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The author is concerned with the polaronic states of a tightly bound particle interacting with the elastic displacements of a linear host crystal. A new variational approach to Holstein's molecular-crystal model is introduced, which includes the 'adiabatic' and the 'dynamic' approximate solutions treated so far separately in the literature. It turns out that the transition from one type of solution to the other does not coincide with the transition from small to large polarons. Instead, there is a continuous transition from adiabatic to dynamic solutions in the small-polaron region while there is a discontinuous crossover in the region polarons, and six different types of polarons have to be distinguished with respect to their size and degree of adiabaticity.

Inelastic neutron scattering studies of the magnetic excitations in the planar Heisenberg random antiferromagnet Rb2Mn0.5Ni0.5F4 at 7K are reported. Two well-defined bands of excitations are observed. A simple mean crystal model is found to predict accurately the measured dispersion relations using essentially the pure crystal parameters while the zone boundary energy widths are well-accounted for by an Ising cluster mode. Intensities, however, are not properly explained using these simple models.

A virtual crystal model has been used to determine energy bands in silver-palladium alloys. Results for densities of states as a function of concentration are calculated and compared directly with experimental measurements of electronic specific heat and magnetic susceptibility. The range of validity of the energy band results is estimated by considering the effects of disorder.

The dielectric properties of crystals are studied on the basis of the weakly anharmonic crystal model. Particular emphasis is placed on the low frequency behaviour of the dielectric susceptibility and on the possibility of a coupling between the dielectric properties and the fluctuations in the phonon density distribution. These fluctuations cannot be treated by low-order perturbation theory but can be discussed by solving the appropriate transport equation. The approximate solution to this equation is obtained following the techniques developed for ultrasonic attenuation.

The cubic anharmonic contribution to the Helmholtz free energy of a face-centred cubic crystal has been evaluated for a nearest-neighbour central force model. The results are expressed in terms of the derivatives of an arbitrary interatomic potential and three sums Sm(a1, TR), (m = 1, 2, 3). Here TR is an appropriate reduced temperature and a1 is essentially the ratio of the first to the second radial derivative of the interatomic potential. The three sums Sm(a1, TR) are tabulated for a representative range of volumes and temperatures as well as TR = 0 and the high temperature limit. For these two limiting cases our results are compared with similar calculations by Flinn and Maradudin and Feldman and Horton. Once the interatomic potential is specified our results yield both the volume and temperature dependence of the cubic anharmonic contribution to the Helmholtz free energy. The temperature dependence of Sm(a1, TR) is discussed in some detail since this determines the cubic anharmonic contribution to the entropy and specific heat.