Extra lines

If a spectrum lacks certain Lines or contains extra lines from additional unknown components, or if the true line positions are blurred, fuzzy set theory can improve the matching. 

A hoisting system, as shown in Figure 4-8, is composed of the drawworks, traveling block, crown block, extra line storage spool, various clamps, hooks, and wire rope. 

In terms of chemical equivalence, (or more accurately, chemical shift equivalence) clearly, Ha is equivalent to Ha. But it is not magnetically equivalent to Ha because if it was, then the coupling between Ha and Hb would be the same as the coupling between Ha and Hb. Clearly, this cannot be the case since Ha is ortho to Hb but Ha is para to it. Such spin systems are referred to as AA BB systems (pronounced A-A dashed B-B dashed). The dashes are used to denote magnetic non-equivalence of the otherwise chemically equivalent protons. What this means in practise is that molecules of this type display a highly characteristic splitting pattern which would be described as a pair of doublets with a number of minor extra lines and some broadening at the base of the peaks (Spectrum 5.6). 

These extra lines are often mistakenly thought to be impurity peaks. An in-depth understanding of how they may arise is not really necessary for the purpose of interpretation. What is important is that you instantly recognise the appearance of such spin systems. Check that the system integrates correctly and check that the two halves of the system are symmetrical. Note This phenomenon has nothing whatsoever... 

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

Attempts to isolate mixed halides of tin from mixtures of tin tetrahalides have been unsuccessful because of apparent rapid redistribution of halogen atoms. Existence of such mixed species has been suggested by extra lines ob-... 

The HCP case exhibits one additional signal of the onset of rapid change in vibrational resonance structure. This is the sudden onset of vibrational perturbations at (0, 32, 0) [5]. Local perturbations, where one rotational term curve crosses another, are manifest as level shifts, extra lines, and intensity anomalies [18]. Such perturbations are typically rare at low vib and... 

The extra lines are not due to promoter phases, since they are also found in the pattern of the synthetic spinel FeOj.au, neither are they due... 

Note that you can further refine the appearance of the plot using the tools to create labels, extra lines and arrows. 

The curves showing the lattice constants as functions of composition reveal the existence of a discontinuity in the immediate vicinity of S/Ti = 1.5. If the monochromator photograph of a sulfide with this composition, Ti2S3, is examined closely, the detection of several extra lines, weak and diffuse, suggests the appearance of a superlattice. If this sulfide, Ti2S3, is then prepared at 800° C., the... 

If the separation between two resonances is A Hz and their coupling is J Hz, then the rales above hold if A J. The multiplet is said to be first-order. When AfJ <5, distortions and extra lines appear, and the multiplet is then second-order. See Abraham et a/3 for a good description of how to analyse such spectra. A first-order analysis is adequate for solving all the problems in this workbook, although many of the multiplets are distinctly second-order. 

Alas, things are not as simple as they may have appeared. From the discussions in Chapters 6 and 7 you might be under the impression that typical H NMR spectra exhibit just one sharp signal line for each 1H nucleus (or each set of equivalent H nuclei) and that the same thing is true for 13C spectra as well as for spectra of any other isotope. Actually, this is not usually the case. Instead, the individual signals expected on the basis of the molecule s symmetry are themselves often split into symmetrical patterns (multiplets) consisting of two or more lines. While these extra lines do make a spectrum appear more complex, they also offer valuable structural information that complements the chemical shift data. This chapter explains the source of these extra lines and shows how useful they can be for confirming the structures of molecules. 

From the above example, you can infer that the extent to which the intensity ratios depart from first-order (Pascal s triangle) expectations is a function of A 8v/7. If this ratio is large (A 5v/7 > 10), we describe the spin system as weakly coupled, and the resulting multiplets will exhibit essentially first-order intensity ratios (as do the triplets and quartets in Figures 8.1 and 8.13). But as A 8v/J decreases, second-order effects (multiplet slanting and even the appearance of extra lines) become increasingly apparent. Such a spin system is said to be strongly coupled. 

As the ratio of A 8v (the difference in chemical shift between two coupled nuclei) to J decreases, the relative intensities of the lines in a multiplet deviate further from first-order (e.g., Pascal triangle) ratios. Inner lines (those facing the coupled multiplet) increase in intensity, while outer lines lose intensity. This slanting of the multiplets is one type of second-order effect. At very small values of A Sv/J, not only may extra lines appear in the multiplets but also apparent line positions and spacings may not equate with true chemical shifts and coupling constants (e.g., deceptive simplicity and virtual coupling). 

The same reasoning shows that non-radial planes acquire an extra line at infinity. It follows that projective space may be regarded as affine space plus a plane at infinity. One of the most elegant properties of projective geometry is the principle of duality which asserts that, in a projective plane every definition or theorem remains valid on the consistent interchange of the words line and point. 

More sensitive ESR measurements over a wider magnetic field range find additional resonances in phosphorus- and arsenic-doped material, examples of which are shown in Fig. 5.11. The extra lines (two for phosphorus and four for arsenic) are due to the hyperfine interaction of the electron bound to the donor (Stutzmann and Street 1985). The ESR spectra have exactly the number of lines and relative intensities expected from the nuclear spins of and for phosphorus and arsenic atoms. The splitting of the lines, is proportional to the electron density at the nucleus and is a measure of the localization length, r, of the donor. 

An additional deuterium plasma treatment at 350 °C results in one additional IR absorption line at 2644.4 cm . The frequency ratio of the 3577.3 cm line and the line at 2644.4 cm is 1.35, which is close to the value expected for a harmonic oscillator consisting of a hydrogen atom bound to an oxygen atom (1.37). Based on this, we identify the 3577.3 cm line as a LVM of an 0-H bond. No extra lines appear in the spectra after H+D plasma treatment. This strongly indicates that the defect responsible for the 3577.3 cm line includes a single hydrogen atom. 

Strong polarized lines at 652 cm" and 585 cm" identify the [XeFsF J tetramer, and this is clearly the principal solute species in concentrated solution. The polarized Raman line at 621 cm" and the depolarized line at 508 cm" increase in intensity (relative to 652 cm" ) in more dilute solution their frequencies, relative intensities, and states of polarization correspond with the extra lines in hot liquid xenon hexafluoride, and, a little less closely, with the Raman spectrum of the vapour, (Table 8) which contains only XeFa molecules. We have little hesitation, therefore, in assigning these lines to a monomeric XeFj molecule. It is noteworthy that the... 

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