Reconstruction and Relaxation

An ideal crystal is characterized by a regular arrangement of its constituent atoms. Its microscopic structure possesses a three-dimensional (3D) translational invariance which means that a crystal can be constructed by an infinite repetition of a unit cell along three independent directions. A surface eliminates this invariance along one of the directions. It retains a symmetry with respect to two-dimensional (2D) translations along the surface itself. 

Upon crystal cleavage the surface atomic layer, as well as a few adjacent layers, have a different local environment compared with the atomic layers deep inside the crystal. The forces from the atoms in the crystal interior acting on the surface atoms are no longer compensated by the removed part of the crystal. As a consequence, the net force applied to the surface atoms tends to rearrange their equilibrium positions. The possible types of surface rearrangements fall into two main classes. A modification of the distances between the atomic planes near the surface is called relaxation. It is not accompanied by changes in the topmost surface layer structure compared with the structure in the bulk. Under a surface reconstruction, however, the surface atoms are shifted along the surface with respect to their positions in the bulk. As a result, the surface unit cell differs from the one which would exist if there were no displacements of surface atoms. 

Which of these surface rearrangements takes place upon cleavage is determined by the surface electronic structure. This follows within the adiabatic approximation which is applicable for a wide range of molecular systems and is based on the fact that the ratio me I Mis small. Here, me and M are the electron and the mean nuclei masses, respectively. In the zeroth-order approximation, which corresponds to infinite masses of nuclei, one can neglect their kinetic energies and consider the states of the electronic subsystem at fixed nuclei positions specified by a multidimensional vector R. Then the electronic energy E(R) plays the role of a potential in which the nuclei move. The equilibrium positions of the nuclei, Rq, are found at the minimum 

In metals, the electron density behaves somewhat like a fluid and tends to smooth out the surface relief created on cleavage. As a result, electronic surface dipoles appear in the surface region which cause inward displacements of surface atomic cores, i.e., relaxation. A qualitatively different case is found at semiconductor surfaces. A terminated semiconductor crystal contains on its surface so-called dangling bonds which originate from hybrid sp -orbitals of surface atoms. Upon their saturation the creation of new bonds between adjacent surface atoms leads to a lowering of the free surface energy. Such a rearrangement causes shifts of the atoms in the surface plane, i.e., a reconstruction. 

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Surface states can be divided into those that are intrinsic to a well ordered crystal surface with two-dimensional periodicity, and those that are extrinsic [25]. Intrinsic states include those that are associated with relaxation and reconstruction. Note, however, that even in a bulk-tenuinated surface, the outemiost atoms are in a different electronic enviromuent than the substrate atoms, which can also lead to intrinsic surface states. Extrinsic surface states are associated with imperfections in the perfect order of the surface region. Extrinsic states can also be fomied by an adsorbate, as discussed below. 

Taking advantage of the intrinsic physical and chemical differences of surfaces introduced by the discontinuity of the bulk enviromuent. Specifically, most solids display specific structural relaxations and reconstructions, surface... 

Fundamental information from vibrational spectra is important for understanding a wide range of chemical and physical properties of surfaces, e.g., chemical reactivity and forces involved in the atomic rearrangement (relaxation and reconstruction) of solid surfaces. Practical applications of HREELS include studies of ... 

Tomanek D, Bennemann KH. 1985. Electronic model for energies, relaxations and reconstruction trends at metal-surfaces. Surf Sci 163 503-515. 

A series of LEED intensity studies, together with ion-scattering spectroscopy, established that a missing row structure was the correct model for the (1 x 2) phase,14 with some small subsurface relaxation and reconstruction.10... 

In the case of multi-component alloys and compounds, the surface composition may also change in addition to surface relaxation and reconstruction. For instance, the first layer of (100) plane on the surface of a nickel-aluminiim alloy enriches itself with aliuninum whose atomic size is larger than nickel. Such an enrichment of some constituents on the soUd surface is called surface segregation [Van Hove, 1993]. It is abo known that surface active minor impurities of oxygen, phosphorus and sulfur in metallic iron segregate to the clean siirface of iron [Nii-Yoshihara,... 

By contrast, surface reconstruction is a surface symmetry-lowering process. With reconstruction, the surface unit cell dimensions differ from those of the projected crystal unit cell. The energy change associated with surface relaxation and reconstruction (as much as 10%) is usually much larger than that associated with surface roughening, especially with ceramics and semiconductors. 

The most important difference between particles inside the bulk and in the interfacial layer comes from the surrounding environment of the particles the particles inside the bulk are in an isotropic environment, while those in the interface are in an anisotropic environment thus, in the interlayer, the forces between the particles are unbalanced. To reduce the resulting surface pressure, some additional processes occur that must be taken into account. On clean surfaces (for example, on a solid surface in vacuum), these processes are the bond-length contraction or relaxation and reconstruction of the surface particles (Somorjai 1994). It results in significantly reduced spacing between the first and second layers compared to the bulk. The perturbation caused by this movement propagates a few layers into the bulk. The other effect is that the equilibrium position of the particles changes that is the outermost layers can have different crystal structure than the bulk. This phenomenon is the reconstruction. 

A variety of model catalysts have been employed we start with the simplest. Single-crystal surfaces of noble metals (platinum, rhodium, palladium, etc.) or oxides are structurally the best defined and the most homogeneous substrates, and the structural definition is beneficial both to experimentalists and theorists. Low-energy electron diffraction (LEED) facilitated the discovery of the relaxation and reconstruction of clean surfaces and the formation of ordered overlayers of adsorbed molecules (3,28-32). The combined application of LEED, Auger electron spectroscopy (AES), temperature-programmed desorption (TPD), field emission microscopy (FEM), X-ray and UV-photoelectron spectroscopy (XPS, UPS), IR reflection... 

The size and shape of ceria NCs are proven fo appreciably change the chemical and physical properties hence, their control in synthesis is one chief objective for study, and various nanoparticles, nanocubes, nanooc-tahedra, nanowires, and nanotubes have been obtained for this purpose. Owing to the cubic fluorite structure, ceria tends to form isometric particles, which present sphere-like morphology and are usually intermediates between the shape of cubes and octahedra. The major exposed crystal surfaces for ceria NCs are low index ones, that is, 100, llOj, and 111, with considerable surface relaxation and reconstructions. Figure 1 shows some typical morphologies of ceria NCs. 

Compared to SRO effects on surface segregation in solid solutions, the role of LRO should be naturally more prominent and common. Its elucidation requires calculations that take into account various factors contributing to the net segregation characteristics in ordered alloys including the temperature dependence the crystal bulk structure and surface orientation, effective bulk and surface interatomic interactions (NN, non-NN) in relation to segregation driving forces, deviation from exact stoichiometry, possible surface relaxation and reconstruction, atomic vibrations, etc. This section attempts to quantify some of these factors and present several possible scenarios of segregation/order interplay. 

The aim of this chapter is to review our understanding of the fundamental processes that yield improved electrocatalytic properties of bimetallic systems. Three classes of bimetallic systems will be discussed bulk alloys, surface alloys, and overlayer(s) of one metal deposited on the surface of another. First, we describe PtjM (M=Ni, Co, Fe, Cr, V, and Ti) bulk alloys, where a detailed and rather complete analysis of surface structure and composition has been determined by ex situ and in situ surface-sensitive probes. Central to our approach to establish chemisorption and electrocatalytic trends on well-characterized surfaces are concepts of surface segregation, relaxation, and reconstruction of near-surface atoms. For the discussion on surface alloys, the emphasis is on Pd-Au, a system that highlights the importance of surface segregation in controlling surface composition and surface activity. For exploring adsorption and catalytic properties of submonolayer and overlayer structures of one metal on the surface of another, we summarize the results for Pd thin metal films deposited on Pt single-crystal surfaces. For all three systems, we discuss electrocatalytic reactions related to the development of materials... 

Despite the limitations of empirical potentials, for the last three decades computer simulations have improved the knowledge on physical properties of metals and alloys. In particular, due to the development of empirical interatomic potentials [18,19], it has become possible to describe by the MD technique a great number of solid properties such as recrystallization, structural relaxation, energetic barriers and mixing [23]. The EAM developed by Foiles et al. [18] has successfully described bulk properties of metal and alloys and some surface relaxation and reconstruction features [17,18,24,25], and the empirical potential developed by Ackland and Vitek has been applied successfully to investigate the structure of the noble metal alloys [19] and the deposition of Cu clusters on Au (111) [26] and of Cu and Au clusters on Cu (001) surfaces [27]. 

True ordered surfaces can be observed at the terrace of ideal single crystals, with practical corrugations less than 0.1 nm that are introduced by the electronic charge density of metal atoms. Thus, the surface ideal ordered domains can only be found in a small portion of the surface due to the induced surface relaxations and reconstructions [23]. 

We have reviewed some of the recent simulations of oxide surfaces by First Principles methods. Our emphasis throughout is on the reliability of simulation - how suitable are the models which are built and how accurate are the quantities calculated Practical aspects of the calculation are outlined, but also the thermodynamic framework in which energies can be interpreted and linked to experiment. Computational studies of surfece relaxation and reconstruction are surveyed and compared against experiment. The link between surface structure and dynamics is illustrated for the cases of reactivity with oxygen and water. 

High-resolution in situ X-ray reflectivity studies of mineral/water interfaces have been published, to date, for calcite, barite, corundum, orthoclase, mica, and quartz. These studies have led to general insights on the extent of relaxation and reconstruction at mineral/water interfaces as well as the structure of interfacial water and other adsorbates (discussed in a subsequent portion of this chapter and in the chapter by Fenter in this volume). 

Two mport mt tmc[uoil changes ihai occur ai solid surfaces are unique and are associatc d with the iwo-diiriensional and anisotropic cnvironnient to wtiich the surface atoms must adjust. These structural changes arc bond-length coniraciitin or relaxation and reconstruct ion- They arc discussed below... 

Relaxation and Reconstruction at Clean Surfaces. The surface atoms are pulled inward at the clean metal surface providing an interlayer spacing between the first and second layer that is shorter than the interlayer distances between subsequent layers. This inward relaxation is increased greatly with increasing surface roughness. 

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