Practical difficulties

In theory, the Hanawalt method should lead to the positive identification of any substance whose diffraction pattern is included in the card file. In practice, various difficulties arise, and these are usually due either to errors in the diffraction pattern of the unknown or to errors in the card file. 

These remarks on abnormal intensities are not meant to suggest that successful use of the Hanawalt method requires extremely accurate intensity measurements. If reasonable care has been taken to minimize preferred orientation, then it is often enough to be able to list the diffraction lines in the correct order of decreasing intensity. 

Errors in the card file itself are generally more serious, because they may go undetected by the investigator and lead to mistaken identifications. Many such errors existed in the earlier editions of the file, but critical editing by members of the JCPDS has resulted in the removal of incorrect data and in the labeling of doubtful data as being of low reliability. Moreover, the JCPDS supports continuing work at the National Bureau of Standards [14.5] and elsewhere, in which the diffraction patterns of pure, well-characterized specimens are carefully prepared and the data added to the file. Most of the high-quality, starred patterns in the card file, such as that in Fig. 14-1, have been obtained at the NBS. 

Whenever any doubt exists in the investigator s mind as to the validity of a particular identification, he should prepare his own standard pattern. Thus, if the unknown has been tentatively identified as substance X, the pattern of pure X should be prepared under exactly the same experimental conditions used for the pattern of the unknown. Comparison of the two patterns will furnish positive proof, or disproof, of identity. 

The Hanawalt method fails completely, of course, when the unknown is a substance not listed in the card file, or when the unknown is a mixture and the component to be identified is not present in sufficient quantity to yield a good diffraction pattern. The latter effect can be quite troublesome, and, as mentioned in Sec. 12-4, mixtures may be encountered which contain more than 50 percent of a particular component without the pattern of that component being visible in the pattern of the mixture. 

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VER in liquid O 2 is far too slow to be studied directly by nonequilibrium simulations. The force-correlation function, equation (C3.5.2), was computed from an equilibrium simulation of rigid O2. The VER rate constant given in equation (C3.5.3) is proportional to the Fourier transfonn of the force-correlation function at the Oj frequency. Fiowever, there are two significant practical difficulties. First, the Fourier transfonn, denoted [Pg.3041]

Though the solution procedure sounds straightforward, if tedious, practice difficulty is encountered immediately because of the implicit nature of the available flux models. As we saw in Chapter 5 even the si lest of these, the dusty gas model, has solutions which are too cumbersc to be written down for more than three components, while the ternary sol tion itself is already very complicated. It is only for binary mixtures therefore, that the explicit formulation and solution of equations (11. Is practicable. In systems with more than two components, we rely on... 

The excess chemiccil potential is thus determined from the average of exp[—lT (r )/fe In ensembles other than the canonical ensemble the expressions for the excess chem potential are slightly different. The ghost particle does not remain in the system and the system is unaffected by the procedure. To achieve statistically significant results m Widom insertion moves may be required. However, practical difficulties are encounte when applying the Widom insertion method to dense fluids and/or to systems contain molecules, because the proportion of insertions that give rise to low values of y f, dramatically. This is because it is difficult to find a hole of the appropriate size and sha... 

Practical difficulties in using concentrated (> 72 % perchloric acid) and the fact that the/f function is known only up to 60 % perchloric acid, reduce the value of these media for the study of nitration. 

For deactivated compounds this limitation does not exist, and nitration in sulphuric acid is an excellent method for comparing the reactivities of such compounds. For these, however, there remains the practical difficulty of following slow reactions and the possibility that with such reactions secondary processes might become important. With deactivated compounds, comparisons of reactivities can be made using nitration in concentrated sulphuric acid such comparisons are not accurate because of the behaviour of rate profiles at high acidities ( 2.3.2 figs. 2.1, 2.3). 

It is, however, much easier to write such statements than to achieve perfection in practice. Some idea of the practical difficulties are vividly illustrated in Figure 8.18 due to Clegg which shows the complex interrelations of process variables in an extrusion process. 

A practical difficulty which arises during injection moulding of reinforced plastics is the increased wear of the moulding machine and mould due to the abrasive nature of the fibres. However, if hardened tool steels are used in the manufacture of screws, barrels and mould cavities then the problem may be negligible. 

Measurements show that the velocity has a fairly constant level in the occupied zone even far downstream from the wall with the cooling device. The flow is plane, and general experience indicates that the velocity in a plane stratified flow is constant and independent of the distance from the inlet device. Prediction of the flow by coinpurational fluid dynamics shows a similar velocity level in the hall. - The full-scale measurements shown in Fig. 12.33 indicate a very low velocity in most of the hall due to the practical difficulties in obtaining a correct load during the full-scale experiment. 

Thomas, G. O., and Oakley, G. L. 1993. On Practical Difficulties Encountered When Testing Flame and Detonation Arresters to BS 7244. Trans. IChemE, 71, PartB, 187-193. 

The use of hexafluoroisopropanol (HFIP) as an SEC eluent has become popular for the analysis of polyesters and polyamides. Conventional PS/DVB-based SEC columns have been widely used for HFIP applications, although the relatively high polarity of HFIP has led to some practical difficulties (1) the SEC calibration curve can exhibit excessive curvature, (2) polydisperse samples can exhibit dislocations or shoulders on the peaks, and (3) low molecular weight resolution can be lost, causing additive/system peaks to coelute with the low molecular weight tail of the polymer distribution... 

Molecular construction for a protein chain is just about impossible using the Z-matrix (unless you are particularly good at crossword puzzles). As 1 mentioned in Chapter 10, there are also immense practical difficulties associated with symmetric, cyclic and linear structures, and as time went by people began to question the use of the Z-matrix. 

The practical difficulties are considerable These include the recording of realtime events and minimization of the duration of the laser pulse. Special mode-locked lasers are used to generate the abrupt pulses needed, and optical delays can use the velocity of light to provide the timing. 

The use of HF is attended by certain practical difficulties. For this reason, HF is often used in the form of a less-volatile complex with an /V-donor base. The... 

The reaction was followed by observing the appearance of the yellow colour of Ce(IV) at 400 m, with Pb(IV) present in excess concentration. Pb(IV) was varied in the region 8.6 x 10 M to 4.4 x 10 M while Ce(III) was kept at 4 x 10 M. A practical difficulty encountered was the photochemical instability of Ce(IV) acetate. Under the above conditions and in the temperature range 30-47 °C, the reaction is strictly first-order in each reactant. The observed rate coefficient at 30.0 °C is 1.48x10" l.mole sec and the apparent activation energy and... 

Undoubtedly the establishment of toxicological research organizations will be costly, but the cost will be much less than the cost of not establishing them. There are many difficulties to be faced, but none is greater than the practical difficulties which manufacturers of modern synthetic chemicals continually face in their visions of new products or in their attempts at more economic production of well known products. 

The method of steepest descent uses only first-order derivatives to determine the search direction. Alternatively, Newton s method for single-variable optimization can be adapted to carry out multivariable optimization, taking advantage of both first- and second-order derivatives to obtain better search directions1. However, second-order derivatives must be evaluated, either analytically or numerically, and multimodal functions can make the method unstable. Therefore, while this method is potentially very powerful, it also has some practical difficulties. 

One fundamental practical difficulty with both the direct and indirect search methods is that, depending on the shape of the solution space, the search can locate local optima, rather than the global optimum. Often, the only way to ensure that the global optimum has been reached is to start the optimization from different initial points and repeat the process. 

Occasionally, a component that already exists in the process can be used as the mass separation agent, thus avoiding the introduction of extraneous material. However, clearly in many instances, practical difficulties and excessive cost might force the use of extraneous material. 

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