NMR lineshape calculation for a linear dipolar chain
Abstract
Numerical calculations have been performed to obtain exact results for the hightemperature space and timedependent transverse spin pair correlation functions G^{x}_{r}(t), where r is the spatial separation of the spins, and the freeinductiondecay function F(t), for a linear chain of N dipolar coupled spins (S=12) for N=7, 9, and 11 with periodic boundary conditions. The range Δ of the dipolar interaction was allowed to take separately the values 1, 2, and 3. The moments of the NMR line shape (M_{2} through M_{20}) were obtained for the infinite chain with Δ=1 and Δ=2 and were found to be in excellent agreement with previous reliable moment calculations (M_{2} through M_{8}). By an evaluation of the contribution of the fourparticle terms to M_{6}, it is shown that the BersohnDas theorem fails in one dimension. We find that G^{x}_{r}(t) for even (odd) values of r are predominantly positive (negative). This gives rise to a damped beat structure for F(t). A study of F(t) for N=7, 9, and 11 shows that our 11spin solution reproduces that of the infinite chain at least up through the fifth node, and is also in good agreement with recent ^{19}F freeinductiondecay measurement in fluoroapatite. The nodes of F(t) were found to shift towards shorter values of time as Δ was allowed to increase. Further, for N=11, a comparison of our exact results for F(t) for Δ=3, with a Gaussian broadening of F(t) for Δ=2, shows that the effect of the weak interactions is not well approximated by a simple Gaussian broadening for this case.
 Publication:

Physical Review B
 Pub Date:
 December 1975
 DOI:
 10.1103/PhysRevB.12.4597
 Bibcode:
 1975PhRvB..12.4597S