Resonance frequency, relationship with

It has to be stressed that the relationship is at best a rough guide. There will almost certainly be contributions to dielectric loss occurring at frequencies between the microwave region and the ionic lattice resonance frequency that complicate the Q(f) relationship. For example, such contributions may arise through polarization processes associated with dislocations and microstructural features. There is no alternative to making the measurement if reliable loss data at a particular frequency are required. 

In a polycrystalline material each crystallite experiences its own effective field, which is determined in part by magnetic anisotropy. Therefore, because of the different orientations of the crystallites, there will be a distribution of resonant frequencies in consequence, narrow linewidths are associated with low anisotropies. Magnetic inhomogeneities - inclusions and pores - also disturb the local effective fields and so lead to line broadening. The effect of porosity on resonance linewidth can be expressed by the relationship... 

It cannot be emphasized too much that the resonant frequency in NMR is proportional to the magnetogyric ratio, y, and to the laboratory magnetic field strength, B0. This relationship forms the basis of nearly every phenomenon observed in NMR. There are two ways to measure the precession rate the angular velocity, co0, in units of radians per second and the frequency, v0, in units of cycles per second or hertz. In this book we will use frequencies in hertz. This frequency is sometimes called the Larmor frequency, and the zero subscript refers to this fundamental frequency, which results from the laboratory magnetic field interacting with the nucleus magnetic field. 

The use of resonating quartz crystals for mass-change determinations is very attractive because a sensitivity of about 10"12 g/cmz is feasible. Mass determinations with resonating quartz crystals have been discussed by Plant (48) and Van Empel et al. (49). The principle (49) of the determination is based on the relationship between the variation, A/ of the resonant frequency, f and the mass added, Am, or... 

The oscillation frequency of a quartz resonator in contact with liquid was also investigated by Kanazawa et al (94,95). The relationship which expresses the change in the oscillation frequency of the quartz crystal in terms of fluid and quartz parameters can be described by ... 

If a quartz crystal is coaled with a polymer that selectively adsorbs certain molecules, the mass of the crystal increases if the molecules are present, thus decreasing the resonant frequency of the quartz crystal. When the molecules are desorbed from the surface, the crystal returns to its original frequency. The relationship between the change in frequency of the crystal A/ and the change in ma.ss of the crystal AiV/ is given by... 

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