W. Cochran’s research while affiliated with Canadian Nuclear Laboratories and other places

The "shell model" of an alkali halide is extended to take into account short-range forces between both first- and second-nearest neighbor atoms in the crystal, the polarizability of both ions, and the possibility that the ionic charge may be less than one electronic charge. The arbitrary parameters of the model have been obtained by means of a least-squares fit to the measured dispersion relations for the lattice vibrations, the dielectric constants, and the elastic constants. For NaI and KBr, models have been found which give excellent agreement both with these measurements and with measurements of the specific heat. This good agreement is, however, obtained only when the simple shell-model concept of the ions is to some extent abandoned. The reasons for this, and the connection with work of other authors, are discussed.

Dispersion curves for the lattice vibrations propagating in the [00zeta], [zetazeta0], and [zetazetazeta] directions in NaI at 100°K and in KBr at 90°K have been measured using neutron spectrometry, and the results compared with calculations based on a simple shell model. Both substances obey the Lyddane-Sachs-Teller relation. In addition, some measurements were made on KBr at 400°K most frequencies showed a decrease of a few percent. At this temperature, the acoustical modes show no significant energy broadening, the transverse optical modes show slight broadening, and the longitudinal optical modes show very considerable broadening. The anomalous broadening of the LO modes is not yet understood and requires further study. It appears to be specimen-dependent as well as temperature-dependent.

A relation is derived between the frequencies of lattice vibrations of long wavelength whose wave vector is in the α-direction in a crystal, the dielectric dispersion frequencies, and the ratio of the static and high-frequency limits of the component ϵαα of the dielectric tensor. In crystals having orthorhombic symmetry or higher, the dielectric dispersion frequencies are equal to the frequencies of transverse optic modes for which the polarization is along a crystallographic axis, and the relation may then be expressed in a simpler form.

Theoretical and experimental studies were made of the lattice dynamics ; of alkali halides. A theory of the lattice dynamics of ionic crystals is given ; based on replacement of a polarizable ion by a mcdel in which a rigid shell of ; electrons (taken to have zero mass) can move with respect to the massive ionic ; core. The dipolar approximation then makes the model exactly equivalent to a ; Born-von Karman crystal in which there are two "atoms" of differing charge at ; each lattice point, one of the "atoms" having zero mass. The model was ; specialized to the case of an alkali halide in which only one atom is ; polarizable, and computations of dispersion curves were carried out for Nal. The ; dispersion nu (q) relation of the lattice vibrations in the symmetric STA001!, ; STA110!, and STA111! directions of Nal at 110 deg K were determined by the ; methods of neutron spectrometry. The transverse acoustic, longitudinal ; acoustic, and transverse optic branches were determined completely with a ; probable error of about 3%. -ine dispersion relation for the longitudinal optic ; (LO) branch was determined for the STA001! directions with less accuracy. The ; agreement between the experimental results and the calculations based on the ; shell model, while not complete, is quite satisfactory. The neutron groups ; corresponding to phonons of the LO branch were anomalously energy broadened, ; especially for phonons of long wavelength, suggesting a remarkably short lifetime ; for the phonons of this branch. (auth);