Bloembergen-Rowland

As shown by Ruderman and Kittel (77) and Bloembergen and Rowland (78), Aij in a solid is dependent on the nature of the energy bands in the solid. For metals A is proportional to the product of the square of the electron density of Fermi surface electrons at the nucleus and the effective mass, and decreases as the inverse cube of the internuclear distance. Insulators have been treated by the energy band method (78) and by a molecular method (79) where each atom is considered to be bonded to its nearest neighbors. Unfortunately, both of these methods involve approximations in the evaluation of An which are quite crude at present. 

Bloembergen and Rowland (78) have also shown that associated with the exchange interaction is a pseudo-dipolar interaction, which as the name implies, has the same functional form as the dipolar interaction. This interaction arises from the presence of the electron-coupled nuclear spin interaction and the dipole-dipole interaction and its magnitude is dependent on the relative amount of p- or d-character of the electronic wave functions in the solid. 

The effect of dislocations has also been studied by Bloembergen and Rowland 106) in cold-worked copper (Cu and Cu resonances), and also the effect of alloying in Al-Zn alloys (Al resonance) by Rowland 107). Otsuka and Kawamura 108) have studied the NMR of 1" in KI, Na in NaCl-NaBr mixed crystals, and Br in KBr-NaBr mixed crystals and have estimated dislocation densities in these materials. 

Figure 11.1. A. Changes in the intensity of the Cu NMR signal in annealed and cold-worked copper and in alloys with zinc and silver. The maximum NMR absorption is corrected for the number of copper nuclei in the sample and plotted as a function of the solute concentration C. Data points for zinc alloys denoted by crosses and by open circles for silver. From Bloembergen and Rowlands (1953) by permission of Elsevier Science. B. " Mg NMR spectrum of pure annealed magnesium (lower), magnesium work-hardened by filing (middle) and a Mg+ 6 % Al alloy (upper). The insets in the upper spectrum shows the satellite powder pattern features enlarged vertically. From Bastow and Smith (1995), by permission of the copyright owner.

According to the calculation of Bloembergen and Rowland,4 the intensity of the NMR signal at the frequency u is expressed as... 

In solids, in addition to the classical dipolar interaction described above, interactions between the nuclear spins are also mediated by the bonding and/or conduction electrons. These exchange and pseudo-dipolar interactions were already included by Van Vleck (1948) in his general treatment, and specific application to NMR in solids was given by Bloembergen and Rowland (1953). These interactions are generally most consequential for relatively heavy nuclei. 

Calculated (N. Bloembergen and T. J, Rowland, Acta Metall. 1, 731 (1953)) absorption lineshapes and representative spectra for polycrystalline samples a) an axially symmetric chemical shielding tensor (a and denote shielding parallel and perpendicular to the symmetry axis) e.g., the spectrum of frozen benzene at -40 C b) a general shielding tensor, e.g., the spectrum of polycrystalline polyethylene. 

---