Free induction decay sampling

After the pulse, we wait for a short whilst (typically a few microseconds), to let that powerful pulse ebb away, and then start to acquire the radio frequency signals emitted from the sample. This exhibits itself as a number of decaying cosine waves. We term this pattern the free induction decay or FID (Figure 1.3). 

The zincblende (ZB), or sphalerite, structure is named after the mineral (Zn,Fe) S, and is related to the diamond structure in consisting entirely of tetrahedrally-bonded atoms. The sole difference is that, unlike diamond, the atoms each bond to four unlike atoms, with the result that the structure lacks an inversion center. This lack of an inversion center, also characteristic of the wurtzite structure (see below), means that the material may be piezoelectric, which can lead to spurious ringing in the free-induction decay (FID) when the electric fields from the rf coil excite mechanical resonances in the sample. (Such false signals can be identified by their strong temperature dependence due to thermal expansion effects, and by their lack of dependence on magnetic field strength). 

Fig. 10.1. The top panel shows the free induction decay (FID) acquired for a sample of strychnine (1) at an observation frequency of 500 MHz. The spectrum was digitized with 16 K points and an acquisition time of 2 s. Fourier transforming the data from the time domain to the frequency domain yields the spectrum of strychnine presented as intensity versus frequency shown in the bottom panel.

The so-called static dephasing regime (SDR) predicts a linear dependence of I/T2 on the magnetic moment of the particles in solution (22, 25). This regime describes the transverse relaxation of homogeneously distributed static protons in the presence of static, randomly distributed point dipoles. The free induction decay rate, I/T2, is then proportional to the part of the sample magnetization due to the dipoles (p), M = rap, where ra is the concentration... 

Nuclear Magnetic Resonance (NMR) Spectroscopy. Longitudinal and transverse relaxation times (Ti and T2) of 1H and 23Na in the water-polyelectrolytes systems were measured using a Nicolet FT-NMR, model NT-200WB. T2 was measured by the Meiboom-Gill variant of the Carr-Purcell method (5). However, in the case of very rapid relaxation, the free induction decay (FID) method was applied. The sample temperature was changed from 30 to —70°C with the assistance of the 1180 system. The accuracy of the temperature control was 0.5°C. 

For large-weight Zn + complexes with broad (50-150 kHz) second-order quadrupolar powder patterns Zn QE NMR may be an experimental challenge. In such cases the sensitivity must be enhanced by isotope enrichment combined with, e.g., cross polarization (CP) from H ", low-temperature acquisition or sampling of the free-induction decay (FID) in the presence of a train of refocusing pulses. ... 

The laser heating technique can be applied to perform temperature jumps by irradiating short laser pulses at the sample container. Ernst et al. (54) used such a temperature jump protocol to perform stop-and-go experiments. After the start of the laser pulse, the temperature inside the sample volume is raised to the reaction temperature, the conversion of the adsorbed reactants proceeds, and the H MAS NMR measurement is performed. After the laser pulse is stopped, the temperature inside the sample volume decreases to ambient temperature, and the C MAS NMR measurement is made. Subsequently, the next laser pulse is started and, in this way, the reaction is recorded as a function of the reaction time. By use of the free-induction decay and the reaction time as time domains and respectively, a two-dimensional Fourier transformation leads to a two-dimensional spectrum, which contains the NMR spectrum in the Ej-dimension and the reaction rate information in the Ts-dimension (54,55). 

Th4Hi5. Three kinds of information are obtained from the samples of Th4H15 information on rigid lattice structure from free induction decays, on proton motion from relaxation time measurements, and on internal fields from peak locations that were found using the multiple pulse techniques. Figure 1... 

The free induction decay following 90° pulse has a line shape which generally follows the Weibull functions (Eq. (22)). In the homogeneous sample the FID is described by a single Weibull function, usually exponential (Lorentzian) (p = 1) or Gaussian (p = 2). The FID of heterogeneous systems, such as highly viscous and crosslinked polydimethylsiloxanes (PDMS) 84), hardened unsaturated polyesters 8S), and compatible crosslinked epoxy-rubber systems 52) are actually a sum of three... 

In addition, some samples also gave a signal at 7.1 ppm from the residual NH4 cations the amount of the latter was determined by thermodesorption and subtracted from the intensity of line (3). Thus the sum of intensities of (2) and (3) gave the true total content of acidic hydroxyl groups. They had T2 of 60-75 ftscc, while sample 500 SB contained an additional free induction decay (FID) component due to extra-framework hydroxyls. 

Figure 10.4 Free induction decay signal, which appears in the receiver coils after a 90° pulse. The FID is a time-domain spectrum, showing RF intensity as a function of time 12- It is a composite of the RF absorption frequencies of all nuclei in the sample. The Fourier transform decomposes an FID into its component frequencies, giving a spectrum like that shown in Fig. 10.1. Figure generously provided by Professor John M. Louis.

How do we extract the chemical shifts of all nuclei in the sample from the free-induction decay signal The answer is our old friend the Fourier transform. The FID is called a time-domain signal because it is a plot of the oscillating and decaying RF intensity versus time, as shown in Fig. 10.4 (the time axis is conventionally labeled t2, for reasons you will see shortly). Fourier transforming the FID produces afrequency-domain spectrum, a plot of RF intensity versus the frequencies present in the FID signal, with the frequency axis labeled v2 for frequency or F2 for chemical shift, as shown in Fig. 10.1. So the Fourier transform decomposes the FID into its component frequencies, revealing the chemical shifts of the nuclei in the sample. 

Beyond imaging, the combination of CRS microscopy with spectroscopic techniques has been used to obtain the full wealth of the chemical and the physical structure information of submicron-sized samples. In the frequency domain, multiplex CRS microspectroscopy allows the chemical identification of molecules on the basis of their characteristic Raman spectra and the extraction of their physical properties, e.g., their thermodynamic state. In the time domain, time-resolved CRS microscopy allows the recording of the localized Raman free induction decay occurring on the femtosecond and picosecond time scales. CRS correlation spectroscopy can probe three-dimensional diffusion dynamics with chemical selectivity. 

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