NNR IN RAPIDLY ROTATED METALS By - Nottingham eTheses ...

- 41 -
of as forming a continuum of sidebands which become unobservably
weak; hence resulting in the characteristic Lorentzian line-
shape. For macroscopic sample rotation at the magic angle the
central component of the absorption spectrum is flanked by a series
of sidebands at integer multiples of vr. As the rotation rate is
increased these sidebands move further out and become less intense.
When yr is greater than the linewidth the intensity of the satellites
falls as Vr -2n for the nth satellite, thus preserving the total
second moment. Both the central component and the satellites have
a finite width which decreases with increasing spinning frequency(43,44)
Accurate adjustment of the magic angle is an important criter-
ion in achieving a minimum linewidth. A reduction of the dipolar
linewidth to 1% of its original value requires that the magic angle
is set to an accuracy of better than half a degree. Such an
adjustment can best be performed empirically by direct observat-
ion of the FID from the rotated sample. With the assumption that
there is no antisymmetric component of the spin-spin interaction
the fully resolved central spectrum for any solid rotated about
the magic axis is determined by the Hamiltonian
, ýl° a -3i yß(1 -a)I. HO +I 3.. I.. Iý
J 1J
the same as that relating to fluids in high resolution NMR.
In practice complete resolution of the central line from the
first spinning sidebands flanking it either side is dependent upon
the frequency of rotation. The faster the sample is spun the
greater likelihood there is of attaining some rotationally invar-
iant limit. There have been several suggestions as to the manner
in which the residual dipolar broadening of the central spectrum
varies with rotation
rate,
(33
34,38,45,46)
,
However experimental
(3.17)