Proceedings of the Physical Society. Section A

The connection between the elastic behaviour of an aggregate and a single crystal is considered, with special reference to the theories of Voigt, Reuss, and Huber and Schmid. The elastic limit under various stress systems is also considered, in particular, it is shown that the tensile elastic limit of a face-centred aggregate cannot exceed two-thirds of the stress at which pronounced plastic distortion occurs.

It is shown that the collective electron and London-Heitler models are not to be regarded as different approximations to the same exact wave function for solids in which, according to the former model, there is a partially filled zone of energy levels. It can thus be shown why nickel oxide in the pure state is a non-conductor, although it contains an incomplete zone. The properties of the metals nickel, palladium and platinum are discussed in the light of these results; platinum differs from nickel in that the orbital contribution to the moment of the elementary magnets is not quenched. A discussion is given of x-ray absorption edges, and it is shown why exciton lines are absent for metals.

An account is given of the methods used to determine the matrix elements of crystal field potentials with particular reference to rare earth ions. Emphasis is laid on the importance of Wigner coefficients in such problems and the idea of using equivalent angular momentum operators is developed. For convenience in applying the results tables of matrix elements are included.

The effect of a uniform magnetic field on the conduction band of metal is investigated, using as model the tight-binding approximation for a simple cubic crystal. The normally discrete magnetic levels pertaining to free electrons are shown to be non-uniformly spaced and broadened as a result of the lattice forces.

The scattering of lattice waves by static imperfections is treated by second-order perturbation theory. The transition matrix is composed of contributions due to the mass difference of lattice points, changes in the elastic constants of linkages between lattice points, and elastic strain. Point imperfections are shown to scatter as the fourth power of frequency, dislocations as the first power, and grain boundaries independently of frequency. The magnitude of the scattering cross section is estimated for a variety of lattice defects in alkali halides, for screw and edge dislocations and for grain boundaries. These results are discussed in relation to thermal conduction by the lattice at low temperatures.

A theory of yielding and strain ageing of iron, based on the segregation of carbon atoms to form atmospheres round dislocations, is developed. The form of an atmosphere is discussed and the force needed to release a dislocation from its atmosphere is roughly estimated and found to be reasonable. The dependence on temperature of the yield point is explained on the assumption that thermal fluctuations enable small dislocation loops to break away; these loops subsequently extend and cause yielding to develop catastrophically by helping other dislocations to break away. The predicted form of the relation between yield point and temperature agrees closely with experiment.

Strain ageing is interpreted as the migration of carbon atoms to free dislocations. The rate of ageing depends upon the concentration of carbon in solution and the estimated initial rate agrees with experiment on the assumption that about 0.003% by weight of carbon is present in solution.

A distinction is made between the surface Helmholtz free energy F, and the surface tension γ. The surface energy is the work necessary to form unit area of surface by a process of division: the surface tension is the tangential stress (force per unit length) in the surface layer; this stress must be balanced either by external forces or by volume stresses in the body.

The surface tension of a crystal face is related to the surface free energy by the relation γ=F+A(dF/dA), where A is the area of the surface. For a one-component liquid, surface free energy and tension are equal. For crystals the surface tension is not equal to the surface energy. The standard thermodynamic formulae of surface physics are reviewed, and it is found that the surface free energy appears in the expression for the equilibrium contact angle, and in the Kelvin expression for the excess vapour pressure of small drops, but that the surface tension appears in the expression for the difference in pressure between the two sides of a curved surface.

The surface tensions of inert-gas and alkali-halide crystals are calculated from expressions for their surface energies and are found to be negative. The surface tensions of homopolar crystals are zero if it is possible to neglect the interaction between atoms that are not nearest neighbours.

Measurements of thermal conductivity at temperatures between 2 and 150°K for several specimens of gold of differing physical and chemical purity are reported. A brief description is given of the cryostat and the experimental technique. Below 35°K the total thermal resistance is given approximately by R = A/T + BT²; apparent small departures from this equation are discussed. The experimental values of B lead to a value of C ≃ 15 in the equation for the ideal resistance R_i = R_∞ CN^2/3 (T/Θ)². At temperatures above Θ/2 the conductivity is sensibly constant and no minimum is observed.

The scintillation response S of organic crystals depends on the nature and energy E of the incident ionizing particle, of residual range r. The specific fluorescence dS/dr is not in general proportional to the specific energy loss dE/dr. By considering the quenching effect of the molecules damaged by the particle on the `excitons' produced by it, it is shown that dS/dr = (A dE/dr)/(1 + kB dE/dr). A and kB are constants, which have been evaluated for anthracene from observations of S and E, and the range-energy data. Curves are computed for the relative response S of anthracene to electrons, protons, deuterons and α-particles of E up to 15 MeV, and these are shown to agree closely with the available experimental results. The method used for evaluating the relative response is applicable to ionizing particles of any nature or energy, and also to the other organic scintillation crystals

The present position of our knowledge of antiferromagnetism, including ferrimagnetism, is reviewed, and some very interesting phenomena concerning the magnetic behaviour of certain ferrites and of pyrrhotite are described and explained.

Corrections to 1957 Proc. Phys. Soc. A 70 769.

The rate coefficient for radiative charge transfer from H atoms to He²⁺ ions is calculated at temperatures in the range 250°K to 64000°K. It is found to be almost independent of temperature and to be very high (the mean value being about 1.6×10^-13cm³sec^-1). As a subsidiary part of the work, earlier computations on the exact two centre wave functions of the 1sσ and 2pσ states of HeH²⁺ and on the transition integral connecting these states are extended to internuclear separations up to 10 atomic units.

A critical examination is made of the hypothesis of model independence in high-energy electron scattering from nuclei. Results are presented which indicate that, contrary to this hypothesis, any differences in nuclear charge distributions result in differences in the electron angular distributions which become more and more pronounced as the energy is increased. The fallacies of the arguments leading to this hypothesis are noted, and comments are made on the scattering process.

The cross section of the reaction ³He(d, p)⁴He has been investigated between 100 keV and 500 keV deuteron energy, using a thin gas target. No significant anisotropy was found up to 500 keV.

The total cross sections σ at deuteron energies E_d assuming isotropic angular distributions were

where E_d is in keV and σ in barns.