SURFACE STRUCTURE AND DIFFUSION BY ROBERT Gem* Dept. of Chemistry and Institute for the Study of Metals, University of Chicago, 5640 Ellis Avenue, Chicago 37, Ill. Received 6th May, 1959 Field emission studies of surface diffusion on clean single crystals of known orientation and structure have shown the existence of several modes of surface diffusion for chemisorbed gases. It is found that there is a definite correlation between activation energy and entropy for diffusion on the one hand and surface structure (on the atomic scale) on the other. The ratio of activation energy to heat of binding shows similar behaviour, increasing with increasing roughness. In addition the size and binding mode of the adsorbate plays an important role. These studies illuminate also the well-known changes in heats of adsorption with coverage and indicate that a large fraction of the effect can be attributed to the inherent atomistic inhomogeneity of metal surfaces.Some detailed correlation can be made. Similar results for physical adsorption and multilayer formation will be discussed. A study of diffusion processes on metal surfaces is not only of intrinsic interest but sheds considerable light on the relations between adsorption energy and surface structure. The paper contains a brief summary of the method 1 and the results obtained to date, and a discussion of their meaning. METHOD The field emission microscope, invented by Muller,2 is a device particularly suited for the study of adsorption phenomena, since the adsorbent consists of a single crystal of known orientation, surface condition, and a high degree of perfection.Since all adsorbates including Ne) change its electron emission, surface diffusion can be studied if a portion of the emitter can be kept clean while another receives a gas deposit. This is accomplished as follows. A sealed-off field emission tube is immersed in a bath of liquid He or H2. The vapour pressure of all gases except He (viz., H2 at 20°K) is < 10-15 mm at these tempera- tures so that high vacuum is automatically attained and the tip can be cleaned by electric heating of a supporting loop. Evaporation from a gas source after the tip has cooled produces a deposit only on that part of it which " sees " the former. This results from the high sticking coefficients of all gases on very cold walls, and the high ratio of wall to tip area.Gas sources either utilize the thermal decomposition of such compounds as CuO or ZrH2 (formed in situ) 1 or depend on the sublimation of gas selectively precondensed on a heatable Pt sleeve.3 In this way the adsorption and diffusion of almost all gases on field emitters can be studied. RESULTS AND DISCUSSION At least three types of diffusion are encountered with chemisorbed gases. (i) Diffusion occurs with a sharp boundary a t very low temperature (2 > T > 70"K, depending on the gas) for initial deposits in excess of a monolayer.l.3-5 The layer formed in this way is not itself mobile ; if the initial deposit is insufficient for complete spreading the sharp boundary at first advances and then stops.If more gas is deposited, movement is resumed at low temperature. There is also an upper temperature limit above which no amount of deposition will advance the boundary. These facts indicate that diffusion occurs in a second (and possibly higher 6s 7) physically adsorbed layer, on top of an immobile chemisorbed one. Physically * Alfred P. Sloan Fellow. 2324 SURFACE DIFFUSION adsorbed molecules are mobile at low temperature, can wander to the edge of the chemisorbate, become incorporated into the latter and thus extend it, thereby permitting further diffusion over the newly covered region. Since there is a sharp discontinuity at the adsorbate-clean substrate edge, a moving boundary will be observed. The upper temperature limit corresponds to desorption of physically held molecules before their migration to the edge of the monolayer and chemisorp- tion on the bare surface can occur.It is possible to estimate the diffusion coefficient of the migration, its activation energy, and the heat of desorption from the relations - X Z dot, (1) D a2vexp [- Edlkq, (2) (3) which are all approximately valid. x represents the linear distance advanced by the boundary, X the average distance traversed before evaporation, D the diffusion coefficient, a the jump length, - 3 A, v a jump frequency, - 1012 sec-1, and Edes and Ed the activation energies for desorption and diffusion respectively. Eqn. (3) can be derived by assuming that the same frequency applies to diffusion and desorption. It is interesting that the coverage after type- 1 spreading is - 80 % of the maximum attainable by prolonged exposure of H and 0 on W.194 This suggests that only - 20 % of all sites require any activation for adsorption.(ii) For initial deposits of - 0.3 to - 1.0 monolayers diffusion with a sharp boundary is observed at temperatures ranging from 180°K for H on W1 to 750°K for CO on W.3~8 The activation energy of these processes varies from 6 to > 40 kcal, depending on the system, so that the phenomenon must involve the chemisorbate. With hydrogen1 and oxygen4 on tungsten a boundary moves radially outward from the central (011) face of the tip, if the initial coverage is 8 0.8. Diffusion occurs at 1 80"-220" and 500"-550"K respectively, and advances most rapidly along zones like (01 1)-(121)-(110) which consist of terraces and steps of 1 10 orientation. For 0 on W, 4 a boundary spreading outward from the cube faces, is also observed at - 400°K.For CO on W 3 . 8 boundaries advance from the centre of the tip in such a way as to close in on the cube faces, so that the CO-free portions of the tip appear convex with the cube faces at the centre of curvature. (iii) For deposits insufficient to permit type-2 migration, or after its cessation, diffusion occurs without a boundary at higher temperatures and with higher activa- tion energies than the corresponding type-2 processes. With the exception of CO,398 diffusion occurs in a temperature range where desorption is slow at the coverages involved. Reasonably accurate values of the activation energies of most type-2 and -3 processes can therefore be obtained from semi-logarithmic plots of the rate against 1/T.Comparison of these values with D, obtained approximately from eqn. (1) and (2) permits an estimate of the activation entropy. The results obtained to date for chemically and physically adsorbed gases are summarized in table 1. The mechanism for H on W serves as a convenient starting point for other cases and will be examined first. It is reasonable to assume that atoms will be least tightly bound and also most mobile on the closest-packed regions of the substrate, i.e. the (011) face for b.c.c. crystals. Atoms migrating over it will reach the edges rapidly but will be precipitated there since this face is surrounded by atomically rough surfaces everywhere except along the directions corresponding to the zones 112-011-121 and 112-01 1-121.These also provide low impedance paths of ingress into the central (01 1) face. This can be demonstrated experimentally by arranging the tip-source geometry to exclude the former from the initial deposit. Although the regions surrounding 01 1 are atomically rough, local saturation of trap sites leaves 01 1-like diffusion paths open to permit further migration if adsorbate E b = Ed + 9-2 Tlogl&/a), This process occurs for initial coverages as low as 6 = 0-3.R . GOMER 25 is available. Consequently diffusion with an activation energy corresponding to that on 011 will occur if there are enough adatoms to saturate traps. A boundary will result if the average precipitation distance is less than the resolution 6 of the field emission microscope (20-30 A).It is easy to show 1 that the trapping distance xt is given by (4) where a is the jump length, Nt and Nd the number of trap and diffusion sites per unit surface area and y a trapping coefficient of the order of unity. A sharp boundary will therefore be observed if Furthermore the coverage so that estimates of the number of trapping sites are possible. Eqn. (6) shows that - 40 % of all sites on atomically rough regions of tungsten emitters are trap sites for H atoms. Eqn. (4) then indicates values of the order of - 3 A for xt, so that eqn. ( 5 ) predicts a boundary. If this mechanism is correct, boundary-free diffusion with increased activation energy, Corresponding to migration from trap to trap, should become rate controlling when there are no mobile ad-particles left.This is the case. With Ni as substrate, type-2 diffusion is not observed for hydrogen3 except vestigially near the (1 10) faces, although the values of the activation entropy, energy, and its ratio to the energy of adsory’ion are very similar to those found for type-2 diffusion of H on W. Examination of a lattice model shows that the surface of an Ni emitter consists almost entirely of slabs and terraces of 100 and 11 1 orientation. In a face-centred structure these are the most closely packed faces, so that almost all portions of the Ni emitter are atomically smoother than the closest packed face of tungsten. A quasi type-2 diffusion can occur, but without a boundary, since the number of traps to be saturated is too small.Eqn. (2) indicates that NJN < 0.01, except in the immediate vicinity ofthe (1 10) faces. where the lattice is somewhat less closely packed. These observations do not conflict with the fact that the activation energy of the desorptiong of H2 from Ni shows a “tail” of 45 kcal at very low average 8, probably corresponding to tight binding sites near 110. It is also interesting to note that there is some evidence for equilibrium between adsorbed H and H2 at very high coverage and low temperature.9 This could easily result from the close proximity of ad-sites on this surface. The mechanism just presented assumes that sites of different binding, or at least activation energy for place change, are built into all but the closest-packed faces of a b.c.c.crystal and correspond to the various atomic surface configurations of the substrate. While there is no question that these occur, some care must be exercised in associating them with adsorption and diffusion sites. It is clear that the effects of this structure must disappear in the limit of very small ad-particles, since it is always possible to pick three surface atoms whose relation to each other corresponds to that of atoms in the (1 10) face. Hydrogen on W begins to approach this situation, although the variation in electronic configuration of the surface on the (110) compared with the (1 11) or (100) face is sufficient to bind hydrogen more tightly on the latter two and to increase the value of Ed/Edes there. However, H is sufficiently small so that it cannot differentiate between the configurations occurring on (1 11) or (100).The situation for 0 on W bears out this argument. The general mechanism seems similar to that for H on W, but the larger size of 0 atoms enables these to “ feel ” variations in the surface structure that are not apparent to H. Thus, after type-2 spreading must be Of Nt/(Nt -/- Nd)r (6)26 SURFACE DIFFUSION type-2 diffusion from the (100) face has a slightly lower activation energy than that from the (110) face. The reason is probably connected with the fact that there are two distinct types of sites for 0 atoms on the former. The first, very strongly binding, corresponds to a position in the interstice between four corner atoms of a face of the unit cell where simultaneous contact with at least four (possibly five) W atoms is possible because of the large size of 0.The second corresponds to contact with only two W atoms, once the interstice is filled. On the other hand, an 0 atom makes simultaneous contact with three W atoms on the smoother (1 10) face and must break one of these " bonds " in the process of changing sites. Diffusion from a " two-atom " site on the (100) face may or may not involve a larger fraction of the corresponding binding energy ; the latter will be considerably lower than on 011 so that the net result is a slightly decreased activation energy. The fairly low coverage at which the process occurs is in accord with the loose spacing of atoms on 100 and the large size and relatively low concentration of interstices, i.e.trap-sites. The case of CO on W is particularly interesting for two reasons. First, CO is non-dissociatively adsorbed under most conditions 8810 and secondly, its very large size provides a useful variation in that parameter from the other cases. Examination of a marble model of the emitter surface indicates that binding will be tightest on the cube faces, a site corresponding to the entire interstice between four W atoms of a unit cell face. Diffusion over a filled row of such sites cannot occur. Tight binding can also take place on 11 1 configurations, but place change there involves almost no relinquishing of contacts with substrate atoms. These facts explain the observed behaviour very well. Migration proceeds rapidly and without a boundary over 0 1 1 and its vicinals and also into 11 1.Along the approaches to the cube faces, 001 traps appear with increasing frequency among the micro-configurations so that the precipitation distance becomes small and a boundary appears around 001, but not around 111, where diffusion occurs relatively easily. When the boundary around 001 has advanced to the point where 001 sites predominate almost completely, the temperature must be increased to the point where diffusion out of 001 trap sites can occur, since filled sites block diffusion past them. The rate of this migration will be slow relative to equilibration of the adsorbate behind the diffusion front and consequently a sharp boundary will still be maintained almost until the (001) face itself is reached. It is interesting to examine the ratio of the activation energy for diffusion to the energy of binding, Table 1 shows that (&/Edes) (where known) increases with Ed in a given system and that it is least for H and greatest for CO on tungsten.TABLE 1 .-SUMMARY OF SURFACE DIFFUSION RESULTS type of diffusion a+exp(AS+lR)cm2lsec Ed(kca1) AS*(cal/mole deg.) Edes (kcal) Ed/Edes - [go]* [0*66] - 52 [70] 0 on W boundary free 4 82 30% 1.5 13 f 5 130 0.24 0 on W 110 boundary 4 3 X 10-2 24.8 & 1 7 & 5 125 0.2 0 on W 100 boundary 4 1 22.7 f 1 13 f 5 125 0.18 H on W boundary free 1 3-2 x 10-4 9.6 - 16 i 3 [- 2 rt 51 65-82 0.20 H on W 110 boundary1 1.8 x 10-5 5.9 f 1 [- 8 f 51 60 0.1 H on Ni boundary free9 3.2 x 10-5 7 i 1 - 7 f 5 68-72 0.1 COZ on C02/W 5 [lo-31 2.4 - 5.5 0.43 - [2*3] 0.39 - 2.3 0.39 CO on CO/W 8 [0.91 0.9 0 2 on O/W 4 - 5.9 [Om181 - 1.9 0.3 KronW8 110-31 [0*91 A o n W 7 [lo-31 0 6 Column 2 gives the pre-exponential part of the diffusion coefficient. Column 4 lists activation entropies.Values in brackets are preliminary or represent only rough estimates. CO on W boundary free (1 10) 8 CO on W boundary (110) 8 - 160 f 51 36 - - 9-10 0.3 [ 10-31 Xe on W 8,11 [lo-31 [3 1 The symbols X/W refer to an X-covered W surface. * for 8 - 0.06 monolayerR. GOMER 27 The first observation can be explained by assuming that the corrugation of the potential structure imitates that of the physical surface. Consequently diffusion on a (subatomically) smooth surface would require no activation energy whatever, regardless of the heat of binding.However, the discreteness of atomic surfaces insures that diffusion out of the tightest binding sites requires the greatest amount of partial desorption. The second observation supports the previous arguments regarding the impor- tance of adsorbate size. Thus the place change of a CO molecule from one interstice of the cube face of a unit cell to another requires that contact be reduced from five to two W atoms, during the process. The large size of CO precludes any squeezing between W atoms and consequently the activation energy approaches > 50 % of the heat of binding. On the (I 10) face, diffusion of CO should similarly require - 33 % of the binding energy there. The small size of H permits a certain amount of squeezing between, rather than over, the substrate atoms during place change, and thus results in a much lower ratio for &/Edes.0 as one might expect lies between these extremes. This confirms that &/&s cannot be predicted from nearest-neighbour arguments except perhaps with very large ad-particles, although such considerations are extremely useful in predicting and corroborating qualitative behaviour. Similar arguments hold for the entropy of activation, although the very great uncertainties in the experimental values make a detailed discussion unwarranted. The adsorption and diffusion of inert gases on field emitters have been studied by Ehrlich 11 and by the author.69 7 The results, although incomplete, can be explained along very similar lines. A detailed correlation was made by Ehrlich 11 for Xe on W and seems to apply also to the other cases.12 CONCLUSIONS These results indicate that a certain amount of heterogeneity is built into all but the most closely-packed faces of any crystal.Since the microstructure consists of various combinations of a very small number of different building units, the same types of sites can appear on many different faces, the variation being chiefly in number. Thus macro-orientation is much less important (in many cases) than one might at first suppose. The extent to which a given adsorbate notices variations in structure depends among other things on size, since this determines both the number and position of the substrate atoms an ad-particle can interact with simultaneously. This picture verges dangerously close on a rather naive pairwise-interaction model. The results for hydrogen adsorption indicate that this would be an over- simplification. However, an increase in adsorption energy with the number of participating substrate atoms can be justified quantum mechanically : either by invoking resonance, or equivalently, the uncertainty principle. If these arguments are correct, it must be concluded that variations in heats of adsorption with coverage and orientation can arise without the need of invoking ad-ad interactions until the coverage becomes quite high. It is a pleasure to acknowledge stimulating discussions with many of my colleagues, particularly Dr. A J. Melmed and Dr. D. 0. Hayward. 1 Gomer, Wortman and Lundy, J. Chem. Physics., 1957, 26, 1147. 2 for a summary and references, see Good and Miiller, Handbuch d. Physik, 1956, vol. 4 Gomer and Hulm, J. Chem. Physics, 1957, 27, 1363. 6 Gomer, J. Physic. Chem., 1959, 63, 468. 7 Gomer, J. Chem. Physics, 1958, 29, 441. 9 Wortman, Gomer and Lundy, J. Chem. Physics, 1957,27, 1099. 10 Ehrlich, Hickmott and Hudda, J. Cheni. Physics, 1958, 28, 506. l 1 Ehrlich and Hudda, J. Chem. Physics, 1959, 30, 493. l 2 Klein, J. Chem. Physics, 1959, 31, 1305. XXI, p. 176. Hayward and Gomer, J. Chem. Physics, 1959, 30, 1617. 3 Gomer, J. Chem. Physics, 1958, 28, 168. 8 unpublished results.