,∗ a b
IFW Dresden, Institute for Metallic Materials, P.O. Box 270116, D-01171 Dresden, Germany TU Dresden, Institut für Festkörperphysik, D-01062 Dresden, Germany
a r t i c l e
i n f o
Article history: Received 29 August 2013 Received in revised form 20 December 2013 Accepted 21 December 2013 Keywords: Surface diffusion Aberration-corrected HRTEM Nanoparticles Platin Diffusion coefficient
a b s t r a c t Aberration-corrected high-resolution transmission electron microscopy allows for the delocalizationfree observation of atomic motions on metallic surfaces and thus enables measurements of the diffusion of single atoms on the surfaces of nanoscopic objects such as nanoparticles. Using this recently introduced method, the diffusion coefficient for surface self-diffusion of Pt nanoparticles is determined through the fluctuating occupation of the particle’s atomic columns. This diffusion coefficient is determined to lie in the range D ∼ (10−17 . . . 10−16 ) cm2 /s. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction The continuing development of aberration-corrected highresolution transmission electron microscopy (HRTEM) led to the possibility to study the structure of specimens at the atomic scale in great detail and with highest precision (Urban, 2008; Van Aert et al., 2012). Apart from these static structural information, dynamic changes of the specimen, e.g., due to the impact of the imaging electron beam, are often observed in (scanning) TEM (Bals et al., 2012), in particular when working at high doses that are frequently mandatory to investigate the structural and chemical properties or even three-dimensional structures at highest magnifications (using holography (Linck et al., 2012) or focal series (Jinschek et al., 2011)). Such dynamic phenomena which are mostly related to unwanted radiation damage (Egerton et al., 2004), may also occur spontaneously without the electron beam and are most easily observable on surfaces. Surface diffusion (Smith and Marks, 1985; Zandbergen et al., 2005; Kisielowski et al., 2008; Wang and Palmer, 2011), Ostwald ripening (Yoshida et al., 2012) and sintering (Lim et al., 2009) have been reported and described qualitatively for different nanostructured thin films and for nanoparticles. It is, however, still an open question whether the observed atomic surface diffusion, which is the main underlying mechanism of most of these processes, can be solely ascribed to the physical properties of the
∗ Corresponding author. Tel.: +49 351 4659 754; fax: +49 351 4659 9754. E-mail address: [email protected] (B. Rellinghaus).
material or if and to which extent it is rather promoted by the impact of the imaging electron beam. Recently, a HRTEM method which allows for the quantitative estimation of the surface diffusion coefficient was introduced, and it was shown that it can be used to quantify the surface self-diffusion on Au nanoparticles (Surrey et al., 2012). The method is based on the analysis of temporal fluctuation in the occupancy of surface atomic columns. In the present paper, it is applied to quantitatively describe the surface self-diffusion on Pt nanoparticles. The possibility of a direct quantitative measurement of the surface diffusion may prove a valuable tool in electron microscopy to better understand the impact of the electron beam on the materials under investigation. 2. Experimental methods Pt nanoparticles produced by inert gas condensation (Dmitrieva et al., 2007; Pohl et al., 2012) are deposited on holey amorphous carbon films supported by copper grids. In contrast to the deposition on a continuous carbon film, the holey support offers the advantage to allow for a more direct interpretation of the weak contrasts at the surfaces of nanoparticles, which partly extend into a hole of the support film and are thus imaged substrate-free in vacuum. Due to the absence of noisy contrast backgrounds arising from the support film this setup allows to easily discriminate between empty and occupied surface atom columns by visual impression (Surrey et al., 2012). The diffusion processes are investigated using a FEI Titan3 80-300 microscope equipped with an image CS -corrector at an
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Please cite this article in press as: Schneider, S., et al., Atomic surface diffusion on Pt nanoparticles quantified by high-resolution transmission electron microscopy. Micron (2014), http://dx.doi.org/10.1016/j.micron.2013.12.011
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acceleration voltage of 300 kV. The aberration corrector was used to set the coefficient of the spherical aberration to CS ≈ 0 m, and the focus was adjusted to a minimal underfocus of about −5 nm. Higher order aberrations are corrected to limit the maximum parasitic phase shift to /4 for an aperture with a semiangle of 20 mrad. At these conditions, atomic columns appear as dark contrasts with minimal delocalization in the HRTEM images. HRTEM image series are continuously acquired with a time delay of 0.8 s between subsequent images. These series are comprised of 31–35 images. The current densities are in the range of j ≈ 5 . . .14 × 106 e− /nm2 /s. Since HRTEM images display a two-dimensional projection of the atomic columns, only atomic movements perpendicular to the imaging electron beam are visible. Atoms changing their position within a column that lies parallel to the electron beam do not cause any “significant” contrast changes and therefore, this motion cannot be detected. Furthermore it has to be taken into account that the atoms in a HRTEM image are indistinguishable, i.e. the trajectories of individual atoms cannot be identified. To quantify the motion of individual atoms the definition of the intrinsic (also called tracer) diffusion coefficient D, as given in the review article of Gomer (Gomer, 1990), is used: 1 D = lim →∞ 2dn n
→ r i () − → r i (0)2
Fig. 1. HRTEM image of the Pt nanoparticle #1 oriented in [1 1 0] direction reaching partly into the vacuum. The visible facets are labeled.
(1)
i=1
Here, n is the total number of adatoms, thetime interval between subsequent images,
→ r i () − → r i (0)2 is the mean
square displacement of the ith adatom in the d-dimensional case of uncorrelated jumps. Given the above mentioned limitations in the evaluation of atomic motions in HRTEM images it is useful to rewrite the expression of the diffusion coefficient (Surrey et al., 2012): D=
a2 2 l
1 il nk n
with l =
(2)
i=1
Here, a is the length for nearest neighbor jumps of an atom and l denotes the lateral jump frequency. The factor k takes into account that some lateral diffusion channels are indistinguishable in the two-dimensional projection of a HRTEM image (for a more detailed explanation, the reader is referred to Surrey et al., 2012). For measurements of the surface diffusion on a {0 0 1} surface along a 1 1 0 direction the factor k is equal to 1. The quantity l contains the number of all lateral jumps il of n adatoms in the time period . The knowledge of the numbers of all lateral jumps, il , and all adatoms participating in the diffusion process, n, would allow for an exact determination of the diffusion coefficient D. However, the exact number of all lateral jumps, il , cannot be determined from a HRTEM image series, but it can be approximated by the number of “significant” contrast changes, f, during . These “significant” contrast changes are defined as contrast changes, where either an atomic column is filled or emptied, which is a direct proof for the atomic motion at the nanoparticle’s surface. These jump events can be either detected by a subjective evaluation of the intensity at the individual atom column or by a quantitative analysis of the intensity. However, both approaches yield comparable results (Surrey et al., 2012). Especially in the absence of a substrate “significant” contrast changes are clearly observable. Any contrast larger than the noise level of 7% can be attributed to one or more Pt atoms. An interval of ≈ 0.8 s between two consecutive images of the temporal HRTEM series is small enough to observe individual jumps (Surrey et al., 2012). While it is also impossible to determine the number of adatoms, n, from the two-dimensional HRTEM images, it had been shown that in order to approximate the diffusion
constant, it is sufficient to count the number of atomic columns, N, which are located at sites, where surface diffusion is most likely to occur and to measure the number of significant contrast changes there. These sites are the steps and edges at the surface of the nanoparticle, because atoms at such positions are minimally coordinated and therefore contribute mainly to the diffusion. Based on these assumptions l can be approximated by the frequency: l∗ =
f Nk
(3)
This frequency may deviate from the exact l due to different reasons, but it was shown that it nonetheless allows for the measurement of the diffusion constant with the precision of one order of magnitude (Surrey et al., 2012). 3. Results The method summarized above is now applied to two Pt nanoparticles #1 and #2 in Figs. 1 and 2 and Figs. 3 and 4, respectively. In order to calculate D, all atomic columns N, where diffusion can occur, are counted in each image of the temporal series. This is shown as an example in Fig. 2, where two subsequent images of the series with magnified sections of the (0 0 1) surface of particle #1 (cf. Fig. 1) are displayed. In Fig. 2a, N = 6 atomic columns at steps or edges are identified (marked with red circles). The quantity f/ can then be calculated from the sum of all “significant” contrast changes of the series. How these contrast changes are identified is also illustrated in Fig. 2. The atom column at position “4” which is marked with a red circle in Fig. 2a is emptied in the consecutive HRTEM image in Fig. 2b, where the position is marked with a blue circle (at position “3*”), because the formerly weak dark contrast has vanished by then. On the other hand, the formerly empty column at position “2*” in Fig. 2b marked with a blue circle is meanwhile (partially) filled, which can be seen from the newly emerged dark contrast. In total, f = 3 “significant” contrast changes can be identified from a comparison of Fig. 2a and b. For particle #1 in Fig. 1 a series of 35 consecutive images is acquired, all image pairs of which are likewise analyzed. Since the diffusion occurs mostly on the (0 0 1) surface of the particle, the value k = 1 is chosen for the calculation of D. Averaging over all 34 lateral jump frequencies of the surfaces results in a mean atomic jump frequency
Please cite this article in press as: Schneider, S., et al., Atomic surface diffusion on Pt nanoparticles quantified by high-resolution transmission electron microscopy. Micron (2014), http://dx.doi.org/10.1016/j.micron.2013.12.011
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Fig. 2. HRTEM images of the (0 0 1) surface of the Pt nanoparticle #1. (a) There are N = 6 atomic columns that could exhibit diffusion. (b) Consecutive HRTEM image of the same Pt nanoparticle acquired 0.8 s after image a. The f = 3 “significant” contrast changes are marked with blue circles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
√ ¯l∗ = 0.15 ± 0.03 Hz. Using Eq. (2) with a = gPt / 2 and the lattice ˚ the diffusion coefficient for the surface constant of Pt, gPt = 3.92 A, self-diffusion on the Pt nanoparticle for jumps to the nearest neighbor is thus estimated to be D1 = (5.7 ± 1.1) × 10−17 cm2 /s. Assuming jumps not only to the nearest, but also to the next nearest neighbors the diffusion coefficient is D2 = (2.3 ± 0.4) × 10−16 cm2 /s. On the Pt nanoparticle #2 displayed in Fig. 3, the diffusion occurs also mainly on a {1 0 0} surface. Even though some rare jump events are detectable on other surfaces such as {1 1 1}, again the value k = 1 is chosen for reasons of simplicity and since the factor k has only a minor influence on the order of magnitude of the results. Based on a temporal series of 31 HRTEM images a mean atomic jump frequency ¯l∗ = 0.26 ± 0.02 Hz is calculated. This leads to
3
Fig. 3. HRTEM image of the Pt nanoparticle #2 reaching partly into the vacuum acquired with a current density j ≈ 14 × 106 e− /nm2 /s. As an example the blue arrow indicates a filled atomic column. On the bottom right the amorphous carbon film can be seen. A temporal HRTEM image series of the red marked region can be seen in Fig. 4. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
the diffusion coefficients D1 = (1.0 ± 0.1) × 10−16 cm2 /s for nearest neighbors and D2 = (4.0 ± 0.4) × 10−16 cm2 /s for next nearest neighbors. Here, all given errors represent the standard deviation of the mean value. It has to be stated that a larger number of images would clearly reduce the error and provide a statistically more robust results. However, during the imaging of the nanoparticle not only single atoms start to move, but also the particle as a whole turns because of the imaging electron beam. This is why the zone axis orientation is not stable and the diffusion can only be observed for a limited period of time. 4. Discussion Surface self-diffusion has been studied extensively using field ion microscopy (FIM) and scanning tunneling microscopy (STM) on flat {1 0 0} (Kellogg and Feibelman, 1990; Kellogg, 1991), {1 1 0}
Fig. 4. Temporal series of the Pt nanoparticle #2. The time delay between two images is 0.8 s. Columns marked with an arrow undergo “significant” contrast changes during the temporal series. Following abbreviations are used: occupied atomic column (o), empty atomic column (e). From the left to right the occupation of the columns changes as follows: turquois: o, o, o, o, e, e; white: o, o, e, e, e, e; green: e, e, o, o, e, e; blue: o, o, e, e, o, e; yellow: o, o, o, o, o, e; red: e, o, e, o, e, o. In (a) N = 9 step columns (marked with red circles) are present and in the consecutive image (b) f = 1 contrast change can be counted. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Please cite this article in press as: Schneider, S., et al., Atomic surface diffusion on Pt nanoparticles quantified by high-resolution transmission electron microscopy. Micron (2014), http://dx.doi.org/10.1016/j.micron.2013.12.011
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(Bassett and Webber, 1978; Linderoth et al., 1997) and {1 1 1} (Kellogg and Feibelman, 1990; Bott et al., 1996; Kyuno and Ehrlich, 1999) surfaces. Especially for the {1 1 1} surfaces the attempt frequencies (or pre-exponential factors) and activation energies measured by FIM and STM are perfectly consistent and were also confirmed by ab-initio calculations using density-functional theory (DFT) by Feibelman (1998). Also the FIM results of the energetically favorable exchange (rather than hopping) diffusion on {1 0 0} surfaces agree very well with DFT calculation by Feibelman (2001). Using Arrhenius’ law, these data can be translated into a diffusion coefficient D and a jump frequency f at room temperature. Accordingly, one would expect D in the range of about 10−12 to 10−8 cm2 /s and f from tens of kHz to tens of MHz. This would mean that the mean residence time of an adatom at a lattice site amounts only to some microseconds or even nanoseconds at {1 0 0} or {1 1 1} surfaces, respectively. Given the time resolution of 0.8 s for the here presented HRTEM image series, such atom migration is impossible to observe. In fact with such a fast diffusion each surface column of the nanoparticle should exhibit a constant and more diffuse contrast, because during the time of image acquisition they are all temporarily occupied. Nevertheless atom diffusion is observable in the here described experiments as recognized by the fluctuation of clearly empty or occupied surface columns. The seeming discrepancy between our results and the data reported for the diffusion of isolated adatoms of more than four orders of magnitude can easily be explained, since this situation simply does not apply to the imperfect and rough surface of the Pt nanoparticles, where steps, kinks and vacancies are present. Using DFT calculations, Feibelman (1998) has in deed shown that the activation energies of downward diffusion at stepped {1 1 1} surfaces increase due to a large Schwoebel barrier (Schwoebel and Shipsey, 1966; Ehrlich and Hudda, 1966). Assuming a typical attempt frequency of 5 × 1012 Hz (Bott et al., 1996) this leads to a diffusion coefficient of D ≈ 10−17 . . . 10−15 cm2 /s at room temperature. This is in good agreement with our result for the diffusion on Pt nanoparticles which is mainly observed at such steps on {1 0 0} surfaces with small {1 1 1} micro-facets. A recent study using a cluster expansion model based on the nudged elastic band method (Verma et al., 2013) has emphasized the importance of the local environment of the adatom on a {1 0 0} surface. For thousands of different local environments the influence of the latter on the activation energy was studied. Here, it was found that it depends strongly on the number and position of up to fourth nearest neighbor atoms and can vary considerably. This variation implies that the corresponding diffusion coefficients span more than fifteen orders of magnitude at room temperature. However, for reasons of simplicity, only hopping processes were studied, but the dominant diffusion process on Pt{1 0 0} is the more complex exchange diffusion. Nonetheless, this study shows that the here observed diffusion on Pt nanoparticles will certainly be influenced by the local environments of the adatoms. On {1 1 0} surfaces, experimental investigations utilizing FIM resulted in smaller diffusion coefficients (Bassett and Webber, 1978) with D ≈ 10−17 cm2 /s, which would be comparable with our present finding, while a more recent STM study (Linderoth et al., 1997) has led to a thousand times smaller pre-exponential factors and accordingly to smaller diffusivities at room temperature. However, in our present study, diffusion on {1 1 0} facets is in deed not observed on the Pt nanoparticles. Due to the complexity of surface diffusion itself and the fact that the diffusion on nanoparticles cannot be attributed to only one migration mechanism or one specific surface, the interpretation of our results is not straightforward and the impact of the imaging electron beam in the here described experiments cannot be quantified at this point. However, a massive heating of the particle is unlikely, since then the thermally enhanced diffusion would not be
visible anymore. Additionally knock-on damage partly promoting the migration of atoms cannot be ruled out. In summary, the diffusion coefficient D for surface selfdiffusion on Pt nanoparticles is estimated to be in the range of D ∼ (10−17 . . . 10−16 ) cm2 /s. This value is clearly smaller than the diffusion coefficient for single adatom diffusion on flat extended surfaces. It can only be explained if additional energy barriers at steps and the influence of the local environment of the adatoms are taken into account. To fully understand the surface diffusion on nanoparticles more experimental as well as theoretical work is required.
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Contents lists available at ScienceDirect
Micron journal homepage: www.elsevier.com/locate/micron
Atomic surface diffusion on Pt nanoparticles quantified by high-resolution transmission electron microscopy S. Schneider a,b , A. Surrey a,b , D. Pohl a , L. Schultz a,b , B. Rellinghaus a,∗ a b
IFW Dresden, Institute for Metallic Materials, P.O. Box 270116, D-01171 Dresden, Germany TU Dresden, Institut für Festkörperphysik, D-01062 Dresden, Germany
a r t i c l e
i n f o
Article history: Received 29 August 2013 Received in revised form 20 December 2013 Accepted 21 December 2013 Keywords: Surface diffusion Aberration-corrected HRTEM Nanoparticles Platin Diffusion coefficient
a b s t r a c t Aberration-corrected high-resolution transmission electron microscopy allows for the delocalizationfree observation of atomic motions on metallic surfaces and thus enables measurements of the diffusion of single atoms on the surfaces of nanoscopic objects such as nanoparticles. Using this recently introduced method, the diffusion coefficient for surface self-diffusion of Pt nanoparticles is determined through the fluctuating occupation of the particle’s atomic columns. This diffusion coefficient is determined to lie in the range D ∼ (10−17 . . . 10−16 ) cm2 /s. © 2013 Elsevier Ltd. All rights reserved.
1. Introduction The continuing development of aberration-corrected highresolution transmission electron microscopy (HRTEM) led to the possibility to study the structure of specimens at the atomic scale in great detail and with highest precision (Urban, 2008; Van Aert et al., 2012). Apart from these static structural information, dynamic changes of the specimen, e.g., due to the impact of the imaging electron beam, are often observed in (scanning) TEM (Bals et al., 2012), in particular when working at high doses that are frequently mandatory to investigate the structural and chemical properties or even three-dimensional structures at highest magnifications (using holography (Linck et al., 2012) or focal series (Jinschek et al., 2011)). Such dynamic phenomena which are mostly related to unwanted radiation damage (Egerton et al., 2004), may also occur spontaneously without the electron beam and are most easily observable on surfaces. Surface diffusion (Smith and Marks, 1985; Zandbergen et al., 2005; Kisielowski et al., 2008; Wang and Palmer, 2011), Ostwald ripening (Yoshida et al., 2012) and sintering (Lim et al., 2009) have been reported and described qualitatively for different nanostructured thin films and for nanoparticles. It is, however, still an open question whether the observed atomic surface diffusion, which is the main underlying mechanism of most of these processes, can be solely ascribed to the physical properties of the
∗ Corresponding author. Tel.: +49 351 4659 754; fax: +49 351 4659 9754. E-mail address: [email protected] (B. Rellinghaus).
material or if and to which extent it is rather promoted by the impact of the imaging electron beam. Recently, a HRTEM method which allows for the quantitative estimation of the surface diffusion coefficient was introduced, and it was shown that it can be used to quantify the surface self-diffusion on Au nanoparticles (Surrey et al., 2012). The method is based on the analysis of temporal fluctuation in the occupancy of surface atomic columns. In the present paper, it is applied to quantitatively describe the surface self-diffusion on Pt nanoparticles. The possibility of a direct quantitative measurement of the surface diffusion may prove a valuable tool in electron microscopy to better understand the impact of the electron beam on the materials under investigation. 2. Experimental methods Pt nanoparticles produced by inert gas condensation (Dmitrieva et al., 2007; Pohl et al., 2012) are deposited on holey amorphous carbon films supported by copper grids. In contrast to the deposition on a continuous carbon film, the holey support offers the advantage to allow for a more direct interpretation of the weak contrasts at the surfaces of nanoparticles, which partly extend into a hole of the support film and are thus imaged substrate-free in vacuum. Due to the absence of noisy contrast backgrounds arising from the support film this setup allows to easily discriminate between empty and occupied surface atom columns by visual impression (Surrey et al., 2012). The diffusion processes are investigated using a FEI Titan3 80-300 microscope equipped with an image CS -corrector at an
0968-4328/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.micron.2013.12.011
Please cite this article in press as: Schneider, S., et al., Atomic surface diffusion on Pt nanoparticles quantified by high-resolution transmission electron microscopy. Micron (2014), http://dx.doi.org/10.1016/j.micron.2013.12.011
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acceleration voltage of 300 kV. The aberration corrector was used to set the coefficient of the spherical aberration to CS ≈ 0 m, and the focus was adjusted to a minimal underfocus of about −5 nm. Higher order aberrations are corrected to limit the maximum parasitic phase shift to /4 for an aperture with a semiangle of 20 mrad. At these conditions, atomic columns appear as dark contrasts with minimal delocalization in the HRTEM images. HRTEM image series are continuously acquired with a time delay of 0.8 s between subsequent images. These series are comprised of 31–35 images. The current densities are in the range of j ≈ 5 . . .14 × 106 e− /nm2 /s. Since HRTEM images display a two-dimensional projection of the atomic columns, only atomic movements perpendicular to the imaging electron beam are visible. Atoms changing their position within a column that lies parallel to the electron beam do not cause any “significant” contrast changes and therefore, this motion cannot be detected. Furthermore it has to be taken into account that the atoms in a HRTEM image are indistinguishable, i.e. the trajectories of individual atoms cannot be identified. To quantify the motion of individual atoms the definition of the intrinsic (also called tracer) diffusion coefficient D, as given in the review article of Gomer (Gomer, 1990), is used: 1 D = lim →∞ 2dn n
→ r i () − → r i (0)2
Fig. 1. HRTEM image of the Pt nanoparticle #1 oriented in [1 1 0] direction reaching partly into the vacuum. The visible facets are labeled.
(1)
i=1
Here, n is the total number of adatoms, thetime interval between subsequent images,
→ r i () − → r i (0)2 is the mean
square displacement of the ith adatom in the d-dimensional case of uncorrelated jumps. Given the above mentioned limitations in the evaluation of atomic motions in HRTEM images it is useful to rewrite the expression of the diffusion coefficient (Surrey et al., 2012): D=
a2 2 l
1 il nk n
with l =
(2)
i=1
Here, a is the length for nearest neighbor jumps of an atom and l denotes the lateral jump frequency. The factor k takes into account that some lateral diffusion channels are indistinguishable in the two-dimensional projection of a HRTEM image (for a more detailed explanation, the reader is referred to Surrey et al., 2012). For measurements of the surface diffusion on a {0 0 1} surface along a 1 1 0 direction the factor k is equal to 1. The quantity l contains the number of all lateral jumps il of n adatoms in the time period . The knowledge of the numbers of all lateral jumps, il , and all adatoms participating in the diffusion process, n, would allow for an exact determination of the diffusion coefficient D. However, the exact number of all lateral jumps, il , cannot be determined from a HRTEM image series, but it can be approximated by the number of “significant” contrast changes, f, during . These “significant” contrast changes are defined as contrast changes, where either an atomic column is filled or emptied, which is a direct proof for the atomic motion at the nanoparticle’s surface. These jump events can be either detected by a subjective evaluation of the intensity at the individual atom column or by a quantitative analysis of the intensity. However, both approaches yield comparable results (Surrey et al., 2012). Especially in the absence of a substrate “significant” contrast changes are clearly observable. Any contrast larger than the noise level of 7% can be attributed to one or more Pt atoms. An interval of ≈ 0.8 s between two consecutive images of the temporal HRTEM series is small enough to observe individual jumps (Surrey et al., 2012). While it is also impossible to determine the number of adatoms, n, from the two-dimensional HRTEM images, it had been shown that in order to approximate the diffusion
constant, it is sufficient to count the number of atomic columns, N, which are located at sites, where surface diffusion is most likely to occur and to measure the number of significant contrast changes there. These sites are the steps and edges at the surface of the nanoparticle, because atoms at such positions are minimally coordinated and therefore contribute mainly to the diffusion. Based on these assumptions l can be approximated by the frequency: l∗ =
f Nk
(3)
This frequency may deviate from the exact l due to different reasons, but it was shown that it nonetheless allows for the measurement of the diffusion constant with the precision of one order of magnitude (Surrey et al., 2012). 3. Results The method summarized above is now applied to two Pt nanoparticles #1 and #2 in Figs. 1 and 2 and Figs. 3 and 4, respectively. In order to calculate D, all atomic columns N, where diffusion can occur, are counted in each image of the temporal series. This is shown as an example in Fig. 2, where two subsequent images of the series with magnified sections of the (0 0 1) surface of particle #1 (cf. Fig. 1) are displayed. In Fig. 2a, N = 6 atomic columns at steps or edges are identified (marked with red circles). The quantity f/ can then be calculated from the sum of all “significant” contrast changes of the series. How these contrast changes are identified is also illustrated in Fig. 2. The atom column at position “4” which is marked with a red circle in Fig. 2a is emptied in the consecutive HRTEM image in Fig. 2b, where the position is marked with a blue circle (at position “3*”), because the formerly weak dark contrast has vanished by then. On the other hand, the formerly empty column at position “2*” in Fig. 2b marked with a blue circle is meanwhile (partially) filled, which can be seen from the newly emerged dark contrast. In total, f = 3 “significant” contrast changes can be identified from a comparison of Fig. 2a and b. For particle #1 in Fig. 1 a series of 35 consecutive images is acquired, all image pairs of which are likewise analyzed. Since the diffusion occurs mostly on the (0 0 1) surface of the particle, the value k = 1 is chosen for the calculation of D. Averaging over all 34 lateral jump frequencies of the surfaces results in a mean atomic jump frequency
Please cite this article in press as: Schneider, S., et al., Atomic surface diffusion on Pt nanoparticles quantified by high-resolution transmission electron microscopy. Micron (2014), http://dx.doi.org/10.1016/j.micron.2013.12.011
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Fig. 2. HRTEM images of the (0 0 1) surface of the Pt nanoparticle #1. (a) There are N = 6 atomic columns that could exhibit diffusion. (b) Consecutive HRTEM image of the same Pt nanoparticle acquired 0.8 s after image a. The f = 3 “significant” contrast changes are marked with blue circles. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
√ ¯l∗ = 0.15 ± 0.03 Hz. Using Eq. (2) with a = gPt / 2 and the lattice ˚ the diffusion coefficient for the surface constant of Pt, gPt = 3.92 A, self-diffusion on the Pt nanoparticle for jumps to the nearest neighbor is thus estimated to be D1 = (5.7 ± 1.1) × 10−17 cm2 /s. Assuming jumps not only to the nearest, but also to the next nearest neighbors the diffusion coefficient is D2 = (2.3 ± 0.4) × 10−16 cm2 /s. On the Pt nanoparticle #2 displayed in Fig. 3, the diffusion occurs also mainly on a {1 0 0} surface. Even though some rare jump events are detectable on other surfaces such as {1 1 1}, again the value k = 1 is chosen for reasons of simplicity and since the factor k has only a minor influence on the order of magnitude of the results. Based on a temporal series of 31 HRTEM images a mean atomic jump frequency ¯l∗ = 0.26 ± 0.02 Hz is calculated. This leads to
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Fig. 3. HRTEM image of the Pt nanoparticle #2 reaching partly into the vacuum acquired with a current density j ≈ 14 × 106 e− /nm2 /s. As an example the blue arrow indicates a filled atomic column. On the bottom right the amorphous carbon film can be seen. A temporal HRTEM image series of the red marked region can be seen in Fig. 4. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
the diffusion coefficients D1 = (1.0 ± 0.1) × 10−16 cm2 /s for nearest neighbors and D2 = (4.0 ± 0.4) × 10−16 cm2 /s for next nearest neighbors. Here, all given errors represent the standard deviation of the mean value. It has to be stated that a larger number of images would clearly reduce the error and provide a statistically more robust results. However, during the imaging of the nanoparticle not only single atoms start to move, but also the particle as a whole turns because of the imaging electron beam. This is why the zone axis orientation is not stable and the diffusion can only be observed for a limited period of time. 4. Discussion Surface self-diffusion has been studied extensively using field ion microscopy (FIM) and scanning tunneling microscopy (STM) on flat {1 0 0} (Kellogg and Feibelman, 1990; Kellogg, 1991), {1 1 0}
Fig. 4. Temporal series of the Pt nanoparticle #2. The time delay between two images is 0.8 s. Columns marked with an arrow undergo “significant” contrast changes during the temporal series. Following abbreviations are used: occupied atomic column (o), empty atomic column (e). From the left to right the occupation of the columns changes as follows: turquois: o, o, o, o, e, e; white: o, o, e, e, e, e; green: e, e, o, o, e, e; blue: o, o, e, e, o, e; yellow: o, o, o, o, o, e; red: e, o, e, o, e, o. In (a) N = 9 step columns (marked with red circles) are present and in the consecutive image (b) f = 1 contrast change can be counted. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
Please cite this article in press as: Schneider, S., et al., Atomic surface diffusion on Pt nanoparticles quantified by high-resolution transmission electron microscopy. Micron (2014), http://dx.doi.org/10.1016/j.micron.2013.12.011
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(Bassett and Webber, 1978; Linderoth et al., 1997) and {1 1 1} (Kellogg and Feibelman, 1990; Bott et al., 1996; Kyuno and Ehrlich, 1999) surfaces. Especially for the {1 1 1} surfaces the attempt frequencies (or pre-exponential factors) and activation energies measured by FIM and STM are perfectly consistent and were also confirmed by ab-initio calculations using density-functional theory (DFT) by Feibelman (1998). Also the FIM results of the energetically favorable exchange (rather than hopping) diffusion on {1 0 0} surfaces agree very well with DFT calculation by Feibelman (2001). Using Arrhenius’ law, these data can be translated into a diffusion coefficient D and a jump frequency f at room temperature. Accordingly, one would expect D in the range of about 10−12 to 10−8 cm2 /s and f from tens of kHz to tens of MHz. This would mean that the mean residence time of an adatom at a lattice site amounts only to some microseconds or even nanoseconds at {1 0 0} or {1 1 1} surfaces, respectively. Given the time resolution of 0.8 s for the here presented HRTEM image series, such atom migration is impossible to observe. In fact with such a fast diffusion each surface column of the nanoparticle should exhibit a constant and more diffuse contrast, because during the time of image acquisition they are all temporarily occupied. Nevertheless atom diffusion is observable in the here described experiments as recognized by the fluctuation of clearly empty or occupied surface columns. The seeming discrepancy between our results and the data reported for the diffusion of isolated adatoms of more than four orders of magnitude can easily be explained, since this situation simply does not apply to the imperfect and rough surface of the Pt nanoparticles, where steps, kinks and vacancies are present. Using DFT calculations, Feibelman (1998) has in deed shown that the activation energies of downward diffusion at stepped {1 1 1} surfaces increase due to a large Schwoebel barrier (Schwoebel and Shipsey, 1966; Ehrlich and Hudda, 1966). Assuming a typical attempt frequency of 5 × 1012 Hz (Bott et al., 1996) this leads to a diffusion coefficient of D ≈ 10−17 . . . 10−15 cm2 /s at room temperature. This is in good agreement with our result for the diffusion on Pt nanoparticles which is mainly observed at such steps on {1 0 0} surfaces with small {1 1 1} micro-facets. A recent study using a cluster expansion model based on the nudged elastic band method (Verma et al., 2013) has emphasized the importance of the local environment of the adatom on a {1 0 0} surface. For thousands of different local environments the influence of the latter on the activation energy was studied. Here, it was found that it depends strongly on the number and position of up to fourth nearest neighbor atoms and can vary considerably. This variation implies that the corresponding diffusion coefficients span more than fifteen orders of magnitude at room temperature. However, for reasons of simplicity, only hopping processes were studied, but the dominant diffusion process on Pt{1 0 0} is the more complex exchange diffusion. Nonetheless, this study shows that the here observed diffusion on Pt nanoparticles will certainly be influenced by the local environments of the adatoms. On {1 1 0} surfaces, experimental investigations utilizing FIM resulted in smaller diffusion coefficients (Bassett and Webber, 1978) with D ≈ 10−17 cm2 /s, which would be comparable with our present finding, while a more recent STM study (Linderoth et al., 1997) has led to a thousand times smaller pre-exponential factors and accordingly to smaller diffusivities at room temperature. However, in our present study, diffusion on {1 1 0} facets is in deed not observed on the Pt nanoparticles. Due to the complexity of surface diffusion itself and the fact that the diffusion on nanoparticles cannot be attributed to only one migration mechanism or one specific surface, the interpretation of our results is not straightforward and the impact of the imaging electron beam in the here described experiments cannot be quantified at this point. However, a massive heating of the particle is unlikely, since then the thermally enhanced diffusion would not be
visible anymore. Additionally knock-on damage partly promoting the migration of atoms cannot be ruled out. In summary, the diffusion coefficient D for surface selfdiffusion on Pt nanoparticles is estimated to be in the range of D ∼ (10−17 . . . 10−16 ) cm2 /s. This value is clearly smaller than the diffusion coefficient for single adatom diffusion on flat extended surfaces. It can only be explained if additional energy barriers at steps and the influence of the local environment of the adatoms are taken into account. To fully understand the surface diffusion on nanoparticles more experimental as well as theoretical work is required.
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