Bo inhomogeneity

Shorter results in less signal. The static field of MR scanners must be very uniform to prevent signal loss and image artifacts. Typically, Bq inhomogeneity of MR scanners is about 10 parts per million (ppm) over perhaps a 40-cm-diameter spherical volume (dsv) for imaging. In spectroscopy, measurements of small fi uency shifts must be accurately made and Bo inhomogeneity is typically limited to perhaps 0.1 ppm over a 10-cm dsv. ... 

Spin- spin relaxation is usually determined applying spin echoes (Hahn-Echo, CPMG method), which delete other influences such as Bo inhomogeneity. The spin-lattice relaxation time Ti is measured by detecting the relaxation after inverting Mo by a 180° pulse (inversion recovery method). 

The quadrupole perturbed NMR spectriun of Rb (I = 312) consists of the central hne and two satelUte Unes. In D-RADP-x the nuclear quadrupole couphng constant decreases linearly with x from 9.6 MHz (x = 0) to 6.6 MHz (x = 0.95) [10], whereas the Larmor frequency amounts to 98.163 MHz in a Bo field of 7 T. Due to the substitutional disorder, and the corresponding loss of the translational invariance, the satelHte transitions are inhomogeneously broadened that much, that only the central transition can be directly observed. The position of the corresponding resonance line can be calculated using standard NMR-NQR theory [16], where the second order shift is given by ... 

In other cases, however, and in particular when sublattices are occupied by rather immobile components, the point defect concentrations may not be in local equilibrium during transport and reaction. For example, in ternary oxide solutions, component transport (at high temperatures) occurs almost exclusively in the cation sublattices. It is mediated by the predominant point defects, which are cation vacancies. The nearly perfect oxygen sublattice, by contrast, serves as a rigid matrix. These oxides can thus be regarded as models for closed or partially closed systems. These characteristic features make an AO-BO (or rather A, O-B, a 0) interdiffusion experiment a critical test for possible deviations from local point defect equilibrium. We therefore develop the concept and quantitative analysis using this inhomogeneous model solid solution. 

Fig. 7.2.20 [Ziml] Comparison of primary and stimulated echoes for a curing series of carbon-black filled NR measured in inhomogeneous Bo and Bj fields. The amplitudes of the primary echoes have been normalized to 100%. The amplitudes of the stimulated echoes are very sensitive to the change in cross-link density with increasing curing time, tn = 15 ms.

Fig. 7.2.22 [Gutl] Pulse sequences for combined determination of T and T2 in inhomogeneous Bo fields, (a) Steady-state inversion recovery filter [Sezl). (b) Steady-state saturation recovery filter [Gutl]. (c) Train of echoes measured by sequence (b) which shows the magnetization build-up with T] and the decay with Ti of unfilled, cross-linked SBR.

In inhomogeneous Bq and B fields the flip angle may be relatively well defined if the Bo gradient is strong. Then the B field is quite homogeneous over the sensitive... 

This relaxation time is very important as it is associated to the natural linewidth . However the time constant T2 cannot be directly quantified, because there are other factors which also contribute to the dephasing process. These factors are experimental factors and are related to the inhomogeneity of the Bo field in the sample. As different molecules in the sample experience slightly different Bo fields, their precession frequency (and resonance frequency, vo) is slightly different, thus the dephasing is faster, T2 becomes shorter, and the actual line in the spectrum is artificially broadened. 

The deuterium lock prevents changes in the static field (Bo) and radiofrequency (fii) by maintaining a constant ratio between the two. It therefore ensures long-term stability of the magnetic field. If the lock is not applied, a drastic deterioration in the shape of the NMR lines is expected, due to magnetic and radiofrequency inhomogeneities, (a) With deuterium lock... 

Superimposing the constant magnetic field Bo with an inhomogeneous magnetic field Radd = gz, the precessional ( Larmor ) frequency (o) = yB) of a spin about the direction of the magnetic field (B) becomes space dependent ... 

The factor 1/2 takes into account the fact that the pairs of nuclei should not be doubly counted in the summation, and naturally all summands with i =j are excluded. Each summand leads to a single component of the inhomogeneous NMR hne. In a rigid lattice, the different directions of the r,j are constant in time. The nuclear spins are directionally quantised in the external magnetic field Bq when Bo Bloc-... 

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