Gram refiner

A few industrial catalysts have simple compositions, but the typical catalyst is a complex composite made up of several components, illustrated schematically in Figure 9 by a catalyst for ethylene oxidation. Often it consists largely of a porous support or carrier, with the catalyticaHy active components dispersed on the support surface. For example, petroleum refining catalysts used for reforming of naphtha have about 1 wt% Pt and Re on the surface of a transition alumina such as y-Al203 that has a surface area of several hundred square meters per gram. The expensive metal is dispersed as minute particles or clusters so that a large fraction of the atoms are exposed at the surface and accessible to reactants (see Catalysts, supported). 

With data averaged in point group m, the first refinements were carried out to estimate the atomic coordinates and anisotropic thermal motion parameters IP s. We have started with the atomic coordinates and equivalent isotropic thermal parameters of Joswig et al. [14] determined by neutron diffraction at room temperature. The high order X-ray data (0.9 < s < 1.28A-1) were used in this case in order not to alter these parameters by the valence electron density contributing to low order structure factors. Hydrogen atoms of the water molecules were refined isotropically with all data and the distance O-H were kept fixed at 0.95 A until the end of the multipolar refinement. The inspection of the residual Fourier maps has revealed anharmonic thermal motion features around the Ca2+ cation. Therefore, the coefficients up to order 6 of the Gram-Charlier expansion [15] were refined for the calcium cation in the scolecite. 

Rhenium is the 78th most common element found on Earth, which makes it somewhat rare. During the early twentieth century, it required the processing of about a 1,000 pounds of earth to secure just one pound of rhenium, resulting in a price of about 10,000 per gram. Thus, there were few uses for rhenium. Later in the century, unproved mining and refining techniques reduced the price. Today, the United States produces about 1,000 pounds of rhenium per year, and the world s total estimated supply is only about 400 tons. 

The actual situation with regard to the purity of most of the actinide metals is far from ideal. Only thorixun (99), uranium 11,17), neptunium 20), and plutonium 60) have been produced at a purity > 99.9 at %. Due to the many grams required for preparation and for accurate analysis, it is probable that these abundant and relatively inexpensive elements (Table I) are the only ones whose metals can be prepared and refined to give such high purities, and whose purity can be verified by accurate analysis. The purity levels achieved for some of the actinide metals are listed in Table II. For actinium (Ac), berkelium (Bk), californium (Cf),... 

The light actinide metals (Th, Pa, and U) have extremely low vapor pressures. Their preparation via the vapor phase of the metal requires temperatures as high as 2375 K for U and 2775 K for Th and Pa. Therefore, uranium is more commonly prepared by calciothermic reduction of the tetrafluoride or dioxide (Section II,A). Thorium and protactinium metals on the gram scale can be prepared and refined by the van Arkel-De Boer process, which is described next. 

Processors make annatto colors available as a refined powder, soluble in water at pH values above 4.0 (solubility about 10 grams in 100 milliliters of distilled water at 25°C). in an acid-soluble form, in an oil-soluble form, in a water- and oil-soluble form, and in a variety of hues ranging from delicate yellows to hearty orange. Annatto extract is frequently mixed with turmeric extract to obtain various hues. 

In the intervening decade since the inception of GRAM, numerous refinements to the basic algorithm have been published. Wilson, Sanchez, and Kowalski [25] proposed three initial improvements. Inserting R, + R2 for R, in Equation 12.8 solves stability problems encountered when R2 contains components absent in R,. Here, the diagonal matrix A now contains the fractional contribution, e.g., Att = 0 if the th species is absent in R2 and Att = 1 if the Hh species is absent in R,. Second, the significant joint row and column spaces of R, and R2 can be more rapidly calculated with a NIPALS-based algorithm than with the SVD. Finally, the joint row... 

Preparative techniques used by industry at a reduced scale of production include adsorption, crystallization, zone refining, filtration, and electrolysis. The techniques of gas and liquid chromatography provide products of relatively high purity but have resisted spectacular scale up they are used in preparative work at a lower level of productivity (usually grams to kilog-rams/day) with columns 0.1 m or more in diameter (see Figure 1.2). 

However, these refinements are made at a heavy cost in the observation-to-parameter ratio. The third-order terms, Cyk, of the Gram Charlier expansion add ten more parameters per atom to the nine Uy terms. These expressions are therefore only used when the experimental data are of exceptionally high quality, as in the neutron diffraction analysis of ice, Ih, discussed in Part IV, Chapter 21. They may also be necessary in experimental deformation density analysis, where a very precise description of the atomic thermal motion is required. 

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