Cells dimensions

Vegard s law In phases in which there is a range of composition of solid solution then the cell dimensions vary linearly with the molar proportions of the constituents. The (aw is rarely followed exactly. 

The elements ay are absorptivities (or are proportional to absorptivities, depending on the concentration units and cell dimensions), x= ( ) is the unknown concentration vector, and y = ( () is the absorbance vector, observed at wavelengths Li and X2. 

One of the things that can be done with a knowledge of the unit cell dimensions is to calculate the crystal density. This is examined in the following example. 

Use the unit cell dimensions cited above to determine the crystal density of polyethylene. Examine Fig. 4.10 to decide the number of repeat units per unit cell. 

Unit cell dimensions (A) Number of repeat units per cell Density (g cm 3)... 

For nosetip materials 3-directional-reinforced (3D) carbon preforms are formed using small cell sizes for uniform ablation and small pore size. Figure 5 shows typical unit cell dimensions for two of the most common 3D nosetip materials. Carbon-carbon woven preforms have been made with a variety of cell dimensions for different appHcations (27—33). Fibers common to these composites include rayon, polyacrylonitrile, and pitch precursor carbon fibers. Strength of these fibers ranges from 1 to 5 GPa (145,000—725,000 psi) and modulus ranges from 300 to 800 GPa. 

Fig. 5. Unit cell dimensions for carbon-carbon nosetip materials, parameters are...

The exchange energy coefficient M characterizes the energy associated with the (anti)paraHel coupling of the ionic moments. It is direcdy proportional to the Curie temperature T (70). Experimental values have been derived from domain-width observations (69). Also the temperature dependence has been determined. It appears thatM is rather stable up to about 300°C. Because the Curie temperatures and the unit cell dimensions are rather similar, about the same values forM may be expected for BaM and SrM. 

Sohd hydrogen usually exists in the hexagonal close-packed form. The unit cell dimensions are = 378 pm and Cg = 616 pm. SoHd deuterium also exists in the hexagonal close-packed configuration, and = 354 pm, Cg = 591 pm (57—59). 

Density. Although the polymer unit cell dimensions imply a calculated density of 1.33 g/cm at 20°C, and extrapolation of melt density data indicates a density of 1.13 g/cm at 20°C for the amorphous phase, the density actually measured is 1.15—1.26 g/cm, which indicates the presence of numerous voids in the stmcture. 

Figure 6 The lateral cell dimensions of the hexagonal cell at 500 MPa. (a) Referred to the hexagonal axes and (b) referred to orthohexagonal axes. (From Ref. 57.) (c) Structural model of the intramolecular defect in the hexagonal crystal. (From Ref. 60.)...

USY Zeolite ( 7 Al Atoms/u.c.) unit Cell Dimension =24.25 A (Si02/Ai203=54)... 

Relate unit cell dimensions to atomic or ionic radii (Examples 9.8,9.9 Problems 49-58) 51,53,56,76... 

Since the first structure determination by Wadsley [56] in 1952 there has been confusion about the correct cell dimensions and symmetry of natural as well of synthetic lithiophorite. Wadsley determined a monoclinic cell (for details see Table 3) with a disordered distribution of the lithium and aluminium atoms at their respective sites. Giovanoli et al. [75] found, in a sample of synthetic lithiophorite, that the unique monoclinic b-axis of Wadsley s cell setting has to tripled for correct indexing of the electron diffraction patterns. Additionally, they concluded that the lithium and aluminum atoms occupy different sites and show an ordered arrangement within the layers. Thus, the resulting formula given by Giovanelli et al. 

Because of anomalous scattering by H the results for the as-precipitated Ni(OH)2 could not be refined. Nevertheless, cell constants and the O-H bond distance could be determined. The results showed that the as-precipitated material was different from the well-crystallized material. The unit cell dimensions were aQ =3.119 and c0 =4.686 A. Also the... 

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