Free induction decay curve

Transverse relaxation is caused by the distribution and fluctuation of the resonance frequency of the A spins. The distribution-induced relaxation is called free induction decay. The free induction decay curve is the Fourier transform of the spectral shape of the A spins. This spectral shape depends on the intensity and the pulse width of the incident microwave, when the total width of ESR spectrum is large as is the case for radical species in solids. Therefore, the analysis of the free induction decay curve gives no information on the nature of radical species in solids unless the pulse width is narrow enough to cover the entire ESR spectrum. 

The NMR signal obtained from the resonating nuclei after the sample has been irradiated by the pulse is the so-called free-induction decay curve. This curve consists of peaks and valleys. The spectrometer samples the free-induction decay curve at set time intervals and records the data, which are in a time domain. NMR spectra, however, are normally given in terms of frequency and therefore the spectrum must be transformed by use of the Fourier transform pairs ... 

Figure 2. Logarithmic free induction decay curve of one fresh silk fabric sample (thin line) and the corresponding degraded sample (thick line)...

FIGURE 213 Examples of FID (free induction decay) curves, prior to perfonning FT (Fourier transform) to get the corresponding spectra shown on the right of each set [37]. Fast acquisition of FID s is important, the shape of which carries the encoded frequencies and amplitudes of the components of the reaction mixture. 

Parker GW. Calculation of moments of NMR absorption lines from free - induction decay curves. J Chem Phys 1973 58 3274. 

NMR relaxometry Free induction decay (T2 ) or solid echo Spin echo decay (T2) Magnetization recovery curve (7)) Eads (1998)... 

Fig. 2. (a) The free induction decay, G(t) for 19F in a single crystal of CaFi for B0 along [1,0,0]. The experimental points are given by circles and crosses from the CW and pulse measurements, respectively, and the theoretical curve is that of Eq. (14), corresponding to an exponential decay multiplied by a sine function. Note that F(t) is equivalent to G(t) in the present notation. Reproduced with permission from A. Abragam, The Principles of Nuclear Magnetism, p. 121, Oxford University Press, London, 1961. (b) The lineshape in the frequency domain corresponding to the Fourier transform of the theoretical curve. 

The procedure was tested on simulated time domain MRS data where the model data consisted of metabolite peaks at 3.2, 3.0 and 2.0 ppm representing choline, creatine and IV-acetylaspartate (NAA) respectively, with corresponding values of Ak of 1.0, 1.0 and 3.0 units.89 White noise of specified standard deviation, crt, was then added. The Levenberg-Marquardt method requires suitable initial values for each of the nine parameters being fitted. The initial values of the three frequencies were taken as their known values. An exponentially decaying curve with a constant offset parameter was fitted, using a nonlinear least-squares fit, to the envelope of the free induction decay, Mv(t), in order to obtain an initial value for T and for the amplitudes, each of which was taken to be one-third of the amplitude of the envelope. The constant offset was added to account for the presence of the noise. 

The phase relaxation curve was recorded by monitoring the peak intensity of the two-pulse ESE signal as a function of the time interval between the two microwave pulses, x. The relative shape of an ESE signal is determined by the free induction decay, so that it does not depend on x. The phase relaxation takes place between the time of the excitation and the observation, so that t2 = 2x is the time for the phase relaxation. The longitudinal relaxation also causes the decrease in the ESE intensity. However this effect is negligible because the rate of the longitudinal relaxation in solids is usually more than two orders of magnitude lower than the phase relaxation rate. 

X-ray diffraction patterns were recorded on a Siemens D5000 diffractometer using CuKa radiation. Thermogravimetric and differential thermal analysis curves were recorded on a Setaram Setsys 12 thermal analysis station by heating in an argon atmosphere from 25 to 1200 -C at a rate of 5 min". Samples were used untreated. The Pt content was determined by the Service Central d Analyse, CNRS (Vernaison, France) and the microanalyses (C, H) were performed at Complutense University (Madrid, Spain). Na isotherms were determined on a Micromeritics ASAP 2000 analyzer. H MAS NMR, Si MAS NMR and C CP MAS NMR spectra were recorded at 400.13, 79.49 and 100.61 MHz, respectively, on a Broker ACP-400 spectrometer at room temperature. An overall 1000 free induction decays were accumulated. The excitation pulse and recycle time for H MAS NMR spectra were 5 ps and 3 s, respectively, those for Si MAS NMR spectra 6 ps and 60 s and those for C CP MAS NMR spectra 6 ps and 2 s. Chemical shifts were measured relative to a tetramethylsilane standard. Prior to measurement, if necessary, samples were dehydrated in a stove at 423 K for 24 h. 

With regard to point (2) mentioned earlier, because of its linearity, the FFT imparts noise as unaltered from the time domain to the frequency domain. Moreover, the FFT has no possibility of separating noise from the true signal. In an attempt to improve resolution, one tries in vain to increase the total acquisition time, but for longer signals, noise becomes the major content to the encoded signals or free induction decay (FID) curves. 

Spin-lattice relaxation times for the protein protons were measured using the 90°-t-90° pulse sequence. Free induction decay amplitude was measured 15-20 microsec after the end of the second pulse by averaging 30 repetitions. To obtain the obvious double exponential relaxation behavior from the water protons, the first pulse of a 180°-t-90° sequence was attenuated so that the 180° pulse width was about 55 microsec while the second pulse remained near 4 microsec. Experimental considerations led us to believe the errors for the protein Ti values and the slow component of the water Ti curve are about 5% although linear least squares fits indicate better precision. 

FID-DECRA free induction decay direct exponential curve resolution... 

We present a new approach for observation of first-order free-induction-decay (fid), which can sensitively be detected by means of polarization selective devices. FID in Cs vapor is measured with picosecond time resolution, and for the first time beats due to the hyperfine splitting of the ground and first excited state with 9-2 GHz and 1.2 GHz can be observed on the fast decay curve. 

Fourier Transform NMR. In Fourier transform NMR (FTNMR), a repetitive radio frequency (RF) pulse is applied in order to excite all of the nuclei of the particular nuclear species being studied. The sum of the free induction decay (FID) curves from each pulse is analyzed by a Fourier transform method in order to generate the familiar frequency domain spectra. Fundamentally, parameters such as the frequency, intensity, application time of the appropriate RF pulse, and time intervals between these pulses are important variables when using this technique. The principle of the pulsed Fourier transform technique can be found in books covering the fundamental concepts of NMR spectroscopy (58,59). 

The problem we must address is how to recover the resonance frequencies present in a free-induction decay. We know that the FID curve is a sum of oscillating functions, so the problem is to analyze it into its component frequencies by carrying out a Fourier transformation. When the signal in Fig. 13.24a is transformed in this way, we get the frequency-domain spectrum shown in Fig. 13.24b. One Hne represents the Larmor frequency of the A nuclei and the other that of the X nuclei. 

From H pulse NMR, the free induction decay (FID) with a large number of data points can be obtained. The curve fitting for the observed FIDs gives the individual T2 characteristics in the crystalline, amorphous, and interfacial phases [6-12]. Such a resolution into several components has been attempted on a broad-line spectrum of solid polyethylene (PE) [13-16], which reflect the sample morphologies. 

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