2555
Langmuir 1991, 7, 2555-2563
Atomic Interactions on Crystals: A Review of Quantitative Experiments Gert Ehrlich' and Fumiya Watanabe'lt Coordinated Science Laboratory and Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 Received April 10, 1991. In Final Form: May 30, 1991 Two types of studies have been pursued to gain insights into atomic interactions at crystal surfaces. Changes in macroscopic surface properties, such as atom desorption as a function of coverage, have been interpreted in terms of the forces operating between atoms. Recently the ability to observe individual atoms on solids, available through several techniques, has also made it possible to directly measure energy changes when two or more atoms are brought together. For adsorbed metal atoms, both approaches have yielded quantitative results, and these are summarized, with special emphasis upon results from direct observationsin the field ion microscope. The latter have revealed several interesting trends: a significant dependence upon the orientation of the atom pair, interactions extending over very long distances (>lo A), and sizable contributions from many-atom effects. Introduction In the rapid development of surface studies during the last few decades, one area has until recently lagged behind-the examination of interactionsbetween adsorbed species. Such interactions are of fundamental as well as practical concern; they are responsible for cohesion in crystals and play an important role in the formation of overlayers, which are currently of great technological interest. Interactions between atoms on a surface will differ from what is familiar through studies in the gas phase. Nevertheless, the latter provide a useful reference point, and in Table I we list dissociation energies measured for gas phase dimers of several different metal atoms. A single atom interacting with a surface will perturb its immediate environment; when more than one atom is adsorbed, these perturbations of the substrate combine to bring about characteristic indirect interactions between the adatoms which can propagate over long distances through the lattice. The theory governing these effects on crystals dates back to the 1960s. Early efforts, succinctly reviewed by E i n ~ t e i n ,have ~ led during the last few years to quantitative predictions for the surface behavior of transition-metal atoms.57 There has also been a continuing low level of effort devoted to experimentally characterizing surface interactions between adatoms, and during the last decade this has culminated in estimates of interaction energies for a variety of different adatoms. Experiments aimed at quantitatively estimating interactions have been of two different types: measurements of macroscopic or semimacroscopic surface phenomena, which are then interpreted in terms of a particular law of atomic interactions, or else direct determinations of interactions by observa+ Present address: IBM Research, Almaden Research Center, 650 Harry Rd, San Jose, CA 95120-6099. (1)Moskovits, M. Metal Clusters; Wiley: New York, 1986;pp 135138. ~~. (2) Kolaczkiewicz, J.; Bauer, E. Surf.Sci. 1986, 175, 508-519. (3)Schlenk, W.; Bauer, E. Surf.Sci. 1980, 93, 9-32. (4)Einstein, T.L. CRC Crit. Reu. Solid State Mater. Sci. 1978, 7, 261-2843. - - - __ -. (5)Bourdin, J. P.;Desjonqudres, M. C.; Spanjaard, D.; Friedel, J. Surf. Sci. 1986,157, L345-354. (6)Bourdin, J. P.;Desjonquhs, M. C.; Ganachaud, J. P.; Spanjaard, D. Surf.Sci. 1987, 179, L77-83. (7) Dreyssb, H.; Tomanek, D.; Bennemann, K. H. Surf. Sci. 1986,173, 538-554.
Table I. Dissociation Energies (eV) gas phase dimer'
cu Ag Au
Ni Pd
Pt
1.97 1.65 2.29 2.38 1.09 3.71
adatom desorption W(110)2 3.2 2.8 3.3 4.35
dimer on W(110)2 0.35 0.45 0.35 0.30
3.63
tions of individual atoms on a surface. For chemisorbed layers, the former approach has proved quite promising: the quantitative interpretation of phase diagrams has yielded information about a number of different systems.* Direct studies, however, have been possible only for metal adatoms. It is therefore upon such adsorbed layers that we focus here, since these allow a comparison of the different approaches. In this brief survey of the experimental facts about atomic interactions at surfaces, we first touch upon large scale observations of metal layers, done by techniques standard for single crystal surface studies. The main emphasis, however, will be on direct probes of interactions, which are now able to provide detailed atomistic information. Macroscopic Measurements
As the concentration n of adatoms in a surface layer increases, interactions among the atoms a t the surface become more important and will alter the energetics of surface phenomena. The energy of atom desorption from the surface is one of the parameters that should reflect such effects. Desorption energies at low adatom concentrations, some of which are given in Table I, are responsive primarily to interactions between an adatom and the substrate. At higher adatom populations, however, the desorption energy will be affected by the interplay between the adatoms. Such effects have been examined for several metals by Kolaczkiewicz and Bauer.2 For silver, copper, gold, and nickel atoms on W(llO), desorption is governed by the usual rate equation dnldt = -nu exp[-Ed,/kT] (1) in which the frequency factor u is responsive to the detailed dynamics of the desorption process and E d w gives the (8) Bauer, E. In Structure and Dynamics of Surfaces XI: Phenomena, Models and Methods; Schommers, W . Blanckenhagen, P. v., Eds.; Springer-Verlag: Berlin, 1987;pp 115-179.
0743-7463/91/2407-2555$02.50/0 0 1991 American Chemical Society
Ehrlich and Watanabe
2556 Langmuir, Vol. 7, No. 11, 1991
I
2.81 0
I
0.1
I
1000(
I
1
I
0.2
I
0.3
0.4
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Figure 1. Desorption parameters for silver atoms at different coverages from W(1101,measured by Kolaczkiewicz and Bauer.z activation energy for desorption. Results for the desorption of silver atoms from the (110) plane of tungsten are shown in Figure 1. Both the desorption energy &w and the frequency factor v increase with coverage 8, but it is the former that is most interesting. As the concentration of silver increases, the energy required for desorption increasesas well, indicatingattractive interactions between adatoms. At a coverage 8 l/10 of a monolayer, there is a plateau in the desorption energy, and this has been attributed to desorption from silver dimers assumed present on the surface. From similar observations for other metal atoms, Kolaczkiewicz and Bauer2 derive the dimer binding energies listed in Table I. The proposed binding energies of two atoms on the surface are almost an order of magnitude smaller than for gas phase dimers. That, of course, is expected as, for the former, interactions are primarily with the substrate and amount to several electronvolts. It is also important to note, however, that the binding energies given by Kolaczkiewicz and Bauer are based on a particular view of what is happening on the surface-namely desorption from dimers-for which there is as yet no direct substantiation. Gollisch? who has made semiempirical predictions about cluster energetics, interprets some of the same desorption experiments rather differently, as stemming from the dissociation of atoms from larger clusters, and finds smaller values of dimer binding. Also, in earlier investigations, Bauer et a1.10 have interpreted desorption studies of copper from W( 110) in terms of much smaller pair interactions, amounting to only 0.15 eV. It appears that the analysis of such desorption experiments is still developing and would benefit from more atomistic information about the structure of the surface and the events on it. Desorption is just one of the many phenomena expected to reveal effects from atomic interactions.ll Under the right conditions of temperature and concentration, interactions between adatoms can be expected to lead to phase transformations in the surface layer. At low concentrations, the adatoms should behave like a lattice gas; as the concentration is raised, however, atomic interactions may lead to the formation of a coexisting condensed layer on the surface. From work function studies, Kolaczkiewicz and Bauer12 have been able to
-
(9) Gollisch, H.Surf. Sci. 1986, 175, 249262. (10) Bauer, E.;Bonczek, F.; Poppa, H.; Todd,G. Surf. Sci. 1976,53, 87-109. (11) The structure of clusters on Pt(100)and Ir(1OO) has recently been interpreted in terms of atomic interactions by Schwoebel, P. R.; Foiles, S. M.; Bisson, C. L.; Kellogg, G. L. Phys. Rev. E Condena. Matter 1988, 40,10639-10642, and Schwoebel, P.R.; Feibelman, P. J. Surf. Sci. 1989, 216,263-269.
Kdaczkiewicz
& Bauer 1985
-
0
0.1
0.2
0.3
Coverage,e Figure 2. Phase boundary for silver on W(110),separating T-8 region in which lattice gas exists by itself from the coexistence region for lattice gas and condensed phase.lZ
0
0 0
0
0
0
E1P
O
O O&
d o b o B Figure 3. Illustration of pair- and many-atom interactions contributing to binding in clusters on W(l10).14 deduce the phase boundary, separating the lattice gas from the region in which gas and condensed phase coexist, for Cu, Ag, Au, Pd, and Ni on W(110). Their results for the low coverage boundary of the coexistence region for silver on W(110) are shown in Figure 2. There is a standard procedure for inferring interactions from such results. The adsorbed atoms are treated as a lattice gas, with interactions between near neighbors, and also many-atom effects, as illustrated in Figure 3 for a body-centered cubic (110) plane. Attempts are then made to fit the observed coexistence curve with that predicted for a lattice gas (usually using Monte Carlo simulations), by treating the interactions in Figure 3 as adjustable parameters. Results obtained in this way by Stoop13for Ag on W(ll0) are given in Table 11. Several aspects of these estimates are of interest. In Stoop’s work, nearest-neighbor interactions are attractive, as are the many-atom contributions tl and t 2 ; interaction between second and third neighbors, however, are repulsive, and longer range effects are negligible. The absolute magnitude of the binding energy is only about l / e of what was estimated for Ag on W(110) from desorption measurements. (12) Kolaczkiewicz, J.; Bauer, E. Surf. Sci. 1986, 151, 333-350. (13) Stoop, L. C. A. Thin Solid Films 1983,103, 375-398.
Langmuir, Vol. 7, No. 11,1991 2557
Atomic Interactions on Crystals Table 11. Interaction Energies (meV) on W(llO)* Ag CU AU Ag a
-74 -222 -293 -177
37 -147 -255 -167
37 -72 -146 -103
-37 8 23 7
-37 52 158
94
-148 -85
Single Atom
13 14 14
ED
Attraction indicated by negative energies.
A start in examining the phase boundaries for Cu and Au on W(110) has been made by Roelofs and Bel10n.l~ Relying on the cluster calculationsof Gollisch? they deduce the pair, trio, and quarto interactions listed in Table I1 and then show that although the phase boundaries calculated from these parameters differ in detail from the experimental results, they do reproduce the general trends found in the experiments of Kolaczkiewicz and Bauer.12 Following Roelofs and Bellon,14 we have also derived parameters for silver on W(110), given in Table 11. These results for Ag, Cu, and Au differ dramatically from what Stoop13found for Ag on W(110): all pair interactions are attractive, and trio effects are repulsive. The magnitudes of the pair interactions are all significantly higher than the values reported by Stoop, and there clearly is a conflict here. Right now, conclusions about interactions drawn from macroscopic experiments are confusing and sometimes contradictory. Nevertheless, these observations are very important: they illustrate the need for more direct information about atomic interactions at surfaces in order to understand the course of macroscopic phenomena in atomistic terms. Direct Observations
Interaction energies on a surface can be deduced in a very straightforward way provided the individual atoms can be visualized. For a system at equilibrium at temperature T,the probability P(R) of finding two atoms separated by the vector R is related to the free energy of interaction F(R) throughlsJ6
P(R) = CPo(R) exp[-F(R)/kT]
(2)
here Po(R)is a geometrical factor, equal to the probability P(R) when there are no interactions, and C is a constant of normalization. If the probability P(R) can be measured in an experiment, then the free energy of interaction can immediately be deduced as a function of the interatomic distance and orientation on the surface. The primary requirement for accomplishing this is the availability of a technique that detects atoms on a surface and allows measurements of the interatomic separation. There are now available a number of methods capable of resolving surface features on the atomic level: scanning tunneling and atomic force m i c r o s ~ o p y , ~scanning ~-~~ transmission electron microscopy,20and field ion microscopy.21-24 The first group of methods is quite new, and (14)Roelofs, L. D.;Bellon, R. J. Surf. Sci. 1989,223,585-598. (15)Hill, T.L.Statistical Mechanics;McGraw-Hill: New York, 1956; Chapter 6. (16)Chandler, D. Introduction to Modern Statistical Mechanics; Oxford University Press: New York, 1987;Section 7.3. (17)Golovchenko, J. A. Science 1986,232,48-53. (18)Hamers, R.J. Annu. Rev. Phys. Chem. 1989,40,531-559. (19)Trump, R.M. J. Phys.: Condens. Matter 1989,1,10211-10228. (20)Crewe, A. V. Science 1983,221,325-330. (21)Muller, E. W.;Tsong, T. T. Field Ion Microscopy Principles and Applications; American Elsevier: New York, 1969. (22)Panitz, J. A. J. Phys. E 1982,15,1281-1294. (23)Panitz, J. A. In Solid State Physics: Surfaces; Park, R. L., Lagally, M. G., Eds.; Academic Press: Orlando, FL, 1985;Chapter 7.
Figure 4. Schematic of barrier to motion of an isolated adatom on a surface, compared to that for dissociation of an adatom in a dimer.30
work is still underway to demonstrate its utility in locating individual adatoms on solids. Crewe and his collaborators have made STEM observations of heavy metal atoms on graphite films,25and initial studies of the distance distribution have been reported.26 These observations are not easy, however, and during the last few years this promising approach has not been pursued. In contrast, the oldest of the techniques offering atomic resolution, the field ion microscope (FIM), is now routinely used to provide quantitative information about individual atoms. Here we will therefore concentrate entirely upon insights about atomic interactions obtained by this technique. Even with the ability to depict individual adatoms, a complete mapping of atomic interactions is not easy; somewhat less ambitious experiments have also provided useful information, and we will therefore examine the available data in order of increasing complexity of the measurements. Dimer Binding Energies. Metal atoms deposited on a surface will, at sufficiently low temperatures, associate into clusters, which are readily seen in the FIM. Measurements of the stability of such clusters offer immediate insights into the interactions between adatoms. Such studies were initiated some time ago by Bassett?' who observed the lifetime to dissociation of various metal dimers on W(110), the most densely packed plane of the bcc lattice. The mean time ( 7 ) to dissociation of a dimer on a surface is given, as is usual for a process occurring over an activation barrier Edb, by
(3) where 70 is a prefactor generally taken to be on the order of s. On a crystal surface, two atoms in adjacent sites face a barrier to dissociation even if there are no interactions between them, as is suggested in Figure 4; in order to move apart, the atoms must overcome the activation energy to diffusion, ED. The dissociation barrier Ed& is therefore written as the sum of the binding energy EBand the activation energy for diffusion (4)
EBis the energy difference for the dimer atoms at their equilibrium separation and so far from each other that interactions are negligible. In principle, the dissociation barrier Edim can be derived in a straightforward fashion from measurements of the lifetime of dimers prior to dissociation into separate adatoms, done at different temperatures. In practice this is a tedious undertaking. Dimers must be recreated on the (24)Ernst, N.; Ehrlich, G. in Microscopic Methods in Metals; Gonser, U., Ed.; Springer-Verlag, Berlin, 1986;pp 75-115. (25)Isaacson, M.; Kopf, D.; Utlaut, M.; Parker, N. W.; Crewe, A. V. Proc. Natl. Acad. Sci. U.S.A. 1977,74, 1802-1806. (26)Utlaut, M.Phys. Rev. B.: Condens. Matter 1980,22,4650-4665. (27)Bassett, D.W.In Surface Mobilities on Solid Materials; Binh, V. T., Ed.; Plenum: New York, 1983;pp 83-108.
2558 Langmuir, Vol. 7, No. 11,1991 Table 111. Directly Observed Dimer Energies (in eV) on
[iii]
W(110) EB
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surface for each observation of a lifetime, so that at any one temperature the statistics for this Poisson process will be limited, and endowed with a significant random error. Only a narrow span of temperatures can be explored before the lifetime becomes either too short to reliably determine temperatures or too long to guarantee surface cleanliness. The usual procedure has therefore been to assume a value for the prefactor, and to derive the barrier height from observations at one temperature only. Such measurements were obtained by Bassett et a1.28em for several transition-metal dimers on W(110). Their dissociation energies, listed in Table 111, were really the first to provide any indication of the magnitude of atomic interactions a t surfaces. It is clear from these direct observations that dimer binding on W(110) is small, amounting to roughly -0.10.2 eV for platinum metals, which is an order of magnitude less than what is observed for gas-phase dimers. The chemical trends noted by Bassett et a1.29on moving along a row in the periodic table are of considerable interest: in going from Ta2 to Re2, the dimer bindig energy falls to essentially zero, and then rises again for the platinum metals. These trends can be correlated with the behavior observed for the binding of individual atoms on the same surface. Plummer and RhodinS2 used field evaporation to characterize the desorption energy for the elements from Ta through Pt. Although quantitative values obtained in this way are open to serious questi0n,3~the trends in the reported desorption energies of the adatoms are opposite to those in dimer binding, which diminishes toward Re-atom binding to the surface is highest in the middle of the period, for Re, and diminishes toward the ends. That is also the trend for the activation energy of atomic diffusion,M which should reflect the strength of atomic interactions with the surface. The trends in dimer binding observed by Bassett et a1.28as the identity of the adatom is changed have been attributed recently by Bourdin et al.5 to the increasing importance of electronic correlations when the center of the periodic table is approached. Although these early studies are important for their qualitative implications about interactions between ada(28) Bassett, D. W.; Chug, C. K.; Tice, D. Vide 1975,176, 39-43. (29) Bassett, D. W .;Tice, D. R. in The Physical Basis for Heterogeneous Catalysis; Drauglis, E., Jaffee, R. I., Eds.; Plenum Press: New York, 1975; pp 231-245. (30) Wrigley, J. D.; Ehrlich, G. Mater. Res. SOC.Symp. h o c . 1985,48, 47-53. (31) Tsong, T. T.; Casanova, R. Phys. Reu. B: Condens. Matter 1981, 24,3063-3072. (32) Plummer, E. W.; Rhodin, T. N.J. Chem. Phys. 1968,49,34793496. (33) Emst, N. Surf. Sci. 1979,87,469-482. (34) Bassett, D. W. In Surface Mobilities on Solid Materials; Binh, V. T., Ed.; Plenum: New York, 1983; pp 63-82.
A
A
J
~
A
A ~ A-
h
Figure 5. Hard-sphere model of the bcc (211) plane; outermost atom layer in white, second in gray. Spacing of close-packed (111) rows serves as unit of length for x , the lateral distance between adatoms (shown in black) along (111).
toms, there are some questions about their quantitative validity. In order to arrive at values of the binding energies, Bassett et had to make assumptions about the prefactor T~ in eq 3, and furthermore relied upon the activation energies for diffusion available a t the time. Both are sources of possibly significant errors. There is an alternative available for gaining information about the energetics of diatom binding. The free energy difference between bound and dissociated pairs can be derived, starting from eq 2, as
hFB/kT = -(In [P(RB)/P(=)] -In [P0(&3)/P0(=)11(5) where P ( m ) gives the probability of finding two atoms when they are beyond the reach of interatomic forces. The ratio of bound to dissociated pairs, P(RB)/P( =) which enters here, can be measured by direct observation, and the geometrical factor Po(R~)/Po( -) is available provided the size and shape of the plane on which measurements are made are known. Bassett et also explored this approach to derive the estimates to -AFB listed separately in Table 111. These free energy values are generally lower than the figures for the binding energy EB. It is doubtful, however, that such differences are outside the limits of error. In these trend-setting early experiments, determiningP(RB)/P( -), for example, would have been fraught with considerable uncertainty. Later measurements of free energy differences (also listed in Table 111)give values smaller still. Despite quantitative discrepancies, the general trend in all these direct studies is the same-binding energies of dimers a t the surface very small compared to the energy of dimers in the gas phase, just as found in the more macroscopic measurements. Interaction Studies in One Dimension. Estimates of the energetics of binding provide information about interactions between two atoms at the equilibrium spacing of the dimer. To get an idea about the range and strength of the interactions, however, the probability P(R) must be explored fully, a formidable problem in data gathering. The difficulties of carrying out such a program are greatly eased by operating in one dimension only, as is appropriate in characterizing atomic behavior on a channeled plane. This approach has been tried on the (211) plane of tungsten; as is apparent from the model in Figure 5,this plane consists of close-packed channels along (111). At the temperatures accessible in the FIM, atom motion on W(211) is alwaysalong the channels; if two atoms are placed in separate channels, they will be forced to remain in these throughout an experiment. Provided the separation of al.28929
Atomic Interactions on Crystals
Langmuir, Vol. 7, No. 11,1991 2559 T (K) 325
300
275
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I
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14
(1) Figure 6. Distance distribution for two tungsten adatoms on W(211). Adatoms are in channels separated by an intervening empty channel, so that minimum distance between them is 8.96 A.35 The lateral separation gives the distance (in units of the nearest-neighbor distance 1) measured along a channel. Distribution for noninteracting atoms is obtained by Monte Carlo simulation under the same conditions as actual experiments.
3.0 -
- 2.0
3.0
3.2
3.4
1000/T
3.6
3.8
(K-')
Figure 8. Temperature dependence of the ratio of rhenium crosschannel dimers on W(211) in staggered (1)as compared to straight state (0): raw data a t the bottom; data after correction for annealing during cool down is shown by dashed curve.% In the temperature range 7' < 325 K, cross-channel dimers are stable to dissociation, and the results for the internal energy difference El -EOas well as the entropy difference St - SOare obtained from eq 7 in keeping with standard thermodynamics.
A t equilibrium at a temperature T,the probability of fmding a dimer in the straight as compared to the staggered configuration is given, in terms of the free energy difference F1- FObetween the two, as Figure 7. Rhenium cross-channel dimer in configuration 1on W(211):38 hard-sphere model on left, with outermost atom layer in dark gray, second layer in white; field ion image a t right.
the channels is known, the behavior of cross-channeldimers can then be characterized entirely in terms of the lateral separation x of the atoms (measured along the channel). The probability P, of finding two atoms separated from each other by x nearest-neighbor spacings, in channels containing L sites, is now given by the simple expression35
P, = C(2 - 6,,)(L - x ) exp[-F,/izT]
(6) where 6, is the Kronecker delta and C the usual normalization constant; Fx represents the free energy of interaction for two adatoms a t a lateral separation x . The prefactor here just gives the number of ways the specified separation x can be realized on a channel of L sites, and corresponds to the term Po in eq 2. The probability P, has been examined in some detail for two tungsten atoms on W(211), separated from each other by an intervening empty channel.35 The results, in Figure 6, are in good agreement with a random distribution and suggest that interactions across the empty channel are not discernible. Measurements on W(321), with tungsten adatoms in adjacent channels which are separated by a distance of 7.08 A,have yielded rather similar results. When atoms are placed in neighboringchannels on W(211), a t a separation of 4.48 A, interactions become so strong that distribution studies have not been possible. The two atoms form a quasi-molecule,illustrated in Figure 7, which exists in two different states: a straight or 0 configuration, in which atoms in adjacent channels are lined up with each other, or else with the atoms displaced from each other by one spacing, in the staggered or 1configuration.36 (35) Graham, W. R.;Ehrlich, G. Phys. Reu. Lett. 1974,23,1309-1311. (36) Stolt, K.; Wrigley, J. D.; Ehrlich, G. J. Chem. Phys. 1978, 69, 1151-1161.
Measurements at different temperatures should then yield information about both the internal energy and entropy differences for the two forms. However, a significant experimental problem intrudes in such determinations. Equilibration is done at a high temperature, a t which diffusive interchange is rapid; observations are made at low temperatures, T
