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The entropy change due to the formation of a vacancy is calculated in the harmonic approximation on the basis of a Debye model which distinguishes between longitudinal and transverse velocities. For Al the calculated value agrees with the experimental result obtained recently.

By the use of second quantization theory, the interactions between the electromagnetic field and the field produced by lattice vibrations in a crystal, are studied. The emphasis is put on the harmonic lattice vibrations,i.e., phonon-photon interactions. Among these the more interesting ones result to be the Bragg scattering, the first-order Raman scattering (including thermal scattering of light) and the secondorder Raman scattering. Cross-sections in terms of lattice properties are given for all these effects.

Using the general theory given in the first part of this work, vacancy-phonon scattering is studied and, for an isotropic medium, the results shown to be identical with the classical values. The emphasis is put on the scattering by a vacancy pair, and the theory is used to evaluate the thermal resistivity of both vacancies and vacancy pairs.

The change of phonon occupation numbers as a consequence of vacancy creation is calculated by a perturbation approach, and used to evaluate the resultant entropy change. For a Debye model, this change is found to be 7/4 k. The method is also applied to the case of a vacancy pair. The total vibrational energy of the crystal is shown to be unaffected by the formation of a vacancy.

A new method is proposed for calculating the displacements due to an edge or screw dislocation in a crystal. The dislocation is represented by a perturbation in the phonon state of a perfect crystal and the treatment is carried out by the use of second quantization. The results agree with the classical ones at large distances from the dislocation core but show a quite different structure in the neighbourhood of the core which eliminates the singularities in the former theory.

The second quantization of the phonon field allows a theory to be developed which gives the reticular centre displacements, produced by vacancy formation. The theory is based on Bravais lattices, and a detailed calculation is carried out for the Debye approximation. Numerical results for argon at 80 °K are compared with those of previous theories.

The problem of thermal diffusion in liquids is treated in the context of a phenomenological theory, where the whole subject of diffusion in liquids is reconsidered. A general formula for the enrichment factor is obtained in terms of four characteristic parameters of the liquid; the average drift velocities of the particles under the action of a thermal gradient are also required. The central Section of the paper is an attempt to define the nature of the force moving the atoms through the liquid when the thermal gradient is established. Arguments are given to retain as a good approximation of this force the simple expressionF=–kB▽T. By using a modified Stokes relation between force and drift velocities, a good agreement between theory and experiment is found for the case of an isotopic mixture.

An edge type dislocation in a simple cubic lattice is studied with the inclusion of a new double row of forces confined to the core. Particular emphasis is given to the distortion in the neighbourhood of the dislocation line. The theory is based on a new formula which gives the lattice distortion arising from the introduction into the crystal of a point force, the discrete structure of the medium being taken into consideration. The resulting displacements are linear functions of some matrices whose values are tabulated for the core atoms. At greater distances from the dislocation line the present solutions are substantially the same as the classical ones.

In this paper we study the kinematics of a system of three particles without spin and without interaction, concerning ourselves withS-waves only. We introduce a set of co-ordinates that allow the separation of the variables in a very simple way. The main result is the partialS-wave Green’s function of the system. We introduce also thetriangular calculus, a useful tool in avoiding lengthy formulas and in making clear the symmetry properties of the system.