Second moment calculation

It should be noted that relaxation effects play an important role on these results. Indeed it is found that, especially for monomers by also for dimers, the relaxation is larger at fault sites than at normal sites when Nd < 8e /atom while the opposite occurs for Nd 8e /atom. This tends to increase the range of stability of the fault site. It must be emphasized that second moment calculations (13) cannot account for this effect since they are quite insensitive to lateral relaxations. Actually, in such relaxation some distances are expanded whereas some others are compressed and the net effect on the second moment nearly cancels. 

As with graphite oxide, there are currently two views as to the structure of carbon monofluoride. Although detailed X-ray diffraction work suggested a chair arrangement of the sp -hybridized, carbon sheets (Ml), second-moment calculations of the adsorption mode of the fluorine nuclear magnetic resonance suggested that a boat arrangement is more plausible iE2). The structures are illustrated in Fig. 3. 

An instructive illustration of the effect of molecular motion in solids is the proton resonance from solid cyclohexane, studied by Andrew and Eades 101). Figure 10 illustrates their results on the variation of the second moment of the resonance with temperature. The second moment below 150°K is consistent with a Dsi molecular symmetry, tetrahedral bond angles, a C—C bond distance of 1.54 A and C—H bond distance of 1.10 A. This is ascertained by application of Van Vleck s formula, Equation (17), to calculate the inter- and intramolecular contribution to the second moment. Calculation of the intermolecular contribution was made on the basis of the x-ray determined structure of the solid. 

Lithium-doped BPO4, another candidate ceramic electrolyte material for lithium batteries has been studied by Li NMR relaxation and linewidth measurements of samples with Li doping levels up to 20 mol % (Dodd et al. 2000). Comparison of the NMR data with values of the second moment calculated for both random and homogeneous models of Li distribution indicate the existence of Li clusters with an intemuclear distance of 3A, possibly consisting of 1 Li ion fixed at a boron vacancy with additional 2 Li ions in the conduction channels surrounding the vacancy. The atomic jump time, determined from measurements of the Li motional narrowing behaviour, indicate a maximum in the Li ionic mobility at the 10 mol % doping level (Dodd et al. 2000). 

The diamagnetic susceptibility anisotropies and molecular second moments of the electronic charge distributions for COCIF have been calculated by Maksic and Mikac [1303a], and these authors suggested that their calculated values showed that the experimentally derived second moments (calculated from the Zeeman effect in the Stark-modulated microwave... 

The M —H distances are approximately equal to the sum of covalent radii as shown by neutron and X-ray studies. In order to find out the precise structure of metal hydrides, both neutron and X-ray studies are needed. The distances obtained from NMR studies in the solid state based on the second moment calculated from the line shape are too small. This results from the inaccuracy of the Van Vleck equation. The Mn-H distance in [MnH(CO)5] calculated from the second moment of the Van Vleck equation is 128 pm. The longer distance (144 pm) was calculated from NMR data based on the modified Van Vleck equation. " A similar distance was calculated from electron diffraction studies in the gas phase. All these distances are lower than the sum of covalent radii which equals 157 pm. The Mn-H distance in [MnH(CO)5] obtained from neutron diffraction studies equals 160.1 pm. Similar distances were found for other hydride complexes. 

Because the experimental determinations of H and N described here are based on Gaussian chromatographic peaks, the calculations are considered esti mates. More accurate methods for dealing with skewed Gaussian peaks have been described in the literature they are based on finding the variance of the peaks using statistical second-moment calculations. ... 

Early ESR data on LaSb Dy were reported by Davidov et al. (1975b) and Oseroff and Calvo (1978). The results were interpreted by a random stress model and were evaluated by second-moment calculations. The resulting /f-value is much higher compared to that observed on LaS Er. The ESR line of the Fe ground state of dysprosium shows a broad asymmetrical structure and therefore the second-moment analysis can be a first approximation only. 

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