Frequency resonant

Table 3.9 gives the resonance frequencies in a 9.4 tesla magnetic, field. . . 

Ultrasonic pulses are generated within the sample on the transducer s resonance frequency, pass through sample and are received by the wideband receiver. After received pulse processing in the computer, results analysis is carried out. 

Another oscillatory method makes use of a drop acoustically levitated in a liquid. The drop is made to oscillate in shape, and the interfacial tension can be calculated from the resonance frequency [113]. 

Modification of an AFM to operate in a dynamic mode aids the study of soft biological materials [58]. Here a stiff cantilever is oscillated near its resonant frequency with an amplitude of about 0.5 nm forces are detected as a shift to a new frequency... 

Figrue BTl 1.1 shows the range of radiolfequencies where resonances may be expected, between 650 and 140 MHz, when Bq = 14.1 T, i.e. when the H resonance frequency is 600 MHz. There is one bar per stable isotope. Its width is the reported chemical shift range (Bl.11.5) for that isotope, and its height corresponds to the log of the sensitivity at the natural abundance of the isotope, covering about six orders of magnitude. The... 

Figure Bl.11.1. Resonance frequencies for different nuclei in a field of 14.1 T. Widths indicate the quoted range of shifts for each nucleus, and heights mdicate relative sensitivities at the natural isotopic abundance, on a log scale covering approximately six orders of magnitude. Nuclei resonatmg below 140 MHz are not shown.

Despite these simplifications, a typical or F NMR spectrum will nomially show many couplings. Figure BTl 1.9 is the NMR spectrum of propan-1-ol in a dilute solution where the exchange of OH hydrogens between molecules is slow. The underlymg frequency scale is included with the spectrum, in order to emphasize how the couplings are quantified. Conveniently, the shift order matches the chemical order of die atoms. The resonance frequencies of each of the 18 resolved peaks can be quantitatively explained by the four... 

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

The heart of an NMR spectrometer is the probe, which is essentially a tuned resonant circuit with the sample contained within the main inductance (the NMR coil) of that circuit. Usually a parallel tuned circuit is used with a resonant frequency of coq = The resonant frequency is obviously the most important probe... 

For large molecules, such as proteins, the main method in use is a 2D technique, called NOESY (nuclear Overhauser effect spectroscopy). The basic experiment [33, 34] consists of tluee 90° pulses. The first pulse converts die longitudinal magnetizations for all protons, present at equilibrium, into transverse magnetizations which evolve diirhig the subsequent evolution time In this way, the transverse magnetization components for different protons become labelled by their resonance frequencies. The second 90° pulse rotates the magnetizations to the -z-direction. 

As before, we note that the resonance frequency of a nucleus at position r is directly proportional to the combined applied static and gradient fields at that location. In a gradient G=G u, orthogonal to the slice selection gradient, the nuclei precess (in the usual frame rotating at coq) at a frequency ciD=y The observed signal therefore contains a component at this frequency witli an amplitude proportional to the local spin density. The total signal is of the fomi... 

Application of an oscillating magnetic field at the resonance frequency induces transitions in both directions between the two levels of the spin system. The rate of the induced transitions depends on the MW power which is proportional to the square of oi = (the amplitude of the oscillating magnetic field) (see equation (bl.15.7)) and also depends on the number of spins in each level. Since the probabilities of upward ( P) a)) and downward ( a) p)) transitions are equal, resonance absorption can only be detected when there is a population difference between the two spin levels. This is the case at thennal equilibrium where there is a slight excess of spins in the energetically lower p)-state. The relative population of the two-level system in thennal equilibrium is given by the Boltzmaim distribution... 

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

FID does not die away before the deadtime has elapsed. In die case of inliomogeneously broadened EPR lines (as typical for free radicals in solids) the dephasing of the magnetizations of the individual spin packets (which all possess slightly different resonance frequencies) will be complete within the detection deadtime and, therefore, the FID signal will usually be undetectable. 

Pulsed-force mode AFM (PFM-AFM) is a method introduced for fast mapping of local stiffness and adliesion with lower required data storage than recording force-distance curves at each point on the x-y plane [115]. A sinusoidal or triangular modulation is applied between the tip and sample (either via lever or sample piezo) at a lower frequency than that of either the piezo or cantilever resonance frequency. Tip and sample then come... 

This corresponds to the physician s stethoscope case mentioned above, and has been realized [208] by bringing one leg of a resonatmg 33 kHz quartz tiinmg fork close to the surface of a sample, which is being rastered in the x-y plane. As the fork-leg nears the sample, the fork s resonant frequency and therefore its amplitude is changed by interaction with the surface. Since the behaviour of the system appears to be dependent on the gas pressure, it may be assumed that the coupling is due to hydrodynamic mteractions within the fork-air-sample gap. Since the fork tip-sample distance is approximately 200 pm -1.120), tire teclmique is sensitive to the near-field component of the scattered acoustic signal. 1 pm lateral and 10 mn vertical resolutions have been obtained by the SNAM. 

We assume that tlie light field is detuned to tlie red of tire J —> J atomic resonance frequency. 

Figure Cl.5.8. Spectral jumping of a single molecule of terrylene in polyethylene at 1.5 K. The upper trace displays fluorescence excitation spectra of tire same single molecule taken over two different 20 s time intervals, showing tire same molecule absorbing at two distinctly different frequencies. The lower panel plots tire peak frequency in tire fluorescence excitation spectmm as a function of time over a 40 min trajectory. The molecule undergoes discrete jumps among four (briefly five) different resonant frequencies during tliis time period. Arrows represent scans during which tire molecule had jumped entirely outside tire 10 GHz scan window. Adapted from...

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