Cell, dimensions volume

The materials for solid solutions of transition elements in j3-rh boron are prepared by arc melting the component elements or by solid-state diffusion of the metal into /3-rhombohedral (/3-rh) boron. Compositions as determined by erystal structure and electron microprobe analyses together with the unit cell dimensions are given in Table 1. The volume of the unit cell (V ) increases when the solid solution is formed. As illustrated in Fig. 1, V increases nearly linearly with metal content for the solid solution of Cu in /3-rh boron. In addition to the elements listed in Table 1, the expansion of the unit cell exceeds 7.0 X 10 pm for saturated solid solutions " of Ti, V, (2o, Ni, As, Se and Hf in /3-rh boron, whereas the increase is smaller for the remaining elements. The solubility of these elements does not exceed a few tenths at %. The microhardness of the solid solution increases with V . Boron is a brittle material, indicating the accommodation of transition-element atoms in the -rh boron structure is associated with an increase in the cohesion energy of the solid. 

Cell dimensions were determined from micrografs and the expansion rates calculated from volume changes as a function of the time during which the leaf advanced from e.g. leaf 5 to 7. 

Vh-amylose shows an increase in water molecules from 4 to 16 per unit cell)51). Eight of these guests occupy interstitial sites and eight are present within the helical canals (Fig. 13). All unit cell dimensions are increased over the Va-form, thereby increasing the unit cell volume from 2304 to 2604 A3. The sixfold helical arrangement has been confirmed for Vh-amylose. 

Vc crystalline Va, amorphous). The densities of the pure crystalline (pc) and pure amorphous (pa) polymer must be known at the temperature and pressure used to measure p. The value of pc can be obtained from the unit cell dimensions when the crystal structure is known. The value of pa can be obtained directly for polymers that can be quenched without crystallization, polyfethylene terephtha-late) is one example. However, for most semi-crystalline polymers the value of pa is extrapolated from the variation of the specific volume of the melt with temperature [16,63]. 

Changes in density, unit cell dimensions, and macroscopic volume have serious effects. In an environment where point defects (or aggregates of point defects) are generated, such as in the components of nuclear reactors, or in vessels used for the storage of nuclear waste, where point defects are produced as a result of irradiation, dimensional changes can cause components to seize or rupture. 

Although the unit cell dimensions shown in Table 11.3 appear to be reasonably close to each other, the calculated cell volumes and crystal densities are divided... 

Since these volumes are determined from external dimensions of the samples, they do not reflect actual changes in the cell wall volumes, and where this is claimed or assumed, the data needs to be treated with caution. Sample geometry is a crucial factor affecting the results obtained. In particular, the orientation of growth rings with respect to the sample... 

One deduces the space group from the symmetry in the crystal s diffraction pattern and the systematic absence of specific reflections in that pattern. The crystal s cell dimensions are derived from the diffraction pattern for the crystal collected on X-ray film or measured with a diffractometer. An estimation of Z (the number of molecules per unit cell) can be carried out using a method called Vm proposed by Matthews. For most protein crystals the ratio of the unit cell volume and the molecular weight is a value around 2.15 AVOa. Calculation of Z by this method must yield a number of molecules per unit cell that is in agreement with the decided-upon space group. 

Over the years, modeling of carbohydrates has emphasized intramolecular rather than intermolecular structures. The same holds true in the study of synthetic polymers and polypeptides. Only one such study for carbohydrates comes to mind (1) where the unit cell dimensions and symmetry were not used. Even there, a volume constraint was used, limiting the possible structures. When such constraints are used, one does not obtain an explanation for why the crystal structure is the stable form. 

From the cubic unit cell dimension a, we can calculate the volume of the unit cell, Elf the density, p, of the crystals are known, then the mass of the contents of the unit cell, M, can also be calculated... 

The theoretical density of a crystal can be obtained from the volume of the unit cell and the mass of the unit cell contents. The results of an X-ray diffraction structure determination gives both of these data, as the unit cell dimensions are accurately measured and the type and number of formula units in the unit cell are also determined. An example of this type of calculation for FeO follows ... 

A particular crystal of FeO was found to have a unit cell dimension of 430.1 pm, a measured density of 5.728 kg m and an iron to oxygen ratio of 0.945. The unit cell volume (which is a cube) is thus (430.1 pm) =7.956x10 (pm) ... 

Fig. 4.41 Density profiles calculated using mean-field self-consistent field theory for a PS587PI647 diblock in toluene at room temperature with a polymer volume fraction

The relative effects of supercitical carbon dioxide density, temperature, extraction cell dimensions (I.D. Length), and cell dead volume on the supercritical fluid extraction (SFE) recoveries of polycyclic aromatic hydrocarbons and methoxychlor from octadecyl sorbents are quantitatively compared. Recoveries correlate directly with the fluid density at constant temperature whereas, the logarithms of the recoveries correlate with the inverse of the extraction temperature at constant density. Decreasing the extraction vessels internal diameter to length ratio and the incorporation of dead volume in the extraction vessel also resulted in increases in SFE recoveries for the system studied. Gas and supercritical fluid chromatographic data proved to be useful predictors of achievable SFE recoveries, but correlations are dependent on SFE experimental variables, including the cell dimensions and dead volume. 

Figure 7. Plot of the relative increase in recovery achieved as a function of the PAH fused ring number as follows 70 vs. 0% dead volume 1 1 vs. 1 20 cell dimensions 100 vs. 75°C and 0.75 vs. 0.50 g/ml.

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