The Direct Method

The diffracted intensity of an aibitraiy (hkl) peak with an aibitraiy phase i is written (see Chapter 1)  

Knowing the crystalline structure of a phase makes it possible to calculate the structure factors and the eell volume of that phase. Based on this information, the phases we are trying to qnantitatively analyze can be compared in pairs by calculating the ratios between the characteristic peak intensities of the various 

If attention at first is confined to the production of methyl silicone from the previously accepted raw materials, the chemical processes must include reduction of silica to silicon, preparation of the methyl chloride from methane or methanol, reaction of the methyl chloride with silicon, and hydrolysis of the methylchlorosilanes. If the same conventions are used as in the discussion of the,Grignard method, and the methanol process for methyl chloride is elected, the steps are  

These four steps may be summarized in one equation in which the relative combining weights are given below the formulas  

It is evident that this process is simpler in its requirements than the Grignard method and involves fewer chemical operations. Since the silicon need not be chlorinated, no free chlorine is required. The hydrochloric acid produced by the hydrolysis of dimethyldichloro-silane is exactly consumed by the reaction with methanol, so that two 

For production of methylchlorosilanes, copper equivalent to about 10 per cent of the weight of the silicon is preferred as a catalyst. This may be added as a powder to the pulverized silicon and the mixture sintered in a hydrogen furnace, or it may be added in other ways. On a molar basis, this copper requirement represents 0.049 mole of copper per mole of silicon entering into the reaction, and all of it remains behind as the silicon is consumed. It Is at least theoretically possible to recover the copper after the reaction has run its course, but the limited recovery value of this small amount allows only the simplest methods to be considered. 

As in other preparative methods for organosilicon compounds, the direct synthesis produces a mixture of methylchlorosilanes rather than the single compound shown in equation 3. Besides dimethyl-dichlorosilane, the mixture usually contains silicon tetrachloride, tri-chlorosilane, methyltrichlorosilane, methyldichlorosilane, trimethyl-chlorosilane, and even silicon tetramethyl. Under proper conditions, dimethyldichlorosilane is the principal product. Of the other compounds, methyltrichlorosilane usually is next in abundance this substance finds use in the cross-linked methyl silicone resins, or it can be methylated further by the Grignard method to increase the yield of dimethyldichlorosilane. There is no way of recycling it in the direct process, and so supplemental operations are required for the conversion. The interconversion of this and the other minor products of the direct synthesis, involving the exchange of methyl and chlorine groups as desired, has been a special study in itself.10 

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Iterative solution methods are more effective for problems arising in solid mechanics and are not a common feature of the finite element modelling of polymer processes. However, under certain conditions they may provide better computer economy than direct methods. In particular, these methods have an inherent compatibility with algorithms used for parallel processing and hence are potentially more suitable for three-dimensional flow modelling. In this chapter we focus on the direct methods commonly used in flow simulation models. 

Determination of Lignin Content. Lignin content in plants (wood) is determined by direct or indirect methods (21). The direct method includes measurement of acid-insoluble (ie, Klason) lignin after digesting wood with 72% sulfuric acid to solubilize carbohydrates (22). The Klason lignin contents of representative lignifted materials are shown in Table 2. 

There is a direct and an indirect method of measuring specific soil resistivity. The direct method is carried out in the laboratoiy on a soil sample using a soil box as shown in Fig. 3-16. The resistivity of a soil specimen of cross-section, S, and length, I, is measured and the specific resistivity determined ... 

The evaluation methods could be direct, e.g., measuring a containment index, or indirect, e.g., measuring pressure loss or velocity distribution. The direct methods are used to measure the performance of a hood or an inlet during periodic preventive maintenance. Indirect methods are used for verifying or checking on a daily basis (routine checks). How often each method is used depends on the availability of instrumentation and qualified personnel, since direct measurement of a hood s performance can be both expensive and difficult. On the other hand, indirect methods are usually easier to use and can sometimes include inexpensive, continuously monitoring instruments (pressure gauges or velocity indicators). 

In the Direct SCF method, we do. not store the two-electron integrals over the basis functions, we recalculate them on demand every cycle of the HF procedure At first sight, this may seem wasteful, but Conventional methods rely on disk input/output transfer rates whilst Direct methods rely on processor power. There is obviously a balance between processor speed and disk I/O. Just for the record my calculation on aspirin (73 basis functions) took 363 s using the Direct method and 567 s using the Conventional method. 

The dose and dose rate of irradiation are important factors in any radiation grafting system. In the direct method the total dose determines the number of grafting sites, while the dose rate determines the number of grafting sites, and the dose rate determines the length of the grafted branches. The length of the branches is also con-... 

Intermediate methods include the earliest procedure based on Stein s equation [33] and one based on Samuels equation [34]. Among the direct methods is an IR spectroscopic method based on the measurement of the dichroic ratio (R), of amorphous absorption bands. In the investigations [35], the amorphous bands 898 cm" and 1368 cm", for which the angles of transition moment are a898 = 39 and aneg = 80 , respectively, were used. Other methods are spectroscopy of polarized fluorescent radiation [35,36], measurement of color di-... 

For the calculation of the LDA ground-state one can proceed either via the direct" methods, i.e. via the glocal minimization of the total free energy with respect to the electronic degrees of freedom, or via the the diagonalization (for large PW basis-sets necessarily iterative diagonalization) of the KS Hamiltonian in combination with an iterative update of chai ge-density and potential. 

Measurements of the adsorption of inhibitors on corroding metals are best carried out using the direct methods of radio-tracer detection and solution depletion measurements . These methods provide unambiguous information on uptake, whereas the corrosion reactions may interfere with the indirect methods of adsorption determination, such as double layer capacity measurements", coulometry", ellipsometry and reflectivity Nevertheless, double layer capacity measurements have been widely used for the determination of inhibitor adsorption on corroding metals, with apparently consistent results, though the interpretation may not be straightforward in some cases. 

In the direct method, a solution of the ammonium salt is treated with a solution of a strong base (e.g. sodium hydroxide) and the mixture distilled. Ammonia is quantitatively expelled, and is absorbed in an excess of standard acid. The excess of acid is back-titrated in the presence of methyl red (or methyl orange, methyl orange-indigo carmine, bromophenol blue, or bromocresol green). Each millilitre of 1M monoprotic acid consumed in the reaction is equivalent to 0.017032 g NH3 ... 

Direct or indirect methods may be used to determine moisture in dehydrated foods. Indirect methods must be calibrated in terms of direct methods—the most common of which are the oven, distillation, and Fischer methods. Accuracy of the direct methods is difficult to evaluate except by comparison with a chosen reference method. Several reference methods are reviewed, but none can be given an unqualified recommendation as most practical and suitable for all foods. An indirect measure of moisture is the equilibrium vapor pressure of water, which can be measured easily and accurately. Arguments are presented to show that vapor pressure may be a better index of the stability of dehydrated foods than the moisture content, which has been frequently used for this purpose. 

The methods used for the determination of moisture in dehydrated foods have been divided into two classes, the direct and the indirect. The indirect methods, such as the electrical ones, must be calibrated in terms of the direct methods. 

The choice of a particular method for routine measurements of moisture will depend on the nature of the food and the requirements of the analysis. The direct methods are generally more suitable where high precision or accuracy are desired and speed is not important. The indirect methods are usually applicable when speed is essential, but high precision is not required. 

There have been several experimental studies of two-phase flow in which the holdup has been measured, either directly or indirectly. The direct method of measurement involves suddenly isolating a section of the pipe by means of quick-acting valves and then determining the quantity of liquid trapped.00111 Such methods are cumbersome and are subject to errors arising from the fact that the valves cannot operate instantaneously. Typical of the indirect methods is that in which the pipe cross-section is scanned by y-rays and the hold-up is determined from the extent of their attenuation.02 13141... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

In the case where C is a rectangle, it is possible to adopt B = R with further reference to one of the direct methods available for determination... 

The gradient search methods require derivatives of the objective functions whereas the direct methods are derivative-free. The derivatives may be available analytically or otherwise they are approximated in some way. It is assumed that the objective function has continuous second derivatives, whether or not these are explicitly available. Gradient methods are still efficient if there are some discontinuities in the derivatives. On the other hand, direct search techniques, which use function values, are more efficient for highly discontinuous functions. 

The relative stereochemistry of stephadiamine (16) was clarified by X-ray diffraction analysis, using the direct method, and the absolute configuration was solved by the heavy-atom method, using the N-p-bromobenzoyl derivative (6). Stephadiamine (16), a C-norhasubanan alkaloid, is not regarded as a hasubanan congener in the strict sense, but as a new member of oe-amino acid derivatives (6). 

The direct method reported in ref. (Yoshikawa et a]., 1986) will be explained briefly so that the reader may understand the reason why an indirect method is proposed in the present work. 

Formation and transport of radon ) In the present work, lead isotopes were chemically separated from the sample gas as lead sulfide since the formation of lead sulfide was inevitable under the presence of H2S in the fumarolic gas. The lead sulfide was then dissolved in a small amount of concentrated HCI and mixed with the Insta Gel(emulsion scintillator solution, Insta Gel, Packard Inc.) for the liquid scintillation counting. The chemical yield and the volume of the collected non-condensing gas were obtained from the measurement of the activities of Pb-214 and its progeny which were in radioequilibrium with their precursor Rn-222 whose concentration was determined separately by the direct method. 

Radioactivity measurement The radioactivities of lead isotopes and their decay products were measured with TRICARB 3380 liquid scintillation counter (Packard Inc.). The radioisotopes concerned, and their decay charateristies are shown in Figure 2. In the case of the direct method, the absolute radioactivity can be obtained by the integral... 

Results and discussion Some results of the indirect method obtained in the field work are shown in Table II., and they are compared with those of the direct method. Results of the two methods are barely in agreement within one standard deviation. The correction factor of Equation 3. used in the direct method was found not in a large error when the sampling time was less than about two half lives of Rn-220. 

It was also demonstrated that the indirect method was superior for the determination of Rn-220 in a sample in which the ratio Rn-220 / Rn-222 was small. In the direct method, the decay analysis of Equation 1. where the build-up of Po-218 (T1/2 = 3.05 m), Pb-214 (T1/2 = 26.8 m), and Bi-214 (T1/2 = 19.7 m) is taken into account brings about a large uncertainty in the evaluation of the Rn-220 concentration even when the activity itself is not small whereas the decay analysis of Equation 5 gives an unambiguous result since the half lives of Pb-214 and Bi-214 are quite different from that of Pb-212. The lower limit of the Rn-220 concentration that can be determined by the indirect method is calculated to be 0.4 nCi/l for the condition that one-1 iter of gas is sampled and that the radioactivity measurement of Pb-212 is con-... 

One suggestion to explain this discrepancy is that two pathways of fat catabolism are available and that ketone body formation is the resultant of only one type of breakdown.177 This latter type, also called the indirect fat utilization, 182 occurs in the liver the catabolism of fat in the muscle, called the -direct method, either involves no ketogenesis or the ketone bodies are immediately utilized and no accumulation occurs. 

The determinations of absolute rate constants with values up to ks = 1010 s-1 for the reaction of carbocations with water and other nucleophilic solvents using either the direct method of laser flash photolysis1 or the indirect azide ion clock method.8 These values of ks (s ) have been combined with rate constants for carbocation formation in the microscopic reverse direction to give values of KR (m) for the equilibrium addition of water to a wide range of benzylic carbocations.9 13... 

The three dimensional structure was obtained by means of single crystal X-ray diffraction. CuKa radiation, a graphite monochromator, and a photomultiplier tube were used to collect 1825 total reflections on an automated diffractometer. Of these, 1162 were used for the analysis. Figure 2 shows a computer generated drawing of halcinonide. The position of the chlorine atom was not clear from the Patterson map, but the direct method program "MULTAN" gave its position. 

The advantage of fluorescent dyes coupled to primary antibodies is the fast result obtained with the direct method. Another advantage is the possibility to label more than one antigen at the same time. In plant material, it is important to take into account the possible autofluorescence of the tissue. Disadvantages can be the lack of orientation in the tissue and photobleaching of the dyes. The latter problem can often be... 

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