Refinement procedure

Pyrometa.llurgica.1 Methods. To prepare blast furnace bulhon for commercial sale, certain standards must be met either by the purity of the ores and concentrates smelted or by a series of refining procedures (r6—r8,r20,r21). These separated impurities have market value and the refining operations serve not only to purify the lead, but also to recover valuable by-products. 

Some of this material is reclaimed by ketde melting and refining. However, most scrap is a combination of metallic lead and its aUoying constituents mixed with compounds of these metals, usuaUy oxides and sulfates. Therefore, recovery as metals requires reduction and refining procedures. 

However, simplification of the refining procedure is not always the end result. IncompatibiUty of different cmde oils, which can occur if, for example, a paraffinic cmde oil is blended with a heavy asphaltic oil, can cause sediment formation ia the unrefined feedstock or ia the products, thereby complicating the refinery process (5). 

B3) These variations are related to the refinement procedures much more than to the experimental data [23] and are generally larger than in high resolution structures of small molecules. In MD calculations with harmonic bond lengths and bond angles they are still higher. 

Raman, V. and Pitsch, H., Large-eddy simulation of a bluff-body-stabilized non-premixed flame using a recursive filter-refinement procedure. Combust. Flame, 142, 329, 2005. 

Confort s [14] refinement procedure. Previous studies show that these functions do not increase the likelihood of retrieving the bioactive conformation on the contrary, they have a negative impact [35],... 

Historically (1960 s and 1970 s) mostly used on single crystals, it has since then been generalised for powders using Rietveld refinement procedures. 

The chitobiose unit has been treated as a rigid body, and by using the full-matrix, least-squares, rigid-body, refinement procedure, the structure was refined to an R factor of 40.7%. Visually estimated intensities were used. The structure was found to be free from short contacts, and to be stabilized by an intrachain OH-3—0-5 hydrogen-bond and one interchain N-H—O hydrogen-bond. 

The above algorithm works well for pure compounds and simple mixtures, but it becomes increasingly difficult to assign all peaks properly when complex mixtures are to be addressed. Additional problems arise from the simultaneous presence of peaks due to protonation and alkali ion attachment etc. Therefore, numerous refined procedures have been developed to cope with these requirements. [102] Modem ESI instrumentation is normally equipped with elaborate software for charge deconvolution. 

Space or plane group determination. There can be ambiguities here especially if data are limited in their sampling of reciprocal space. In this case all the possibilities need to be explored with respect to solution and refinement procedures. 

The use of constraints and restraints arise from unrealistic bond lengths and angles. It is a reasonable use of statistical analysis to include prior information in a refinement procedure, and geometry is one such restraint/constraint. Poor geometries are often a consequence of missing data down one axis, invariably the result of the missing cone or lack of an epitaxially grown crystal. This lack of data has a profound effect on the refinement process... 

Diffraction patterns may always be multiplied by a constant factor without changing the physics of the system. In MSLS this is a scaling factor which is needed to scale the observed and calculated intensities to the same order of magnitude. This scaling factor is one of the relinable parameters. However, one has to take care with the definition of this factor. It should be defined in such a way that it is not dependent on the change of any other parameter in the refinement procedure, in particularly the crystal thickness and the absorption parameter. Therefore the actual scaling factor, C, was expressed as function of c, the parameter which was used in the refinement process ... 

Five isotopomers of Sia were studied in Ref (20), and are labeled as follows Si- Si- Si (I) Si- Si- Si (II) Si- Si- Si (III) Si- "Si- Si (IV) Si- Si- °Si (V). Rotational constants for each (both corrected and uncorrected for vibration-rotation interaction) can be found towards the bottom of Table I. Structures obtained by various refinement procedures are collected in Table II. Two distinct fitting procedures were used. In the first, the structures were refined against all three rotational constants A, B and C while only A and C were used in the second procedure. Since truly planar nuclear configurations have only two independent moments of inertia (A = / - 4 - 7. = 0), use of B (or C) involves a redundancy if the other is included. In practice, however, vibration-rotation effects spoil the exact proportionality between rotational constants and reciprocal moments of inertia and values of A calculated from effective moments of inertia determined from the Aq, Bq and Co constants do not vanish. Hence refining effective (ro) structures against all three is not without merit. Ao is called the inertial defect and amounts to ca. 0.4 amu for all five isotopomers. After correcting by the calculated vibration-rotation interactions, the inertial defect is reduced by an order of magnitude in all cases. 

The "refine" procedure starts by assigning a trial set of observations as seedpoints it then tests the remaining observations to see if they are better seedpoints than those already chosen. The test is carried out as follows. The distance from the observation... 

Diamond, R. (1971). Areal-space refinement procedure for proteins. Acta Crystallogr. A 27,436-452. 

The electrostatic Hellmann-Feynman theorem states that for an exact electron wave function, and also of the Hartree-Fock wave function, the total quantum-mechanical force on an atomic nucleus is the same as that exerted classically by the electron density and the other nuclei in the system (Feynman 1939, Levine 1983). The theorem thus implies that the forces on the nuclei are fully determined once the charge distribution is known. As the forces on the nuclei must vanish for a nuclear configuration which is in equilibrium, a constraint may be introduced in the X-ray refinement procedure to ensure that the Hellmann-Feynman force balance is obeyed (Schwarzenbach and Lewis 1982). 

Data analysis procedures have developed substantially over the last few years. In particular, use of least square refinement methods have been developed. Recent progress with theoretical development for the treatment of multiple scattering has resulted in Ugand group refinement such as an imidazole. We can expect further development in this area which ought to lead us to restrained least square refinement procedures for EXAFS data analysis. This type of restrained refinement is commonly used for macromolecular crystallographic structure determination where a similar problem of imderdeterminancy exists... 

One investigation 1) sought more definite information on the effect of molecular structure on toxicity. Although it had been well established that aromatic and olefin compounds were toxic as compared to alkanes, it seemed worth while to pursue this study further, with the idea that if some one compound or series of compounds could be identified as the significant factor in toxicity, it could either be isolated by some refining procedure or be synthesized from other substances. 

The difficulty with this procedure is that simple refinement routines, such as simplex or least squares, lead only to the nearest minimum in the cost function which is unlikely to be the global minimum. The refinement procedure therefore has to be one that randomly samples different parts of configuration space so as to be able to reach different minima, ultimately selecting the global minimum. Two refinement methods have been proposed, simulated annealing and the genetic algorithm. 

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