Table of contents

It is predicted on theoretical grounds that additional charge carriers may be injected into a semiconductor by a thin region of high electric field in which avalanche multiplication occurs. The voltage drop across the region may be quite low and associated with a negative resistance for certain values of the current. The observation of the predicted phenomena in germanium is described; it is found that the negative resistance region may cover some hundreds of volts and the response time be as short as 3 × 10^-9 sec. The implications of avalanche injection are discussed in connection with solid-state phenomena involving a large current density, and it is shown that any sufficiently small contact is capable of rectification independently of the presence of potential barriers.

It is shown that if high surface recombination rates can be corrected for or eliminated, then the travelling light spot method is very suitable for measurements of lifetimes in silicon since no ambiguities due to trapping effects are involved and since the measurement can readily be made on large sections of ingots instead of on carefully fashioned rods of rectangular section. Experimental results are given and treatments for the reduction of recombination velocities at surfaces of both n- and p-type silicon are described.

The Hall effect and resistivity of n-type single crystals of natural galena containing from 6 × 10¹⁵ to 10¹⁹ extrinsic electrons per cm³ have been measured from room temperature down to liquid helium temperatures. No appreciable change in the number of extrinsic electrons has been observed down to 4°K in any crystal.

While the mobility is proportional to T^-5/2 down to a temperature of about 70°K, the low temperature mobility varies with the number of extrinsic electrons in a manner which cannot be explained by current theories of scattering.

It is estimated that at room temperature a purely intrinsic crystal of PbS would contain 2 × 10¹⁵ conduction electrons per cm³.

A general theory is given of the gross electrical conductivity (or thermal conductivity, dielectric constant or magnetic permeability) of a composite medium having its isotropic granular components distributed spatially in a disordered way. It is shown that the gross conductivity is a weighted superposition of the component conductivities with weights containing the volume fractions of the components and an intensity factor depending on the average electric field for the whole medium and for each component. By introducing a suitably defined `average electrostatic problem', the case of grains spherical in the mean and suspended in a uniform medium is examined in detail, and the gross conductivity explicitly found. The limiting case in which the suspending fluid is withdrawn and the grains coalesce is shown to give rise to a discontinuity in the gross conductivity. Coated grains, e.g. oxide-coated metallic grains, are also treated.

In a continuation of a previous paper, it is shown here how the gross bulk and shear moduli of a composite material consisting of a suspension of grains or a compact of grains may be deduced. The grains are assumed to be perfectly bonded to the suspending medium or to each other, and are taken to be spheres in the mean. By using an averaging procedure due to Bruggeman, and analysing the effect of a uniform hydrostatic compression and of a uniform tension on an average grain, a pair of de-coupled equations for the gross moduli is found for suspensions. When the suspending medium vanishes and the grains are packed, these equations become coupled and there is exhibited a discontinuity in the gross moduli. The bulk coefficients of linear expansion of the two kinds of composites are found from an analysis of the dilatation and bulk stress for average spherical grains when the composite as a whole is subjected to some small temperature change. All results are free of any limitation on the number of components.

The propagation of a sound wave through a liquid can be described in terms of the absorption per wavelength μ and the velocity c. It is generally accepted that an important part of the absorption is due to the relaxation of internal degrees of freedom, and the aim of this paper is to derive relationships between the acoustic quantities μ and c and the thermodynamic parameters which describe specific molecular processes.

The analysis is based on an expansion of the adiabatic compressibility. It is valid for the general case of structural relaxation involving changes both in internal energy and in volume as a molecule passes from one stable equilibrium state to another. Attention is given to the combined effects of more than one relaxing process, where each process has a different relaxation time. The equations are derived in a form suitable for the analysis of experimental results.

A satisfactory picture of the three-dimensional intensity distribution near focus in the aberration-free diffraction image of a monochromatic point object was first given by Zernike and Nijboer in 1949. No corresponding general picture of the phase relations between different parts of the image seems to have been worked out, although Gouy's discovery in 1890 of the so-called phase anomaly at focus aroused an interest in this topic which, as a succession of publications shows, has not decreased in the intervening 66 years.

In the present paper a sharpened version of Lommel's classical analysis is applied to obtain a general picture of the phase distribution near focus and to examine in detail, in the special case of an F/3.5 pencil, its peculiarities near the geometrical focal point, the Airy dark rings and the axial nodes (points of zero intensity) of the diffraction image. The `phase anomaly' near focus and the singular behaviour of the phase along the axis of the pencil become more readily intelligible when they are considered against the background of this general picture.

Corrections to 1956 Proc. Phys. Soc. B 69 21.