Cell parameters defined

Case study theophylline anhydrate and monohydrate The type of structural information that can be obtained from the study of the x-ray diffraction of single crystals will be illustrated through an exposition of studies conducted on the anhydrate and hydrate phases of theophylline (3,7-dihydro-l,3-dimethyl-LH-purine-2,6-dione). The unit cell parameters defining the two phases are fisted in Table 7.2, while the structure of this compound and a suitable atomic numbering system is located in Fig. 7.3. 

Vector notation is being used here because this is the easiest way to define the unit-cell. The reason for using both unit lattice vectors and translation vectors lies in the fact that we can now specify unit-cell parameters in terms of a, b, and c (which are the intercepts of the translation vectors on the lattice). These cell parameters are very useful since they specify the actual length eind size of the unit cell, usually in A., as we shall see. 

Irrespectively of the iron content, the applied synthesis procedure yielded highly crystalline microporous products i.e. the Fe-ZSM-22 zeolite. No contamination with other microporous phases or unreacted amorphous material was detected. The SEM analysis revealed that size and morphology of the crystals depended on the Si/Fe ratio. The ZSM-22 samples poor in Fe (Si/Fe=150) consisted of rice-like isolated crystals up to 5 p. On the other hand the preparation with a high iron content (Fe=27, 36) consisted of agglomerates of very small (<0.5 p) poorly defined crystals. The incorporation of Fe3+ into the framework positions was confirmed by XRD - an increase of the unit cell parameters with the increase in the number of the Fe atoms introduced into the framework was observed, and by IR - the Si-OH-Fe band at 3620 cm 1 appeared in the spectra of activated Fe-TON samples. 

Crystallographic parameters defining the unit cells of theophylline anhydrate and theophylline monohydrate phase... 

The calculated intensities depend on several parameters which may be refined and defined these include the structural characteristics (the cell parameters, see Chapter 3) of the phase, its quantity in a multiphase sample, etc. 

Figure 24. X-ray diffraction pattern (in the inset the 2D image) of the polyethylene sample recovered by the laser-assisted high-pressure reaction in the pure liquid monomer. The two measured sharp lines nicely fit the polymer diffraction pattern having a orthorhombic cell (Pnam) defined by the lattice parameters reported in the figure.

Wang15 investigated heat and mass transport and electrochemical kinetics in the cathode catalyst layer during cold start, and identified the key parameters characterizing cold-start performance. He found that the spatial variation of temperature was small under low current density cold start, and thereby developed the lumped thermal model. A dimensionless parameter, defined as the ratio of the time constant of cell warm-up to that of ice... 

The second process of water vapor removal down the channel can be described by the convective flux, Q(pw,Sat PvMet)KRTA), representing the maximum amount of water vapor removed with the purge gas when the exit purge gas is fully saturated with vapor. In the above definition Q is the purge gas volumetric flow rate and A the active area of the fuel cell. Both parameters defined above have the unit of mol/s per unit of the fuel cell active area. It follows that... 

Numerical simulations produce force-deformation data whose shape and magnitude is dependent on the initial parameters defined within the model, including the elastic modulus (E), the uninflated cell radius (rQ) and the initial stretch ratio (ls). Experimental data are fitted to these numerical simulations allowing intrinsic material properties to be derived. 

A carbon SWNT can be visualized as a hollow cylinder formed by rolling a planar sheet of hexagonal graphite (unit-cell parameters a = 0.246, c = 0.669 nm). It can be uniquely described by a vector C = nn + m 2, where ai and a2 are reference unit vectors as defined in Fig. 14.1.9. The SWNT is generated by rolling up the sheet such that the two end-points of the vector C are superimposed. The tube is denoted as (n, m) with n>m, and its diameter D... 

Toraya s Method. The WPPD as implemented by Toraya et al.11 decomposes the peak profiles and background functions to obtain the best fit to the experimental powder pattern of the individual pure phase data by least-squares refinement. The integrated intensities of the pure phases are then stored with the other refined parameters, such as the profile parameters and the unit-cell parameters of the phases to be quantified. During quantification step, the integrated intensity of the phase being quantified is scaled, as defined in Eq. (12.4), such that the total of the scale factors for the component phases sum to unity. The scale factors of the individual components are then refined by least-squares methods until a best fit is observed with respect to the pattern of unknown composition. 

In all the applications of structure solution discussed here, we assume that the unit cell parameters a, b, c, a, /J, y and space group S are already known from prior analysis of the experimental powder diffraction pattern. We also assume that the contents of the unit cell (e.g. the types and number of atoms, ions or molecules) are known, at least to a sufficiently good approximation, but that the positions and structural arrangement of these constituents within the unit cell are not known. The structure is defined in terms of a structural fragment , which represents an appropriate collection of atoms within the asymmetric unit, and is coded using a set (denoted T) of variables that represents the positions of the atoms and/or molecules in the unit cell. For a collection of independent... 

Figure 6 Temperature dependence of the (new) cell parameter a defined in the text for TEA(TCNQ)2. (These data are recalculated from those of Ref. 22 and the unpublished results of A. Filhol and H. Grassi.) Inset Geometrical relation between a and the cell parameters a and b chosen in Ref. 22.

In the layered misfit structures each layer set A and B can be described in terms of three basic translations, i.e. by its own component lattice. [The existence of the third vector is contingent upon a strict sequence in the layer stacking. If this is absent, the two three-dimensional subcells/lattices will, in the following discussion, be replaced by two two-dimensional subcells, i.e. by submeshes (nets) built only on the intralayer vectors.] In normal layered structures the unit cells of A and B are commensurate, i.e. their unit vectors are commensurable and the periodicity of the entire structure may be described in terms of a single unit cell. In contrast, we deal with those less-frequent cases in which this is not so at least one of the basic periodicities of A and of B are incommensurate. Then the component unit cell of set A has at least one intralayer unit cell parameter which is not commensurable with the corresponding parameter of set B. Such structures have two incommensurate, interpenetrating, component lattices and can be defined as composite) layered structures with two incommensurate component unit cells. Intermediate cases, in which the nodes of the two component lattices coincide at relatively large... 

Table 8.2. Cell parameters from Smith (1974) and values for u and w defined in Eq. (8.4) for plagioclase feldspars of several compositions...

Atomic parameters A set of numbers that specifies the position of an atom in the unit cell (atomic coordinates), the extent of its displacement about an equilibrium position (vibration), and an occupancy factor (generally 1.0). Three parameters define position, one parameter can be used to define isotropic displacements, or six to define anisotropic displacements and one parameter defines the site occupancy. 

---