Unit cell size determination

The framework aluminum (FAL) was estimated from the unit cell size (determined by XRD) and using the Fichtner-Schmittler equation [framework Al=l 12.4(ao-24.233)]. 

The synthesis of silicates that contain metal cations other than aluminium in framework positions results in solids with modified adsorptive and catalytic properties. The criteria for successful incorporation of cations into tetrahe-drally coordinated silicate frameworks are that they should exhibit solubility under synthesis conditions without the formation of an insoluble oxide or oxyhydroxide and that the substituting species should be able to adopt tetrahedral coordination. Preparation of a phase that is shown to contain other metals (by selected area chemical analysis in an electron microscope, for example) is no guarantee that the metal has adopted a framework site. Physicochemical methods must be used to determine whether this is the case. This is complicated when the metal adopts more than one site or is present at very low levels. Confirmatory evidence for framework substitution may be available from unit cell size determination (substitution of a cation larger than Si" will in general result in an increase in unit cell dimension), and determination of coordination geometry by NMR, UV-visible and EXAFS spectroscopies (Chapter 3), which are able to distinguish whether the metal is within the... 

The different forms of carbynes were assumed to be polytypes with different numbers of carbon atoms in the chains lying parallel to the hexagonal axis and different packing arrangements of the chains within the crystallite. Heimaim et al [23] proposed that the sizes of the unit cells were determined by the spacing between kinks in extended carbon chains, Fig. 3A. They were able to correlate the Cg value for the different carbyne forms with assumed numbers of carbon atoms, n (in the range n = 6 to 12), in the linear parts of the chains. 

Aluminum distribution in zeolites is also important to the catalytic activity. An inbalance in charge between the silicon atoms in the zeolite framework creates active sites, which determine the predominant reactivity and selectivity of FCC catalyst. Selectivity and octane performance are correlated with unit cell size, which in turn can be correlated with the number of aluminum atoms in the zeolite framework. ... 

Fig. 8. Illustration of the use of periodic boundary conditions in the determination of molecular electronic structure. The unit cell is shown by the dashed line. As the unit cell size is increased the calculated properties converge toward those of the isolated molecule...

Increasingly, Rietveld refinement is also used as a more accurate way for determining the other types of information discussed above, including phase identification, phase quantization, unit cell size determinahon and crystallite size analysis. 

J.H., and O Donnell, D.J. (1985) Determination of framework aluminum content in dealuminated Y-type zeolites a comparison based on unit cell size and wavenumber of i.r. bands. Zeolites, 6, 225-227. 

The zeolite unit cell size was determined by X ray diffraction according to ASTM-D-3942-80 at SINTEF (SINTEF, Oslo, Norway). For data see Table 4.2. 

The size and shape of the unit cell is determined, usually from rotation photographs and... 

Analysis of Fractions. Surface areas and pore size distributions for both coked and regenerated catalyst fractions were determined by low temperature (Digisorb) N2 adsorption isotherms. Relative zeolite (micropore volume) and matrix (external surface area) contributions to the BET surface area were determined by t-plot analyses (3). Carbon and hydrogen on catalyst were determined using a Perkin Elmer 240 C instrument. Unit cell size and crystallinity for the molecular zeolite component were determined for coked and for regenerated catalyst fractions by x-ray diffraction. Elemental compositions for Ni, Fe, and V on each fraction were determined by ICP. Regeneration of coked catalyst fractions was accomplished in an air muffle furnace heated to 538°C at 2.8°C/min and held at that temperature for 6 hr. 

Techniques of transmission electron microscopy have proved valuable in many areas of solid state science. Use of electron diffraction permits identification of crystal types, determination of unit cell sizes and characterization of crystal defects in the phases. Measurement of Energy Dispersive X-ray (EDS) line intensity allows calculation of the elemental composition of the phases. It is difficult to overestimate the value of such applications to metallic alloys, ceramic materials and electron-device alloys (T-4V Applications to coal and other fuels are far fewer, but the studies also show promise, both in characterization of mineral phases and in determination of organic constituents (5-9. This paper reports measurements on a particular feature of coal, the spatial variation of the organic sulfur concentration. 

Stephens et al. determined the lattice structure of powdered TDAE-C60 to be monoclinic C2/m with one formula unit per unit cell [84]. However, a structural analysis performed on single crystals [85] showed the room temperature structure to be monoclinic with unit cell dimensions a=15.858(2) A, b=12.998(2) A, c=l9.987(2) A, (3=93 37° and four formula units per unit cell. The correct space group was found to be C2/c and not C2/m as originally reported from the powder data. The unit cell in fact consists of two subcells, which are stacked along the c-direction so that the unit cell size in the c-direction is doubled (Fig. 13). In one of the subcells the TDAE ion is shifted by about 0.02 A along... 

The discovery of x-rays provided crystallographers a powerful tool for the thorough determination of crystal structures and unit cell sizes [20-26], X-rays have wavelengths between 0.2 and 10 nm. As x-rays possess dimensions comparable to the interplanar distances in crystals, x-ray crystallography is an ideal nondestructive method for material characterization, since nanometer parameters as well as macroscopic properties of the tested samples can be determined from x-ray diffraction data. 

Powder X-Ray Data. We believe that S1 NMR provides a more accurate determination of framework composition than elemental analysis since the measurement Is essentially Independent of any Impurities that may be occluded In the zeolite pores. Therefore, we used the values of Sl/Al derived from the NMR data to follow the variation of unit-cell size with composition. 

The next stage of characterization focuses upon the different phases present within the catalyst particle and their nature. Bulk, component structural information is determined principally by x-ray powder diffraction (XRD). In FCC catalysts, for example, XRD is used to determine the unit cell size of the zeolite component within the catalyst particle. The zeolite unit cell size is a function of the number of aluminum atoms in the framework and has been related to the coke selectivity and octane performance of the catalyst in commercial operations. Scanning electron microscopy (SEM) can provide information about the distribution of crystalline and chemical phases greater than lOOnm within the catalyst particle. Differential thermal analysis (DTA) and thermogravimetric analysis (TGA) can be used to obtain information on crystal transformations, decomposition, or chemical reactions within the particles. Cotterman, et al describe how the generation of this information can be used to understand an FCC catalyst system. 

Dealuminated Y zeolites which have been prepared by hydrothermal and chemical treatments show differences in catalytic performance when tested fresh however, these differences disappear after the zeolites have been steamed. The catalytic behavior of fresh and steamed zeolites is directly related to zeolite structural and chemical characteristics. Such characteristics determine the strength and density of acid sites for catalytic cracking. Dealuminated zeolites were characterized using X-ray diffraction, porosimetry, solid-state NMR and elemental analysis. Hexadecane cracking was used as a probe reaction to determine catalytic properties. Cracking activity was found to be proportional to total aluminum content in the zeolite. Product selectivity was dependent on unit cell size, presence of extraframework alumina and spatial distribution of active sites. The results from this study elucidate the role that zeolite structure plays in determining catalytic performance. 

In addition, structural similarities can often be determined from careful interpretation of XRD powder patterns. The powder patterns of offretite and erionite look quite different, but are easily understood in terms of the crystallographic consequences of a change in the ordered layer stacking sequence (11), cf. Figure 4. In offretite, the layers are stacked in an AAB sequence, while in erionite, they are ordered in an AABAAC arrangement that doubles one of the crystallographic unit cell parameters. The doubled c-parameter is readily deduced from an analysis of the XRD powder pattern of erionite. Another framework structure effect, isomorphous substitution, can result in changing unit cell sizes, observed as shifts in XRD line positions for such systems as X and... 

The stractures of the alkali metal fullerides may be considered to be intercalation compounds of the fee lattice of the Ceo host formed by filhng the interstitial sites. Superconductivity has been investigated in detail for the alkali metal and mixed alkah metal phases of composition AgCeo where the conduction band is half filled. Critical temperatures as high as 31.3 K (in Rb2CsCeo) have been observed. A clear correlation between unit cell size and Tc is observed, and it has been suggested that the conduction bandwidth controlled by the separation between the molecules is the dominant factor in determining Tc. 

Solid-state NMR can distinguish between lattice and nonlatdce species, but is difficult to use in some cases. Ion exchange capacity is simple however, caution must be used since ion exchange capability has been observed for high-silica materials. The size of the unit cell determined by x-ray diffraction is widely used to determine lattice concentrations, but may be unreliable if the unit cell size is affected by more than lattice concentrations. ... 

Commercially deactivated FCC Beats of varying matrix types and containing a wide range of sodium were characterized by t-plot surface area (ASTM D4365-85) to determine the effect of Na on zeolite and matrix area stability. The Beats were also examined by electron microprobe (Cameca SX50) to determine the Na distribution within a catalyst particle. Some of the Beats were separated into eight age fractions based on a modified sink/float procedure described in the literature (13,14). Bach age fraction was analyzed by ICP, t-plot and zeolite unit cell size (ASTM D3942-91). 

To determine if we could simulate in the laboratory the effect of sodium on conunercially deactivated FCC catalysts, we prepared catalysts containing Na in the range of 0.22 to 0.41 wt% by modifying the catalyst washing procedure and deactivated the samples at 1088 K fa- 4 hours under 1 atm of steam This steaming procedure is commonly used to prepare deactivated catalysts with physical properties (zeolite and matrix surface areas and unit cell size) that match conunercial Beats. 

Besides the asymmetry between monolayers in cytomembranes, two of the more obvious differences between cubic phases and membranes are the unit cell size and the water activity. It has been argued that tire latter must control the topology of the cubic membranes [15], and hence tiiat the cubic membrane structures must be of the reversed type (in the accepted nomenclature of equilibrium phase behaviour discussed in Chapters 4 and 5 type II) rather than normal (type I). All known lipid-water and lipid-protein-water systems that exhibit phases in equilibrium with excess water are of the reversed type. Thus, water activity alone cannot determine the topology of cubic membranes. Cubic phases have recently been observed with very high water activity (75-90 wt.%), in mixtures of lipids [127], in lipid-protein systems [56], in lipid-poloxamer systems [128], and in lipid A and similar lipopolysaccharides [129,130]. 

Many different kinds of errors can affect the measurement of X-ray diffraction data. Incorrect assignment of the space group, badly applied absorption corrections, insufficient data (possibly because the unit cell size was not correctly determined), and the misinterpretation of the Miller indices of Bragg reflections may give rise to data sets unsuitable for a structure determination. In other words, if the experiment is not done properly, the structure will not be determined with the necessary precision, or, perhaps, even at all. 

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