Refinement problems

The command MORE m sets the amount of output into the. 1st file. MORE 0 gives the least and MORE 3 the most verbose output. The default value for m is 1. 

The interface between the crystallographer and author of a scientific publication involving a crystal stmcture on one side and the reader of this publication as well as electronic databases on the other side is the Crystallographic Information File (also known as the. cif file) as introduced by the International Union of Crystallography (Hall etal. 1991). 

If the command ACTA appears in the header of an. ins file, SHELXL generates such a. cif file. ACTA automatically sets the BOND, fmap 2, plan and LIST 4 instructions and ACTA cannot be combined with other fmap or LIST commands. Torsion angles defined by CONF and hydrogen bonds defined by HTAB are also written into the. cif file, while quantities defined by RTAB and MPLA are only tabulated in the. 1st file. 

There are many more or less difficult problems a crystallographer can encounter when refining a crystal stmcture. The most prominent problems are twiiuiing, disorder, pseudo-symmetry and atom type ambiguities. A whole set of additional difficulties is related to the refinement of protein structures. 

The following chapters are intended to address the most common problems in a way that can easily be understood by scientists who have basic crystallographic knowledge and a minimum of experience refining simple crystal stmctures. 

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Refining problems resulting from Federal and State... 

The effect of grey boundary condition (partial reflection caused by particle contact) in the A+A -A 0 ld-lattice reaction was simulated in [106] whereas more refined problem for the combined reaction... 

Most of the refinement problems on peptides obtained from polymer phase are characterized by the molecular similarity of the main product and its contaminations. It is... 

Following certain refining processes like catalytic cracking, sizeable amounts of nitrogen can appear in light cuts and cause quality problems such as instability in storage, brown color, and gums. 

The refining industry generally seeks either to eliminate asphaltenes or to convert them to lighter materials because the presence of heteroelements cause pollution problems, e.g., sulfur and nitrogen, catalyst poisoning, and corrosion (formation of metal vanadates during combustion). 

Separation of families by merely increasing the resolution evidently can not be used when the two chemical families have the same molecular formula. This is particularly true for naphthenes and olefins of the formula, C H2 , which also happen to have very similar fragmentation patterns. Resolution of these two molecular types is one of the problems not yet solved by mass spectrometry, despite the efforts of numerous laboratories motivated by the refiner s major interest in being able to make the distinction. Olefins are in fact abundantly present in the products from conversion processes. 

For a long time the official specifications for diesel fuel set only a mciximum viscosity of 9.5 mm /s at 20°C. Henceforth, a range of 2.5 mm /s minimum to 4.5 mm /s maximum has been set no longer for 20°C but at 40°C which seems to be more representative of injection pump operation. Except for special cases such as very low temperature very fluid diesel fuel and very heavy products, meeting the viscosity standards is not a major problem in refining. 

Finally, there are some limits regarding LPG fuels butadiene content (0.5 wt. % maximum, ISO 7941), the absence of hydrogen sulfide (ISO 8819) and copper strip corrosion (class 1, ISO 6251) which are not usually problems for the refiner. 

It is mainly in cold behavior that the specifications differ between bome-heating oil and diesel fuel. In winter diesel fuel must have cloud points of -5 to -8°C, CFPPs from -15 to -18°C and pour points from -18 to 21°C according to whether the type of product is conventional or for severe cold. For home-heating oil the specifications are the same for all seasons. The required values are -l-2°C, -4°C and -9°C, which do not present particular problems in refining. 

For the refiner, the main problem is to meet the specifications for kinematic viscosity and sulfur content. Dilution by light streams such as home-heating oil and LCO, and selection of feedstocks coming from low-sulfur crude oils give him a measure of flexibility that will nevertheless lead gradually to future restrictions, most notably the new more severe antipollution rules imposing lower limits on sulfur and nitrogen contents. 

To avoid these problems, refiners commonly use additives called detergents" (Hall et al., 1976), (Bert et al., 1983). These are in reality surfactants made from molecules having hydrocarbon chains long enough to ensure their solubility in the fuel and a polar group that enables them to be absorbed on the walls and prevent deposits from sticking. The most effective chemical structures are succinimides, imides, and fatty acid amines. The required dosages are between 500 and 1000 ppm of active material. 

For the refiner, the reduction in benzene concentration to 3% is not a major problem it is achieved by adjusting the initial point of the feed to the catalytic reformers and thereby limiting the amount of benzene precursors such as cyclohexane and Cg paraffins. Further than 3% benzene, the constraints become very severe and can even imply using specific processes alkylation of benzene to substituted aromatics, separation, etc. 

The presence of these acids in crude oils and petroleum cuts causes problems for the refiner because they form stable emulsions with caustic solutions during desalting or in lubricating oil production very corrosive at high temperatures (350-400°C), they attack ordinary carbon steel, which necessitates the use of alloy piping materials. 

Spectroscopy is the most important experimental source of infomiation on intemiolecular interactions. A wide range of spectroscopic teclmiques is being brought to bear on the problem of weakly bound or van der Waals complexes [94, 95]. Molecular beam microwave spectroscopy, pioneered by Klemperer and refined by Flygare, has been used to detemiine the microwave spectra of a large number of weakly bound complexes and obtain stmctiiral infomiation... 

In most engineering problems the boundary of the problem domain includes curved sections. The discretization of domains with curved boundaries using meshes that consist of elements with straight sides inevitably involves some error. This type of discretization error can obviously be reduced by mesh refinements. However, in general, it cannot be entirely eliminated unless finite elements which themselves have curved sides are used. 

All numerical computations inevitably involve round-off errors. This error increases as the number of calculations in the solution procedure is increased. Therefore, in practice, successive mesh refinements that increase the number of finite element calculations do not necessarily lead to more accurate solutions. However, one may assume a theoretical situation where the rounding error is eliminated. In this case successive reduction in size of elements in the mesh should improve the accuracy of the finite element solution. Therefore, using a P C" element with sufficient orders of interpolation and continuity, at the limit (i.e. when element dimensions tend to zero), an exact solution should be obtaiiied. This has been shown to be true for linear elliptic problems (Strang and Fix, 1973) where an optimal convergence is achieved if the following conditions are satisfied ... 

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