Magnetization transverse

As shown in Fig. 2.1 (b), the nuclear moments still precess with Larmor frequency v0 about the z axis in the xy plane, as does the resultant transverse magnetization (Figs. 2.1(b) and 2.2(b)). In the rotating frame (Section 1.7.3), the transverse magnetization with reference frequency v0 stands while faster or slower components with v( v0 or v, v0 will rotate clockwise or counterclockwise, respectively, as shown in Fig. 2.3. 

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Writing the electromagnetic field in terms of transverse electric (TE) and transverse magnetic (TM) components, the electric field has the form ... 

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. 

Farrar T C and Stringfellow T C 1996 Relaxation of transverse magnetization for coupled spins Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 4101-7... 

The transverse magnetization may be described in this frame by a complex variable, m, the real and imaginary parts of which represent the real and imagmary components of observable magnetization respectively ... 

The z-component of the magnetization is constant. The evolution of the transverse magnetization is given by... 

Figure Bl.14.2. Gradient-recalled echo pulse sequence. The echo is generated by deliberately dephasing and refocusing transverse magnetization with the readout gradient. A slice is selected in the z-direction and v- and y-dimension are frequency and phase encoded, respectively.

If temis of higher order than linear in t are neglected, the transverse magnetization evolves in the presence of the first bipolar gradient pulse according to (equation Bl.14.2 and equation B 1.14.61 ... 

The phase of the transverse magnetization is inverted by tire 180° pulse and the magnetization after the second gradient pulse and therefore at the echo centre is ... 

In electron spin echo relaxation studies, the two-pulse echo amplitude, as a fiinction of tire pulse separation time T, gives a measure of the phase memory relaxation time from which can be extracted if Jj-effects are taken into consideration. Problems may arise from spectral diflfrision due to incomplete excitation of the EPR spectrum. In this case some of the transverse magnetization may leak into adjacent parts of the spectrum that have not been excited by the MW pulses. Spectral diflfrision effects can be suppressed by using the Carr-Purcell-Meiboom-Gill pulse sequence, which is also well known in NMR. The experiment involves using a sequence of n-pulses separated by 2r and can be denoted as [7i/2-(x-7i-T-echo) J. A series of echoes separated by lx is generated and the decay in their amplitudes is characterized by Ty. ... 

At equilibrium, the transverse magnetization equals zero. A net magnetization vector rotated off the -axis creates transverse magnetization. 

Fig. 1. Representative device configurations exploiting electrooptic second-order nonlinear optical materials are shown. Schematic representations are given for (a) a Mach-Zehnder interferometer, (b) a birefringent modulator, and (c) a directional coupler. In (b) the optical input to the birefringent modulator is polarized at 45 degrees and excites both transverse electric (TE) and transverse magnetic (TM) modes. The appHed voltage modulates the output polarization. Intensity modulation is achieved using polarizing components at the output.

Dehberate stirring can be imposed on conductors with a transverse rotating magnetic field or by passage of electric current axially with a transverse magnetic field. Conversely, a constant magnetic field with no current imposed greatly reduces natural convection. 

Langer et al. [10] measured also electrical resistance of individual MWCNTs at very low temperatures and in the presence of a transverse magnetic field. As for the case of the microbundle, the CNTs were synthesised using the standard carbon arc-discharge technique. Electrical gold contacts have been attached to the CNTs via local electron beam lithography with an STM. The measured individual MWCNT had a diameter of about 20 nm and a total length of the order of 1 im. 

M. Mihelcic, K. Wingerath. Threedimensional simulations of the Czochralski bulk flow in a stationary transverse magnetic field and in a vertical magnetic field Effects on the asymmetry of the flow and temperature distribution in the Si-melt. J Cryst Growth S2 318, 1987. 

The transverse magnetization and the applied radiofrequency field will therefore periodically come in phase with one another, and then go out of phase. This causes a continuous variation of the magnetic field, which induces an alternating current in the receiver. Furthermore, the intensity of the signals does not remain constant but diminishes due to T and T2 relaxation effects. The detector therefore records both the exponential decay of the signal with time and the interference effects as the magnetization vectors and the applied radiofrequency alternately dephase and re-... 

The relaxation rates of the individual nuclei can be either measured or estimated by comparison with other related molecules. If a molecule has a very slow-relaxing proton, then it may be convenient not to adjust the delay time with reference to that proton and to tolerate the resulting inaccuracy in its intensity but adjust it according to the average relaxation rates of the other protons. In 2D spectra, where 90 pulses are often used, the delay between pulses is typically adjusted to 3T] or 4Ti (where T] is the spin-lattice relaxation time) to ensure no residual transverse magnetization from the previous pulse that could yield artifact signals. In ID proton NMR spectra, on the other hand, the tip angle 0 is usually kept at 30°-40°. 

Transverse magnetization represents a particular type of coherence involving a change in quantum number p of 1. Each coherence a is equal to the difference in magnetic quantum numbers of the nuclei r and 5, i.e., the coherence order is M,—M and pulses cause transitions to occur... 

The spin-echo is used to suppress the production of spurious signals due to field inhomogeneities or to eliminate errors in the setting of pulse widths. It is also possible to use the spin-echo to follow the decay of transverse magnetization and to determine the transverse relaxation time (7 2). How might we do this in practice ... 

After the 90° pulse, the transverse magnetization vectors of C nuclei of C, CH, CH2, and CHj do not rotate synchronously with one another but rotate with characteristically different angular velocities during the same delay interval. This results in their appearing with differing (positive or negative) amplitudes. This forms the basis of the APT experiment. 

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