Table of contents

The tolerance on aberration is made subject to the criterion that the response of the optical system for a given spatial frequency shall not be less than 0.8 of the response of the same system in the absence of aberration. In this way the tolerance on aberration is related to the number of lines to be resolved with good contrast. The method is applied to defect of focus, spherical aberration, coma and astigmatism. The best form of correction and focal plane according to this criterion are determined by the same method. The results are expressed by approximate formulae for the lower spatial frequencies which are those of importance in other than very highly corrected systems.

The specific heat of a specimen of cerium of face-centred cubic structure has been measured between 1.5° and 20°K and anomalous effects, expected as a result of the susceptibility measurements of Lock, have been found. The specific heat shows a marked maximum at 12.5°K, the magnitude of which increases with the number of times the specimen has been cooled. The anomaly is probably due to antiferromagnetism.

The susceptibility of ytterbium metal has been measured at room temperature and between 1 3°K and 80°K. Its magnitude seems to indicate that the atoms are mostly in the ¹S state with the 4f shell completely filled, only about 1 atom in 260 being in the ²F_7/2 state with 13 electrons in the 4f shell. The paramagnetic saturation effect at the lowest temperatures seems to confirm this. The material has been tested for superconductivity down to 1.24°K in fields as low as 10 oersteds, with a negative result.

The surface conductance of germanium may be modulated by an external electric field. If the electrode used for applying the field does not cover the full extension of the specimen a boundary effect appears. In the presence of longitudinal currents the transition regions between the field-free and field-applied surfaces behave as junctions, giving rise to carrier concentration disturbances and also to rectification. The properties of a single field-induced junction have been investigated experimentally.

The problem of designing a light or electron optical system specifically for the imaging of periodic objects, such as real crystals, is discussed. A qualitative appeal to communication theory suggests that it should be possible to devise systems of higher efficiency than the conventional microscope by using the a priori knowledge of periodicity.

The possibility of deforming the incident wavefront in such a way that the periodic object acts as its own imaging system is considered and a formalism is set up. The particular case of the spherical wavefront is then examined in detail and it is predicted that a new type of image should be formed on certain planes. Since this image is in many ways analogous to the Fourier projection of crystallography, and since it can only be formed by periodic objects, it is named the Fourier image.

Fourier images produced experimentally with light optics are presented and shown to be in agreement with theoretical predictions. Patterns on planes other than Fourier image planes are described briefly, but detailed treatment is deferred until Part II.

The possibility of application to the imaging of crystal lattices by electron optics is discussed, but a quantitative treatment of the crucial problems of finite source size and coherence are deferred until Part III.

The theoretical and experimental investigation of Fourier images described in Part I is extended to the patterns on planes other than focal planes.

The theory is developed from a new statement of the diffraction equations correct to the Fresnel approximations, and experimentally observed patterns are shown to be in good agreement with the results of the theory.

It is concluded that, at least within the angular range of the experiments, some fifteen degrees, the Fresnel approximation gives an adequate description of the phenomenon.

The theoretical and experimental investigation of Fourier images, described in Parts I and II, is extended to the case of finite sources. The Fourier images produced by a pair of point sources, a rectangular source and a Gaussian source are considered in detail. The dependence of focus on source dimensions for the first two of these cases is confirmed experimentally with light optics.

From the results obtained for these idealized sources, the contrast and resolution of Fourier images from experimentally realizable sources is deduced.

The possibility is considered of an improvement in resolution in the electron microscopy of thin crystals when the first stages of magnification are performed by forming magnified Fourier images. It is shown that the resolution that can be attained depends on the sharpness with which the boundaries of the source are defined. In particular, if the effective source is formed by using electron lenses to demagnify a larger source, the resolution may be improved by a factor of 2^-1/2.

The paramagnetic resonance spectrum in crystals of GdCl₃ diluted with LaCl₃ and CeCl₃ has been examined. The splitting of the ground level ⁸S_7,2 of Gd³⁺ in zero magnetic field is small, and has a remarkable temperature dependence. A theory to account for the experimental results is developed, and it is shown that perturbation mechanisms both linear and quadratic in the crystalline field potential are important.

In extension of earlier studies on the production of percussion marks on diamond surface using a diamond sphere as indenter, it is now found that much softer materials than diamond can be used to produce pressure crack figures on diamond surfaces. Tungsten carbide and sapphire balls have produced cracking on an octahedral face of diamond, this face having been already shown to be the face of least resistance to this type of deformation. The cracks are of the same nature as those previously produced by a diamond indenter and the critical stress necessary is of the same order, but the cracks are on a bigger scale and have greater associated disturbance. The full development of a pressure crack is traced and multiple beam interference pictures show the extent of the surface damage. Three distinct types of cracking are found associated with each percussion mark and the mechanism of each is discussed in terms of cleavage, crystallographic shatter and cracks due to shock-wave propagation.