Surface relaxation effects

In dynamic ETEM studies, to determine the nature of the high temperature CS defects formed due to the anion loss of catalysts at the operating temperature, the important g b criteria for analysing dislocation displacement vectors are used as outlined in chapter 2. (HRTEM lattice images under careful conditions may also be used.) They show that the defects are invisible in the = 002 reflection suggesting that b is normal to the dislocation line. Further sample tilting in the ETEM to analyse their habit plane suggests the displacement vector b = di aj2, b/1, 0) and the defects are in the (120) planes (as determined in vacuum studies by Bursill (1969) and in dynamic catalysis smdies by Gai (1981)). In simulations of CS defect contrast, surface relaxation effects and isotropic elasticity theory of dislocations (Friedel 1964) are incorporated (Gai 1981). 

Geometry optimizations allowed adsorbates and the central fottr Pt atoms of the first layer to optimize completely while keeping all other Pt-Pt distances fixed to the bulk crystal value of 2.775 A. By doing so, we minimized tmphysical border effects to reproduce the (semi-)irrfinite Pt(lll) surface. This model includes major surface relaxation effects, which were significant for some adsorbates. 

In slab calculations, a finite number of layers mimicks the semi-infinite system, with a two-dimensional (2D) translational periodicity. A minimal thickness dmin is required, so that the layers in the slab centre display bulk characteristics. Practically speaking, dm-,n should be at least equal to twice the damping length of surface relaxation effects, which depend upon the surface orientation. In plane wave codes, the slab is periodically repeated... 

We will successively discuss surface relaxation effects, changes of covalency in the outer layers, partial fillings of surface states and stoichiometry changes. 

Later work on diffusion rates led Wu et al. [86] to reject diffusion as the rate-limiting step on Si(lOO). They fit a potential surface to results of their calculations and used Monte Carlo transition state theory to calculate rate constants. Surface relaxation effects that were neglected in their first prin-... 

Teraoka Y (1990) Surface relaxation effects on surface segregation and order-disorder transition temperatures of binary alloys. Surf Sci 238(1-3) L453-L456... 

Equations (4-6) are by no means rigorous but they essentially form the basis for analyzing CTR data from the three low-index surfaces of fee transition metals. The equations are easily modified to include surface relaxation effects, surface roughness, or adsorbed adlayer species and are used in the analysis of the results presented in Sects. 4.1.3 and 4.1.4 of this report. 

Modem surface crystallographic studies have shown that on the atomic scale, most clean metals tend to minimize their surface energy by two kinds of surface atom rearrangements - relaxation and reconstmction [22-26]. In this review, the term surface reconstruction applies to the case in which there is lateral (i.e. in the surface plane) movement of surface atoms such that the surface layer has a symmetry that is different from that of the underlying bulk of the crystal. Hence, the surface layer has a two-dimensional unit cell that is different from the corresponding two-dimensional unit cell of a layer in the bulk. The periodicity of the surface can be defined by Woods notation for example, an unreconstructed surface would be termed as (1x1), whereas if the surface unit cell size was doubled in one of the primary vector directions, it would be termed as (2 x 1), and so on. On the other hand, surface relaxation apphes to the case in which the surface layer is in a (1 x 1) state but the layer is displaced along the surface normal direction from the position expected for bulk termination of the crystal lattice. In this section, both surface reconstruction and surface relaxation effects are described with specific examples chosen to illustrate the phenomena as they are observed in the electrochemical environment. 

Ag(hkl), Au(hkl), and Ft(hkl) surfaces in electrochemical environments [40, 46, 49]. As opposed to UHV systems, in the electrochemical environment, it is not possible to perform LEED experiments and surface relaxation effects can only be probed using X-ray diffraction techniques. As shown in Sect. 4.1.2.1, the analysis of CTR data is relatively simple to perform and can provide accurate values of surface relaxation in both the UHV environment and when the surface is in contact with the electrolyte. Additionally, the potential dependence of the surface relaxation can be probed by performing XRV measurements at suitable reciprocal lattice positions (see Sect. 4.1.2.1). The results can give good insight into the nature of the interaction between species that can be adsorbed from the electrolyte solution and the metal surface. 

This paper presents a discussion of our present understanding of the structure of ionic crystal surfaces. Both theoretical predictions and experimental observations will be reviewed. Emphasis will be placed on surface relaxation effects, point defects in the top monolayer and long range point defect distributions. The role of space charge regions in ionic transport and other processes will be reviewed. Attention will also be given to impurity distribution near interfaces in doped systems. 

DV calculations by Hoshino and Tsukada (1983), as a model for the polar (lll)-(l X 1) TiC surface. These authors made an attempt to take into account the surface relaxation effects. It was found that the decrease in the interlayer distances promoted charge polarisation between the different types of atom in the layers and between the atoms of the first and second layers. Moreover, at the same time, the relaxation greatly influences the outer electronic states of the surface. 

One usually observes faster relaxation rates for fluids inside a solid porous structure than for bulk fluids. This can be described as a surface relaxation effect, two or three fluid molecular layers having a specific relaxation rate much shorter than the bulk value. The origin of this shorter relaxation rate, for most mineral materials like rocks, is the presence of paramagnetic centres (usually iron). It is also considered that a reduction of molecular mobility or orientation could play a role. Whatever the origin of the surface relaxation, it can be shown that, under conditions of fast exchange, the relaxation rate measured for the fluid inside the pore space is proportional to the surface to volume ratio S/V, i.e. is inversely proportional to a characteristic pore size. The proportionality constant is the surface relaxation strength p characteristic of the solid-liquid pair under consideration, its order of magnitude for water in sandstone is 8 x 10 4 cm s . ... 

The surface relaxation effects do not affect the second-order magnetic properties of AIMs such as magnetic susceptibility and chemical shielding. The transferability of these properties provides a theoretical basis for the empirical Pascal rules. A Hilbert space approach to the partitioning of magnetic susceptibility into atomic contributions has also been proposed. ... 

P. Cordoba-Torres, M. Keddam, and R. P. Nogueira, On the intrinsic electrochemical nature of the inductance in EIS. A Monte Carlo simulation of the two-consecutive steps mechanism The rough 3D case and the surface relaxation effect, Electrochim. Acta 6779-6787 (2009). 

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