Larmor frequency, NMR

NMR has become such an invaluable technique for studying the structure of atoms and molecules because nuclei represent ideal noninvasive probes of their electronic environment. If all nuclei of a given species responded at their characteristic Larmor frequencies, NMR might then be useful for chemical analysis, but little else. The real value of NMR to chemistry comes from minute differences in resonance frequencies dependent on details of the electronic structure around a nucleus. The magnetic field induces orbital angular momentum in the electron cloud around a nucleus, thus, in effect, partially shielding the nucleus from the external field B. The actual or local value of the magnetic field at the position of a nucleus is expressed as... 

Precession frequency. Syn. Larmor frequency, NMR frequency. The frequency at which a nuclear magnetic moment rotates about the axis of the applied magnetic field. 

Greatly enhanced sensitivity with very short measuring time is the major advantage of PFT (pulse Fourier transform) experiments. In the CW (continuous wave) experiment, the radiofrequency sweep excites nuclei of different Larmor frequencies, one by one. For example, 500 s may be required for excitation over a 1-KHz range, while in a PFT experiment a single pulse can simultaneously excite the nuclei over 1-KHz range in only 250 jits. The PFT experiment therefore requires much less time than the CW NMR experiment, due to the short time required for acquisition of FID signals. Short-lived unstable molecules can only be studied by PFT NMR. 

The basic principle underlying the development of images is simple (Lauterber, 1973). Consider a body cavity containing two pools of water in different quantities. In a uniform magnetic field, the NMR spectrum will consist of a single peak, since all the water molecules will process at the same frequency, irrespective of their spatial location. If, however, a linear field gradient is applied in the x -direction, the Larmor frequency of the water will increase linearly across the sample as a function of the x -coordinate, thereby creating a one-dimensional profile, or spectrum, of the sample (Fig. 7.21). 

The quantity of interest is the precession of the components perpendicular to B0 that are measured in the experiment by induced voltage in the coil, which is subsequently amplified and demodulated. We can write them either as individual components Mx, M, or by a vector M+, which combines both of them. In the static field, the precession about B0 occurs with the Larmor frequency w0 = /B0. If we neglect those processes which dampen the amplitude of the rotating transverse magnetization as precession proceeds, this already describes the frequency that we pick up with our receiver coil, and it is the third and perhaps the most important of our three fundamental equations of NMR ... 

The Larmor frequency rf reference signal is generated using a DDS (direct digital synthesizer) board (FSW01, DST Inc., Asaka, Japan). This board can generate coherent and spectrally pure rf signals from 5 to 200 MHz, of which the frequency is controlled via the ISA bus. This board has an essential role in the NMR lock process. 

P and 27A1 MAS NMR spectra of aluminophosphate powders and of samples scratched from films were recorded on 600 MHz Varian NMR system equipped with a Varian 3.2 mm MAS probe. Fifty two-faced films deposited on glass slides were needed to obtain sufficient amount of material for NMR measurements. Larmor frequencies for phosphorus and aluminium at 14.1 T are 242.89 and 156.35 MHz, respectively. 

It will be useful to outline the basic features of solid state 2H NMR spectra. Deuteron is a spin 7= 1 nucleus possessing an electric quadrupole moment. The EFG interacts with the electric quadrupole moment to produce a frequency shift. Frequencies of the symmetric line shape centred around the Larmor frequency >0, which depend on the relative orientation of an external magnetic field B0 and the EFG tensor, are given by1 7... 

A way out of this dilemma is to perform an NMR-type experiment on the paramagnetic centre. NMR provides an inherently higher resolution than EPR, since only one line pair at frequences v is obtained for each nucleus (or set of magnetically equivalent nuclei). The lines appear, to first order, symmetrically spaced around the Larmor frequency v of the respective nucleus for nuclei with I = i and a hfc A the resonance condition is... 

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