Face-centered cubic lattice model

Estimating inter-aggregates distances through a face-centered cubic lattice model. 

Estimating Inter-Aggregates Distances with a Face-Centered Cubic Lattice Model... 

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. ... 

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]. 

Construct a single face-centered cubic lattice unit cell. Using dots to represent spheres draw a diagram to represent your model. 

At this point it is necessary, as in the previous discussion, to introduce a model for the anharmonic crystal. The authors choose a face centered cubic lattice with central forces between nearest neighbor ions only. The necessary derivatives of the anharmonic potential are then calculated for a lead crystal and fit to experimental values of the thermal expansion, compressibility, and the lattice parameter. 

In the following, only the face-centered cubic lattice (fee) will be discussed. For this lattice, a ball-and-stick model is shown in Figure 2.4. The bottom view shows the stacking arrangement in the two different cavities, while the side view shows the ABCAB. . . stacking. Some building blocks have been color coded to indicate the unit cell to be discussed in Section 2.1.2. 

Sodium chloride has a face-centered cubic lattice. W The unit cell shown here (as a space-filling model) has Cl ions at the corners and at the centers of the faces of the cube.The Cl ions are much larger than Na" ions, so the Cl ions are nearly touching and have approximately a cubic close-packed structure the Na" ions are in cavities in this structure. (6) The alternative unit cell shown here has Na ions at the comers and the centers of the faces of the unit cell. 

The Elements Handbook (Appendix A) contains a table of properties for each group that includes information on the crystal structures of the elements. Most metals crystallize in one of three lattice arrangements body-centered cubic, face-centered cubic, or hexagonal close-packed. Figure 3.2 shows a model of the face-centered cubic lattice for sodium chloride. Use this figure and the information in the Elements Handbook (Appendix A) to answer the following. 

We will consider that each molecule of a liquid or an amorphotis organic polymer is centered on a normal site in a face centered cubic lattice and that all interactions may be described in terms of van der Waals interactions. The total potential of a molec ile will be calculated by summing over a large number of nei bors. Similarly, calcxilations of various properties of such a system will be peiv formed in terms of the fee lattice array. There is, of course, no physical basis for the selection of any one of the isotropic crystalline models except from the standpoint of simplifying the subsequent calculations. One cotild also perform calculations using a radial distribution function and integrating rather than performing lattice sums. Clearly these calculations are of an approximate na-ttare and are used only to demonstrate that several properties of liquids and polymers may be described in teims of van der Waals interactions. ... 

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. 

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). 

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... 

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,... 

---