INDEX cubic

Understand the principles of the diffraction technique and index cubic materials... 

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...

All of the observed reflections could be indexed on the basis of a cubic unit cell with Oo = 11.82 A the estimated probable error is 0.01 A. The only systematic absences were hhl with l odd this is characteristic of the space group 0 -PmP>n, which also was reported by von Stackelberg from his single-crystal work on sulfur dioxide hydrate. For 46 H20 and 6 Cl2 in the unit cell the calculated density is 1.26 densities reported by various observers range from 1.23 to 1.29. 

Reciprocal spacings (1 jdm — qm = (2 sin 6)1 X) were calculated from the positions of the powder lines, and the lines were indexed on the basis of a face-centered cubic lattice. Analysis of a few lines in the back-reflection region gave a preliminary value of 0-081409 A-1 for 1 ja0. A refinement of l/a0 was carried out by... 

The oxide of trivalent iron, Fe203, has a cubic structure, a density of 5.2 g/cm, a melting point of 1565°C, and a refractive index of 3.0. It is an optical material. It is formed by CVD mostly on an experimental basis. 

The structure of PuB,qq is not yet clear. A satisfactory indexing can be made for a primitive cubic cell with a = 23.42 A, but with 10 reflections not characteristic of space group Fm3c . ... 

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... 

FIG. 58. (a) Refractive index 2.07cV- Ih) cubic bandgap E. (c) hydrogen content Ch. and (d) microstnicture parameter R as function of frequency at optimum pressures (see Fig. 54) at three power densities. 

Molecular Shape Analysis. Once a set of shapes or conformations are generated for a chemical or series of analogs, the usual question is which are similar. Similarity in three dimensions of collections of atoms is very difficult and often subjective. Molecular shape analysis is an attempt to provide a similarity index for molecular structures. The basic approach is to compute the maximum overlap volume of the two molecules by superimposing one onto the other. This is done for all pairs of molecules being considered and this measure, in cubic angstroms, can be used as a parameter for mathematical procedures such as correlation analysis. 

Index 7-point smoothing with quartic fitting function 5-point first derivative with cubic fitting function 5-point second derivative, quadratic fitting function... 

X-ray diffraction patterns were recorded on a Philips PW1820 diffractometer with Cu-Ka radiation (X = 0.154 nm). The collected sample was indexed very well as cubic a-Mn203 bixbyite (JCPDS 41-1442, la-3, a = 0.941 nm) (Fig. 1). The morphologies were visualized by scanning electron microscopy (SEM) (Fig. 1). The abundant well-defined hexagonal-like plates with the sizes from several hundred nanometers to a few micrometers were formed during hydrothermal treatment, which kept initial shape after 700 °C-calcination (Fig. 1). The hexagonal plates are about 50 nm thick with smooth surfaces. 

VTO, and that of the G structure (Ia3d symmetry, Fig. 4) index to /6 /8 /l4 VT6 V O V"22 /7A. Finally the measurements of the surface area inside the cubic cell can yield partial information about a topology of the structure. One can expect a small unit cell and the small surface area per side of... 

Figure 12.10c shows a contour plot of the nanolaser index profile superimposed on a cross-section of the modal field intensity profile in the center of the active medium. As shown in the figure, the modal profile of the nanocavity is confined almost completely in the 300-nm wide central pillar with a modal volume of 0.213 (1/n)3 (0.024 pm3) only 1.75 times the theoretically possible limit of a cubic half... 

The shape of the single crystal obtained by the method described above is a sphere with several flat facets as drawn in Fig. 2-6. Usually seven large facets, which are assigned to seven of possible eight (111) surfaces, are seen on the apex positions of a cube. Five small facets, which are assigned to five of possible six (100) surfaces, are also seen on the center of the faces of a cube. The missing (111) and (100) facets are supposed to be located where the shaft is attached. Figure 2—7 shows the relative positions of the three low index surfaces of platinum, which is a face-centered cubic lattice. 

Fig. 2-7 Three low index surfaces of Pt (face centered cubic lattice) si e crystal and their surface atom arrangement and atomic density.

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