Half maximum intensity

In the simplest approach T is the full width of the peak (measured in radians) subtended by the half maximum intensity (FWHM) corrected for the instrumental broadening. The correction for instrumental broadening is very important and can be omitted only if the instrumental broadening is much less than the FWHM of the studied diffraction profile, which is always the case in presence of small nanoclusters. The integral breadth can be used in order to evaluate the crystallite size. In the case of Gaussian peak shape, it is ... 

Figure 5.4 Typical total ion chromatogram by pyrolysis MAB/Tof MS for deposition of 0.5 pi of suspension (about 50,000 cells). The cells were a thermostable direct hemolysin producing V. parahaemolyticus serotype 04 K12. Peak width at half maximum intensity is 20 scans ( 4 seconds).

The reason why one chose to follow the main liquid-crystalline to gel phase transition in DPPC by monitoring the linewidth of the various or natural abundance resonance is evident when we consider the expressions for the spin-lattice relaxation time (Ti) and the spin-spin relaxation time T2). The first one is given by 1/Ti oc [/i(ft>o) + 72(2ft>o)] where Ji coq) is the Fourier transform of the correlation function at the resonance frequency o>o and is a constant related to internuclear separation. The relaxation rate l/Ti thus reflects motions at coq and 2coq. In contrast, the expression for T2 shows that 1/T2 monitors slow motions IjTi oc. B[/o(0) -I- /i(ft>o) + /2(2u>o)], where /o(0) is the Fourier component of the correlation function at zero frequency. Since the linewidth vi/2 (full-width at half-maximum intensity) is proportional to 1 / T2, the changes of linewidth will reflect changes in the mobility of various carbon atoms in the DPPC bilayer. 

In the parallel orientation at a given pore size we observe a gradual increase in the linewidths corresponding to mj values of -3/2, -1/2, 1/2 and 3/2. For a given mj value, the linewidth increases with pore size. The linewidth at half maximum intensity of the mj = -3/2 and mj = -1/2 transitions as a function of pore diameter can be measured directly from the ESR spectra"l5 and are given in Table I. 

The linewidth at half maximum intensity H// is composed of the residual width and a contribution from the distribution 6H, as shown in eq. 6. 

Fig. i.4. (a) Action of a radio-frequency field Bl on a nucleus precessing about direction B0. (b) NMR signal (Av1,2 is the half-maximum intensity line width). 

Since spin-spin relaxation reduces the life-time of a nucleus in a particular spin state to T2 g Tj, the half-maximum intensity line width is expressed more precisely by eq. (1.13), which accounts for spin-spin relaxation. 

By adding eqs. (1.13) and (1.14) one obtains the observed half-maximum intensity line width Avl/2(ohsy. 

Using the temperature dependence of NMR spectra, thermodynamic data of interconversions due to intramolecular mobility can be determined. If the coalescence temperature is known, the rate constant at Tc is calculated according to eq. (3.10). Often, Tc and (vA — vB) are not known exactly. In this case, a rough value for kr can be calculated by measuring the half maximum intensity line widths dv1/2(T, at temperatures near Tc and using eq. (3.11) [107, 108],... 

Very slow molecular motion (tc > 10 9 s/rad at B0 x 2.1 Tesla) leads to an increase in T, while T2 decreases (Fig. 3.20). The signals then broaden (line width at half-maximum intensity zlv1/2 1/7V). Therefore, the more sluggish macromolecules usually give poorly resolved 13C NMR spectra having a bandlike shape. 

Generally it is found that PPT fibres are highly oriented and that those variants with the lowest values of orientation angle exhibit the highest tensile modulus. Indeed the average crystallite orientations derived from azimuthal peak widths at half maximum intensities of the 200 reflections in Kevlar 49 and Kevlar 29 are found to be nine and eleven degrees respectively. 

The rocking curve full width at half maximum intensity (fwhm) was characterized at the 100/001 diffraction for pzt 52/48 thin films with gixrd geometry. Figure 6.12 shows the calculated diffraction pattern distribution for pzt 52/48 thin films based on the lattice parameters obtained from xrd-rsms shown in Figure 6.6. As shown in Figure 6.12, the 1001001 diffraction includes 100 diffraction of c-domains, the 001 diffraction of a-domains and the 100 diffraction of the pseudocubic phase. Therefore, fwhm obtained by this measurement indicates a twist of all these phases. 

The complete desorption analysis described above is rarely used in TPD. Many authors rely on simplified methods, which make use of easily accessible spectral features such as the temperature of the peak maximum, Trrl lx, and the peak width at half-maximum intensity, W. We describe these methods briefly and evaluate their merits. 

Fig. 10 Representative SLS power spectra from water at 25 °C. The three diffraction orders, 4th, 5th and 6th, correspond to k = 26295, 32431 and 38548 m1, respectively. The frequency shift for the 4th order is indicated by/s while the full width at half-maximum intensity for the 5th order is indicated by Afs...

The temperature-dependent Raman spectra are depicted in Fig. 4-27a, b. Figure 4-27a shows the spectra of H2O-I (the water molecules in the inner coordination sphere) from 133-223 K. Figure 4-27b shows the spectra of H2O-II (the water molecules in the outer sphere). The spectra above 223 K are not shown because of the overlap with fluorescence that is observed with the 514.5 nm excitation. Plots of the variations of band frequency with temperature are illustrated in Fig. 4-28a, b for H2O-I and H2O-II. Two discontinuities are observed at 195 5K and 140 5K, indicative of three distinct phases occurring in the temperature range studied, as indicated in Fig. 4-28a. The higher-frequency OH stretch region, as shown in Fig. 4-28b does not show any discontinuities for H2O-I. A plot of full width at half maximum intensity (FWHM) vs. T for H2O-I shows a discontinuity at 140 K (Fig. 4-28c, d). Additional support for these phase transitions was found from the temperature dependences of the UO vibrational mode, lattice vibrations and the NO3 ion vibrations (translations and rotations). 

The precise definition of resolution depends on the lineshape, but usually resolution is taken as the full line width at half maximum intensity (FWHM) on a wavenumber, 8v, or frequency, 8v, scale. 

The rocking-curve method has been applied to semiconductor materials by several workers. Weissmann(8) estimated 5ft as the depth of damage on germanium lapped with No. 305 abrasive (3200 mesh alundum, having nominal particle size of 5fi). On silicon Andrus and Bond (9) found l/2ft depth for a fine polish, 3ft for No. 305 lap, and 10ft for a diamond saw-cut the widths at half-maximum intensity before any etching were 13<... 

The degrees of orientation for the crystallites in the injection-molded specimens of PECs were determined from the azimuthal breadth at half-maximum intensity in the strongest equatorial reflection by X-ray diffraction. Figure 6 showed the degrees of crystallite orientation of the as-molded and the annealed specimens. 

Theoretically, thermal vibration of the atoms causes a very slight increase in the breadth B, measured at half-maximum intensity, of the diffraction lines. However, this expected effect has never been detected [4.2], and diffraction lines are observed to be sharp right up to the melting point, but their maximum intensity gradually decreases. 

By use of Eq. (6-9), we can calculate the resolving power, for the 321 reflections, of the camera used to obtain Fig. 6-9. The camera radius is 2.00 in. (5.08 cm), and the mean 9 value for these reflections is about 65.7°. The line breadth at half maximum intensity is about 0.04 cm. The two component lines of the doublet will be clearly resolved on the film if their separation is twice their breadth (Fig. 6-10). Therefore... 

Many diffraction problems require an accurate measurement of the integrated intensity, or the breadth at half maximum intensity, of a diffraction line on a powder photograph. For this purpose it is necessary to obtain a curve of intensity vs. 20 for the line in question. 

The chief problem in determining particle size from line breadths is to determine B from the measured breadth fiv/ of the diffraction line. Of the many methods proposed, Warren s is the simplest. The unknown is mixed with a standard which has a particle size greater than 1000 A, and which produces a diffraction line near that line from the unknown which is to be used in the determination. A diffraction pattern is then made of the mixture in either a Debye camera or, preferably, a diffractometer. This pattern will contain sharp lines from the standard and broad lines from the unknown, assumed to consist of very fine particles. Let Bg be the measured breadth, at half-maximum intensity, of the line from the standard. Then B is given, not simply by the difference between B and B, but by the equation... 

As we saw in Fig. 6-10, resolution depends both on A20, the dispersion, or separation, of line centers, and on B, the line breadth at half-maximum intensity. The resolution will be adequate if A26 is equal to or greater than 2B. By differentiating the Bragg law, we obtain... 

Line positions cannot be measured with sufficient precision on a chart recording made with a ratemeter. Instead, a scaler is used to determine the count rate at several positions on the line profile, and from these data the position of the line center is calculated. This procedure is particularly necessary when the lines are broad, as they are from hardened steel the line width at half-maximum intensity is then 5°-10° 29. If the line is 8° wide and the stress constant AT, is 86.3 ksi/ deg A20, as given above, a stress of 50 ksi will cause the line to shift by only 7 percent of its width when the specimen is turned through 45°. Measurement of such a small shift requires that the line center be accurately located at each angle ij/. 

The spectral resolution of a detector is defined here as equal to its spatial resolution (in urn ) times the reciprocal linear dispersion of the spectrometer (in nm/um ). It was measured to be 1.5 - 2.5 and 2-4 times poorer for the SPD and SIT, respectively, compared to that of a PMT. All measurements were performed with the same spectometer, utilizing 20 urn slit widths. Because, the proximity focused, microchannel plate (MCP) intensi-fier broadens the line images, the spectral resolution of the ISPD was found to be significantly worse than that of the SPD. Peak widths measured at half maximum intensity were four diodes wide even when only a single diode width was illuminated. 

Classical analysis of the two-state model using parabolic diabatic surfaces produces a Gaussian-shaped IV band having a full-width at half-maximum intensity that is only determined by Umax 14,55... 

Precipitates were smear-mounted and dried on a glass slide for x-ray diffraction analysis using a General Electric x-ray diffractometer and FeKa radiation. An estimate of the size of crystalline particles in the precipitates was made by measurement of the width of the major diffraction peak for the mineral of interest at half-maximum intensity (24). 

In the preceding sections, we have assumed that an absorption line has a Lorentzian shape. If this is not true, then the linewidth cannot be defined as the full width at half maximum intensity. Transitions from the ground state of a neutral molecule to an ionization continuum often have appreciable oscillator strength, in marked contrast to the situation for ground state to dissociative continuum transitions. The absorption cross-section near the peak of an auto-ionized line can be significantly affected by interference between two processes (1) direct ionization or dissociation, and (2) indirect ionization (autoionization) or indirect dissociation (predissociation). The line profile must be described by the Beutler-Fano formula (Fano, 1961) ... 

The quantum efficiency was only given in cd units. The % efficiency listed here was estimated by approximating the EL spectrum as a Gaussian lineshape with a 70 nm full width at half maximum intensity centered at the reported Amax-... 

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