Table of contents

A general statistical mechanical method for introducing temperature dependent `energy levels' is developed. Previous discussions of this problem are included as particularizations of the general treatment and are unnecessarily restrictive. It is shown that appropriate definitions and procedures depend upon the nature of the information available or, alternatively, on the nature of the information it is desired to obtain. Simple and typical problems are considered in illustration of the general results.

In alkali halide crystals the discharge paths formed when electric breakdown occurs about a point electrode follow definite crystallographic directions, but many believe that the intrinsic electric strength of these materials does not depend on the direction of the applied field. This belief is difficult to reconcile with the above fact and examination of the literature shows that it is based on very scanty evidence.

The experiments described in this paper were made to extend the available information, and measurements of intrinsic strength were made with both KCl and NaCl between - 200°C and + 230°C. The results of the measurements provide little support for the above belief. A fair measure of agreement existed between the discharge track directions and the directions of smallest electric strength. This result suggests that the mechanism of breakdown is dependent on the properties of high-energy conduction electrons.

The d.c. Hall coefficient and resistivity of six semiconducting diamonds have been measured as a function of temperature from 200 to 800°K. All the diamonds were p-type semiconductors. From the measurements the effective mass of the charge carriers, the concentration of donor and acceptor centres, the activation energy of the acceptors (close to 0.34 eV) and the temperature dependence of the Hall mobility have been calculated. At high temperatures the mobility varies as T^-2.8.

The relative strengths of certain peaks in the infra-red absorption spectrum are the same in different specimens. It is concluded that all these peaks are due to the same centre. These peaks are not detected in type I and type IIa diamonds. There is a strong correlation between the strength of the strongest peak at 0.346 eV and the number of vacant acceptor levels at room temperature, from which it is concluded that the centre giving rise to the peaks is also responsible for conduction.

The real and imaginary parts of the complex permeability have been measured for a series of iron-nickel alloys in the frequency range 300-400 Mc/s. The frequency of the internal resonance observable in this region has been investigated as a function of composition and is found to pass through a minimum in the neighbourhood of 70% Ni. The value of the principal anisotropy coefficient is also known to be very small in this region and a qualitative comparison provides additional support for the view that this resonance is attributable to the equivalent magnetic field associated with the anisotropy energy.

A formal proof is given that, in the critical region, the predictions of the model are the same whether the atoms are considered to be arranged on a torus, on a cylinder or on a plane. The latter arrangements involve `raw' edges, and are hard to handle by matrix methods, but can be dealt with by a slight modification of Kac and Ward's treatment. The conclusion is not trivial, because critical assemblies are known to be abnormally sensitive to perturbations, and it is in principle possible that, since correlation distances are large, an alteration in the boundary constraints might affect the entire assembly.

It is shown that the friction of a bituminous material decreases with increasing sliding velocity, and that this decrease is due to the creep behaviour of the material.

A new type of fracture experiment is described. The specimen is a flat strip, which is split lengthwise by gradually propagating a crack down the middle. The crack is made stable in direction by holding the specimen in a state of lengthwise compression. The energy balance of the system can be established by simple beam theory. Given Young's modulus for the material, the fracture energy is found from the length of the crack and from its width at the open end. Measurements made on plastics, with specimens of varying size, show that the crack propagation is governed by a constant specific fracture energy, which is invariant with respect to scale transformations of the stresses. For a sample of polymethylmethacrylate the specific fracture energy was 4.9 × 10⁵ dyn cm^-1. For a sample of polystyrene it was 25 × 10⁵ dyn cm^-1 for slow cracks, but dropped to 3 × 10⁵ dyn cm^-1 for fast-running cracks.

The properties of high power pulsed discharges in hydrogen have been studied. The time for the discharge to reach steady state conditions was investigated as a function of its parameters. Without a magnetic field the time was of the order of 100 μsec. At high pressures, longitudinal magnetic fields up to 23 000 oersteds caused little change in the time to reach equilibrium, but at low pressures (e.g. 0.46 mm Hg) the time was considerably increased and values up to 2.5 msec were recorded. Observations of the arc diameter showed that a strong uniform magnetic field produced a constriction, unless the natural arc diameter was much greater than the tube diameter. Non-uniform magnetic fields, on the other hand, caused the discharge to become diffuse where the field was diverging.

The electrode falls and positive column gradient of the steady state discharges were measured. Without a magnetic field the electrode falls were 58 v, and the positive column gradient was 60p^{0 34}i^{-0 5} where p is the pressure in mm Hg and i the current in amperes. This expression is in reasonable agreement with the theoretical value. The electron densities were found to lie in the range 10¹³ to 10¹⁵ electrons per cm³. These densities correspond to ionization of from 0.5% to 12% of the gas atoms. The addition of a magnetic field considerably increased the electrode falls and values as high as 400 v were recorded. At low pressures a magnetic field, as predicted by theory, reduced the positive column gradient. At high pressures, on the other hand, the gradient was increased. For example, with a 100 A arc at 10 mm pressure the gradient was increased from 13 v per cm to 25 v per cm by an intense magnetic field. Again this change is consistent with theory. This change in gradient was accompanied by a 13^o_o increase in the discharge temperature.

A simple model of a semiconductor with one trapping level in equilibrium with one band only is defined through the lifetime τ and two trapping time constants τ_c and τ_s. A rectangular pulse of minority carriers is injected at one end and the drift of this pulse in a constant electric field is studied, neglecting diffusion effects. Analytical expressions are derived for the densities of free carriers N and of trapped carriers N_t, as functions of distance and time. Graphs are plotted of the time dependence of N at a collector point, corresponding to drift-decay measurements, and of the spatial distribution of N and N_t at different times, which are relevant in photoconductive measurements. It is concluded that the attenuation of the drifting pulse corresponds to an apparent lifetime which is shorter than the true lifetime τ and that the shape of the (N, time response) curve depends critically not only on the parameters τ, τ_c and τ_s but also on the distance of the collector point from the emitter and on the duration of the injecting pulse. In the case of heavy trapping most of the trapped and free charge is confined to the immediate neighbourhood of the emitter. In the steady state it is shown that, on this model, the density distribution of free carriers is entirely independent of trapping.

The steady-state diffusion of minority carriers is studied for the case of continuous injection (d.c.) and sinusoidally variable injection (a.c.) for a simple model of a semiconductor containing one trapping level in equilibrium with one band only. It is shown that the d.c. diffusion is affected only very little by the presence of trapping in extrinsic material. In the extreme case of heavy trapping in near-intrinsic material the effective diffusion length becomes L^* = radical2L, where L is the diffusion length for the trap-free case. In the case of sinusoidally variable carrier density the effective diffusion length is the same as for the trap-free a.c. case at low frequencies and again at very high frequencies but may become appreciably less at intermediate frequencies.

Experiments are described which show that it is possible to transfer barium from an anode as a thin film to a cathode by simple electron bombardment. This effect appears to occur with the anode cold. The `threshold' bombarding energy is about 300 volts for barium; the corresponding current density at the target is of the order of 1 mA cm^-2. The gradual build-up of thin film activity of a pure strontium oxide cathode was followed with time. The final result was an emitter whose performance matched that of the standard BaO/SrO cathode in every way; the thin film emitter, however, exhibits a large temperature dependence but has high tenacity.