1. A. MORRISON National Research Laboratories, Ottawa, Canadas
Tm major interest of chemistry in the surfaces of solids is in their use as sites for chemical reaction* the so-called heterogeneous reactions. These may be reactions of normally gaseous components at the surface or they may involve the solid itself as one reacting component. A full understanding of the processes requires a detailed knowledge of the properties of the surfaces but so far this has not been achieved. To some extent properties of the surface may be inferred from those of the bulk, hut surfaces have additional features (e.g., asymmetric potential fields) which have proved difficultto treat. Possibly the most significant recent development in the study of surfaces is the realization of the importance of imperfections. A discussion of some of these will comprise a large part of this paper. No attempt will he made to describe particular surfaces in detail, but rather emphasis will be placed upon what general deductions can be made with present information. THE STRUCTURE OF SURFACES
An understanding of surface structure requires a consideration of both the gross topographical features and the details of the atomic and molecular arrangements a t the surface. An ideal solid surface is easy to visualize as a perfect low-index crystallographic plane such as would be formed by cleavage, with edges and corners as the only nonuniformities. All experimental evidence indicates that the occurrence of such ideal structures is extremely rare even under the most favorable experimental conditions. A large proportion of the solid surfaces of special interest to chemistry are surfaces of very small particles or of porous solids. Unfortunately, direct observation of their structure is virtually impossible. At best their nature can only be deduced indirectly. For example, the variation of the differential heat of physical adsorption of simple adsorbed molecules with amount adsorbed can, under certain circumstances, be taken as reflecting the energy profile of the surface (I). However, relation of the magnitude of the adsorption energy to structural detail has so far been ruled out by uncertainties as to the nature of the forces acting between the surface and the adsorbed atoms or molecules. In general, the profiles which have been obtained show a broad spectrum of energies (for example, (2)) indicating a wide variety in the atomic or molecular arrangements in the sur-
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'Presented as part of the Symposium on Recent Develop ments in the Solid State before the Division of Chemical Education a t the 129th Meeting of the American Chemical Society, Dallas, April, 1956. 2 N.R.C. NO. 4276. 230
With more extensive single surfaces, such as cleavage planes, direct observation has had more success, and several elegant observational techniques have been developed. Much of the work on single surfaces has been in connection with studies of crystal growth, which, as will be seen, have yielded valuable information about surface structure. It is appropriate to summarize briefly here some of the experimental findings. Direct Obseruation of Surfaces. Because of its low resolving power, the ordinary light microscope is limited to the observation of gross structure on surfaces, such as overgrowths of one crystal upon another. I t may he modified, however, to make use of the principle of phase contrast (5) and is then capable of showing much surface detail. A number of striking photographs, taken by means of this technique, have been published (4, 5). Figure 5 is an example. The electron microscope affords higher resolution and in addition the means-?f studying surfaces by electron diffraction. A concise review of recent diffraction studies has been given by Thomson (6). Precise interpretation of the diffraction patterns is difficult but not vital. Rough and smooth surfaces show markedly different patterns and distortion can be readily recognized. Only cleavage planes of crystals provide the occasional example of a smooth surface. I n most instances even these show steps and protrusions. I t is interesting that electron diffraction can sometimes reveal that a surface has a chemical composition differentfrom that of the bulk substrate. The smoothness of a surface can also be investigated by comparing it with an optical flat using Fizeau interference fringes either in transmission or in reflection. Thrpugh use of multiple beams a resolution of about 30 A. can be had for the examination of surface contours (7). This added dimension to the study of surfaces has been of great value. The heights of steps and promontories on surfaces have been measured ( 5 ) ,and it has been shown that step heights are characteristic of crystals, being the size of the unit cell or a multiple thereof. Another recently developed instrument for surface studies is the field emission microscope (8). Here cold emission of electrons from a rounded metal point (commonly of tungsten) is used to display the topography of the point on a fluorescent screen. The surface of the point can be cleaned rigorously by flashing under high vacuum so that one is certain of observing the metal surface and not a contaminating layer. The usual field emission point exposes a number of different crystal facets and these can be identified unambiguously. One sees directly, then, surface JOURNAL OF CHEMICAL EDUCATION
nounuiformity of one kind a t least. The different reactivity of the different facets has been demonstrated in a number of ingenious experiments (9, 10). Very recently (10a) a modification of the microscope has achieved a resolution of about 4 A. This raises the exciting possibility of studying directly the details of the lattice structure of a surface. From the various results of direct observation we must conclude that nonuniformity of solid surfaces is the rule. If this proved to be due to various haphazard circumstances, no general understanding of surfaces could be expected. Fortunately there is now ample evidence that this is not so. Known imperfections in real solids can account for many of the experimental observations. We shall now consider the effects of two types of imperfections, those arising from thermal disorder and those due to gross displacements in the bulk solid lattice.
Thermal Disorder. In a solid in equilibrium a t 0°K. no thermal disorder exists, so that ideally the surface has the structure depicted in Figure 1. Unless the number of atoms or molecules is just right the surface layer is incomplete leaving a step, and the step in turn is incomplete leaving a kink. At higher temperatures the flat surface and the step are roughened by thermal vibrations as indicated in Figure 2. At the same time vacant lattice sites are created in the interior as discussed by Houig (If). An equilibrium exists between the vapor and the surface so that kinks, adsorbed atoms, and vacancies are continually shifting their positions. It is obvious that the various types of positions will have different binding energies associated with them. Depending
Figure 2.
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VOLUME 34, NO. 5, MAY, 1957
(after
upon the nature of the forces, the difference in binding energy for an adsorbed atom and one built into the surface may be as large as 100 kcal./mole. Knowing the approximate binding energies for the different surface species, one can readily estimate their concentrations from the Boltzman equation. These turn out to be small. For example, a concentration of one adsorbed molecule for about lo4 surface sites may be expected a t ordinary temperatures (12). Such concentrations seem too small to account for observed molecular scale surface heterogeneity. Crystal Growth. Growth of a crystal may be visualized with reference to Figure 2. As the vapor pressure is increased, atoms or molecules are adsorbed, diffuse over the surface and are incorporated into the step a t a kink. With growth the step moves over the surface until the layer is complete. A new step must now he created, and it might be supposed that this could be done by thermal vibrations. Actually, it has been shown (IS) that this is unlikely except a t temperatures near the melting point. Alternatively the nucleus of a new layer might be formed by aggregation of adsorbed molecules, hut this process only occurs at a sufficient rate a t high vapor supersaturations, say of the order of 25% or 50% (IS). Experimentally it is observed that crystals grow at easily measurable rates at supersaturations as low as ly0 or less, so another mechanism must exist. I n 1949, Frank (14) showed how a screw dislocation in the bulk crystal could give rise to a nondisappearing step at the surface. The emergence of the dislocation at the surface is depicted in Figure 3. It is seen that a ramp-like structure r e s ~ l t s . ~As mdecules are added from the vapor the step moves around and does not disappear. For a straight step each point advances with the same speed, but the section near the origin of the dislocation has a higher angular velocity. The net effect is the formation of a spiral or a pyramidal growth on the surface. Many such growths have been photographed and their dimensions measured in detail. Numerous examples have been published (4, 6); two are shown in Figures 4 and 5. The spirals are most readily observed on layer type crystals, but sufficient have been found on other types of crystals, e.g., cubic crystals such as ' T h e origin of screw dislocations will he discussed in the second of the papers by Honig ( 1 1 ) .
F;BUFB 3. The Emergence of e Screw Dislocation et e Surface (aft.. Read (37))
Figure 4.
Growth Spiral on th. Surface of n-CdIa. Cr~stalliredfrom Petrolsum Ether (Forty (4)). X Z 4 . m (opprox.)
CdI? (4), to show that their cause is a general one. We have considered only a single screw dislocation, but detailed descriptions of the consequences of multiple and interacting dislocations can be given (6). These give a general account for observed gross topographical nonuniformities of solid surfaces. Isotopic Exchange Reactions. Recently it has been observed that a variety of solid surfaces will undergo rapid isot,opic exchange with a surrounding gas a t t.emperatures as low as of the hulk melting temperature. For example, O2 gas and HrO vapor will exchange oxygen with oxides such as NiO, CaO, MnO?, COO and y-Al,O, (15, 16, 17, 18). For some of the oxides, e.g., COO and NiO, exchange occurs in the rnngr where t hf. oxidth art BS ~ x i d i ~ t i~rn~iconductors. m~ Ilrllvc tht: I I I ~ ~ I : I I I ~ S of I I I exrhmgc might he thought of as electron transfer between oxygen gas chemisorbed on the surface and oxygen ions in the lattice. On t,he other hand, some of the oxides (e.g., y-Al,O,) apparently do not chemisorb oxygen in the temperature range where exchange is observed. I n addition they act as reduction semiconductors a t higher temperatures. Analogous rapid exchange has been observed hetween COr and CaCOI (19) and between HCI and Clz gases and the surfaces of alkali chlorides (20, 21). The dissimilarity of these various systems suggests looking for a single explanation which does not involve detailed electronic mechanisms. An attractive supposition is that real solid surfaces are more or less completely disordered on a molecular scale. If the surface is not of a regular lattice structure, rapid isotopic exchange can he readily imagined. Otherwise, the only easily conceivable mechanism of exchange is surface diffusion. The kinetics of the exchange do not agree with this latter mechanism (17, 21). Complete disordering or "melting" in the twodimensional surface is a cooperative phenomenon (IS). Although certain faces of a crystal may "melt" a t low temperatures, the "melting" point of the dominant face would seem to he of the same order as the hulk melting point. However, the transition temperature may be lowered considerably by the presence of foreign material adsorbed on the surface (22). Perhaps the observed rates of isotopic exchange will he explicable on this basis, but more experimental information is necessary.
Figure 5.
Growth Spirals on the Surface o f Sic Werrna (5))
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THERMODYNAMICS OF SOLID SURFACES
Every solid surface will have a certain energy, free energy, and entropy associated with it. Determination of these quantities both experimentally and theoretically may be expected to yield useful information on the constitution of the surface. Both the experiments and the theoretical calculations have proved difficult, and broad general deductions from them are not yet possible. However, it i% perhaps useful to summarize some of the recent work. Experimental Determination. A procedure for obtaining the thermodynamic properties of solid surfaces has been suggested by Jura (23, 24). Two types of experimental information are required: (i) measurements in the region of room temperature of heats of solution of the same substance in various states of aggregation, and (ii) measurements of the heat capacities of the same materials from as low a temperature as possible up to room temperature. From (i) one obtains the enthalpy of the surface, i.e., h,. = A H / A a where A H is the difference in heat of solution at temperature T* and A @ the difference in surface area. From (ii) the change in enthalpy or entropy with temperature can be derived. The surface enthalpy a t any temperature can be readily calculated from
where AC, is a difference in heat capacity a t constant pressure corresponding to a difference in surface area Aa. From arguments which will not he reproduced here, Giauque (24a) has concluded that the surface entropy is very likely zero at O°K. Hence the entropy calculated from
is the total entropy of the surface. The surface free energy, y, may he computed from h aud s by means of the relation y = h - Ts. These quantities have been determined for MgO by Jura and Garland ( 2 4 , and their results are reproduced in Figure G . JOURNAL OF CHEMICAL EDUCATION
Dependence of the Heat Capacity upon Particle Size. It is possible to analyze in more detail the change in the heat capacity of a solid due to extension of surface. Moutroll (25) and others have considered what happens to the lattice frequency spectrum of a solid when the solid is subdivided. The effect of subdivision is to shift the spectrum to lower frequencies which means that the heat capacity is increased. However, at high temperatures where all of the vibrations are classically excited the difference between the heat capacity of small particles and that of the bulk solid disappears. A consequence is that the surface enthalpy reaches a constant value. Assuming a distribution function for the lattice frequencies, e.g., that of the Debye model, numerical values for the dependence of the heat capacity upon particle size can be derived and compared with experimental values. I t can he shown (26) that, for temperatures and particle sizes readily attainable experimentally, the results should be essentially independent of the particle size distribution, particle shape, etc. This removes a criticism which had been made of the general scheme of determining extensive thermodynamic properties of solid surfaces (27). A limited number of measurements of the effect of particle size on the heat capacity of solids other than
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Figure 1. The E x o w of the Heat Capscity of Partiel- of NnCL h e r That of the Bulk e. e Function of Tempuature (after Morrison and pntterson (33)) experimental. 59 m.*/g.. theoretical (25) 53 rn.'/..
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VOLUME 34, NO. 5, MAY, 1957
MgO has been made (28, 29, SO). For one case, that of particles of NaCl (SO), a quantitative comparison between theory and experiment has been made. A much oversimplified presentation of the results is shown in Figure 7. The salient point is that the heat capacity of the particles a t low temperatures is three or four times larger than is predicted by Montroll's theory. The parameters in the theory cannot be altered to fit the experimental results, and it must be supposed that another heat capacity contribution comes in a t low temperatures. I t has been suggested (SO) that it is due to loose surface structure. Calculations of Su~faceEnergies. The first exteusive theoretical calculations of the surface energy of crystals were made by Lennard-Jones and collaborators (e.g., (31, 82)) a number of years ago. Since then, further calculations of varying degrees of refinement have been made by others. Essentially what is done is to identify the surface energy with the difference in potential energy arising from splitting a crystal along a particular crystallographic plane and separating the two parts to infinite distance. No account is taken of the thermal vibrational energy of surface and bulk atoms so that the calculations of surface energy pertain to the state at O°K. The refinements are concerned with what forces are assumed to be operative and what allowance is made for changes in lattice spacing at the surface. The computed surface energies of a number of inert gas and alkali halide crystals are given in a paper by Shuttleworth ($3). Experimental data suitable for comparison with calculated surface energies are sparse. For the case of MgO there appears to be good agreement between theory and experiment. However, some experimental uncertainties exist which have been discussed by Jura and Garland (24). For NaCI, a difference of about a factor of two is found, the experimental value being the larger (34). Recently the bases of the classical calculations have been examined in more detail (55, 36). Adoption of more realistic models unfortunately seems to increase the discrepancy with experiment. SUMMARY
The foregoing brief discussion attempts to summarize recent studies of the physical nature of solid surfaces. The important outcome is the recognition that real surfaces are imperfect structures. Many gross structural features of surfaces can now be unambiguously ascribed to the occurrence of dislocations in the bulk solid. There is evidence that considerable molecular disorder is a natural complement of real surfaces but the reason is not yet understood. Thermal disorder apart from actual surface melting would not appear large enough to account for it. Nonstoichiometry introduces another class of imperfections which has not been dealt with here. These are electronic defects. Their effect upon surface properties is more complicated because they are dependent upon the composition of the whole solid. ACKNOWLEDGMENT
I am grateful to Mr. Donald Patterson of the University of Montreal for many helpful comments on this paper.
LITERATURE CITED
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..
. .
(lCl.56) \----,-
(11) HONIO,J. M., J. CHEM.EDUC.,34, 224 (1957). W. K., Penguin Seiaee News, 21, 26 (1951). (12) BURTON, AND F. C. FRANK, Phil. (13) BURTON,W. K., N. CABRERA, Trans. Roy. Soc., 243A, 299 (1951). (14) FRANK,F. C., Discu~~iuns Faladay Soc., 5, 48 (1949). (15) MORITA,N.,Bull. Chem. Soc. Japan, 15, l(1940). (16) ALLEN,J. A., AND I. LAUDER, Nature, ,164, 142 (1949). G., AND E. R. S. WINTER,Nature, 164, 1130 (17) HOUGHTON, (1949). E., A N D E. R. S. WINTER,J . Chem. Soe., 50, (18) WHALLEY, 1175 (1950).
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(1055)
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