Single line method

Calculation of mean crystallite size, lattice strain and frequency distributions of crystallite sizes from the same XRD line-profiles used for crystallinity determinations. In addition to the application of the Scherrer equation, two single-line methods were used the variance method of Wilson (1963) (Akai and To th 1983 Nieto and Smchez-Navas 1994), and the Voigt method of Langford (1978) in combination with single-line Fourier analysis (Akai et al. 1996, 1997, 2000 Warr 1996 Jiang et al. 1997 Li et al. 

Two newer areas of implantation have been receiving attention and development. Focused ion beams have been iavestigated to adow very fine control of implantation dimensions. The beams are focused to spot sizes down to 10 nm, and are used to create single lines of ion-implanted patterns without needing to create or use a mask. Although this method has many attractive features, it is hampered by the fact that the patterning is sequential rather than simultaneous, and only one wafer rather than many can be processed at any one time. This limits the production appHcations of the technique. 

By incorporating the entire analytical scheme (enzyme reaction and electrochemical detection) into the flow system a great improvement in precision can be realized. Sample manipulation is minimized because only a single injection into the flow system is required versus sampling of aliquots for the off-line method. Precision is also improved because the timing of the enzyme reaction and detection are much better controlled in the flow system. Finally, less of both enzyme and sample are needed with on-line enzyme reactor methods. 

The most direct information on the state of cobalt has come from Mossbauer spectroscopy, applied in the emission mode. As explained in Chapter 5, such experiments are done with catalysts that contain the radioactive isotope 57Co as the source and a moving single-line absorber. Great advantages of this method are that the Co-Mo catalyst can be investigated under in situ conditions and the spectrum of cobalt can be correlated to the activity of the catalyst. One needs to be careful, however, because the Mossbauer spectrum one obtains is strictly speaking not that of cobalt, but that of its decay product, iron. The safest way to go is therefore to compare the spectra of the Co-Mo catalysts with those of model compounds for which the state of cobalt is known. This was the approach taken... 

Differences in calibration graph results were found in amount and amount interval estimations in the use of three common data sets of the chemical pesticide fenvalerate by the individual methods of three researchers. Differences in the methods included constant variance treatments by weighting or transforming response values. Linear single and multiple curve functions and cubic spline functions were used to fit the data. Amount differences were found between three hand plotted methods and between the hand plotted and three different statistical regression line methods. Significant differences in the calculated amount interval estimates were found with the cubic spline function due to its limited scope of inference. Smaller differences were produced by the use of local versus global variance estimators and a simple Bonferroni adjustment. 

The single and centroid linking methods do not always join clusters in. the same order as in the previous example. Figure 4.12 shows an example where these methods yield different dendrograms. If the single-link method is used, the clustering proceeds as follows (solid lines in Figure 4.12) ... 

One method of analysis of an element is based on the assumption that it can be measured using a single line, provided that line can be isolated from the rest of the spectrum. This is the basis of the method that uses equilibrated filters. The technique, used to relate the concentration of interest to the difference between two measurements, uses filters placed between the sample (or reference) and a counter of the Geiger-Muller type ... 

There are several reports of T1 measurement techniques in specialized applications such as single line spectra, where the FID is directly integrated (Cantor and Jonas, 1976 Matson, 1977), a rather fast single scan FT method to observe relaxation times of unstable compounds (Kaptein et al., 1976), and a very special technique to measure extremely long 7j values of very weak signals such as that from 109Ag and other metal nuclei (Kronenbitter and Schwenk, 1977). 

It is important to appreciate that the colorants in products other than commercial sugars have been successfully defined by the new colorimetric techniques. Application to vegetable oils was made by McNicholas,36 who showed existence of a spread of the chromaticity points over an appreciable area instead of along a single line, but there was a sufficient degree of correlation for the method to be useful. The grading of lubricating oils has also been successfully performed, as shown by a study by Judd, Plaza and Belknap.39... 

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