Lateral lattice constant

In order to calculate adsorbed SO3 configuration on Pt surface, we used the first-principles calculation code PHASE [9] with a slab model in a periodic boundary condition along the surface plane to simulate the Pt (111) surface. A four-layer slab model was used for main calculations. In these calculations, the atoms at the bottom are fixed at a bond distance d=2.83 A, which is the optimized value in Pt fee crystal with PHASE. A p(4 x 4) lateral supercell was used for the computation of the most energetically stable configuration. The p(4 x 4) surface supercell has 16 Pt atoms per layer with a lateral lattice constant of 11.31 A. 

Model Lattice The model lattice L has to incorporate the Pt25Rh75(100) substrate, the C adsorbate, and the C vacancies [111]. So in total, four different atomic species are distributed over the lattice and a priori k = 4. Our choice for L is a symmetric surface slab with three bulklike layers and five surrounding surfacelike layers. The former fixed the lateral lattice constant, and the latter provided room for both the substrate (four layers) and the adsorbate (one layer). 

Like in the case of a clean (100) surface, the four substrate layers can accommodate arbitrary Pt and Rh occupations in fcc-Hke positions. Again, the substrate layers build around three buUdike fee layers with fixed Pt25Rh75 occupation, arranged in an LI 2 structure. Those three layers mimic the bulk behavior of the system and fix the lateral lattice constant of the whole slab. This setup leaves us with 11 slab layers for the Pt25Rh75(100) substrate and a 2 x 1 lateral unit cell due to the LI2 bulk structure [111]. The concentration of Pt in the four substrate layers will be denoted by x. On top of the substrate layers, one additional layer accommodates the C contaminants. In our model, the C atoms can be placed on different fee sites the lateral 2x1 substrate lattice allows for two top, four bridge, and two hollow adsorption sites. So the maximum coverage in our model is 0 = 4 ML (monolayers) [111]. 

The effects due to the finite size of crystallites (in both lateral directions) and the resulting effects due to boundary fields have been studied by Patrykiejew [57], with help of Monte Carlo simulation. A solid surface has been modeled as a collection of finite, two-dimensional, homogeneous regions and each region has been assumed to be a square lattice of the size Lx L (measured in lattice constants). Patches of different size contribute to the total surface with different weights described by a certain size distribution function C L). Following the basic assumption of the patchwise model of surface heterogeneity [6], the patches have been assumed to be independent one of another. 

The fact that the structure that I formulated for this alloy from chemical arguments with no knowledge about the X-ray diffraction diagram was found later to agree quantitatively with that diagram has convinced me that the structure is correct. I emphasize that I formulated only one structure, and that the X-ray diagram was not involved in any way in its formulation. The probability of chance agreement of the lattice constant to 0,1 A and of adherence to the selection rules for intensities is surely less than 1 in 1,000. 

The example demonstrates that the instability and consequent energy dissipation, similar to those in the Tomlinson model, do exist in a real molecule system. Keep in mind, however, that it is observed only in a commensurate system in which the lattice constants of two monolayers are in a ratio of rational value. For incommensurate sliding, the situation is totally different. Results shown in Fig. 21(b) were obtained under the same conditions as those in Fig. 21 (a), but from an incommensurate system. The lateral force and tilt angle in Fig. 21(b) fluctuate randomly and no stick-slip motion is observed. In addition, the average lateral force is found much smaller, about one-fifth of the commensurate one. 

Simulations of incommensurate surfaces showed a similar dependence on Vi, with first-order instabilities occurring if Vi < Vj, where Vj is some positive, critical value that depends on the degree of mismatch between the lattice constants of the top and bottom surfaces. This process leads to nonvanishing Fk as l o goes to zero. In the case where Vi < V, the atoms are dragged with the wall that exerts the maximum lateral force. It, in turn, leads to friction that scales linearly with the sliding velocity. As a result, the friction force will go to zero with vq. 

Later, Tieke reported the UV- and y-irradiation polymerization of butadiene derivatives crystallized in perovskite-type layer structures [21,22]. He reported the solid-state polymerization of butadienes containing aminomethyl groups as pendant substituents that form layered perovskite halide salts to yield erythro-diisotactic 1,4-trans polymers. Interestingly, Tieke and his coworker determined the crystal structure of the polymerized compounds of some derivatives by X-ray diffraction [23,24]. From comparative X-ray studies of monomeric and polymeric crystals, a contraction of the lattice constant parallel to the polymer chain direction by approximately 8% is evident. Both the carboxylic acid and aminomethyl substituent groups are in an isotactic arrangement, resulting in diisotactic polymer chains. He also referred to the y-radiation polymerization of molecular crystals of the sorbic acid derivatives with a long alkyl chain as the N-substituent [25]. More recently, Schlitter and Beck reported the solid-state polymerization of lithium sorbate [26]. However, the details of topochemical polymerization of 1,3-diene monomers were not revealed until very recently. 

The rhombohedral lattice constants of some compounds LiMeFg and NaMeFg, isostructural with NaOsFg, were already stated by Boston and Sharp 46). The structure analysis of this type was performed somewhat later in the case of the compound LiSbFg 59). According to the investi-... 

Let us now consider the ideal case of the BFS (see Fig. 1.18). In the absence of anions and neglecting sulfur- or selenium-induced lateral molecule-molecule interactions, the organic molecules can be modelled as forming an ideal ID chain with orbitals aligned in the direction of the chain with a lattice constant a given... 

As early as 1943, Sommer (101) reported the existence of a stoichiometric compound CsAu, exhibiting nonmetallic properties. Later reports (53, 102, 103,123) confirmed its existence and described the crystal structure, as well as the electrical and optical properties of this compound. The lattice constant of its CsCl-type structure is reported (103) to be 4.263 0.001 A. Band structure calculations are consistent with observed experimental results that the material is a semiconductor with a band gap of 2.6 eV (102). The phase diagram of the Cs-Au system shows the existence of a discrete CsAu phase (32) of melting point 590°C and a very narrow range of homogeneity (42). 

The accessible deepness of donor centers extraction remains to be relatively small (probably, no more than several oxide lattice constants) because of its limitation by the low diffusion of oxygen, which is necessary for the oxidation of donor centers. To explain the experimentally observed appearance of a rather small concentration of relatively big Ag particles on the Ti02 electrodes, account must be given to the possibility of the lateral electron transfer from the neighboring donor centers, that is the electrochemical mechanism being of widespread occurrence in the processes of the chemical deposition of metals. In any case, metal nanoparticles deposited via the interaction of semiconductor donor centers with soluble metal ions prove to be localized at the sites of the electrode surface exposure of donor centers including continuous donor clusters. 

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