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- Surfaces en c! Interfaces INTRODUCTION The outermost layer of atoms in the surface of a crystal has been studied for over five decades, since the observation of diffraction of electrons by the two-dimensional array of atoms in the surface of a nickel crystal established the wave nature of the electron in a clear and unambiguous fashion. For years, the field was plagued by the inability to prepare surfaces sufficiently clean and well characterized to ensure the reproducibility of data. This problem was solved by the develop- ment of ultrahigh-vacuum techniques during the past two decades. Now, when a surface is prepared, it can be maintained perfectly clean for 1 hour or longer, while a variety of precise measurements are performed on it. In the past 10 years many new experimental probes have been used for the study of the structural and dynamical properties of the crystal surface and of atoms or molecules adsorbed onto it. These new probes are summarized in Table 7.1. In parallel with these developments, there have been rapid advances in surface-physics theory. Numerous examples now exist where important new conclusions have followed from the interplay between theory and experiment. In addition, we see substantial progress in the development of both ab initio descriptions of the electronic structure of clean and adsorbate-covered surfaces and of the dynamics of crystal surfaces. 144

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S UREA CES A ND I N TERFA CES 145 TABLE 7.1 Experimental Techniques Used in the Study of Physical Properties of Surfaces and Interfaces Physical Property Studied Elementary Interface Excitations Atoms and Between on the Molecules on Solids and Experimental Technique Structure Surface the Surface Dense Media Ion beams Raman spectroscopy Scanning vacuum tunneling X X X X X microscope Synchrotron radiation X X Electron energy-loss X X spectroscopy Electron microscopy X Atom/surface scattering X X X Low-energy electron X X diffraction Neutron scattering X X X X rays X Infrared spectroscopy X X X Spin-dependent electron X scattering Brillouin scattering X X Diffusion of adsorbed X species Molecular beams X Laser-induced desorption X or fluorescence Inelastic electron-tunneling X spectroscopy This chapter is concerned primarily with the physics of the outer- most atomic layer or two of single crystals in an ultrahigh-vacuum environment, along with that of monolayer quantities of adsorbate atoms or molecules upon it. The adsorbates may be chemisorbed, i.e., bound to the surface tightly via chemical bonds similar to those encountered in molecules, or physisorbed, where only a much weaker van der Waals attraction traps the adsorbate near the surface. A1SO7 a substantial interest exists in the microscopic nature of the solid-gas or the solid-liquid interface, where the first few layers in the low-density phase may have properties modified profoundly by their proximity to the solid interface. Some of the new methods of studying the interface

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146 A DECADE OF CONDENSED-MATTER PHYSICS between a crystal and vacuum are directly applicable to the analysis of the liquid-solid or the gas-solid interface, as we shall see. If one considers the outermost atomic layer of a perfect crystal, one may inquire whether it is a replica of a plane of bulk atoms or whether it differs importantly. The latter is frequently the case. The atoms may shift off the sites expected from the bulk structure to form a new, low-symmetry phase unique to the surface. This is known as surface reconstruction and is observed on many surfaces. The electronic structure of the surface may be unique, because of unsaturated dangling bonds. Such electronic states are often responsible for the particular chemical reactivity of the crystal surface. Adsorbate overlayers are a rich area for study. The environment of a chemisorbed species differs greatly from that in an isolated molecule, and this leads to new electronic configurations. At finite coverage, adsorbates may interact directly via the overlap of their wave func- tions, indirectly via the perturbation of the electronic structure of the substrate, or by local strains induced by chemisorption. Such lateral interactions control ordering of the overlayers, and thus control the thermodynamic phase diagram of the adsorbate/substrate combination. Physisorbed rare-gas atoms are weakly bound to the surface and may move parallel to the surface relatively unhindered. One may view the substrate as a passive entity whose role is to confine the atoms to a plane parallel to its surface; hence the absorbate system constitutes a realization of two-dimensional matter. From recent theory we know that physics in two dimensions differs profoundly from that in three dimensions. Hence, study of physisorbed overlayers offers insight into basic issues of statistical mechanics in two dimensions. We have outlined why, from the point of view of fundamental physics, the study of surfaces is of great interest. In addition, advances in our understanding of surface physics have a direct impact on other areas of science. In the chemical industry, solid-state catalysts are extremely important in many manufacturing processes. While a par- ticular catalyst often proves highly efficient for a limited range of reactions, little is understood about the origin of this specificity. Knowledge of the basis for efficient catalytic activity will allow the design of new catalytic structures. Practical catalysts are typically complex, multicomponent systems, prepared in powder form, and operating in a high-pressure environment; they differ substantially from a single-crystal surface, prepared and cleaned in ultrahigh vacuum. However, the fundamental principles elucidated in the study of the single-crystal surface and its interaction with atoms or molecules will form the basis of a deeper understanding of how real catalysts function. Also, diagnostic methods developed in surface physics have been

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SURFACES AND INTERFACES 147 applied to the analysis of real catalysts. In the past 3 years, a com- bination of surface-physics methods (Auger spectroscopy, low-energy electron diffraction, and electron energy-loss spectroscopy) has been used to study the decomposition of hydrocarbons on single-crystal platinum surfaces. This has allowed us to trace out, in a step-by-step fashion, how their decomposition leads to formation of a carbonaceous layer, and the consequent poisoning of the surface as a catalyst. In materials science, there is great interest in new multilayered structures formed by deposition of two or more materials and consti- tuting a macroscopic material with unique properties. In idealized form, such a structure consists of single-crystal films, with the thick- ness of each controlled and in the range of a few tens to a few hundreds of angstroms. Semiconductor superlattices are one example of such materials. There are also new superlattices formed from metals or from combinations of (ferromagnetic) metals and semiconductors. The study of the single-crystal surface, and of adsorbates on it, may be viewed as the study of the first atomic layer of a new constituent in a superlattice structure. Thus, research in surface physics has a direct impact on this exciting new area of materials science. THE STRUCTURE OF THE CRYSTAL SURFACE If one is to understand properties of, and bonding to, the outermost layer of a crystal, a first step is the elucidation of the geometrical arrangement of the constituents. Thus, considerable effort is spent on the development of probes that provide structural data and on theo- retical descriptions of the interaction of the probe with the surface. To extract structural information from the data is formidable. The problem is that the probe must either reflect off the outermost layer or backreflect after penetrating only a small number of layers. This means that it interacts strongly with the crystal. Hence full utilization of information in the data requires a sophisticated theory that treats the strongly interacting probe completely. (In contrast, in the study of bulk structures, the probing quanta x rays or neutrons, for ex- ample-travel long distances in the crystal; their interaction with any one constituent is weak. This leads to simple theories for interpreting data.) It proves difficult to determine a surface structure unambiguously from one set of data. Consequently, several methods are often used to study a single structure. There is no single probe or method, such as x-ray scattering used in bulk studies, that solves surface-structure problems. Many surface structure studies employ either low-energy electron

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148 A DECADE OF CONDENSED-MATTER PHYSICS beams, with energy in the range of a few to a few hundred electron volts, or neutral atom or ion beams. The electrons sample a small number of layers, three or four in number, while neutral atom beams sample only the outermost contours of the electron charge density. Both have a deBroglie wavelength comparable to lattice spacings, or bond lengths, and thus serve as sensitive probes of microscopic aspects of surface geometry. Of the electron spectroscopies. low-energy electron diffraction (LEED) has been a mainstay for many years. Through its use one may identify systematic structural trends. Recently it has been established that on most metal surfaces there is a contraction between the first and second layer, with the more open faces contracted the greatest. Observations such as these have provided a major stimulus to theory. A major development of the past decade is the utilization of synchrotrons as intense sources of electromagnetic radiation with a continuous spectrum of wavelengths, which extends from the visible, through the ultraviolet, and into the x-ray region. Many new surface- sensitive spectroscopies based on these sources have emerged during the past decade. Among them photoemission has developed rapidly. Here a photon, which penetrates many atomic layers, will eject an electron from the crystal. One measures the total current emitted by the crystal, the energy distribution of the emitted electrons, or their angular distribution. Sensitivity to the surface arises because the mean free path of the excited electron is a few lattice constants. Thus, only those excited close to the surface emerge. Ultraviolet photons excite electrons from the valence orbitals of the atomic constituents of crystals. One finds here surface electronic states revealed by photoemission; these states are markedly affected by the surface geometry, so their spectroscopy provides important informa- tion on surface structure. A decade ago, we had few data in hand in this area, but now the influence of a surface on the electronic structure of materials has been explored experimentally for many semiconductors and many metals. Other spectroscopies employ synchrotron radiation as the basic probe. A photon may eject a core electron from an adsorbed atom or molecule. The emitted electron wave propagates to the detector, at the same time that a backscattered portion reflects off the surrounding structure to interfere with the direct wave. Study of the energy and angular variation of the cross section for this process provides infor- mation on the local environment of the atom or molecule involved. X-ray absorption edges exhibit fine structure, with a closely related origin. Since the synchrotron's output is in the form of a broad, continuous band of radiation, these features may be explored in detail.

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S UREA CkS A ND /NTERFA CkS 1 49 New areas of synchrotron-radiation-based spectroscopy are in early stages of development. For example, while x rays have not generally been considered a surface-sensitive probe, at glancing incidence their electromagnetic fields are evanescent in the substrate. Thus, the Bragg beams reflected from the crystal contain information about the outer- most region of the crystal. In particular, if the surface reconstructs, new Bragg beams are induced by the reconstruction process. These beams provide information about the magnitude of the atomic displace- ments parallel to the surface. Recently, more complete analyses have provided information on the vertical displacement of atoms. The method may be unique in providing access to displacements associated with reconstruction, without recourse to the theories required in electron- or atom-beam studies. Glancing-incidence neutron spectroscopy also offers the possibility of surface sensitivity, though the method has yet to be implemented fully. One exciting new probe has appeared recently: the tunneling elec- tron microscope. This device operates on the basis of a fundamentally new principle. If two metals are placed ten or so angstroms apart, with a potential difference between them, an electron may transfer from one to the other via quantum-mechanical tunneling. One metal is a sharp tip, while the second is the sample to be studied and is nominally flat. The current that flows is sensitive to the distance between the tip and the sample; if the tip is scanned across the sample, the current will fluctuate in magnitude in response to protrusions on the surface that change the distance from the probe tip to the sample. Features in the surface profile that influence the current are steps or defects on a length scale of a few to a few tens of angstroms, or possibly the bumps in the electron density produced by the individual atomic constituents. A direct, real space map of the surface geometry is produced. The current spatial resolution of the device renders large-scale surface features, such as steps, readily visible. Since steps and other defects on the surface play a major role in catalysis, in the nucleation of reconstructed phases, and in other surface processes, this is an exciting development. The spatial resolution allows studies of atomic arrangements in open surface structures. Thus, the 7 x 7 reconstruc- tion of the ( 1 1 1 ) surface of silicon has been probed directly (Figure 7. 1), as has the (110) surface of gold. As remarked earlier, low-energy atoms have a de Broglie wavelength comparable to crystalline lattice constants, and such atoms are backscattered from the outermost portions of the electron charge- density contours. Recently there has been a great improvement in our ability to prepare monoenergetic beams of light atoms, such as He. At

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150 A DECADE OF CONDENSED-MATTER PHYSICS FIGURE 7.1 Relief of two complete 7 x 7 unit cells on a reconstructed silicon (111) surface, with nine minima and twelve maxima each, taken at 300C. Heights are enhanced by 55 percent; the hill at the right grows to a maximal height of 15 A. The (21 1 ) direction points from right to left, along the diagonal. (Courtesy of H. Rohrer, IBM Research Laboratory, Zurich.) present, beams with energy spreads well below 0.1 meV are readily available. The study of elastic- or Bragg-scattered beams is rich, with scattering resonances evident that are associated with bound states of the atom/surface interaction potential. These are sensitive to the details of the potential, including its variation in the two dimensions parallel to the sample surface. New high-energy ion backscattering studies place important con- straints on surface geometry and provide quantitative information on whether surface atoms are shifted off high symmetry sites or if there is a contraction or expansion of the distance between outermost layers of the crystal. Here classical trajectory analyses are sufficient to analyze the data. A set of qualitative concepts based on the shadowing of interior atoms by those in the surface has developed that may be used

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S UREA CES A ND INTERFA CES 1 5 1 to interpret data. This is an experimental technique that will continue to be developed in the coming years. Electron microscopy is another technique emerging as a surface probe of substantial importance. Transmission of electrons through thin films offers the possibility of studying electron diffraction under conditions where a single scattering description is appropriate. A dark-field imaging method can pick out only superlattice reflections and thus can be used to examine the dynamics of formation of the (7 x 7) structure on the Si ( 1 1 1 ) surface. It is even possible to observe nucleation of the new phase near steps on the surface with this technique. Electron microscopy will become an important tool for exploring a range of issues such as the nature of defects on the surface, dynamical aspects of the surface environment, and also microscopic aspects of surface structure. A final probe that is being used extensively in surface studies is the field ion microscope. It employs a needle-shaped specimen with an electric field at its tip so strong that inert gas atoms are ionized; the ions subsequently follow the electrostatic field to an imaging screen. Since the fields are strongest at the surface and are sensitive to surface features on an atomic scale, the pattern of ion impacts on the screen images atomic details of the sample tip. Surface structure, atomic diffusion on surfaces (Figure 7.2), and chemical groupings of adatoms are the types of surface properties that are now investigated In a direct way by field ion microscopy. In addition, however, by means of strong field pulses it is possible to strip away successive surface atoms and reveal underlying structure. This makes depth profiling a feasible, if tedious, procedure. When coupled with a time-of-flight mass spectrom- eter the field ion microscope thus permits a structural and chemical map of the tip surface and underlayers to be built up sequentially at atomic resolution. The past decade has clearly been one in which classical methods of deducing surface geometry have advanced in a qualitative manner, while a number of new and potentially powerful methods of analysis are under active development. SPECTROSCOPY AND ELEMENTARY EXCITATIONS ON THE SURFACE A major advance in understanding the physics of bulk solids oc- curred when inelastic neutron scattering became widespread. The neutron may scatter inelastically oD of any elementary excitation such as a spin wave or phonon, and an analysis of the kinematics of the

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152 A DECADE OF CONDENSED-MATTER PHYSICS FIGURE 7.2 Movement of a single Re adatom didusing on the central (21 I) plane (dark circular area) of a tungsten crystal field ion microscope tip. The four images taken at successive times show the Re adatom progressively displaced. (Courtesy of K. Stolt and G. Ehrlich, University of Illinois.) scattering event allows one to map out their dispersion curves. Since the de Broglie wavelength of thermal neutrons is of the order of a lattice constant, one may study the dispersion relations throughout the entire Brillouin zone. Such data have led to a qualitative expansion in our understanding of perfect and imperfect crystals. During the past 2 years, two methods-inelastic scattering of helium atoms and electron energy-loss spectroscopy have been developed to the point where they can now be used for detailed measurements of surface phonon dispersion curves. In the previous section we noted that we now have in hand highly monoenergetic beams of slow, neutral He atoms. These not only allow one to study fine detail in the elastic cross section but have led to the realization of high-resolution inelastic scattering studies of surface phonons. We now have data available for several insulating and metallic surfaces. Shortly before 1970, electron energy-loss spectroscopy was used to study high-frequency vibrational motions of light adsorbates, and in

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SURFACES AND INTERFACES 153 1970 the method was used to study vibrational spectra of clean surfaces. This technique has developed into one of the standard working tools of surface science during the past decade. As the surface atoms or adsorbates vibrate, oscillating electric dipole moments asso- ciated with the motion lead to intense inelastic scattering of the electron through small angles. Virtually all of the experiments study these near-specular losses. In this configuration one studies only modes whose wave vector lies close to the center of the corresponding two-dimensional Brillouin zone. During the past S years, the first studies of electrons that suffer inelastic scattering through large angles have appeared. A selection rule that applies to near-specular scattering breaks down in the large- angle studies, with the consequence that many more modes can be explored. The first experiments explored the vibrational spectrum of ad- sorbates. When off-specular spectra are combined with the near-specu- lar data, a rather complete picture of the adsorbate geometry emerges. Within the past year off-specular electron energy-loss studies have been employed to obtain surface phonon dispersion curves for a clean surface and also for a surface covered with an ordered adsorbate layer. We thus have two methods that may be utilized to explore surface phonon dispersion curves, and the coming years should prove to be an exciting era in the spectroscopy of surface vibrations. It should be remarked that the two methods discussed above will surely emerge as complementary approaches to the problem. One area of surface spectroscopy in an early stage of development, with great future promise, is the spin-dependent scattering of electrons from a surface. One may now produce beams of spin-polarized electrons, through the use of GaAs emitters appropriately pumped with laser radiation. With these beams, elastic scattering data are obtained from ferromagnetic substrates. One may align the spin of the beam electrons either parallel or antiparallel to the substrate magnetization and detect the difference in scattering intensity. It is believed that this difference is in essence proportional to the magnetization in the crystal surface. The new data have been used to infer the temperature variation of the magnetization in a ferromagnet below the bulk Curie temperature and to provide the first results for this quantity close to the Curie temperature. Neither inelastic atom/surface scattering nor electron energy-loss studies have provided information on the linewidths of the various modes that have been probed. It is unlikely that the electron energy- loss method will achieve sufficient resolution in the near future to generate such information, and while atom/surface studies may be able

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154 A DECADE OF CONDENSED-MATTER PHYSICS to realize sufficient resolution to measure linewidths in favorable cases, this has not been done as yet. However, both infrared and Raman spectroscopy offer high resolution' when applied to the study of bulk excitation spectra of condensed matter, and one may look toward either of these as possible high-resolution probes of surface vibrations. Both suffer from weak signals, a disadvantage if the aim is to study monolayer or submonolayer quantities of material on the surface of a single crystal. Despite this basic difficulty, recent years have seen substantial progress in each area. There have been impressive new methods in infrared studies of adsorbate vibrations. In one version of this method the frequency of a surface electromagnetic wave (surface polariton) is swept through a vibrational resonance of the adsorbate and the resulting attenuation studied. One may achieve an appreciable enhancement here over the signal level expected in a one-bounce reflection experiment. A second, multiple-reflection, method in which the sample serves as a waveguide has been utilized to obtain beautiful high-resolution spectra of submonolayer quantities of hydrogen on a silicon surface. Finally, the thermal emission of a warm sample placed in a cryogenic environment has been employed to explore the vibrational motion of CO on a single-crystal Ni surface. In all these cases, the data yield the linewidth of the normal mode explored. These experiments employ state-of-the- art equipment of a sophisticated nature. Since infrared spectroscopy is at the moment the only experimental method that has provided data on the intrinsic linewidths of simple adsorbates on single-crystal surfaces, further application of these new approaches to a broader class of systems is of paramount importance. Great excitement was generated a few years ago by the discovery of giant Raman signals from adsorbed molecules. The effect was discov- ered by electrochemists, who were exploring the interface between an electrolytic liquid and a silver electrode. The Raman cross section per adsorbed molecule was found to be larger than that observed in the gas or liquid phase by a factor of 105 to 106. This enhancement, if present for a wide range of adsorbate/substrate combinations, would render Ra- man spectroscopy a viable high-resolution probe of surface vibrations. An essential element necessary for the giant signals is the presence of roughness on the silver surface. The physical picture that emerges is that such roughness couples the incident photon to surface electronic resonances, whose origin may be the protrusions themselves. Excita- tion of surface resonances enhance the electromagnetic field of the incoming photon, and since the Raman cross section scales as the

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SURFACES AND INTERFACES 155 fourth power of the field strength, a modest enhancement in the field leads to a large enhancement in the signal realized. Since roughness plays an essential role in generating the giant Raman intensities, quite clearly this form of spectroscopy is difficult to apply to high-quality single-crystal surfaces. Also, the surface resonances must lie in the visible, and the damping that they experience must be modest. These two requirements limit the effect to only a limited number of substrates, with silver a particularly favorable material. Systematic control of the enhancement effect can be achieved utilizing a surface on which a diffraction grating is present. The resulting enhanced fields can be exploited to enhance a wide variety of linear and nonlinear optical interactions near surfaces and interfaces, in addition to the Raman effect. For example, the intensity of second-harmonic radiation obtained from an illuminated metal surface can be enhanced by a factor of 104, through use of surface roughness. It is quite possible to detect Raman signals from adsorbed molecules in the absence of the giant enhancement discussed above. While the signals are weak, spectra from monolayer quantities of molecules adsorbed on high-quality, single-crystal surfaces have been observed. Raman, like infrared, spectroscopy can be carried out in a high-pres- sure environment or can be used to explore the liquid-solid interface, if the liquid is transparent. Thus, development of either tool to the point where it may be used to explore a diverse range of systems will be an important step. A third optical spectroscopic technique that has experienced sub- stantial development is Brillouin scattering of light from surface phonons, surface spin waves, and other surface excitations. One may now explore backscattering of light from metals where the skin depth is only 150 A. Kinematical considerations restrict its application to waves with very long wavelengths (typically a few thousand ang- stroms), so the technique is not a microscopic probe of the surface. However, one can measure elastic and spin-wave stiffness constants in thin films and explore the influence of a surface on the acoustic or magnetic response of the medium. INTERACTIONS OF ATOMS AND MOLECULES ON THE SURFACE . The understanding of the physical origin of various features in the . . atom/surface interaction potential will clarify many aspects of surface chemistry. One source of quantitative information on the atom/surface

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156 A DECADE OF CONDENSED-MATTER PHYSICS interaction potential is the analysis of the intensities of atoms scattered elastically from crystal surfaces. As mentioned earlier, recent ad- vances allow the preparation of highly monoenergetic, highly colli- mated atom beams. The resulting improvement in the quality of scattering data is truly impressive, and the theory of atom scattering from a rigid, possibly deeply corrugated, surface has undergone considerable development in the same period of time. A consequence is that semiempirical interaction potentials have been constructed that describe the interaction of rare-gas atoms with several surfaces. There are two distinct limiting cases in the discussion of rare-gas atom/surface interactions. A surface of an insulating or semiconducting material is highly corrugated, and one must understand in detail the magnitude of this corrugation whose influence on many aspects of atom motion on or near the surface is a crucial consideration. On the other hand, the low-index surfaces of simple metals are smooth, so the rare-gas atoms are trapped on the surface, but they are free to move parallel to the surface impeded only modestly by the corrugation. The physics of overlayers adsorbed at finite coverage is then dominated by lateral interactions between the adsorbate atoms. In recent years, much has been learned of the physical nature of these lateral interactions. It is now clear that the van der Waals interactions are influenced importantly by the close proximity of the atoms to the surface. Much attention has been devoted to the phase diagram of monolayer or near-monolayer quantities of rare-gas adsor- bates, in the limit where the influence of the corrugations in the substrate potential may be ignored. The phase diagram of chemisorbed systems has also been studied both experimentally and theoretically, and the strengths of the various lateral interactions deduced from it. Information on the atom/surface potential can be obtained from experiments other than scattering experiments. The primary mecha- nism for the diffusion of atoms over a surface is thermal activation over the barrier between the initial and final site. This activation energy provides information about saddle points in the potential energy surface. Computer simulations of such dynamical processes are impor- tant to carry out, since they can test whether a given semiempirical atom/surface potential provides results that fit the data. The interaction of molecular beams with surfaces has been studied actively and will yield important results in the near future. Small diatomic molecules can impact the surface, and a new element in such scattering studies is the presence of the rotational and vibrational degrees of freedom in the molecule. The molecule may now scatter off the surface with a change of rotational quantum number, and in fact the

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S UREA CES A ND INTERFA CES 157 molecule-surface interaction potential itself may depend on the rota- tional quantum state of an incoming molecule or of one adsorbed on the surface. Recent experiments that study the scattering of H2 molecules from an Ag surface show that the positions of the fine-structure resonances, and hence the bound-state energies of the molecules, depend on the rotational quantum number. Lasers have also found applications in the study of various proper- ties of atoms and molecules on solid surfaces. In the past few years, nonlinear optical techniques have been exploited to probe surfaces and interfaces. Second-harmonic generation in reflection from a surface has been shown to have enough sensitivity to detect submonolayers of atomic and molecular adsorbates. The technique is versatile. It can yield information about the dynamics of molecular adsorption and Resorption, the changing of adsorption sites, the spectrum of adsorbed molecules, and the arrangement and orientation of adsorbates, for example. That it can be extended to the infrared region makes high- resolution vibrational spectroscopy of adsorbed molecules also a possi- bility. Several other laser surface probes have also been developed recently. One may learn much about the kinetics of molecules on the surface by analyzing the population of various rotational and vibrational states of species desorbed or scattered from the surface; here laser-induced Resorption or fluorescence and photoacoustic spectroscopy may be useful probes. When one combines such information with theory generated by computer simulations based on molecular-dynamics routines, one gains considerable insight into those aspects of the dynamics of molecule/surface interactions crucial to the understanding of chemical interactions on surfaces. One may monitor the rotational and vibrational statistics of species that come off the surface. A non-Boltzmann distribution is frequently found, and there has been considerable success in the comparison between such data and theory based on computer simulations. THE INTERFACE BETWEEN SOLIDS AND DENSE MEDIA In many instances, one is interested in surfaces placed in a high-pres- sure environment or in the interface between a surface and a dense medium such as a liquid. Catalysts operate in a high-pressure environ- ment. In electrolytic cells, a dense fluid overlies the interface. In such systems, many experimental methods used in ultrahigh- vacuum environments are inapplicable. Any method based on the use of electron beams, or of atoms or ions, fails because the mean free path

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158 A DECADE OF CONDENSED-MATTER PHYSICS of these entities in the dense medium above the substrate is too short; the same is true of photoemission spectroscopies because the mean free path of the photoemitted electron is too short for the electron to emerge from the dense medium above the solid. Thus, many of the methods discussed above cannot be applied to the systems discussed in the opening paragraph of the present section. However, new methods may be applied to these systems. If the dense medium is transparent, then any photon spectroscopy may be used to explore the interface, provided the signal from the species of interest (at the interface) may be detected, in the presence of the possibly large background from the dense medium. If one seeks a species not present in the liquid, then the feature of interest may lie in a frequency domain removed from that dominated by the dense medium. In these situations, techniques such as infrared or Raman spectroscopy may be employed. If the solid substrate is transparent, then the interface may be probed by bringing the probe beam into the interface through the substrate. If it strikes the interface at an angle of incidence greater than that required for total internal reflection, the optical wave field is evanes- cent in the liquid, so the backscattered or reflected radiation provides information only on the near vicinity of the interface. In Raman or Brillouin studies with visible radiation as a probe, one may examine the o first 200 A of the liquid by this means. Signals may be enhanced by either fabricating the substrate into a waveguide, and employing an integrated-optics geometry, or by overcoating the waveguide by an evaporated film and coupling the incident and scattered photons to surface polaritons in the film. Some early experiments using these techniques show them to be promising for future surface studies. In an earlier section we mentioned that, under certain circum- stances, the Raman signal from adsorbed molecules may be enhanced enormously over that appropriate to the gas phase. However, since surface roughness combined with the presence of long-lived surface resonances is necessary to realize these large signals, the effect is of limited utility for the study of single crystals in high vacuum. Fortu- nately, just these conditions are realized in electrolytic cell environ- ments, where, in fact, this remarkable phenomenon was discovered. The spectra so obtained are impressive: the Raman signals from the adsorbed molecules are so strong that they are comparable with those produced by the solution itself. Since roughness is present on electro- lytic cell electrodes as a consequence of cycling the applied voltage, Raman scattering will serve as a powerful probe of the interface in these systems.

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S UREA CES AND INTERFA CES 159 Practical catalysts employ the active material in the form of small particles suspended on a substrate. These high surface-to-volume systems may be probed with infrared spectroscopy; indeed, the earliest infrared spectra of adsorbed species were obtained on such systems. A new method of vibrational spectroscopy applicable to them has been developed in the last decade. This is inelastic-electron-tunneling spec- troscopy. It has been known for many years that if an electron tunnels from one metal to another, through an insulating barrier between them (the insulating barrier is commonly the oxide of one of the constitu- ents), then features in the l-V curves of the structure are produced at voltages that correspond to the energies of vibrational modes of molecular species trapped in the oxide. Analysis of these features allows one to deduce the nature of the molecular entities trapped in the oxide. The method has now been applied to systems that mimic practical catalysts, to obtain the vibrational spectra of the adsorbed species. The resolution of the method is high, if the data are taken at low temperatures (4 K is sufficient). Thus, while many of the experimental methods of surface physics rely on the use of particle beams with constituents that have a short mean free path in matter (this is why such beams are useful for probing the surface, of course), so that they are not applicable to the study of the interface between a solid and any dense medium, new spectroscop- ies are being developed that are directly applicable. The latter will surely continue to evolve in the coming years and will provide an important supplement to more traditional methods. THEORY Advances in experimental techniques for the study of structural and dynamical properties of crystal surfaces, particularly through the use of external probes such as electrons and rare-gas atoms, require parallel theoretical efforts for their interpretation owing to the strong interaction of these probes with the system being studied. The exper- imental advances of the past decade described in the preceding four sections have been accompanied by significant theoretical achieve- ments. The theory of atom/surface scattering has made significant advances in recent years. It is now possible to calculate the intensities of the diffracted beams fairly accurately, given the potential. Calculations based on model potentials can be brought into impressive agreement with data, and a detailed understanding of the physical origin of the scattering resonances often observed has emerged.

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160 A DECADE OF CONDENSED-MATTER PHYSICS A fundamental problem in the interpretation of atom/surface scat- tering data for the determination of surface structures is to relate the interaction potential to the actual nuclear positions in the crystal. It has recently been shown that to a good approximation the repulsive part of this potential is proportional to the electron charge density in the surface layers of the crystal and is consequently short ranged, while the attractive part is of the van der Waals type and is long ranged. Ab initio calculations now can generate electron-charge-density contours 3-4 A outside the surface, which is as close as a helium atom incident on a crystal approaches its surface. During the past decade, there has been a major advance in our understanding of the electronic structure of surfaces. From early theoretical studies, and simple pictures based on chemical intuition, it was clear that under a variety of circumstances one should find two-dimensional bands of electronic states localized on the surface. The development of the technique of angle-resolved photoemission has allowed the direct study of the surface state bands on a wide variety of clean and adsorbate-covered surfaces. During this period, largely through application of the density functional formalism, theorists have carried out self-consistent studies of the electronic structure of sur- faces. Agreement between theory and experiment can allow one to draw firm conclusions about the structure of the clean surface or the bonding sites of adsorbates. In the largest number of such theoretical calculations a structure for the surface is assumed, and a self-consistent calculation is then carried out of the one-electron energy states, with the nuclei held fixed. The results are then placed alongside the data, and, if necessary, the calculations are repeated for several different surface geometries until a match between theory and experiment is achieved. In a major development theorists are now actively engaged in calculations of the total energy of the surface structure, within a framework that allows the nuclear positions to be varied. Then one may seek the configuration of lowest energy to predict the surface structure of a given material. OPPORTUNITIES The achievements of the past decade provide some indications of the areas in which research in surface physics will be carried out in the next decade. Surface Brillouin spectroscopy, the emergence of Raman spectros- copy as a surface-sensitive probe, and the use of field enhancement in a variety of optical interactions near surfaces and interfaces constitute

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SURFACES AND INTERFACES 161 a new field of experimental endeavor with substantial promise. A factor-of-2 improvement in the spatial resolution of the scanning vacuum tunneling microscope will be a major advance; this device will offer surface physics a new probe that will greatly expand our understanding of a variety of features of surface geometry. The technique of second-harmonic generation of laser light can be used for in situ measurements at interfaces between two condensed media with a picosecond time resolution. This opens up many inter- esting and exciting possibilities for surface studies in, for example, high-pressure catalysis, electrochemistry, photolithography, and even biophysics. In spin-dependent scattering of electrons from a surface we have a new surface probe that for the first time can be used to probe magnetism in the outermost atomic layers of crystals. For example, antiferromagnets should be readily studied by this technique, since new Bragg beams will appear if the surface orders in such a manner that the appropriate two-dimensional unit cell increases in size. One may also envision inelastic scattering of spin-polarized beams where a spin wave rather than a surface phonon is responsible for the loss. Since we have no information on the behavior of surface spin- correlation functions in the near vicinity of a bulk phase transition, there would be great interest in the study of the diffuse background to such scattering produced by spin fluctuations, particularly near a magnetic phase transition. However, there has been little theoretical attention paid to calcula- tions of the magnitude and the energy and angular dependences of cross sections associated with spin-dependent electron scattering. Such analyses should prove helpful, by elucidating optimum scattering geometries. There are other questions that need to be addressed by theorists. LEED data show that on most faces of metal single crystals there is a contraction in the spacing between the first and second layer, with the greatest contraction occurring for the more open faces. These results are in disagreement with the predictions of simple pair-potential models of the crystal. Sophisticated theory is required to provide a framework for interpreting the data. Thus, as our ability to carry through ab initio calculations of surface structure improves, the information will be of direct value to LEED theorists and others engaged in other studies of electron spectroscopy of the surface region. The implications are exciting; LEED theorists will have in hand clear theoretical guidance when an obvious choice of structure fails to fit the data. The effort will lead to more reliable potentials for integration into

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162 A DECADE OF CONDENSED-MATTER PHYSICS a variety of analyses of the interaction of electron probes with the surface. It will also be possible to calculate, in an ab initio fashion, the force constants that enter models of surface lattice dynamics. A complete understanding of the photoemission process requires knowledge not only of the electron energy states, their wave functions, and the sensitivity of both to surface structure, but it also requires knowledge of the electromagnetic field of the incoming photon in the near vicinity of the surface. This is an area where further theoretical understanding is both required and will prove fundamental not only to photoemission spectroscopy but to other surface spectroscopies ad- dressed in this report. In a great deal of the theoretical work on the interaction between an atom and a crystalline substrate the latter is treated as if it is a perfectly rigid structure, whose only role is to provide an effective potential that influences the motion of the atom. In fact, if an atom is placed in an adsorption site, there is a distortion of the lattice in its near vicinity. Also, if the atom is adsorbed on a particular site and it hops to a neighboring site, there will be a local distortion of the lattice that will be dragged along with it, during diffusion on the surface. As an atom approaches a crystal, to resect off it in a scattering experiment, there will be a local distortion in the near vicinity of the impact site. As the atom recoils, a substantial fraction of its energy may be transferred to the lattice. This whole sequence of phenomena requires for its eluci- dation a description of the interaction of the atom with the vibrational quanta of the substrate (phonons) and a theory that provides a valid description of the consequences of this coupling. Our ability to describe atom/phonon interactions, and to exploit their consequences, is at a primitive stage at present, yet these couplings may play a crucial role in many aspects of the atom/surface interaction. Computer simu- lations may prove useful here. So far, we have discussed only the scattering of atoms off the surface or their motion on it, under circumstances where the electronic configuration of the atom remains unchanged during the interaction process. For rare-gas atoms interacting with the surface, this picture is surely sufficient in most circumstances. However, when atoms (or ions) with lower ionization potentials or electron affinities strike the surface, it is possible for an electron to be transferred from the atom to the surface or for the incoming particle to pick up an electron. A rigorous description of these processes poses a real challenge. At present, classical trajectory analyses form the basis for most theories, but a fully quantum-mechanical description of the atom motion may be required.

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S UREA CES AND INTERFA CES 1 63 Our discussion of the last two topics has focused primarily on the need for further development of the theory. The absence of predictive theories limits our ability to appreciate the full significance of existing data, and if definitive developments occur in the theory, surely the direction of experimental research will be affected positively. Another area where the absence of theory limits our ability to appreciate the full significance of data is electron- or photon-stimulated Resorption, in which adsorbed atoms are detached from a surface on excitation by incident electrons or photons. Our knowledge of the origin and even the magnitude of lateral interactions, particularly in chemisorbed systems, is sketchy. Since these interactions play a key role in stabilizing the various surface phases encountered in chemisorbed systems, and control the degree of short-range order present in a disordered overlayer, a more complete understanding of the underlying physics that controls their strength and magnitude is important to have. The study of the interaction of small molecules with surfaces, with emphasis on the interchange of vibrational or rotational energy, is expected to be a lively and active area in the coming years. As our understanding of the interaction of atoms with surfaces becomes increasingly quantitative, we acquire a base upon which a clear understanding of molecule/surface interactions may be based. As one moves from small, simple diatomic molecules to more complex entities such as hydrocarbons, we approach issues of direct interest to surface chemists. There is at present a rather limited amount of structural data on the adsorption geometry of hydrocarbons and hydrocarbon fragments. The complexity and variety of adsorption geometries possible for these systems renders a full quantitative interpretation of the data difficult, but we are seeing the beginnings of active research in the area, with attention to quantitative results. Several laboratories are actively exploring the use of time-resolved methods to probe the kinetics of molecule/surface interactions in real time. Such data could lead to a qualitative expansion in our under- standing of the kinetics involved, by direct observation rather than indirect inference. It is possible to envisage the construction of apparatus that can resolve surface kinetics at the submillisecond level, with microsecond resolution as a lower bound owing to limitations on one's ability to chop a molecular beam. Activated rate processes are easily slowed down by cooling the sample, so millisecond-resolution experiments will suffice to provide a major step forward in our understanding of surface kinetics. This is an area, virtually unexplored at present, that should prove exciting in the coming years.