Nuclear magnetic resonance linewidths

In a nuclear magnetic resonance measurement in solution, the direct dipolar interaction Xo actually disappears because, due to rapid molecular motion, the interspin (internuclear) vectors are rapidly space-averaged within the time-scale of a measurement. Hence, the terms Xs and Xj are detectable as sharp lines or splittings in a high-resolution spectrum of H or and they can be related to detailed molecular structure or conformation of the substance investigated. In a solid, on the contrary, the directions of the internuclear vectors are stationary even if they are distributed randomly in space. Then, X gives a very wide linewidth to the zeroth-order absorption line and completely masks all lines due to Xs and Xj. 

The parameters characterizing the nuclear magnetic resonance in a solid, in particular the linewidth, second moment, and the spin-spin and spin-lattice relaxation times, are strongly affected by molecular reorientations and atomic diffusive motions. Application of NMR methods to the study of hydrogen (and deuterium) diffusion in the non-magnetic rare-earth hydrides has been extensive. 

R. Weiss and R. N. Grimes, J. Amer. Chem. Soc., 1978, 100, 1401. Sources of linewidth in boron-11 nuclear magnetic resonance spectra. Scalar relaxation and boron-boron coupling in tetraborane(lO) and pentaborane(9). 

One of the most striking and characteristic features of nuclear magnetic resonance (n.m.r.) is that the spectra from solids are so very much broader than those from liquids. An excellent example is provided by water, whose proton n.m.r. linewidth at room temperature is about 0.1 Hz, while for ice at low temperatures it is about 10 kHz, six orders of magnitude broader. 

The temperature-dependent shift of the resonance line is strongly connected with the nuclear magnetic relaxation times and the linewidth. The fluctuating magnetic field at the nucleus usually has components perpendicular to the external magnetic field. The Fourier spectrum of these field components contains terms with resonance frequencies, which induce transitions between nuclear energy levels. One may foresee the temperature... 

---