Jump processes in surface diffusion

Transcription

1 Surface Science Reports 62 (2007) Jump processes in surface diffusion Grazyna Antczak a,b,, Gert Ehrlich a a Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA b Institute of Experimental Physics, University of Wroclaw, Wroclaw, Poland Received 2 December 2006; accepted 4 December 2006 Abstract The traditional view of the surface diffusion of metal atoms on metal surfaces was that atoms carry on a random walk between nearest-neighbor surface sites. Through field ion microscopic observations and molecular dynamics simulations this picture has been changed completely. Diffusion by an adatom exchanging with an atom of the substrate has been identified on fcc(110), and subsequently also on fcc(100) planes. At elevated temperatures, multiple events have been found by simulations in which an atom enters the lattice, and a lattice atom at some distance from the entry point pops out. Much at the same time the contribution of long jumps, spanning more than a nearest-neighbour distance, has been examined; their rates have been measured, and such transitions have been found to contribute significantly, at least on tungsten surfaces. As higher diffusion temperatures become accessible, additional jump processes can be expected to be revealed. c 2007 Elsevier B.V. All rights reserved. Keywords: Atom jumps; Surface diffusion; Field ion microscopy; Molecular dynamics Contents 1. Introduction Surface diffusivities Atom exchange On fcc(110) planes On (100) planes Via multiple events Long and rebound jumps Theoretical work Experimental studies Summary Acknowledgements References Introduction Surface diffusion plays a significant role in crystal and film growth, in evaporation and condensation, in surface chemical Corresponding author at: Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. Tel.: address: antczak@mrl.uiuc.edu (G. Antczak). reactions and catalysis, in sintering as well as in other surface processes. As such there has been considerable interest in how diffusion occurs; during the last few decades much novel and significant material has been discovered. Here we will briefly review what has been learned about how diffusion of single metal atoms takes place on metal surfaces, what sort of atomic jumps occur and how information about these processes has been obtained /$ - see front matter c 2007 Elsevier B.V. All rights reserved. doi: /j.surfrep

2 40 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 1. Hard-sphere models of bcc (a) (110), (b) (211), and (c) (321) planes Surface diffusivities Diffusion is characterized by the material parameter D, the diffusivity in the (one-dimensional) diffusion equation: J = D c x connecting the adatom flux J to the concentration gradient c/ x. The diffusivity is given by the usual Arrhenius relation ( D = D o exp E ) D, (2) kt where the prefactor D o, usually considered a constant, and the activation energy E D are obtained from the temperature dependence. Langmuir [1], in 1933, already viewed the atoms in surface diffusion as hopping between elementary spaces at a separation a, and was able to show that for an individual adatom the diffusivity was given in terms of the lifetime τ at a particular site by D = a 2 /2τ. (3) In transition-state theory the one-dimensional diffusivity is written more elaborately as: ( ) ( D = υl 2 SD exp exp E ) D, (4) k kt where υ gives the effective vibrational frequency of the adatom, l its jump length, and S D as well as E D the entropy and activation energy for diffusion. We can, however, introduce the abbreviation: ( ) SD υ o = υ exp, (5) k so that the diffusivity appears as in Eq. (2), but with D o = υ o l 2. (6) On surfaces it would be difficult to measure atom fluxes and gradients. The mass flux of material over a surface can of course be detected, but it is not clear how to disentangle interactions between the atoms. The diffusivity is therefore obtained alternatively from the Einstein relation, which ties the diffusivity to the mean-square displacement x 2, x 2 = 2Dt, (7) (1) Fig. 2. Models of fcc (a) (111) and (b) (100) planes. where t is the time interval of the measurements. The elementary formalism is now in hand, and using it much data has been gathered about diffusion kinetics [2]. But what are the jump processes participating in surface diffusion? If atoms always jump between nearest-neighbour sites, then since a typical vibrational frequency at the surface is s 1, and the spacing is 3 Å, the prefactor D o should, if we neglect entropy contributions, be of magnitude 10 3 cm 2 /s. It turns out that this is close to the value of the prefactor for many diffusion systems [2], starting with one of the first studied, W on W(110), for which a value of cm 2 /s was found [3, 4]. This agreement suggested that this simple view of diffusion processes had considerable merit. However, the story has turned out to be much more interesting than that. 2. Atom exchange 2.1. On fcc(110) planes Early studies of individual metal atoms diffusing on metals were with tungsten atoms on (110), (211), and (321) planes of bcc tungsten, models of which are shown in Fig. 1. Also studied somewhat later were rhodium atoms on rhodium, an fcc metal [4]. Examined were (111) and (100), as well as (110), (311) and (331) planes, shown in Figs. 2 and 3. What is clear is that the (321) and (211) planes on tungsten and (311), (331) and (110) planes on rhodium are channelled, and that an adatom moving along one of these channels might be expected to stay in such a channel and execute strictly one-dimensional diffusion. That was in fact found to be the case as shown in Fig. 4 for W(211), making predictions of the direction in diffusion seemingly straightforward.

3 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 3. Models of fcc (a) (110), (b) (311), and (c) (331) planes. Fig. 5. Mechanism for cross-channel diffusion of adatom on Pt(110) proposed by Bassett and Webber [5]. (a) Adatom in channel. (b) Vacancy forms in channel wall. (c) Adatom has moved into vacancy, lattice atom is now in channel site. Fig. 4. Location of sites on W(211) at which Rh adatom has been detected after diffusion at 197 K. Motion is strictly one-dimensional. Shown at the bottom is a count of the number sighted at each site. This simple picture was suddenly destroyed, however, by the work of Bassett and Webber [5] in 1978, who studied another fcc metal, platinum. On (331) and (311) planes diffusion occurred, as expected, along the channels of the surfaces. On the (110) plane, however, diffusion was two-dimensional! The activation energy for in-channel motion was 0.84 ± 0.1 ev, for cross-channel movement it was smaller, only 0.78 ± 0.1 ev. Similar results were found with the diffusion of iridium atoms on these surfaces. What had been established here was that diffusion on channelled surfaces could occur in two dimensions, depending on the particular system. Predicting the direction in which diffusion occurred was not just a matter of looking at surface geometry. The question still remained how cross-channel motion took place. Bassett and Webber [5] had two ideas. One was that large fluctuations occurred in the rows of atoms constituting the channel walls, creating holes through which adatoms could easily jump. A more likely possibility was that the movement of a channel atom created a hole that could be filled either by the adatom or a surface atom, as shown in Fig. 5. They concluded that Further experimental and theoretical studies are required to clarify the nature of inter-channel diffusion. Even without an understanding of the mechanism of cross-channel motion, the phenomenon of cross-channel diffusion had been established. What actually happened in cross-channel atom movement was soon uncovered in experiments by Wrigley and Ehrlich [6]. They took advantage of the atom probe [7], to measure the chemical identity of atoms on Ir(110)-(1 1). In this work the system was calibrated by first depositing an iridium and separately a tungsten atom on the surface kept at 50 K. The mass of the individual atoms was then obtained by measuring the time of flight to a detector 1 m away by field desorbing the atoms; the results are shown in Fig. 6. With this information in hand, a tungsten atom was placed on the clean surface, which was heated until cross-channel diffusion took place. The atom observed by field ion microscopy after diffusing into the adjacent channel was then field evaporated, and as also shown in Fig. 6 proved to be iridium, an atom from the lattice. Thereafter the top layer of the surface was field evaporated and analyzed, as in Fig. 7, and usually a tungsten atom was detected in the surface layer, as expected if atom exchange had occurred. This was not the case when the surface was probed after crosschannel motion had not been seen. These experiments were the first direct proof of an interchange between a substrate and an adsorbed atom during cross-channel diffusion. A number of theoretical investigations were stimulated by the results on Pt(110). Halicioglu [8,9] carried out calculations for diffusion on Pt(110) with Lennard-Jones twobody potentials and found that in cross-channel diffusion an adatom interacts with an atom in the channel wall to form a dumbbell, as in Fig. 8(b). This could decompose by the adatom incorporating into the surface and the surface atom going into the adjacent channel, or else by returning to the original channel, as indicated in Fig. 8(c). Just slightly later, DeLorenzi et al. [10,11] did molecular dynamics calculations, again using Lennard-Jones potentials, on fcc surfaces. Most interesting were the results for (110) planes, shown in Fig. 9, on which both in-channel and

4 42 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 6. Distribution of atomic weights of individual atoms field evaporated from Ir(110) surface [6]. Top: after deposition of Ir atom. Bottom: after deposition of W atom. Center: After deposition of W atom, followed by heating and observed cross-channel diffusion event; material desorbed is iridium. Fig. 7. Atomic weight distribution of material field evaporated from first Ir(110) layer [6]. Left: after cross-channel diffusion has occurred, a W atom is detected in the first substrate layer. Right: when no cross-channel motion was detected, iridium is desorbed. cross-channel motion was discovered, the latter with a lower activation energy. In cross-channel diffusion they again envisioned a dumbbell intermediate, as shown in Fig. 8(b), in which a pair of atoms sat across the ridgeline. When this decomposes, the adatom can move back to its original channel, or else it can move into the channel wall, placing a lattice atom in the adjacent channel. Additional simulations of diffusion across channels on a Lennard-Jones fcc crystal were done by Mruzik and Pound [12]. On the (110) plane, cross-channel motion again occurred by exchange with a lattice atom, but movement on the (113) plane was along the channels. Garofalini and Halicioglu [13] did similar estimates on the Pt(110) plane at both low and high temperatures. At lower temperatures both iridium and gold atoms diffused along the channels, but at higher temperatures exchange took place for iridium, and a platinum lattice atom appeared in the next channel. Gold at this temperature also formed a dumbbell with an atom from the channel wall, but returned to continue diffusion in its original channel, so diffusion was really onedimensional. More experimental work was reported in 1982 by Wrigley [14], who examined the temperature dependence of cross-channel motion, as shown in Fig. 10, with an activation energy of 0.74 ± 0.09 ev and a prefactor 1.4( 16 ±1 ) 10 6 cm 2 /s. Data were obtained at only five temperatures, and keeping in mind the low prefactor, must be viewed with some doubt. What was not clear at this point was the reason for the magnitude of the prefactor. Was it associated with the complicated mechanism, or were the measurements not detailed enough? At essentially the same time, Tung and Graham [15] looked at self-diffusion on various surfaces of nickel. The behaviour of the (110) plane varied depending on whether it had been cleaned thermally, or had been subjected to field evaporation in hydrogen gas. Diffusion measurements were made after the hydrogen treatment and some field evaporation, as well as after thermal cleaning only, and gave the results shown in Fig. 11. For both treatments self-diffusion was two-dimensional on Ni(110); however, diffusion after thermal treatment led to very low diffusion prefactors cm 2 /s, with an activation energy of 0.23 ± 0.04 ev for in-channel movement and 0.32 ± 0.05 ev across the channels. After hydrogen treatment, the characteristics for in-channel motion were a diffusion barrier of 0.30 ± 0.06 ev and a prefactor of 10 1 cm 2 /s; for crosschannel diffusion the barrier was lower, 0.25 ± 0.06 ev, with a prefactor of 10 1 cm 2 /s. In the temperature range K, cross-channel motion predominated. On Ni(331) and (113), however, movement was always one-dimensional. Tung [16] also briefly studied self-diffusion on Al(110), determining the temperature for the beginning of atom movement. Twodimensional diffusion was observed on the (110) plane, at a temperature of 154 K for both directions, leading to an estimate of 0.43 ev for the activation energy. It should be noted that the diffusion characteristics, both for nickel and aluminum (110) are uncertain, and the data have been reanalyzed [17]. Nevertheless, these observations firmly established crosschannel motion on these surfaces. Another five years later, in 1986, Kellogg [18] measured the rates of in- and cross-channel self-diffusion on Pt(110) over a range of temperatures. From an Arrhenius plot, shown in Fig. 12, he found an activation of 0.72 ± 0.07 ev with a prefactor of cm 2 /s for diffusion along the channels,

5 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 8. Schematic of atom exchange process in self-diffusion on fcc(110) surface: (a) Atom in the equilibrium position. (b) At the saddle point, atom pair sits as a dumbbell across [1 10] row of substrate atoms. (c 1 ) (c 4 ) After diffusion, atoms distributed uniformly over allowed sites. and 0.69 ± 0.07 ev with a prefactor of cm 2 /s for motion across the channels. It appeared that the prefactors for in- and cross-channel motion were similar and normal. Chen and Tsong [19] again looked at self-diffusion on Ir(110) in 1991, and as shown in Fig. 13, observed crosschannel diffusion with an activation energy of 0.71 ± 0.02 ev and a prefactor ±1.8 cm 2 /s; the values for inchannel motion were 0.80 ± 0.04 ev and a prefactor of ±0.8 cm 2 /s, so cross-channel jumps occurred more rapidly. Earlier work by Wrigley [14] was reasonably close in the diffusion barrier, but the present prefactor value is clearly preferable. Above and beyond the usual measurements, Chen and Tsong also looked at the distribution of displacements to get additional information about the diffusion process. These observations are shown in Fig. 14, with x indicating in-channel diffusion and y cross-channel jumping. What is especially interesting here is the fact that 80% of the jumps were in the 112 direction, shown in Fig. 8, with the remainder along 100. According to all the simulations of such self-diffusion done at that time, a cross-channel transition should have the same probability in four directions, whereas in the experiments, transitions in the direction of the moving adatom were favoured. These results were not accidental, however. Kellogg [20] in the same year, looked at the diffusion of platinum on the (110) plane of nickel. For these measurements nickel was not cleaned in hydrogen; instead a combination of thermal cleaning, sputtering and evaporation was found to be essential for a good image of the (110) plane. Although

6 44 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 11. Arrhenius plot for in- and cross-channel diffusion of Ni on Ni(110) plane [15]. Left: Substrate after thermal treatment. Right: Nickel substrate had been hydrogen fired and field evaporated before experiments. Fig. 9. Adatom trajectories in diffusion on fcc(110) plane at 0.4T m [11]. Transitions across the [1 10] channels are apparent. Fig. 12. Self-diffusion of Pt on Pt(110) surface [18]. In-channel diffusion: E D = 0.72 ± 0.07 ev, D o = cm 2 /s. Cross-channel diffusion: E D = 0.69 ± 0.07 ev, D o = cm 2 /s. Fig. 10. Early Arrhenius plot for the cross-channel diffusion of iridium atoms on Ir(110) [14]. Kellogg did not rely on an atom probe, he was able to discriminate between Ni and Pt atoms through differences in the voltages necessary for field evaporation the platinum atoms were removed at significantly higher voltages; they also had a much larger image spot. When a Pt atom was deposited on the cold surface, the image looked as in Fig. 15(a). After heating to 112 K, the image in Fig. 15(b) yielded a much smaller spot size, indicative of Ni. Upon removing the adatom, in Fig. 15(c), and field evaporating the topmost layer, as is shown in Fig. 15(d), a platinum atom was retrieved from the surface layer. Clearly exchange had occurred between a Fig. 13. Self-diffusion of Ir on Ir(110) plane [19]. Both in-channel and crosschannel motion is observed. platinum adatom and a nickel atom from the substrate, and the atom entering the lattice was platinum not nickel. Assuming a prefactor of cm 2 /s, a barrier of 0.28 ev was determined for the displacement of platinum. The distribution of displacements was also observed in these experiments and it was found that in 62.5% the replacement atom appeared in the 112 direction, never along 001 ; the remaining experiments

7 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 14. Distribution of displacements in diffusion of Ir on Ir(110) at different temperatures [19]. Transitions in direction of moving atom are favoured, contrary to theoretical predictions. Fig. 16. Exchange between Re adatom and Ir(110) substrate illustrated in field ion images [21]. In (b), Re atom has been deposited on the clean Ir(110) surface in (a), giving a round image spot, a schematic of which is in (e). After one minute at 255 K, oblong atom, Ir, is found in (c), also illustrated in (f). Substituted Re atom is revealed on partial field evaporation, in (d). Fig. 15. Neon field ion images showing exchange of Pt adatom with Ni from Ni(110) surface [20]. (a) Single Pt adatom on Ni(110) plane. (b) After one minute at 112 K, adatom has changed to Ni, judged from lower desorption field. (c) Adatom has been removed by field evaporation. (d) After removal of one layer of nickel, Pt adatom is again apparent. ended with an atom in the original row. Kellogg speculated that this was due to the atom from the channel wall maintaining its cohesion with the adatom, but this conclusion was not reached in previous molecular dynamics simulations. The mechanism of cross-channel movement is still wreathed in uncertainty. A year later, Chen et al. [21] carried out field ion microscopic studies of rhenium atom diffusion on the Ir(110) surface. They were able to distinguish between Re and Ir atoms, as rhenium gave a circular image spot and iridium yielded an elongated image. A rhenium atom was deposited on the surface and then heated to 256 K. This moved the atom spot one space over and elongated the image, suggesting that an atom replacement had occurred. The top layer of the substrate was then field evaporated, as shown in Fig. 16, revealing a bright rhenium atom, and demonstrating that exchange with a lattice atom had indeed taken place. Finally, it should be noted that in 2002, Pedemonte et al. [22] were able to detect some cross-channel movement in helium scattering experiments on Ag(110) at temperatures above 750 K, but did not derive energetics for such movement. At the beginning of the nineties there started quite a large number of efforts to calculate diffusivities of metal atoms on metals. Such estimates, usually using semi-empirical interactions, were done for the (110) planes of Al [17,23 25], Ni [17,26 28], Cu [17,27 33], Pd [17,27,28,34], Ag [17, 28,30,32,34,35], Ir [28,36,37], Pt [17,27,28,38,39], Au [17,27, 28,32], and Pb [40]. In all of these the barrier to diffusion along the channels was lower than the barrier for cross-channel transitions, despite the fact that for Al, Ni, Ir and Pt the opposite had been demonstrated in experiments. In short, diffusion by atom exchange on fcc(110) is well established, if not yet well understood. What is still not clear is why a particular system undergoes exchange while another one does not, and why a particular direction is favoured in diffusion.

8 46 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 19. Map of sites on Pt(100) at which Pt adatom was found after diffusion at 175 K [46]. A c(2 2) net is formed, indicative of jumps by atom replacement. Fig. 17. Atom migration on bcc (100) surface, shown in molecular dynamics simulations modelled by Price potential [42,43]. Straight arrows j indicate nearest-neighbour jumps, curved arrows e show adatom exchange with substrate [41] On (100) planes While all this work studying atom exchange on fcc(110) planes was going on, DeLorenzi and Jacucci [41] had been continuing their efforts to examine atomic jumps in surface diffusion. Their attention turned to bcc materials, which meant they had to resort to a different type of interaction for simulations. They relied on a metallic potential devised by Price [42,43] to describe sodium, and used this in examining diffusion on various planes of a bcc lattice. Of specific interest here is what was observed on the (100) plane. In the usual course of events, we expect diffusion to take place by an atom jumping from its normal binding site, at the centre of four surface atoms, to a neighbouring binding site in a straight line at right angles to the border of the unit cell. What frequently happened in the simulations, however, was different and is shown in Fig. 17, where short straight arrows indicate normal jumps, between nearest neighbours, and curved ones reveal an atom-exchange process. In this exchange an adatom moves into the outer lattice layer, dislodging a lattice atom which ends up on the surface in a position diagonal to the starting point, as suggested in the schematic in Fig. 18. In their own words, DeLorenzi and Jacucci found that In addition to conventional nearest neighbour jumps between surface sites, the adatom undergoes migration events reminiscent of exchange processes of the intersticialcy in the bulk. In these events, atom A belonging to the surface layer is replaced by atom B originally constituting the adatom. As a result, atom A ends up as an adatom located at a site displaced from the one originally occupied by the point defect. This is the first observation, in simulations or real experiments, of the occurrence of exchange events between adatom and a substitutional atom as a quantitatively important process contributing to atomic diffusion on isotropic crystal surfaces. A new exchange event had been discovered; one question remaining was the generality of this process. Would it occur in practical systems? Regrettably, nothing was done to test the work of DeLorenzi and Jacucci, until five years later two studies appeared: Kellogg and Feibelman [44] studied Pt(100) and Chen and Tsong [45] simultaneously looked at Ir(100). They both examined the displacements carried out on the surface, and found that atoms moved diagonally and not just to nearest neighbors, creating a c(2 2) map of binding sites, as shown in Fig. 19. From the mean-square displacement at 175 K, the activation energy for diffusion on Pt(100) was estimated as 0.47 ev, assuming the usual prefactor of 10 3 cm 2 /s. Chen and Tsong did better in studying iridium. From an Arrhenius plot of the meansquare displacement per unit time, shown in Fig. 20, they found a barrier of 0.84 ± 0.05 ev and a diffusivity prefactor of 6.3( 11 ±1 ) 10 2 cm 2 /s. Just like Kellogg and Feibelman, they observed diagonal atom movement for iridium. On these two surfaces, diffusion occurred by atom exchange, as had been found earlier by DeLorenzi and Jacucci [41]. Fig. 18. Schematic showing exchange between adatom and substrate atom on (100) plane: (a) Adatom at equilibrium site. (b) Adatom and lattice atom in transition state. (c) Adatom incorporated into lattice; atom from lattice has turned into adatom.

9 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 20. Arrhenius plot for diffusion of Ir adatom on Ir(100) observed in field ion microscope [45]. Fig. 23. Interaction of Re adatom with Ir(100) surface [48]. Re atom is placed on (100) plane in (b) and is then heated to 230 K, yielding an oblong image spot in (c), which rotates on heating to 262 K. This sequence is shown schematically in (e) (g). Fig. 21. Dependence of Pt atom diffusivity on Pt(100) upon 1/T [46]. Fig. 22. Binding sites for Pd on Pt(100) after diffusion at 265 K, indicating ordinary hopping [47]. Further studies of self-diffusion on Pt(100) were carried out in 1991 by Kellogg [46], who again found a diagonal map of displacements for platinum atoms, indicating an exchange process. The diffusion barrier obtained from the Arrhenius plot in Fig. 21 was 0.47 ± 0.01 ev, with a prefactor 1.3( 10 ±1 ) 10 3 cm 2 /s. Subsequent work [47] showed that palladium atoms carried out the usual atomic jumps, as indicated in Fig. 22, while nickel and platinum underwent atomic exchange reactions in diffusion. In the next year, Tsong and Chen [48] put a rhenium atom on Ir(100). When heated to a temperature of 230 K, the Re displaced an Ir atom from the surface layer to form a dimer above the vacancy, as in Fig. 23. Above 280 K the dimer decomposed and the rhenium entered the lattice, with an iridium atom left to continue surface diffusion, another example of atom exchange. Kellogg [49] also studied the behavior of platinum atoms on Ni(100). He was able to distinguish between the two in terms of the higher voltage required to field evaporate platinum than nickel atoms. After depositing platinum on the surface at 77 K, and then heating to 250 K, the platinum disappeared. On field evaporating the surface layer platinum appeared again, as in Fig. 24, revealing that an exchange process had taken place. Additional confirmation for iridium diffusion on Ir(100) by atom exchange was provided by the work of Friedl et al. [50] in They plotted the sites visited in diffusion and found a c(2 2) net, as expected if exchange took place between an adatom and a lattice atom. However, they proposed an alternative explanation: the surface could reconstruct and create a c(2 2) sub-lattice for diffusing atoms. This explanation did not survive the test of time, however, since reconstruction should occur independent of the type of diffusing atom. Some years later, Fu and Tsong [51] again looked at self-diffusion on Ir(100) and again observed a c(2 2) net. In the meantime, quite a number of calculations were made for surface diffusion on a variety of fcc(100) planes, with a mixture of results. More then ten estimates have been carried out for Al(100). Most of them considered exchange

10 48 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 24. Replacement of Pt adatom on Ni(100) by Ni atom [49]. (a) Pt atom deposited on Ni(100) at 77 K. (b) After heating to 250 K for one minute, Pt adatom disappears. (c) After partial field evaporation. (d) On complete field evaporation of one layer of nickel, Pt atom reappears. as a possible mechanism [17,23,25,52 59], and roughly half favored atom exchange during diffusion. For Ni(100) [17,59 71], out of a total of nineteen estimates, only eight considered exchange as an option, and fewer than half of these indicated an exchange of atoms as primary in the diffusion process. Here it is important to note the observation of Perkins and DePristo [65] as well as of Chang and Wei [60] that the activation energy for exchange depends strongly on the size of the cell used in the calculations, while the hopping energy is not sensitive to this factor. Much more work has been done to understand diffusion on Cu(100) [17,29,53,58 68,70 90, ]. Half the investigations considered exchange as an option, but only three studies gave an indication of atom exchange taking place. For Pd(100) [17,27,59 62,64,66,69 71,92,93], three estimates favored hopping as the principal mechanism, but after increasing the size of the cell in the calculations three favoured exchange [17,60,65]. Only one out of six studies considered exchange in diffusion on Ag(100) [17,27,59 62,64 71,76,91,94 97, ] possibly indicating a rate of atom exchange comparable to atom hopping; the remainder gave hopping as the mode of diffusion. Not too much calculational work has been done to evaluate diffusion characteristics on Ir(100) [37,92], Pt(100) [17,92,98], and Au(100) [17,66,99], but all of them indicate that the preferred path for diffusion was by atom exchange. Although the outcome of some of the theoretical estimates is not that certain, the evidence is firm that exchange between an adatom and a lattice atom occurs in diffusion on (100) planes of Ir [45], Pt [44], and Ni [49], and probably also on Au [17,66,99]. There have been attempts to rationalize the conditions under which exchange will dominate in diffusion. For Al(100), Feibelman [100] pointed out that the transition state for atom exchange was stabilized by the covalent nature of aluminum. Kellogg et al. [47] correlated exchange diffusion with the relaxation of surface atoms around the binding site of the adatom. Yu and Scheffler [94] argued that tensile surface stress plays the key role for the exchange diffusion on fcc(100) surfaces, and is important not only for Au(100), but also for Fig. 25. Multiple atom exchange process in molecular dynamics simulation of adatom on Cu(100) at 900 K [75]. Adatom (black) moves into substrate, causing eventual emergence of a substrate atom at some distance from the original entry. Al(100) and 5d metals. However, Feibelman and Stumpf [92] have done detailed density functional calculations for the (100) surfaces of Rh, Ir, Pd, and Pt, and found no clear relation between surface stress and the diffusion barrier. Instead, they concluded that exchange diffusion was favored, as proposed by Kellogg et al. [47], when the relaxation of the substrate around an adatom was largest. Right now, however, it appears that predicting from experimental information which systems will undergo atom exchange in surface diffusion is an uncertain matter Via multiple events The results for exchange processes in diffusion described so far have been obtained at reasonably low temperatures, and have revealed a single event. Experiments at higher temperatures, to explore the possibility of multiple processes, are difficult and have not yet been explored. However, these conditions are accessible to molecular dynamics simulations, and have been probed starting in 1993 with the work of Black and Tian [75], who studied copper on Cu(100) relying on embedded atom potentials [101]. At 900 K, a high temperature for copper, they found that an atom adsorbed on the surface entered into the surface layer, straining the adjacent surface atoms as indicated in Fig. 25. The strain caused a surface atom to leave, popping out, not adjacent to the original entry point, but farther away. This peculiar event was again found in the work of Cohen [76], who did similar simulations on Ag, Al, Au, Cu, Pd, Pt, and Ni. On the (100) plane of aluminum she found that an atom entered the surface and travelled two sites and then over one before emerging again. The barrier for this novel diffusion was much higher than for ordinary hopping, and for all the metals above except for nickel would only become important above half the melting point. For nickel, the temperature for this diffusion process was expected to be even higher. An Arrhenius plot of the different diffusion processes is given in Fig. 26, and shows clearly that at elevated temperatures the new type of diffusion event makes significant contributions.

11 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 26. Arrhenius plot for three different mechanisms of diffusion for Ag on Ag(100) derived in molecular dynamics simulations [76]. New refers to multiple displacement exchange process, which has a higher activation energy and therefore only contributes at elevated temperatures. Fig. 28. Arrhenius plot for frequency of jumps in self-diffusion on Cu(100) [82]. Filled squares single jumps; open squares double jumps. Filled circles simple exchange; filled and open triangles double and triple exchange. Rhombic squares quadruple exchange. Table 1 Jump characteristics of Cu on Cu(100) [82] Jump Migration barrier (ev) D o (cm 2 /s) Single 0.43 ± ±0.2 Double 0.71 ± ±0.5 Simple exchange 0.70 ± ±0.3 Double exchange 0.70 ± ±0.6 Triple exchange 0.82 ± ±1.0 Quadruple exchange 0.75 ± ±0.9 Fig. 27. Molecular dynamics simulation of self-diffusion on Cu(100) at 950 K [82]. Adatom squeezes into the surface layer, and eventually a surface atom pops out at a considerable distance from the first entry. A more detailed examination of high temperature surface processes was carried out by Evangelakis and Papanicolaou [82] for copper atoms on the Cu(100) plane. They used the quite reliable RGL [102,103] potential to carry out their molecular dynamics simulations, which were done at 700 K and higher. At more elevated temperatures they observed double jumps, as well as exchange processes. Most interesting, however, were events such as shown in Fig. 27: an adatom enters the surface layer, disturbing a row of surface atoms, the last of which exits the surface to become an adatom. From observations of the jump frequency at different temperatures they were able to construct the Arrhenius plot in Fig. 28, yielding the diffusion characteristics of the different processes, shown in Table 1. It is important to recognize that the atom exchange events all have much the same kinetics, independent of the length of the process, which may be related to the extent of Fig. 29. Schematics showing atom movement in correlated jump-exchange (je), exchange-jump (ej), and finally jump-exchange-jump (jej) [104]. Dark grey indicates atom initially placed in channel; light grey shows atom from surface row taking part in exchange. the strain field; these transitions also occur over barriers much higher than for ordinary jumps. Also to be noted is the work of Ferrando on Ag(110) [104], who at temperatures above 600 K observed not only exchange but also correlated exchange-jump movements, as sketched in Fig. 29. He also observed a drastic change in the frequency of events when correlation between jumps and exchange occurred. Correlated jump and exchange processes were also observed on Cu(110) [32].

12 50 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 30. Temperature dependence of length of correlated jumps in diffusion of adatom on Lennard-Jones fcc(100) surface [107]. Fig. 32. Adatom trajectories on bcc(110) plane modelled with Price potential [42,43] during 200 ps at 0.4T m [41]. (a) Single jumps. (b) Double jumps. (c) Complicated trajectories. 3. Long and rebound jumps 3.1. Theoretical work Fig. 31. Adatom trajectories on Lennard-Jones (100) surface at T = 0.34T m, revealing non-nearest neighbour transitions [11]. The study by Evangelakis and Papanicolaou [82] has been the most detailed work on multiple exchange events, but these processes were rediscovered several years later by Xiao et al. [105,106]. Using EAM potentials they found multiple atom exchange events for strained Cu(100) and Pt(100), which were designated as crowdions. Although as yet there are no experiments to demonstrate such large scale exchange processes, there is little doubt that they will be found at elevated temperatures. However, detailed theoretical studies of such complicated processes will have to wait until procedures for investigating simple exchanges become reliable. One thing is certain: much more extended cell sizes will be needed for such calculations. From the experimental point of view, STM should be the most suitable tool to uncover such transitions. The view that in diffusion over a surface, atoms jump at random between nearest-neighbor sites, remained widespread until the end of the seventies. At that time a number of simulations appeared which suggested a more complicated picture of atomic events. Tully et al. [107] in 1979 carried out ghost particle simulations for a (100) surface of a Lennard- Jones crystal at different temperatures below the melting point T m. They discovered that, as shown in Fig. 30, the average jump length more than doubled as the temperature increased from 0.2T m to 0.6T m. More extensive molecular dynamics were carried out at much the same time by DeLorenzi et al. [10,11], again on an fcc Lennard-Jones crystal. Most interesting was the fact that on the (100) plane at 0.3T m long jumps were observed, between sites as much as three to four spacings apart. This is clear from the atom trajectories in Fig. 31. Corrections to diffusion rates predicted by transition-state theory for Rh(100) stemming from transitions to sites farther away than a nearest-neighbour distance were done by Voter and Doll [108], again with Lennard-Jones interactions. Only in the vicinity of 1000 K were jumps to other than nearestneighbour positions found. In the same year, 1985, DeLorenzi and Jacucci [41] published molecular dynamics simulation on various bcc surfaces modelled with a metallic potential developed by Price [42,43] for sodium. On the most densely packed surface, the (110), at a temperature of 0.4T m, they found not only jumps between nearest-neighbour sites, as in Fig. 32(a), but also double and more elaborate transitions, shown in Fig. 32(b) and (c). Evangelakis and Papanicolaou [82] also saw that double jumps started to be active on the (100) plane of copper, an fcc metal, at temperatures above 750 K. Above 800 K, more complicated processes, such as quadruple exchange began playing a role as well.

13 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) the length of atomic jumps can be obtained, as the probability that after a time t an atom will be at a displacement x from the origin was given by Wrigley et al. [114] as Fig. 33. Schematic of single, double and triple transitions in one-dimensional atom motion. In 1996, Ferrando [104] looked at self-diffusion on Ag(110) and found that single jumps represented 90% of the total, the rest were double or more complicated transitions. Investigations of long jumps were done by Montalenti and Ferrando [32] who looked at self-diffusion on the (110) planes of gold, silver and copper. Although the activation energy for movement on gold and silver is almost the same, and for copper slightly lower, their behaviour with respect to long jumps differed greatly. At 450 K, long jumps were absent on gold, there were 3% long jumps on silver, and 6% on copper. For copper, the fraction of long jumps increased to 15% at 600 K, but never got to this value on the Ag(110) surface. Ferrón et al. [113] saw long jumps as well as rebound jumps in self-diffusion on Cu(111). They claimed that at 500 K, 95% of jumps were correlated; at 100 K this decreased to 50%. What is quite clear from these simulations is that at elevated temperatures, larger than 0.2T m, long jumps should participate significantly in surface diffusion. The question still remained, however, how to detect the transitions in an experiment Experimental studies Information about the characteristics of surface diffusion has usually been obtained from measurements of the meansquare displacement. However, these measurements provide no simple connection to the types of transitions carried out by atoms diffusing over the surface. Usually an increase in the diffusivity is expected due to long transitions, since the diffusivity in Eq. (4) depends on the jump length squared, but so far this expectation has not been realized in experiments. More information is definitely needed. From measurements of the distribution of displacements in one dimension insight into p x (t) = exp[ 2(α + β + γ )t] I k (2γ t) k= j= I j (2βt)I x 2 j 3k (2αt). (8) Here it is assumed that single jumps at the rate α, double jumps at the rate β, and triple jumps at the rate γ take place on the surface, as is illustrated in Fig. 33; I m (u) is the modified Bessel function of the first kind, of order m and argument u. The jump rates clearly affect the probability of finding a set of atom displacements, and that is more immediately evident from the plots in Fig. 34, where single and double transitions participate in diffusion. All that needs to be done is to carry out an adequate number of observations of atomic displacements, and from these deduce the probability p x (t). To derive the individual jump rates, Eq. (8) is not all that useful, however, as it holds for diffusion on an infinite plane. For experiments in the field ion microscope the individual planes are quite small, and may extend over only 20 spacings, so that Monte Carlo simulations must be employed to extract rates. The first attempt to derive jump rates from the measured distribution of displacements was made in 1989 by Wang et al. [115] in one-dimensional diffusion on W(211). Tested were Re, Mo, Ir, and Rh atoms. As shown for rhenium in Fig. 35, the best fit to the distribution measured at 300 K was obtained assuming only single jumps. Even though long jumps were not found, for the first time the picture of diffusion as occurring by random jumps between nearest-neighbor sites had been demonstrated. Much the same also held for the other atoms studied, although for iridium and rhodium there were negligibly small contributions from double jumps. The next step was taken by Senft [ ], who surmised that energy transfer between the moving adatom and the lattice would affect the participation of long jumps in surface diffusion. She therefore elected to study palladium as well as nickel, with low values of the diffusion barriers amounting to 0.314±0.006 ev for Pd and 0.46±0.06 ev for Ni, which imply rather poor energy transfer. The displacement distribution was tested for self-diffusion of tungsten on W(211) at 307 K, and as Fig. 34. Effect of double jumps on the distribution of atomic displacements in diffusion with a mean-square displacement of two.

14 52 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 35. Distribution of Re adatom displacements at 300 K on W(211), obtained from field ion observations [115]. Best fit to experiments obtained with an entirely negligible contribution from long jumps. Fig. 36. Displacement distribution for W adatom on W(211) at 307 K [117]. Best fit to field ion experiments derived with negligible contribution of β double or longer jumps. Fig. 37. Distribution of Pd atom displacements on W(211) at 133 K [118]. Best fit with double/single jumps equal to 0.20, and triple/single of shown in Fig. 36 was found to be due entirely to single jumps between nearest-neighbor sites, as expected at the time. The same was found for the diffusion of palladium at 114 and 122 K. However, at 133 K, the distribution in Fig. 37 for the first time gave a clear indication of significant contributions from long jumps; the ratio of double to single jumps was 0.20, Fig. 38. Distribution of Ni adatom displacements on W(211) plane at 179 K [117]. Best fit of observations with double/single jumps equal to and even triple jumps were detected, at a ratio of 0.13 for triple to single transitions. In the diffusion of nickel atoms on W(211), Senft [117] found a distribution shown in Fig. 38, best fit with a ratio of doubles to singles of at T = 179 K. What was surprising about these findings is not just the detection of long jumps, but long jumps at quite a low temperature, < 0.1T m, and at a rate very temperature sensitive. For palladium, a diminution of the temperature by 11 K sufficed to eliminate all long transitions. With long jumps now firmly established in surface diffusion, Linderoth et al. [119] decided to explore their rates in selfdiffusion on the reconstructed Pt(110)-(1 2) plane, shown in Fig. 39. Jumps were observed with the scanning tunneling microscope, which yielded the distribution at 375 K in Fig. 40, with a ratio of double to single jumps of They also made measurements over a temperature range of 60 K to come up with the Arrhenius plot in Fig. 41, which gave a barrier of 0.81 ± 0.01 ev for single jumps and a somewhat higher value, 0.89 ± 0.06 ev, identified as coming from doubles. This identification turned out to be premature, however. A year passed and Montalenti and Ferrando [120] did simulations of diffusion on Au(110)-(1 2), relying on RGL interactions [102, 103]. They discovered two prevalent jumps, illustrated in

15 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 39. Hard-sphere model of (1 2) reconstructed fcc(110) surface, in which every second 111 row has been removed. Fig. 41. Arrhenius plot for single and double jump rates presumed to occur in self-diffusion on Pt(110)-(1 2) [119]. Fig. 40. Distribution of atomic displacements in self-diffusion on Pt(110)- (1 2) plane [119]. Best fit obtained with ratio of double to single jumps of Fig. 42: transitions along the bottom of the diffusion channel, and in addition transitions in which the atom jumps to the (111) sidewalls and continued diffusion there. The number of these metastable transitions exceeded that of long jumps in the channel. Another year later, Lorensen et al. [121] published density functional estimates for diffusion on Pt(110)-(1 2), which confirmed what had previously been found for gold metastable jumps were the likely explanation for the findings of Linderoth et al. [119]. Up to this point, long jumps had been identified experimentally only on the channeled, one-dimensional surface of the W(211) plane, and only for rapidly diffusing atoms. Oh et al. [122] in 2002 undertook tests to see if they also occurred on W(110), in the two-dimensional diffusion of palladium. Of course this is a rather more complicated system, and jumps may take place in quite a number of ways, as indicated in Fig. 43. The Arrhenius plot in Fig. 44 did not show any evidence of long jumps. However, an Arrhenius plot is not a good indicator of the jump processes in diffusion. For this we have to rely on the distribution of displacements, shown in Fig. 45. At a Fig. 42. Trajectories of Au adatom on reconstructed Au(110) surface with 110 rows missing, obtained in molecular dynamics simulations at 450 K [120]. Left column: in-channel jumps single, double, and triple. Right column: metastable transitions single, double, and triple. temperature of 210 K this distribution gave a significant number of double β jumps along 111 as well as vertical δ y transitions. After correction for effects due to transient temperatures during sample heating and cooling, the ratio of β/α proved to be 0.12 ± 0.06, and 0.11 ± 0.10 was found for δ y /α, the first experimental demonstration of long jumps in two-dimensional diffusion. Worth noting here is the difference between vertical

16 54 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 43. Schematic of possible atom jumps on W(110) plane. Fig. 45. Displacement distribution of Pd adatom on W(110) plane at 210 K [122]. Double/single jump rate β/α is 0.12, δ y /α is Fig. 44. Dependence of the diffusivity of single Pd adatom on W(110) upon the reciprocal temperature [122]. Data corrected for edge effects as well as for migration during transients. and horizontal jumps, which is huge. It has been possible to derive a significant energy difference between the two kinds of jumps. Oh et al. [123] also examined the self-diffusion of tungsten atoms on W(110), and surprisingly found behaviour similar to that of palladium. At 365 K, the distribution yielded β/α = 0.22, δ x /α = 0.36, and δ y /α = Half of the transitions now were long jumps. Of particular interest are the vertical δ y and horizontal δ x transitions. It is not yet clear how they take place, but they can be envisioned as starting as jumps in the 111 direction, which are then deviated either toward the x- or y-axis. Although long jumps had now been found for a variety of atoms in both one- and two-dimensional diffusion, nothing was known about the rates of these transitions. This matter was tackled by Antczak [124]. In 2004 she examined in detail the distribution of displacements of tungsten atoms on W(110) Fig. 46. Arrhenius plot for diffusivities of W atom on W(110) along 100 and 110 direction [124]. Best fit is obtained with a straight line. over a range of temperatures and with very good statistics of 1200 observations. From an Arrhenius plot of the diffusivities, in Fig. 46, she obtained straight lines, indicating a barrier of 0.92 ± 0.02 ev for diffusion along 100 and much the same barrier of 0.93 ± 0.01 ev along 110. Again there were no indications in the diffusivity of anything to suggest contributions from long jumps. However, the distribution of displacements at elevated temperatures clearly showed such transitions, as is evident from Fig. 47. It must be noted that at these high temperatures significant displacements occur during the temperature rise before the diffusion interval and during the fall at the end. The distribution of displacements during these temperature transients therefore has to be determined and is also shown in Fig. 47. The final rates were obtained using the relation r = Rt r ot o t e (9)

17 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Table 2 Jump rate parameters for W on W(110) [124] Rate Activation energy (ev) Frequency factor υ o (s 1 ) α (low temperature) 0.94 ± ( 2.5 ±1 ) β 1.24 ± ( 8.1 ±1 ) δ x 1.28 ± ( 8.6 ±1 ) δ y 1.37 ± ( 4.4 ±1 ) Fig. 49. Arrhenius plots for δ x and δ y jumps of W adatom on W(110) [124]. Fig. 47. Distribution of W displacements on W(110) at 364 K [124]. Best fit obtained with significant contributions from long jumps. Inset gives distribution during temperature transients. Rates not corrected for effects from transients. Fig. 48. Arrhenius plots for rates of single α jumps and double β jumps of W adatom on W(110) [124]. Single jump rate is fitted at low temperatures. At elevated temperatures, rate drops significantly below this straight line. where R is the rate measured in the experiment for an interval t, r o and t o give these quantities determined for the transients, and t e is the effective time interval. In Fig. 48 are shown the Arrhenius plots for the rates of tungsten single jumps α and double jumps β. What is most interesting here is that above 340 K, the rate α drops below the straight line extrapolated from low temperatures. This is not the case for the other rates β, nor for δ x or δ y shown in Fig. 49. Clearly the rate of single transitions is influenced by the occurrence of the other jumps. The kinetics of these transitions are listed in Table 2. The barriers to the long jumps are all considerably higher than for single transitions; so are the frequency prefactors, s 1 for single jumps and s 1 for vertical transitions. How can all of this be understood? The important thing to recognize is that the various rates are not independent. If the sum of all the rates is displayed on an Arrhenius plot, as in Fig. 50, a straight line is obtained, not a line curved concave upward. This can be understood in terms of the schematic in Fig. 51. An atom starts a transition toward a nearest-neighbor site, but may continue beyond this. Every time one of these other transitions β, δ x, or δ y occurs, the number of single jumps is diminished. At higher temperatures, where the higher barriers to these transitions can be overcome, the rate α will therefore become smaller. How can we account for the high barriers and prefactors of the long transitions? For the range of temperatures in the experiments, we can write the rate r i of transition i as r i = R p i, (10) where R is the basic jump rate, given by ( R = υ o exp E ) o, (11) kt

18 56 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 50. Arrhenius plot of the sum of all jump rates for W adatoms on W(110), giving a straight line fit [124]. Fig. 52. Arrhenius plot for Ir adatom diffusivities on W(110) plane along 100 and 110 [125]. Fig. 51. Schematic of jump rates on W(110) plane [124]. Basic jump is α transition along 111. At elevated temperatures, this can proceed beyond nearest neighbour end point, giving β, δ x, or δ y. and p i is the probability of a particular transition i. This probability is given by a normalized expression similar to Eq. (11), so that the activation energy for the given rate r i is just the sum of the barriers, and the prefactor the product of the separate prefactors, which makes the results obtained understandable. The diffusion of tungsten on W(110) is not the only system considered so far. Antczak [125] also examined the behaviour of iridium atoms on W(110). Arrhenius plots in Fig. 52 for diffusion along 100 and 110 are again quite straight, without any indication of multiple jump processes. Nevertheless, longer jumps occur frequently, as is clear from the distribution of displacements during experiments at 366 K, shown in Fig. 53 together with zero-time experiments, to catch displacements during temperature transients. For the long jumps were found β/α = 0.15, δ x /α = 0.38, and δ y /α = Just as previously with tungsten atoms above 350 K, the rate of single α transitions falls below the straight extrapolation from low temperatures; the other jump rates β, δ x, and δ y fit on normal Arrhenius plots. The explanation is the same as for tungsten atoms the Fig. 53. Distribution of Ir adatom displacements on W(110) surface at 366 K [125]. Both normal experiments, and experiments during transient temperatures are shown. Values for ratios of jump rates shown obtained after corrections for transient effects. jumps are not independent and arise by conversion from one elementary process. What is important here is that the long transitions of both iridium and tungsten replace the single jumps on W(110) gradually and at quite a low temperature, less than a tenth of the melting point. There they start playing a leading role in diffusion, and at higher temperatures single transitions disappear completely. Surprising is the difference in the activation energies of vertical and horizontal jumps on W(110), which as shown in Fig. 54 is huge for palladium atoms, much lower for tungsten, and disappears for iridium atoms. It turns out that this difference has a linear dependence on mass, but it is so far based on only three points.

19 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 54. Differences in the activation energies for vertical and horizontal jumps of Pd, W, and Ir adatoms on W(110). Fig. 56. One-dimensional distribution of W adatom displacements at 325 K on W(211) [126]. Zero-time measurements to detect transient contributions (in inset) have been used to give listed rates. Fig. 55. Arrhenius plot for self-diffusion of W adatom on W(211) plane [126]. On tungsten, long jumps are not limited to two-dimensional diffusion. Senft [ ] already showed this for Pd and Ni on W(211), but with tungsten she came to the conclusion that long jumps did not occur. More recently Antczak [126] has probed one-dimensional self-diffusion on W(211), but at higher temperatures than Senft, and longer transitions were discovered for this system as well. A normal Arrhenius plot for tungsten, with an activation energy of 0.81 ± 0.02 ev and a prefactor of 3.41( 2.40 ±1 ) 10 3 cm 2 /s was found, as shown in Fig. 55. At an elevated temperature of 325 K the distribution of displacements in Fig. 56 now revealed a ratio β/α of double to single jumps of 0.66; transitions during the temperature transients are given in the same figure. The plot of the single jump rate α in Fig. 57 drops sharply at temperatures of 300 K and above. At 325 K the rate of single jumps has gone Fig. 57. Arrhenius plot for α single jumps of W on W(211) [126]. At 320 K, rate α has decreased so much it is no longer discernable. to zero and only long jumps contribute to diffusion; the rate of β double jumps behaves normally with temperature, as is evident from Fig. 58. Long jumps are clearly demonstrated in this onedimensional system, but there is also a big surprise. As indicated in Fig. 59, the sum of the two rates measured does not plot as a linear Arrhenius graph, as had been found on W(110); it appears that here not all types of jumps have been detected. What is missing are rebound transitions, illustrated in Fig. 60. An atom starts on a jump; at the adjacent site it can settle down, creating a single jump. It can also continue on to the next site to form a double transition, or else it can rebound to return to the starting point. No displacements arise from

20 58 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 60. Schematic of different types of jump processes for an adatom on W(211) [126]. β R denotes rebound transition. Fig. 58. Normal Arrhenius plot for β double jumps of W adatom on W(211) [126]. Fig. 61. Rate of rebound jumps, obtained as the difference between the sum of single plus double jumps and total jump rate extrapolated from low temperatures [129]. Fig. 59. Arrhenius plot for the sum of all jump rates measured for W adatom on W(211). For temperatures 310 K, rate falls below linear plot [126]. such a rebound transition, and it is therefore not detected in the normal diffusion measurements, but rebounds were found in molecular dynamics simulations in 1989 by DeLorenzi [127], and a few years later by Sanders and DePristo [128] and Ferrón et al. [113]. A way to measure such rebounds has recently been discovered. Antczak [129] has pointed out that the sum of the measured jump rates has to be subtracted from the straightline Arrhenius plot obtained by extrapolating the sum from low temperatures. The rebound rate so obtained is shown in Fig. 61; it has an activation energy of 1.03 ± 0.06 ev and a frequency prefactor of 1.40( 10.3 ±1 ) s 1, and thus lies midway between single and double jumps. What is surprising is that rebounds were not detected in twodimensional diffusion on W(110) at all, suggesting it may be an effect tied to the channelled structure of W(211) that is involved in these transitions. However, they have been seen previously in simulations of self-diffusion on the Cu(111) plane [113]. It should be noted that long jumps are not limited to the movement of single atoms. As is apparent from Fig. 62, long jumps were observed by Wang [130,131] for clusters of iridium atoms on Ir(111), and for the large organic molecules decacyclene and hexa-tert-butyl-decacyclene by Schunack et al. [132]. However, information about the kinetics of these processes is limited and crying for more work. Finally, it should be said that theoretical predictions about long jumps have been very important in pointing to their contributions in diffusion. However, even the limited number of experiments done so far have already revealed that these transitions are rather more varied and more significant than predicted, especially at low temperatures. 4. Summary This survey should make it clear that a whole variety of different jumps contributes to surface diffusion on metals. Atom exchange processes are of course very much affected by the chemistry of the interacting partners, but have so far only been observed in experiments with fcc metals. On channelled surfaces the direction favoured in diffusion is still puzzling.

21 G. Antczak, G. Ehrlich / Surface Science Reports 62 (2007) Fig. 62. Centre-of-mass displacements for Ir 19 cluster during 10 s intervals at 690 K [131]. Observed number of displacements shown bold, best fit in outline numerals just below. α, β, as well as γ transitions contribute significantly. Very interesting are the multiple exchange processes seen in simulations at elevated temperatures, but these have not yet been found in experiments. The situation may well be different for the rate of long jumps. These have so far only been detected in experiments on tungsten surfaces, on which it has been possible to determine jump rates. There it is clear that in self-diffusion these jumps already occur at low temperatures less than 1/10 the melting point; at more elevated temperatures they supplant single atom jumps as carriers of the diffusion process. So far these long transitions have not been observed on other metals, even though the expectation is that long jumps will prove to be quite general, independent of the substrate, and important at elevated temperatures, where new types of jumps may also be found. Surface diffusion has now been explored on the atomic level for forty years, but new effects are still being discovered, and that suggests important work is ahead. Acknowledgements This work was done while supported by the Petroleum Research Fund, administered by the ACS under Grant ACS PRF AC5. We are also indebted to Mary Kay Newman for her help with the literature. References [1] J.B. Taylor, I. Langmuir, The evaporation of atoms, ions and electrons from caesium films on tungsten, Phys. Rev. 44 (1933) 423. [2] G.L. Kellogg, Field ion microscope studies of single-atom surface diffusion and cluster nucleation on metal surfaces, Surf. Sci. Rep. 21 (1994) 1. [3] G. Ehrlich, F.G. Hudda, Atomic view of surface self-diffusion: Tungsten on tungsten, J. Chem. Phys. 44 (1966) [4] G. Ayrault, G. Ehrlich, Surface self-diffusion on an fcc crystal: An atomic view, J. Chem. Phys. 60 (1974) 281. [5] D.W. Bassett, P.R. Webber, Diffusion of single adatoms of platinum, iridium and gold on platinum surfaces, Surf. Sci. 70 (1978) 520. [6] J.D. Wrigley, G. Ehrlich, Surface diffusion by an atomic exchange mechanism, Phys. Rev. Lett. 44 (1980) 661. [7] E.W. Müller, T.T. Tsong, Field Ion Microscopy Principles and Applications, American Elsevier, New York, [8] T. Halicioglu, An atomistic calculation of two-dimensional diffusion of a Pt adatom on a Pt(110) surface, Surf. Sci. 79 (1979) L346. [9] T. Halicioglu, G.M. Pound, A calculation of the diffusion energies for adatoms on surfaces of FCC metals, Thin Solid Films 57 (1979) 241. [10] G. DeLorenzi, G. Jacucci, V. Pontikis, in: D.A. Degras, M. Costa (Eds.), Proc. ICSS-4 and ECOSS-3, Cannes, 1980, p. 54. [11] G. DeLorenzi, G. Jacucci, V. Pontikis, Diffusion of adatoms and vacancies on otherwise perfect surfaces: A molecular dynamics study, Surf. Sci. 116 (1982) 391. [12] M.R. Mruzik, G.M. Pound, A molecular dynamics study of surface diffusion, J. Phys. F 11 (1981) [13] S.H. Garofalini, T. Halicioglu, Mechanism for the self-diffusion of Au and Ir Adatoms on Pt(110) surface, Surf. Sci. 104 (1981) 199. [14] J.D. Wrigley, Surface Diffusion by an Atomic Exchange Mechanism, Ph.D. Thesis, University of Illinois at Urbana-Champaign, [15] R.T. Tung, W.R. Graham, Single atom self-diffusion on nickel surfaces, Surf. Sci. 97 (1980) 73. [16] R.T. Tung, Atomic Structure and Interactions at Single Crystal Metal Surfaces, Ph.D. Thesis, University of Pennsylvania, Philadelphia, 1981, 171. [17] C.L. Liu, J.M. Cohen, J.B. Adams, A.F. Voter, EAM study of surface self-diffusion of single adatoms of fcc metals Ni, Cu, Al, Ag, Au, Pd, and Pt, Surf. Sci. 253 (1991) 334. [18] G.L. Kellogg, Field-ion microscope observations of surface selfdiffusion and atomic interactions on Pt, Microbeam Anal. (1986) 399. [19] C.L. Chen, T.T. Tsong, Self-diffusion on the reconstructed and nonreconstructed Ir(110) surfaces, Phys. Rev. Lett. 66 (1991) [20] G.L. Kellogg, Direct observations of adatom surface-atom replacement: Pt on Ni(110), Phys. Rev. Lett. 67 (1991) 216. [21] C.L. Chen, T.T. Tsong, L.H. Zhang, Z.W. Yu, Atomic replacement and adatom diffusion: Re on Ir surfaces, Phys. Rev. B 46 (1992) [22] L. Pedemonte, R. Tatarek, G. Bracco, Surface self-diffusion at intermediate temperature: The Ag(110) case, Phys. Rev. B 66 (2002) [23] P.A. Gravil, S. Holloway, Exchange mechanisms for self-diffusion on aluminium surfaces, Surf. Sci. 310 (1994) 267. [24] R. Stumpf, M. Scheffler, Ab initio calculations of energies and selfdiffusion on flat and stepped surfaces of aluminum and their implications on crystal growth, Phys. Rev. B 53 (1996) [25] Y.-J. Sun, J.-M. Li, Self-diffusion mechanisms of adatom on Al(001), (011) and (111) surfaces, Chinese Phys. Lett. 20 (2003) 269. [26] C.L. Liu, J.B. Adams, Diffusion mechanisms on Ni surfaces, Surf. Sci. 265 (1992) 262. [27] P. Stoltze, Simulation of surface defects, J. Phys.: Condens. Matter 6 (1994) [28] U.T. Ndongmouo, F. Hontinfinde, Diffusion and growth on fcc(110) metal surfaces: A computational study, Surf. Sci. 571 (2004) 891. [29] L. Hansen, P. Stoltze, K.W. Jacobsen, J.K. Nørskov, Self-diffusion on copper surfaces, Phys. Rev. B 44 (1991) [30] C. Mottet, R. Ferrando, F. Hontinfinde, A.C. Levi, A Monte Carlo simulation of submonolayer homoepitaxial growth on Ag(110) and Cu(110), Surf. Sci. 417 (1998) 220. [31] G.A. Evangelakis, D.G. Papageorgiou, G.C. Kallinteris, C.E. Lekka, N.I. Papanicolaou, Self-diffusion processes of copper adatom on Cu(110) surface by molecular dynamics simulations, Vacuum 50 (1998) 165. [32] F. Montalenti, R. Ferrando, Jumps and concerted moves in Cu, Ag, and Au(110) adatom self-diffusion, Phys. Rev. B 59 (1999) [33] S. Durukanoglu, O.S. Trushin, T.S. Rahman, Effect of step step separation on surface diffusion processes, Phys. Rev. B 73 (2006) [34] L.S. Perkins, A.E. DePristo, Self-diffusion of adatoms on fcc(110) surfaces, Surf. Sci. 317 (1994) L1152.