Nuclear precession frequency

Chemical shift The difference between the nuclear precession frequency and the carrier frequency. 

Larmor frequency The nuclear precession frequency about the direction of Bo. Its magnitude is given by yBo/27T. 

Modulation The variation in amplitude and/or phase of an oscillatory signal by another function, e.g., modulation of the nuclear precession frequency of one nucleus by the nuclear precession frequency of a correlated nucleus in COSY spectra. 

The SIN defined by Equation 7.6 for a given NMR resonance is proportional to the square of the nuclear precession frequency (mo, rad/s), the magnitude of the transverse magnetic field (Bi) induced in the RE coil per unit current (/), the number of spins per unit volume (Ns), the sample volume (Vs), and a scaling constant that accounts for magnetic field inhomogeneities. The SIN is inversely proportional to the noise generated in the RE receiver and by the sample (Vnoise) as defined by the Nyquist theorem,... 

In pulsed NMR, the magnetic field is turned on for the time necessary to rotate the magnetization vector into a plane called the 90° rotation or 90° pulse. The field is turned off and the magnetization vector rotates at a nuclear precession frequency relative to the coil. This induces an NMR signal that decays with time as the system returns to equilibrium. This signal is called the free induction decay (FID). 

In Mossbauer spectroscopy, we encounter two types of expectation values for the electronic spin4 6 that we illustrate briefly for an iron site with S = 1/2 and g 2, taking the applied field along z. If the spin relaxation rate (spin flips between the Ms= + 1/2 and Ms= —1/2 sublevels) is slow compared to the nuclear precession frequency (which is typically 10—30 MHz Larmor precession around Bint or quadrupole precession), the nucleus senses the Fe atom in either the Ms= + 1/2 or Ms =1/2 state during the absorption process. In this case, we have (Sz) = + 1/2 for spin up and (Sz) = —1/2 for spin down. Each electronic level produces a Mossbauer spectrum, and these two spectra are weighted by the probability (given by the... 

In this expression r is the inter-chain hopping time and ts is the phonon scattering time along a chain. The quantity s = (d2/a2) is the ratio of the anisotropic to isotropic contribution of the hyperfine interaction and /(cd) is the spectral density of the interaction, with coe and con being electron and nuclear precession frequencies respectively,... 

The exact value of v0 is designed to be slightly offset from the range of nuclear precession frequencies to be examined (the spectral width, SW, in hertz). Therefore, the SW can be no greater (and preferably less) than Av, leading to the relationship... 

The simplest theoretical approach to exchange is via the Bloch equations, to which terms are added to reflect the rate phenomena. The spectra shown in Fig. 2.14 are obtained from such a treatment. It is apparent that the line shapes depend on the ratio R/ vA — vB), where the exchange rate R = 1/t. Thus fast and slow are measured with respect to differences in the nuclear precession frequencies in the two sites. Exchange rates can be measured by analysis of line shapes and by certain pulse experiments, as described in later chapters. 

The Larmor relation, Eq. 2.45, is the basis for determining the nuclear precession frequency. In many instances we are concerned only with the magnitude of the... 

It was shown in the previous section that the emitted rf signal from excited nuclear spins (the FID) is detected as a time dependent oscillating voltage which steadily decays as a result of spin relaxation. In this form the data is of little use to us because it is a time domain representation of the nuclear precession frequencies within the sample. What we actually want is a display of the frequency components that make up the FID as it is these we relate to transition energies and ultimately chemical environments. In other words, we need to transfer our time domain data into the frequency domain. 

Larmor frequency. Syn. precession frequency, nuclear precession frequency, NMR frequency, rotating frame frequency. The rate at which thexy component of a spin precesses about the axis of the applied magnetic field. The frequency of the photons capable of inducing transitions between allowed spin states for a given NMR-active nucleus. 

Nuclear magnetic resonance spectroscopy first aroused the chemist s Interest when the discovery was made that the exact nuclear precession frequency is dependent upon the chemical environment of the nucleus. The displacement of the resonance frequency relative to an arbitrary standard is commonly referred to as chemical shift. Without this property, NMR would be without practical utility to the chemist as an analytical tool and it would probably long be extinct. 

The electromagnetic radiation must be of precisely the same frequency as the nuclear precession frequency for absorption of energy to occur and thus achieve resonance. 

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