High-symmetry site

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

Figure 2.15 High-resolution STM image (a) [30] and AFM image (b) [49] of the alumina film on Ni3AI(l 1 1). The high-symmetry sites marked by triangles (circles) and the hexagons correspond to the network and dot structure, respectively.

The results for Pd and V lead to the conclusion that the high-symmetry sites of the alumina film on Ni3Al(l 1 1) can act as template for the growth of nanostructured model catalysts. They also prove that kinetic control of the growth is of utmost importance. 

Fig. 1. Location of various high-symmetry sites in the diamond structure. T is the tetrahedral interstitial site, H is the hexagonal interstitial site, B the bond center, and C is at the center of a rhombus formed by three adjacent Si and the nearest T. The M site is midway between two C sites it is also located midway between B and a neighboring H site.

We can avoid this symmetry-induced trap by deliberately breaking the symmetry of our atom s coordinates. One easy way to do this is to repeat our calculations after moving the H atom a small amount (say, 0.2 A) in some arbitrary direction that does not coincide with one of the symmetry directions on the surface. What we find, if we run calculations in which we start the H atom at a point about 0.2 A away from each of the high-symmetry sites mentioned above is that the H atom relaxes to the fourfold hollow site even if it is started quite near the top and bridge sites. This shows that the top and bridge sites are not minima for this system. 

The lowest energy atomic site for H chemisorbed on Cu(l 11) is the fee hollow site with W = 2.3 eV. Smaller and different W exists at the other high symmetry sites. Thus, the PES is very laterally corrugated, both in energy and geometry. In addition, there are metastable subsurface sites inside the surface plane, e.g., one site exists below the fee hollow with W 0.9 eV above that of the most stable surface adsorption site [140]. This is made metastable by abarrier of 0.4 eV relative to the bottom of the subsurface well. Bulk octahedral absorption sites have essentially the same stability as the subsurface sites, with presumably similar barriers to migration into the bulk. Thus, populating the subsurface site represents the initial step in bulk absorption of H. 

Figure 1 Computed potential energy curves for a single H atom over three high-symmetry sites on Ni(l 0 0). Results for H over the hollow (open circles), bridge (filled diamonds) and atop (filled circles) sites are plotted as a function of z, the distance of the H atom above the surface.

At this time, the locations of cations in zeolites have been determined primarily by X-ray diffraction (XRD) techniques. Unfortunately, this method has the drawback of being able to locate only the most stationary cations in zeolites. In some studies of hydrated zeolites, less than 50% of the total cation population can be accounted for. A higher percentage of the cations can be located in dehydrated samples, but the effect of the dehydration step on the location of the cations is generally not well known. NMR measurements, on the other hand, are most sensitive to mobile cations and cations in high symmetry sites. 

The spectroscopy of the SD0 level is also a valuable tool to investigate the point symmetry of Eu3+ ions in materials. It is well-known that the 5D0 - 7F2 transition is electric-dipole in nature, while 5D0- -7Fi shows a magnetic-dipole character. 5D0-> 7F2 is totally forbidden in presence of an inversion center and it is allowed in the opposite case. Usually, in vitreous phases, where the symmetry is low, electric dipolar transitions exhibit the strongest intensity. The fluorescence spectra displayed in Fig. 8 show that both transitions have about the same intensity indicating that Eu3+ ions are in high-symmetry sites in fluorozirconate glasses, relatively to oxide glasses. 

Figure 1. Plan view of the Pt(lll) surface. The anows indicate the location of the four high symmetry sites and the straight Iinesap(3x2) unit celt Qnb two layers of metal atoms are shown for clarity.

TABLE 4. Chemisorption energies in eV for 1/6 monolayer C, N, O, and H adsorption on the four high symmetry sites of a fixed three layer Pt slab. 

Pt(l 11) surface were performed. Tables 4 and 5 list chemisorption energies for C, N, 0, and H and CHx(x=i- 3)> NHx(x=i- 3), OHx(x=i->2) on the four high symmetry sites of Pt(lll). From Table 4 we see that the atomic adsorbates have a strong preference for adsorption at three-fold hollow sites, with the exception of H which has a very smooth potential energy surface (PES). Table 5 reveals that the molecular adsorbates do not exhibit quite the same preference for adsorption at three-fold hollow sites, binding preferentially at a variety of sites CH and NH favour adsorption at fee three-fold hollow sites CH2, NH2 and OH at bridge sites and CH3, NH3 and H2O at top sites. 

Fig. 24. Model of ZnO(lOTO) surface, with the bond geometries of formate and carbonate proposed in Ref. 122. The tilts out of high symmetry sites have been neglected, and for formate only one azimuthal orientation is shown.

The EPR spectra in the crystalline phase are explained by analogy with the work of Durville et al. who attribute the sharp absorption at 1580 Gauss to Cr " in high symmetry sites of the crystalline phases. The appearance of 1460 G narrow peaks in all samples is due to the ferric impurity and at 3300 Gauss, to pairs. 

Fig. 2.5. High-symmetry sites (small spheres) in a III-V sphalerite lattice oriented along a < 111 > vertical axis (the simple substitutional sites are not indicated). BC bond-centred, AB antibonding, T tetrahedral interstitial, H hexagonal sites are located along the <111> axis. The Ti and AB sites are noted according to the atoms closest to these sites. The C site, midway between two next nearest neighbours along a <110> axis, is observed according to these atoms. The M site (not shown) is midway between two adjacent Cm and CV sites and also midway between a BC site and a H site...

This means that the point symmetry of H changes from to D2h ( L and H stand for low- and high -symmetry site, respectively, as should now be evident). The first step in the construction of the benzene dimer is to modify force constants of the two sites according to Eqs. (5.1) and (5.2). A similar study can be easily and systematically implemented within the one-dimensional algebraic model by taking the Hamiltonian operator for CH stretching modes of the benzene molecule (Section III.C.2),... 

Fig. 4.12 (a) Definition of lattice planes in a fcc-lattice (b) hydrogen adsorbed on Ni(lll) (c) high symmetry sites of low index surfaces. 

Static line shapes arising from chemical shift anisotropy (CSA) and quadrupolar coupling also reflect the local symmetry of the nucleus. Isotropic lines occm for high-symmetry sites, such as tetrahedral, cubic, or octahedral, where these interactions are zero [e.g., in the Cu-NMR of tetrahedral copper centers in N(CH3)4-CuZn(CN)4 and N(CH3)4CuCd(CN)4 guest framework-], -whereas the lines have characteristic shapes for sites with axial symmetry or for lower-symmetry sites. In the case of the sign of an axial CSA line... 

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