Residual index

The residual index, or R factor, gives a measure of the difference between the observed and calculated structure factors and therefore of how well the structure has refined. It is defined as... 

The progress of iterative real- and reciprocal-space refinement is monitored by comparing the measured structure-factor amplitudes IFobsl (which are proportional to (/obs ) /2) with amplitudes IFca(c I from the current model. In calculating the new phases at each stage, we learn what intensities our current model, if correct, would yield. As we converge to the correct structure, the measured Fs and the calculated Fs should also converge. The most widely used measure of convergence is the residual index, or R-factor (Chapter 6, Section V.E). 

Changes in parameters are found that increase the agreement between measured data and those calculated from the revised model that results from these changes. The positions x, y, and z and the atomic displacement (thermal) parameters B derived for each atom in a preliminary crystal structure are adjusted so as to improve the agreement between the observed structure amplitudes, F hkl) o, and those calculated from the determined model F hkl) c. The progress in improving this agreement is usually monitored by a residual index known as the R value, defined as ... 

The most widely used measure of convergence is the residual index or R-factor, expressing the disagreement between the Fo hkl) and the Fc hkl) values. The most common R-indices are based on F and F. 

The validation of the model obtained ean be made in various ways. A eon-secrated method consists in the evaluation of the so-ealled residual index R, a measure of the global relative error of the ealeulated strueture factor... 

The calculation of Rp in this fashion, while slightly artificial, leads to values for the residual index which can be meaningfully compared to those values found in the literature. When used in conjunction with the large body of crystallographic knowledge available this number provides a useful criterion with which to assess the correctness of the structure. By convention, Rp is normally calculated using only observable reflections and it should be pointed out that adherence to items (2) and (5) above will produce... 

Contributions to the Least Squares Residue and Residual Index... 

It has become customary in X-ray crystallography to describe the agreement between the observed and calculated structure factors by using the residual index, Rp, defined by... 

In a single stage, without liquid recycle, the conversion can be optimized between 60 and 90%. The very paraffinic residue is used to make lubricant oil bases of high viscosity index in the range of 150 N to 350 N the residue can also be used as feedstock to steam cracking plants providing ethylene and propylene yields equal to those from paraffinic naphthas, or as additional feedstock to catalytic cracking units. 

This form of limited-conversion hydrocracking is a process that selectively prepares high quality residues for the special manufacture of base oils of high viscosity index or treating residues having low BMCl for the conversion of heavy fractions to ethylene, propylene, butadiene and aromatics. 

American Petroleum Institute atmospheric residue atmospheric residue hydroconversion American Society for Testing and Materials Association pour la Valorisation des Huiles Lourdes Anstalt fur Verbrennungskraftmaschinen List Bureau of Mines Correlation Index bromine number... 

Figure C2.5.10. The figure gives tire foldability index ct of 27-mer lattice chains witli sets containing different number of amino acids. The sets are generated according to scheme described in [27], The set of 20 amino acids is taken as a standard sample. Each sequence witli 20 amino acids is optimized to fulfil tire stability gap [5]. The residues in tire standard samples are substituted witli four different sets containing a smaller number of amino acids [27]. The foldability of tliese substitutions is indicated by tire full circles. The open diamonds correspond to tire sequences witli same composition. However, tire amino acids are chosen from tire reduced representation and tire resultant sequence is optimized using tire stability gap [5].

Potassium nitrate is being used increasingly on intensive crops such as tomatoes, potatoes, tobacco, leafy vegetables, citms, and peaches. The properties that make it particularly desirable for these crops are low salt index, nitrate nitrogen, favorable N K20 ratio, negligible CU content, and alkaline residual reaction in the soil. The low hygroscopicity of KNO (Table 9) leads to its use in direct appHcation and in mixtures. It is an excellent fertilizer but the high cost of production limits its use to specialty fertilizers. 

Amino acid Three- letter code One- letter code Mass of residue in. b proteins Accessible surface area, 2 nm Hydrophobicity index ionizable side chain Occurrence in n/ proteins, /o Relative mutabihty... 

Concurrent bombardment during film growth affects film properties such as the film—substrate adhesion, density, surface area, porosity, surface coverage, residual film stress, index of refraction, and electrical resistivity. In reactive ion plating, the use of concurrent bombardment allows the deposition of stoichiometric, high density films of compounds such as TiN, ZrN, and Zr02 at low substrate temperatures. 

Esteis aie often chaiacteiized by theic physical piopeities. These include boiling point, freezing point, melting point, density, refractive index, residue or ash... 

Bromine (128 g., 0.80 mole) is added dropwise to the well-stirred mixture over a period of 40 minutes (Note 4). After all the bromine has been added, the molten mixture is stirred at 80-85° on a steam bath for 1 hour, or until it solidifies if that happens first (Note 5). The complex is added in portions to a well-stirred mixture of 1.3 1. of cracked ice and 100 ml. of concentrated hydrochloric acid in a 2-1. beaker (Note 6). Part of the cold aqueous layer is added to the reaction flask to decompose whatever part of the reaction mixture remains there, and the resulting mixture is added to the beaker. The dark oil that settles out is extracted from the mixture with four 150-ml. portions of ether. The extracts are combined, washed consecutively with 100 ml. of water and 100 ml. of 5% aqueous sodium bicarbonate solution, dried with anhydrous sodium sulfate, and transferred to a short-necked distillation flask. The ether is removed by distillation at atmospheric pressure, and crude 3-bromo-acetophenone is stripped from a few grams of heavy dark residue by distillation at reduced pressure. The colorless distillate is carefully fractionated in a column 20 cm. long and 1.5 cm. in diameter that is filled with Carborundum or Heli-Pak filling. 4 hc combined middle fractions of constant refractive index are taken as 3-l)romoaccto])lu iu)nc weight, 94 -100 g. (70-75%) l).p. 75 76°/0.5 mm. tif 1.57,38 1.5742 m.]). 7 8° (Notes 7 and 8). 

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