FWHH

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

FIGURE 4.4 Line shapes. Lorentzian (broken lines) and Gaussian (solid lines) line shapes and their first derivatives are given. The outermost vertical lines delimit full width at half height (FWHH) of the absorption lines. 

FIGURE 9.1 Linewidth versus standard deviation. A gaussian distribution of unit amplitude is plotted on an x-axis scale in units of the standard deviation (or sigma). At 3.15x0 the unit intensity has dropped to 0.1%. The linewidth in simulations is usually expressed as the halfwidth at half height (HWHH), which is equal to circa 1.17x0, or as twice this value that is, the full width at half height (FWHH). 

FIGURE 9.3 Linewidth as a function of microwave frequency. The linewidth (FWHH) of the low-field gj-feature is plotted versus the frequency in L-, S-, X-, and Q-band. The left-hand panel is for the ferric low-spin heme in horse heart cytochrome c, and the right-hand panel is for the [2Fe-2S] cluster in spinach ferredoxin. (Data from Hagen 1989.)... 

Figure 54-1 Two Gaussian absorbance bands and their respective first and second derivatives (finite differences). The top spectrum represents a synthetic Gaussian absorbance spectrum, the middle a first derivative and the bottom a second derivative . Note that the ordinate of the first derivative has been expanded by a factor of 10 and the second derivative by another factor of 10. The wavelength spacing between data points is 1 nm. The narrow band has a bandwidth (FWHH) of 20 nm, the broad one is 60 nm.

For a le couple, the Nemstian behavior predicts a peak full width at half-height (FWHH) of 90.6 mV. Real peak FWHH usually differs from that value. This... 

An intriguing and exciting chapter of modem astrophysics was opened by Gillett, Forrest and Merrill in 1973 [1] with their discovery that some astronomical objects emitted a broad band which peaks near 3050 cm". In the ensuing years, astronomers around the world found that this was part of a family of infrared emission features which were emitted by a large number of very different types of astronomical objects. Reviews of the ground breaking observations are in Ref [2] and [3], The other prominent, well-known bands, or features as they are often called, peak near 1610, 1310 , 1160 and 890 cm-1. They are broad, with a FWHH on the order of 30 to 50 cm-1 or more. The peak frequencies do not seem to vary by more than a few wavenumbers from object to object except for the case of the 1310 cm-1 feature in which it can differ by as much as 50 cm-1. 

ISOBARIC IONS AT NOMINAL MASS 124 RESOLUTION 24,000 FWHH... 

To further characterize the mobility of the IRE loop, time-resolved isotropic fluorescence emission decay components of the IRE RNAs were determined as a function of temperature. Some details of the measurements and data assessment will be necessary here to appreciate both the utility of the information and caveats about its literal interpretation. Considering first the TCSPC instrument itself, some uncertainty in the measurements arise from its intrinsic parameters. With 300 nm incident light, the IRF of the photomultiplier tube ranged from 190 to 276 ps full-width at half-height (FWHH). The width of the IRF and the time resolution (32.5 ps/channel) limit the short components that can be reliably extracted from the fit, and certainly those <200 ps will have large errors on their amplitudes and lifetimes. Fluorescence emission decay components as short as 9—20 ps (Larsen et al., 2001) and 30—70 ps (Guest el al., 1991) (and much shorter by Wan et al., 2000) have been measured for 2AP in a stacked conformation, but in our instrument, a fit to such a short lifetime would be inaccurate. 

The photophysical properties of terphenyl-based acyclic (22a) and cyclic hemispherands (22c, 22d, see fig. 27) have been investigated in organic solvents and in KBr pellets (1 wt%) with the purpose of introducing them later in optical amplifiers (Sloofif et al., 1998). Absorption cross sections for the 1.54 pm emission, which is quite broad with fwhh = 70 nm, amount to 0.62, 1.1, and 0.93 x 10 20 cm2 for [Er(22a)], [Er(22c)] and [Er(22d)], respectively. The best photoluminescence intensities are obtained with the cyclic ligands. The optical gain of the complexes doped into a polymer channel waveguide is on the order of 1.7 dB cm-1, while the threshold power is as low as 1.4 mW. 

The intensity ratio and the ratio of the full widths of the half height (FWHH) of the CH2 antisymmetric and symmetric stretching bands for x = 0 and 1.0 are 1 1.08 and 1 1.19 (intensity ratio) and 1 0.813 and 1 0.813 (FWHH ratio), respectively. In addition, the intensity of the CH3 asymmetric stretching band for x = 0 is appreciably lower than that for x = 1.0. These results... 

The linewidth of VH spectrum for the fluid at 7.0 MPa is as broad as about 54 cm (FWHH), from which the rotational relaxation time is calculated to be as short as about 0.3 ps. This may be based upon the fact that the density of the fluid is so low that the molecule can reorientate with small perturbation the collision rate is still low at this density compared with that in the liquid. 

FIGURE 12.14 (a) Plot of the wave number and bandwidth (full width at half height) of the C-C raman peaks for different SiC fibers after various thermal treatment in air or in nonoxidizing atmospheres, (b) Comparison between ultimate tensile strength and sp peak FWHH as a function of thermal treatment for SiC Hi Nicalon fibers. (Adapted from Colomban, P., Raman microscopy and imaging of ceramic fibers in CMCs and MMCs, Ceramic Trans., 103, 517, 2000. With permission.)... 

The corrected FWHHs can be used to ftirther characterize the crystal size (more precisely the size of the mean coherently scattering domain, MCD) in the various crystallographic directions if this is smaller than ca.lOO nm. For example, small hematite crystals are often less developed in the [001]... 

Fig. 3-10. Apparent shift of major XRD peaks as a function of corrected width at half height (FWHH) for goethite (upper) and hematite (lower). From Schulze, (1984) with permission and Stanjek, (1991) with permission.

Figure 5 shows the results for model T. The calculated spectra were obtained from Gaussian convolution applied to the election transition probabilities Irom the Ni Is orbital with a full-width at half-height (FWHH) of 1.0 eV. The energy scale for the ceilculated spectra was calibrated by assigning the calculated Is —> 3d transition to the energy of the pre-edge peak in the each recorded XANES spectra. The calculated spectra have three peaks, which however, have a poor fit to the observed one at the positions arrowed, especially, the point II. 

Reactant gases can be introduced into the microreactor as steady flow s or transient inputs with pulse widths (FWHH) of 250 fdsec. Reaction products are analyzed in realtime using a quadrupole mass spectrometer. Pulses from separate valves can be introduced as sets of pulses of predetermined length or in a pump-probe format alternating between two valves. 

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