Face center cubic models

The volume elements placed at each lattice site in the face centered cubic model were assumed to be bound to each other by van der Waals forces alone. We realize that this is not an accurate representation for polymer chains and should result in theoretical estimates for thennal expansion coefficients and compressibilities... 

Face-centered cubic crystals of rare gases are a useful model system due to the simplicity of their interactions. Lattice sites are occupied by atoms interacting via a simple van der Waals potential with no orientation effects. The principal problem is to calculate the net energy of interaction across a plane, such as the one indicated by the dotted line in Fig. VII-4. In other words, as was the case with diamond, the surface energy at 0 K is essentially the excess potential energy of the molecules near the surface. 

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

Particles of face-centered cubic metals of diameter 5 nm of more have been studied extensively by high resolution electron microscopy, diffraction and other methods. It has been shown that such particles are usually multiply twinned, often conforming approximately the idealized models of decahedral and icosahedral particles consisting of clusters of five or twenty tetrahedrally... 

The ion lattice model of Ref.20, applied to metals, leads to the values of 360, 210, and 730 erg/cm2 for the 111 face of lithium, sodium, and aluminum, respectively, all of which crystallize in the face-centered cubic lattices. See also Ref.21. ... 

Ideal Surfaces, A model of an ideal atomically smooth (100) surface of a face-centered cubic (fee) lattice is shown in Figure 3.13. If the surface differs only slightly in orientation from one that is atomically smooth, it will consist of flat portions called terraces and atomic steps or ledges. Such a surface is called vicinal. The steps on a vicinal surface can be completely straight (Fig. 3.13a) or they may have kinks (Fig. 3.13b). 

In an early paper, Demuth and Ibach (6) suggested that the type A spectrum of ethyne on Ni(lll) may correspond to a surface species involving four metal atoms by adsorption across the central M-M bond of the (111) unit cell of the face-centered cubic (fee) crystal. This involves interactions with the two somewhat different threefold sites on either side of the central M-M bond. This model implies that the plane of the HCCH group is perpendicular to the (111) face so that, as found experimentally, the -yCH... 

Ideal Surfaces. A model of an ideal, atomically smooth (100) surface of a face-centered cubic (fee) lattice is shown in Figure 3.13. If the surface differs only... 

Since most of the methods and examples in this review are focused on metals, this section will be shortened. Albeit, it is important to note that multiscale modeling has been applied to basic metal alloy structures such as face center cubic aluminum alloys, hexagonal close pack magnesium alloys, and body center cubic iron and... 

FIG. 4. Thirteen-atom cluster model for face-centered cubic geometry. 

In the case of rock salt, the cations form a face-centered-cubic (f.c.c.) array. Such an array is not compatible with a two-sublattice model, and there are four different types of magnetic order that can be considered (see Fig. 18). An f.c.c. structure is composed of four interpenetrating, simple-cubic (s.c.) sublattices. In ordering of the first kind, each s.c. sublattice is ferromagnetic and Mi = — M2, M3 = -M4 so that each cation has eight antiparallel and four parallel near neighbors. Then equation 101 becomes (all interactions assumed negative)... 

The (a) simple cubic (sc), (b) body-centered cubic (bcc), and (c) face-centered cubic (fee) closest packing models. The spheres are considered as touching, but in the upper structures they are shown... 

The (a) hexagonal and (b) face-centered cubic closest packing models. The spheres are considered to... 

FJ clusters (in FJ units, or as a model for specified rare-gas atom clusters) continue to be used as a benchmark system for verification and tuning in method development. With the work of Romero et al. [52], there are now proposed global minimum structures and energies available on the internet [53], up to n=309. This considerably extends the Cambridge cluster database [54], but the main body of data comes from EA work that used the known FJ lattices (icosahedral, decahedral, and face-centered cubic) as the input. This is obviously dangerous,... 

In the present work, the interaction of the ethylene molecule with the (100) surfaces of platinum, palladium and nickel is studied using the cluster model approach. All these metals have a face centered cubic crystal structure. The three metal surfaces are modelled by a two-layer M9(5,4) cluster of C4V symmetry, as shown in Fig. 6, where the numbers inside brackets indicate the number of metal atoms in the first and second layer respectively. In the three metal clusters, all the metal atoms are described by the large LANL2DZ basis set. This basis set treats the outer 18 electrons of platinum, palladium and nickel atoms with a double zeta basis set and treats all the remainder electrons with the effective core potential of Hay and Wadt... 

Cubic closest packed (cep) structure a solid modeled by the closest packing of spheres with an abcabc arrangement of layers the unit cell is face-centered cubic. (16.4)... 

The Raman spectra of solids have a more or less prominent collision-induced component. Rare-gas solids held together by van der Waals interactions have well-studied CILS spectra [656, 657]. The face-centered, cubic lattice can be grown as single crystals. Werthamer and associates [661-663] have computed the light scattering properties of rare-gas crystals on the basis of the DID model. Helium as a quantum solid has received special attention [654-658] but other rare-gas solids have also been investigated [640]. Molecular dynamics computations have been reported for rare-gas solids [625, 630, 634]. 

Synchrotron-x>ray powder-diffraction and differential-scanning-calorimetry measurements on solid Cso reveal a first-order phase transition from a low-temperature simple-cubic structure with a four-molecule basis to a face-centered-cubic structure at 249 K. The free-energy change at the transition is approximately 6.7 J/g. Model fits to the diffraction intensities are consistent with complete orientational disorder at room temperature, and with the development of orientational order rather than molecular displacements or distortions at low temperature. 

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