Atomic sites

Knowing the lattice is usually not sufficient to reconstruct the crystal structure. A knowledge of the vectors (a, b, c) does not specify the positions of the atoms within the unit cell. The positions of the atoms withm the unit cell is given by a set of vectors i., = 1, 2, 3... u where n is the number of atoms in the unit cell. The set of vectors, x., is called the basis. For simple elemental structures, the unit cell may contain only one atom. The lattice sites in this case can be chosen to correspond to the atomic sites, and no basis exists. 

This potential will lead to a single water molecule adsorbing at the PZC on Pt with the dipole pointmg axi ay from the surface and the oxygen atom pointing directly at a Pt-atom site (on-top configuration). 

The SME process can be illustrated by the Cu—Zn system, one of the first SMAs to be studied. A single orientation of the bcc P-phase on cooling goes through an ordering process to a B2 phase. In a disordered alloy, the lattice sites are randomly occupied by both types of atoms, but on ordering the species locate at particular atomic sites, yielding what is called a supedattice. When the B2 phase is cooled below the Mp it transforms to... 

Physically, diffusion occurs because atoms, even in a solid, are able to move - to jump from one atomic site to another. Figure 18.4 shows a solid in which there is a concentration gradient of black atoms there are more to the left of the broken line than there are to the right. If atoms jump across the broken line at random, then there will be a net flux of black atoms to the right (simply because there are more on the left to jump), and, of course, a net flux of white atoms to the left. Pick s Law describes this. It is derived in the following way. 

The entire formulation of a chemical question can involve a number of issues, some of which are often obscure to the user. Questions such as what components can be substituted at a given atom site, what types of bonds are favorable for a given chemical fragment query (single, double, ring, chain, aromatic, etc.), and should the query contain explicit or implicit substitution, are just a few of the issues facing a user. 

The local and partial den.sitie.s of. state have been calculated u.sing projections of the plane-wave components of the eigenstates onto spherical waves centred at the atomic sites[.53]. 

At each atomic site we place a set of hard core spheres with radii We do... 

It is known that Cr23Q can contain up to 25% iron on the metal atom sites, and Cr Cj up to about 60% iron Therefore the minimum activities of CrjjQ and Cr, have been calculated for these phases of maximum iron content using the ideal laws to calculate activities from carbide composition. The free-energy lines which were thus obtained are shown as A and... 

In disordered materials such as amorphous silicon, the mobility is so low that it would correspond to a mean free path lower than the distance between atomic sites, which is not physically pertinent. In a classical paper, Anderson [20 has shown that disorder in a solid may result in a localization of the states, in which case the one-electron wave function takes an exponential form... 

The interest of physicists in the conducting polymers, their properties and applications, has been focused on dry materials 93-94 Most of the discussions center on the conductivity of the polymers and the nature of the carriers. The current knowledge is not clear because the conducting polymers exhibit a number of metallic properties, i.e., temperature-independent behavior of a linear relation between thermopower and temperature, and a free carrier absorption typical of a metal. Nevertheless, the conductivity of these specimens is quite low (about 1 S cm"1), and increases when the temperature rises, as in semiconductors. However, polymers are not semiconductors because in inorganic semiconductors, the dopant substitutes for the host atomic sites. In conducting polymers, the dopants are not substitutional, they are part of a nonstoichiometric compound, the composition of which changes from zero up to 40-50% in... 

Occupation Probabilities of the Copper Atomic Sites in CuTeX Compounds... 

Atomic site Number of equivalent positions Occupation probabilities ... 

As schematically represented in Fig. 3 the structure can be considered two interpenetrating fee lattices of 8,2(8,2)12 units the 8,2(8,2)12 units of each fee lattice differ only by the 90° rotation of these units. Thus there are eight of these 8,2(8,2)12 units or 1248 8 atoms in the unit cell. The metal atom positions and the location of the remaining 8 atoms in the structure can be pictured in the octant of the cell shown in Fig. 3. Six metal atom sites exist in each octant of the ceil, and these are statistically half-filled. The sites are located 1.27 10 pm (for YB g) inside the cell from the center of each face of an octant one such site is depicted in Fig. 3. The center of each octant is occupied by either a 36- or a 48-8 atom group, which are labeled, respectively, configurations I and II (Fig. 4). Half of the octants contain configuration I, and half contain 11 in a random fashion. ... 

The rapid rise in computer power over the last ten years has opened up new possibilities for modelling complex chemical systems. One of the most important areas of chemical modelling has involved the use of classical force fields which represent molecules by atomistic potentials. Typically, a molecule is represented by a series of simple potential functions situated on each atom that can describe the non-bonded interaction energy between separate atomic sites. A further set of atom-based potentials can then be used to describe the intramolecular interactions within the molecule. Together, the potential functions comprise a force field for the molecule of interest. 

Force fields split naturally into two main classes all-atom force fields and united atom force fields. In the former, each atom in the system is represented explicitly by potential functions. In the latter, hydrogens attached to heavy atoms (such as carbon) are removed. In their place single united (or extended) atom potentials are used. In this type of force field a CH2 group would appear as a single spherical atom. United atom sites have the advantage of greatly reducing the number of interaction sites in the molecule, but in certain cases can seriously limit the accuracy of the force field. United atom force fields are most usually required for the most computationally expensive tasks, such as the simulation of bulk liquid crystal phases via molecular dynamics or Monte Carlo methods (see Sect. 5.1). 

The structure was solved by the multiple isomorphous replacement technique using four heavy atom derivatives uranyl acetate, plati-nous chloride, tetramethyllead acetate, and p-chloromercury benzoate. All four derivatives gave interpretable heavy atom Patterson syntheses. The heavy atom sites could be correlated between the de-... 

Here, we have expressed the concentration as the ratio of defects to the number of M- atom sites (this has certain advantages as we will see). We can than rewrite the defect equilibria equations of Table 3-3 and 3-4 in terms of numbers of intrinsic defect concentrations, shown as follows ... 

This crystal is quite defective since 1 out of 7 Ti-atom-sites (0.14 i) is a vacancy, and likewise for the oxygen-atom-sites. 

This means that 1 out of 42 hydride atoms is interstitial, cuid 1 out of 84 hydride-atom-sites is vacant. 

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