Symmetric lineshapes

The amorphous lineshape becomes axially symmetric by -60° and then begins to collapse into a symmetric lineshape. The transformation of the amorphous lineshape from asymmetric to axially symmetric is imprecisely defined because the process which transforms it into a symmetric lineshape becomes dominant before the lineshape becomes completely axially symmetric. 

To describe symmetric lineshapes, Maltempo80 defined linear combinations of normalized Lorentzian and Gaussian lineshapes (hybrid lineshapes) as the function... 

For symmetric lineshapes integrals with odd powers in t vanish, and the moments are given by... 

Figures 14.1(a,b) show typical CP/MAS spectra of two types of PET yarns, an amorphous yarn wound at relatively low speed and a 36% crystalline yarn wound at relatively high speed, respectively [2]. The ethylene and carbonyl carbon peaks of the amorphous yarn are shifted about 1 ppm downfield with respect to the semicrystalline yarn, as opposed to the aromatic carbons which are shifted slightly upheld. Besides differences in chemical shift, the spectrum of the 36% crystalline yarn shows narrower lines with a better S/N ratio than the spectrum of the amorphous yarn. The broader lines in Fig. 14.1(a) are attributed to a broader orientation distribution of polymer molecules, which results in a larger distribution of isotropic chemical shifts. Additional differences between both spectra are observed in the lineshape the ethylene and carbonyl carbon peaks in Fig. 14.1(a) have a symmetric lineshape, whereas, these lines in Fig. 14.1(b) are asymmetric. The asymmetric lineshape is resolvable into two partially overlapping resonances a relatively broad low-field component and a relatively narrow high-field...

The lineshape of an isolated anticrossing is related to the variation with F of (2M 1M,F 2, the fractional 2M) basis function character admixed into the nominal 1 M,F) eigenfunction. The shape of an anticrossing signal depends on the specific methods of excitation and detection (Miller, 1973), but (2M 1M, F) 2 is a crucial factor. For case (1) crossings, each isolated anticrossing signal will have a symmetric lineshape,... 

An underlying question in many of the ESR measurements of the lineshape of the N-donor and its temperature dependence is the possible existence of an additional broad line at a similar g-value to the three-line spectrum. Most authors agree that the three lines in the isolated N-donor spectrum should have symmetric lineshapes and, since there is a slight asymmetry to the full spectrum, this leads to the conclusion that there is another relatively broad ESR line shifted slightly from the three-line spectrum. This could be due to a second donor, a conduction electron spin resonance or a structural defect. A weak signal, possibly due to a Si vacancy, is also observed at higher temperatures (T > 50 K) in some samples. 

In Fig. 13, a difference spectrum which was obtained by subtracting the spectrum at t, = 140 jus from the spectrum at t, = 0-5 fi% is shown. The difference spectrum (C) is considered to represent the other non-crystalline component with the contribution from the crystalline component with shorter T. By subtracting the crystalline contribution, we have a rather broad but symmetric lineshape centring at 31-3 ppm, as is indicated by the broken line in curve C. Since the lineshape can be well approximated by a single Lorentzian distribution function, this non-crystalline component is also assumed to comprise a monophase. The very short transverse relaxation time (which disappeared completely within 100/xs) and the downfield chemical shift characterize this non-crystalline phase as comprising somewhat rigid methylene sequences in a trans-rich conformation. 

Fig. 3 a) 2H NMR static spectnim Pake pattern for the case of an axially symmetric EFG. The symmetric lineshape is a result of the superposition of two transitions, indicated by the dashed and the dotted lines. The angles correspond to the dashed spectrum, b) Definition of vectors and angles in an amphiphilic... 

Experimentally the continuous-wave (CW) EPR experiment is a field-swept experiment in which the microwave frequency (Vc) is held constant and die magnetic field varied. Computer simulations performed in field space assume a symmetric lineshape function,/in Eq. (3) (J(B - B es), CTg), which must be multiplied by dv/dB and assume a constant transition probability across a given resonance [1,29]. Sinclair and Pilbrow [30,31] have described the limitations of fliis approach in relation to asymmetric lineshapes observed in high-spin Cr(III) spectra and the pres-... 

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