By W G Frankenberg
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Additional info for Advances in Catalysis and Related Subjects, Volume 12
This environment will causc a difference 6w in the precessional frequency of the spin which may be positive or negative from some average value w . During the time rethe spin acquires a phase angle 64 = rc6w in addition to that acquired by the uniform precession a t w . )and when (A42)N 1, t may be considered to be equal to T z for the system. Thus 1/T2 = (6w)2rc (12) If the motion is sufficiently slow so that the spin stays in a particular environment for a time long compared to T2,then rc by definition is Tz and 1/Tg = 60 (13) which is the rigid lattice value of T2.
33 11. Nuclear Magnetic Resonance.. . . . . . . . . . . . . . . . . . . . . 34 A. Principles and Methods of NMR.. B. Interactions of Nuclei in the Solid State. C. Applications. . . . . . . . . . . . . . . . . . . . . . . . . Ill. Electron Paramagnetic Resonance. . . . . . . . . . . . . . . . . . . . 76 A. Principles and Methods of E P R . .................................... 76 B. Influence of Atomic Environment on EPR Spectra..
The figure is drawn for a case where rc-I is large compared with the resonance frequency Y O . For such a case the intensity of the coupling with the surroundings is proportional to r e ; the proportionality coefficient turns out t o be ( S W ) ~as in Equation (12), and TI = Tz, as may be verified by computation of the square of the energy matrix elements of the dipolar interaction for the transitions involved ( 3 ) . 5. Spectral density caused by Brownian-type motions versus frequency. rc is the correlation time for the random motion and YO is a NMR frequency.