Magnetic field inhomogeneity

Figure 2.2 Effect of 180 pulse on phase imperfections resulting from magnetic field inhomogeneities. Spin-echo generated by 180 refocusing pulse removes the effects of magnetic field inhomogeneities.

Since these terms are proportional to tr, they increase with decreasing temperature.1 There are several line-width contributions, included in oc0, which do not depend on m,-. These include magnetic field inhomogeneity and the spin rotation interaction, the latter increasing with 1/tr and thus with increasing temperature. These and other line-width effects have been studied in some detail and are discussed elsewhere.13... 

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,... 

The optimization procedure must take into account constraints such as maximum admissible local power dissipation and maximum tolerable magnetic field inhomogeneity. In this way, such constraints influence, often quite seriously, the final performance of the magnet. 

Users of any NMR instrument are well aware of the extensive employment of what is known as pulse sequences. The roots of the term go back to the early days of pulsed NMR when multiple, precisely spaced RF excitation pulses had been invented (17,98-110) and employed to overcome instrumental imperfections such as magnetic field inhomogeneity (Hahn echo) or receiver dead time (solid echo), monitor relaxation phenomena (saturationrrecovery, inversion recovery, CPMG), excite and/or isolate specific components of NMR signals (stimulated echo, quadrupole echo), etc. Later on, employment of pulse sequences of increasing complexity, combined with the so-called phase-cycling technique, has revolutionized FT-NMR spectroscopy, a field where hundreds of useful excitation and detection sequences (111,112) are at present routinely used to acquire qualitatively distinct ID, 2D, and 3D NMR... 

There are several other sources of line width in nuclear magnetic resonance. An experimentally caused width occurs when the laboratory static magnetic field inhomogeneity exceeds the true line width. In this case the... 

Magnetic field inhomogeneities and chemical shifts additionally dephase each doublet component in Fig. 2.38. These effects are also refocussed by a 180" pulse, provided it rotates the components about the x -axis, as is the case in experiments (a) and (c) of Fig. 2.38. 

VIII. Factors Governing Line-Widths and Shapes of Bands The theory of line-widths and shapes, other than those resulting from instrumental limitations such as magnetic field inhomogeneities, is complicated and will not be discussed here. The purpose of this short section is simply to describe qualitatively some of the factors involved and to indicate that this field is of importance to the chemist and may well influence his results adversely unless due care is taken. Also the study of changes in the line-widths and shapes may well give information of considerable use to the investigator. 

The mass calibration law gives mass measurement accuracy of ca. 2 ppm and a precision of ca. 1 ppm. Errors are still systematic, but the measurements are much less sensitive to space charge effects than those made with the cubic cell. One possible cause of the systematic errors may be magnetic field inhomogeneity caused by... 

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