Amorphous solids, magnetism

The dipole-dipole (Keesom) interaetion eomes about from the faet that on the average, two freely rotating dipoles will align themselves so as to result in an attraetive foree, similar to that eommonly observed with bar magnets. In order to ealeulate the net dipole-dipole interaetion, it is neeessary to examine all the possible orientations of the dipoles with respeet to one another. It is also neeessary to determine any jr effeets due to the field assoeiated with a point eharge, in order to determine the net effeet when amorphous solids are plaeed side by side. We also need to eonsider what happens if the dipoles ean reorient in eaeh other s fields. 

NMR and EPR techniques provide unique information on the microscopic properties of solids, such as symmetry of atomic sites, covalent character of bonds, strength of exchange interactions, and rates of atomic and molecular motion. The recent developments of nuclear double resonance, the Overhauser effect, and ENDOR will allow further elucidation of these properties. Since the catalytic characteristics of solids are presumably related to the detailed electronic and geometric structure of solids, a correlation between the results of magnetic resonance studies and cata lytic properties can occur. The limitation of NMR lies in the fact that only certain nuclei are suitable for study in polycrystalline or amorphous solids while EPR is limited in that only paramagnetic species may be observed. These limitations, however, are counter-balanced by the wealth of information that can be obtained when the techniques are applicable. 

The chemical shift anisotropy broadening arises from the fact that the chemical shift of a given C atom in a molecule will vary to some extent as a function of the orientation of the molecule in the magnetic field. In liquid samples this variation is averaged out to a single isotropic value however, in amorphous solids and powders the true linewidth of a given chemical shift... 

As molecular motion in a gas or liquid is free and random, the physieal properties of these fluids are the same no matter in what direetion they are measured. In other words, they are isotropic. True amorphous solids, beeause of the random arrangement of their constituent molecules, are also isotropic. Most crystals, however, are anisotropic, their mechanical, electrical, magnetic and optical properties can vary according to the direction in which they are measured. Crystals belonging to the cubic system are the exception to this rule their highly symmetrical internal arrangement renders them optically isotropic. Anisotropy is most readily detected by refractive index measurements, and the striking phenomenon of double refraction exhibited by a clear crystal of Iceland spar (calcite) is probably the best-known example. 

To describe the magnetic properties of amorphous alloys containing rare earth elements with non-zero orbital moment (L 0) the Hamiltonian of eq. (25) is no longer suited. Harris et al. (1973) have proposed a model in which they assume that there is a local uniaxial field of random orientation at each of the rare earth atoms in an amorphous solid. This local uniaxial field of random orientation is closely associated with the presence of an equally random crystalline electric field. The Hamiltonian for this random anisotropy model (RAM) can be written as... 

It will have become clear after perusal of the many papers that have appeared on amorphous solids that the knowledge of solid state physics has been greatly enriched by this research, not only in the field of magnetism but also in numerous other fields such as mentioned in sections 8 and 9. In some cases solid state physics has profited from the amorphous state in a rather indirect way. We will conclude this chapter by illustrating this point with two examples. 

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