Cell dimensions, determination

X-ray powder patterns were calculated (13) for the four idealized structures, using the atomic parameters and cell dimensions determined by Meier (11), Although these parameters will be slightly different for the four structures, they have been used here as a first approximation. 

Single-crystal precession data indicate orthorhombic symmetry with the crystallographic space group Fddd. This system is not isostructural with any other known metal oxyfluoride or metal dioxide. The cell dimensions, determined from Guinier data, are a = 8.370 1 A. b = 10.182 1 A. and c = 7.030 1 A. The indexed powder data are given in reference 6. 

Recently, a detailed study4,5 of AB02 compounds confirms that AgFe02 has the CuFe02 (delafossite) structure. The cell dimensions, determined with a Guinier camera, are found to be a = 3.0391 2 A. and c = 18.590 2 A. Single crystals are used to measure resistivity as a function of temperature.6 Silver fer-rate(III) exhibits semiconductor behavior with an activation energy of 0.7 e.V. An unusual anisotropy in resistivity is found withp(j c) = 3 X 107 S2-cm. and P( c) = 2 X 1010 J2-cm. 

The unit-cell dimensions determine the reciprocal-lattice dimensions, which in turn tell us where we must look for the data. Methods like oscillation photography require that we know precisely which reflections will fall completely and partially within a given oscillation angle so that we can collect as many reflections as possible without overlap. So we need the unit-cell dimensions in order to devise a strategy of data collection that will give us as many identifiable (by index), measurable reflections as possible. 

The unit cell dimensions determined by least squares refinement of the observed and calculated d-spacings are given in Table I for the four structures considered below. 

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. 

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. 

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... 

The distance of each reflection from the center of the pattern is a function of the fiber-to-film distance, as well as the unit-cell dimensions. Therefore, by measuring the positions of the reflections, it is possible to determine the unit-cell dimensions and, subsequently, index (or assign Miller indices to) all the reflections. Their intensities are measured with a microdensitometer or digitized with a scanner and then processed.8-10 After applying appropriate geometrical corrections for Lorentz and polarization effects, the observed structure amplitudes are computed. This experimental X-ray data set is crucial for the determination and refinement of molecular and packing models, and also for the adjudication of alternatives. 

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. 

The crystal structures of four chlorinated derivatives of di-benzo-p-dioxin have been determined by x-ray diffraction from diffractometer data (MoKa radiation). The compounds, their formulae, cell dimensions, space groups, the number of molecules per unit cell, the crystallographic B.-factors, and the number of observed reflections are given. The dioxin crystal structures were performed to provide absolute standards for assignment of isomeric structures and have been of considerable practical use in combination with x-ray powder diffraction analysis. 

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. 

The crystal properties of pseudoephedrine hydrochloride were determined with a GE model XRD-6 x-ray diffractometer using Zr filtered MoK radiation on a crystal grown from water.8 Pseudoephedrine hydrochloride has an orthorhombic crystal system belonging to the P212121 space group. The cell dimensions are a=25.358 A, b=6.428 A, c=6.901 A with each cell containing four molecules. 

The atomic arrangement within the unit cell is more difficult to determine than the cell dimensions. Trial structures deduced from these dimensions and a knowledge of the chain conformation,... 

The crystallinity of organic pigment powders makes X-ray diffraction analysis the single most important technique to determine crystal modifications. The reflexions that are recorded at various angles from the direction of the incident beam are a function of the unit cell dimensions and are expected to reflect the symmetry and the geometry of the crystal lattice. The intensity of the reflected beam, on the other hand, is largely controlled by the content of the unit cell in other words, since it is indicative of the structural amplitudes and parameters and the electron density distribution, it provides the basis for true structural determination [32],... 

A chemical bond factor can be considered to control the structure when interatomic distances, and as a consequence unit cell dimensions, can be said to be determined by a particular set of chemical bonds. 

Globular proteins were much more difficult to prepare in an ordered form. In 1934, Bernal and Crowfoot (Hodgkin) found, that crystals were better preserved if they were kept in contact with their mother liquor sealed in thin-walled glass capillaries. By the early 1940s crystal classes and unit cell dimensions had been determined for insulin, horse haemoglobin, RNAase, pepsin, and chymotrypsin. Complete resolution of the structures required identification of the crystal axes and some knowledge of the amino acid sequence of the protein—requirements which could not be met until the 1950s. 

In summary, it is important to determine crystal quality, unit cell dimensions of the crystal (a larger crystal absorbs X rays more strongly, 0.3-0.5 mm is considered the optimal size), the crystal s space group, and how many protein molecules are in the unit cell and in one asymmetric unit. Actually, the great majority of crystals useable for X-ray crystallography are not ideal but contain lattice defects. This is true for protein crystals, which are also weak scatterers since the great majority of the component atoms are light atoms, C, N, and O. 

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