V Resonance frequency

The sample (500 mg) was packed into 5 mm OD pyrex tubes for the NMR measurements, which were performed with a Chemagnetics CMX300 Spectrometer, operating at Li and V resonance frequencies of 116.8 and 79.2 MHz respectively. Single pulse excitation sequence was employed. A typical B/2 pulse width was 2.5 ps. For Li, typically 1200 spectral acquisitions were required. Chemical shift references were aqueous solutions of LiCl. 

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

In practice the laser can operate only when n, in Equation (9.2), takes values such that the corresponding resonant frequency v lies within the line width of the transition between the two energy levels involved. If the active medium is a gas this line width may be the Doppler line width (see Section 2.3.2). Figure 9.3 shows a case where there are twelve axial modes within the Doppler profile. The number of modes in the actual laser beam depends on how much radiation is allowed to leak out of the cavity. In the example in Figure 9.3 the output level has been adjusted so that the so-called threshold condition allows six axial modes in the beam. The gain, or the degree of amplification, achieved in the laser is a measure of the intensity. 

Bq field along the -axis, the resonant frequency V is defined by... 

The bracketed term in Eq. (4-60b) describes a Lorentzian line shape for the NMR absorption band. The maximum in the band occurs at the resonance frequency, wq. Expressed in units of X0W0T2/2, the maximum value of x" s 1 at one-half this maximum peak height we find, by substitution, that (wq — w) = IIT. Using w = 2 ttv to convert to frequency (in Hz) gives (vq — v) = 3-7 T 2. However, the peak width is twice this, or... 

As illustrated in Figure 44.42, a resonance peak represents a large amount of energy. This energy is the result of both the amplitude of the peak and the broad area under the peak. This combination of high peak amplitude and broad-based energy content is typical of most resonance problems. The damping system associated with a resonance frequency is indicated by the sharpness or width of the response curve, ci) , when measured at the half-power point. i MAX is the maximum resonance and Rmax/V is the half-power point for a typical resonance-response curve. 

In these equations A and np are the molar fractions of A and P (8 v) = v - vp is the difference between the resonance frequencies of the nuclei in positions A and P, usually determined from the low-temperature limit A is the full-width at half height in the absence of exchange (r - °°) and v is the variable radio frequency of the NMR experiment. 

Fig. 1.24 Two examples of frequency-depen-dent relaxation times - 7"i is plotted as a function of the proton resonance frequency V = ou/2 JI, which was obtained from measurements at different magnetic fields strengths. Left polyisoprene (PI) melts and solutions of the same samples at 19wt-% concentration in cyclohexane. Numbers indicate the average molecular weight. The difference between the melt and solution increases towards lower magnetic fields strengths, the frequency dependence is more pronounced for melts.

We should also remember that a capacitor is only a capacitor for frequencies below its internal self-resonant frequency. That is the point where the impedance of its capacitive portion equals its inductive impedance. Since the two impedances always produce opposite V-/phase relationships (180° apart), at the resonant frequency, they effectively cancel out. 

Take a look at some data I extracted from the Murata database in Figure 4-5. All these are 1 pi 725 V capacitors in the 1206 size, but I am varying their material. You see that though their resonant frequency does not change with material, the better materials have better ESRs, too. So X7R could give you an ESR almost 10 times lower. However, the difference in ESR due to material was not so obvious for lower values of capacitance (probably because then a major part of the ESR is located outside of the actual material (in the interconnects, terminations, etc.). 

Tesla, which corresponds to H resonance frequencies of 8.5 to 900 MHz, respectively) result in large differences in resonance frequency (see Table V for frequencies at B0 = 2.35 T), making it possible to observe each NMR-active nucleus independently. 

The chemical shift (8) is defined as the difference between the resonance position of a nucleus and that of a standard reference compound. It is normally expressed in terms independent of Ho (or the related applied resonance frequency v) ... 

An application of an electrochemical quartz crystal microbalance (EQCM) in the study of the A11/HCIO4 system shows that even at a potential about 0.5 V more negative than the onset of AuO formation (the so-called preoxide region), the resonant frequency of the Au-covered quartz crystal decreases as that of the surface mass increases. A comparison of a voltammogram with the potential dependence of the micro-balance frequency for an Au electrode is shown in Figs. 6a and 6b. 

The shear-mode acoustic wave sensor, when operated in liquids, measures mass accumulation in the form of a resonant frequency shift, and it measures viscous perturbations as shifts in both frequency and dissipation. The limits of device operation are purely rigid (elastic) or purely viscous interfaces. The addition of a purely rigid layer at the solid-liquid interface will result a frequency shift with no dissipation. The addition of a purely viscous layer will result in frequency and dissipation shifts, in opposite directions, where both of these shifts will be proportional to the square root of the liquid density-viscosity product v Pifti-... 

Both the V and Li NMR spectra show multiple vanadium and lithium local environments for the as-synthesized material x = 0.15), and the spectra cannot be explained by using a simple model based on the number of crystallographically distinct vanadium sites. On Li-ion intercalation, the V resonances sharpen and shift to higher frequencies (Figure 15) three sharp resonances along with two broader resonances are clearly resolved for the samples prepared at potentials of 3.4 and 3.0 V (x = 0.3 and 0.5, respectively). This behavior is consistent with solid—solution behavior in this potential range and is ascribed to the presence of localized defects at X close to 0 and electron delocalization for 1 > x > 0.05. Three lithium sites were observed in the Li... 

The displacement in the magnetic resonance frequency of a nucleus as a consequence of the electronic environment in which the nucleus resides. Because moving electrons generate their own magnetic fields, a nucleus surrounded by these electrons experiences an effective field, Neff, which is defined by (1 - a)No, where a is the so-called screening constant and No is the applied magnetic field. A chemical shift is typically reported as a dimensionless displacement (units = parts per million, or simply ppm) from a reference standard. If the magnetic field is varied while the radio frequency v is held constant, then the chemical shift (ppm) equals [//sample ... 

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