Table of contents

In continuation of former work on a simple model in which two molecules may not occupy neighbouring sites on a plane square lattice, various portions of the virial series are derived. The series is split up, not into individual cluster-sums, but into contributions from various types of groups of sites, in the manner introduced by Rushbrooke and Scoins in 1953. It is concluded that the main contributions to the virial series come from single sites, neighbouring pairs and `open' rings of sites, and that contributions from other types of domains of sites are small in comparison, some vanishing identically.

The work of part I suggests that the contributions to the virial series from domains of sites that are not rings or pairs can be neglected. The consequences of this approximation, named the `necklace' approximation, are studied. Enough information is available for these consequences to be worked out almost completely for the plane square lattice. The contributions from rings of four and eight sites are worked out explicitly, while the effect of longer rings of sites can be allowed for also. It is concluded that the correct consequence of this model is a first-order phase change, despite the fact that simpler approximations predict a second-order change. Comparison with a matrix calculation for an 8 × infinite lattice shows satisfactory agreement, and enables the influence of boundaries on the phase change to be estimated.

Approximate self-consistent calculations on solid helium are reported, based on the state k = 0. The analytical form of spherical potential thus obtained is employed to calculate the equation of state at very high pressures. Some important electronic eigenvalues are also discussed as a function of the lattice parameter for a face-centred cubic crystal, both the Wigner-Seitz cellular method and an expansion in plane waves being used. Our results indicate that a transition to a metallic state would occur at a pressure of approximately 10⁸ atmospheres. This is a factor of 2 lower than an earlier estimate made by ten Seldam in 1957.

The unrestricted Hartree-Fock integro-differential equations for the ground state 1s²2s ²S of lithium-like ions are solved by a perturbation expansion in ascending powers of 1/Z. The zero- and first-order functions are obtained analytically and energies up to the third order are calculated. These are compared with the corresponding expansion for the restricted Hartree-Fock energy, obtained by Linderberg (1961). Some of the difficulties in using these functions for calculating the hyperfine splitting are briefly discussed.

The electroluminescence of types I and IIa diamonds has been investigated and as a result of observations made on over one hundred crystals some differences were noted in the response of the different types. The spectrum and temperature dependence of the emission have been determined and are compared with those obtained by α-scintillation and cathodoluminescence of diamond. A linear dependence of emission intensity upon current was found for type IIa diamond, whereas for type I the relationship was superlinear.

By the introduction of BaCl₂ into a pressure-driven shock in argon, and the use of a flash-tube as a source of background continuum, a well-developed spectrum of Ba I and the stronger lines of Ba II have been obtained in absorption.

The spectrum contains all but the weakest lines of Ba I in the spectral range studied. The majority of the lines start on the 5d6s ^1,3D metastable or on the 6s6p ^1,3P⁰ levels, which lie between 1.1 and 1.7 eV above the ground state. Contrary to expectation, the auto-ionizing 5d8p ¹P₁⁰ and higher 5dnp levels, which converge on Ba II 5 ²D and are known to produce strong absorption lines by double-electron transitions from the ground state, make no detectable combinations with the metastable levels.

The spectrum contains the first recorded example of `forced auto-ionization'. A depression of the normal ionization potential by ionic microfields causes the level 5d8p ³P₁⁰ to auto-ionize into the 6sE(p) continua. Correspondingly, the series 6¹S₀-6snp ¹P₁⁰ breaks off at n = 12.

A number of hitherto unclassified lines of Ba I and several new lines ascribed to forced dipole transitions are present in the spectrum.

Insight into ferroelectric phenomena has been gained using lattice dynamical arguments. Early infra-red measurements were misleading. More recent infra-red and neutron work coupled with the theoretical results of Kurosawa permit the assignment of L.O. and T.O. modes that are in good agreement with peaks observed in the neutron spectrum of BaTiO₃.

The r-centroids for some of the bands of v' = 0, 1 and 2 progressions have been reported. Utilizing the experimental intensity data of Treanor and Wurster, the variation of electronic transition moment in this system has been studied following the methods of Nicholls and Jarmain, and of Schuler. It has been found that, in the range 1.51 Å < r < 1.71 Å, the variation of the electronic transition moment is represented by the following equation: R_e(r) = const (1-0.555r).

¹¹B nuclear magnetic resonance has been observed in a series of rare earth hexaboride intermetallic compounds (LaB₆, CeB₆, PrB₆, NdB₆, SmB₆, GdB₆, DyB₆, HoB₆ as well as ScB₆ and YtB₆) above their magnetic transition temperatures. Shifts in the field for resonance of the ¹¹B nuclei were found which depended in sign and magnitude on the magnetic properties of the rare earth atoms. The shifts are qualitatively similar to, but smaller than, the ²⁷Al shifts previously observed in rare earth aluminium compounds. The results in both series of intermetallic compounds can be explained by the exchange interaction between localized rare earth ion core moments and conduction electrons, which results in a magnetic polarization of the conduction electrons and thus in a shift in the field for resonance.

Using a vortex-stabilized arc in chloroform, transition probabilities have been obtained for all classified Cl I lines from 3900-5200 Å and for the strongest Cl II lines in this region. New C I measurements are reported in satisfactory agreement with means from previous works. A strong continuum associated with the chloroform plasma is attributed mainly to the Cl I recombination spectrum in the 3900-5200 Å region. Transition probabilities for Cl lines average 23% above those of Hey.

Several different definitions of the coherence time Δτ can be found in the literature and it is generally assumed that, in cases of practical interest, the different definitions give values of the same order of magnitude. The same remark applies also to definitions of the effective bandwidth Δν. Moreover it is generally supposed that these two quantities are related by the order of magnitude formula Δτ similar 1/Δν.

It is shown from a detailed examination of one particular case of practical interest that the bandwidths as defined by two of the previously proposed formulae are of quite different orders of magnitude, although the correspondingly defined coherence times differ only by a factor of order unity. Similarly it may happen that the two values of Δr differ greatly, whereas the corresponding values of Δν are nearly equal. This discussion shows that the reciprocity relation Δτ similar 1/Δν must be treated with caution, especially in the case of multiple-peaked distributions, such as arise in optical masers.

Ionization currents in spectroscopically pure helium between plane parallel silver electrodes at separations up to 0.75 cm were measured in the range 6 leq E/p leq 100 v cm^-1 mmHg^-1 and 3 leq p leq 115 mmHg where E is the applied electric field and p the gas pressure. The values of the primary ionization coefficient α/p deduced from these measurements were lower than previously published experimental values, particularly at the lowest range of E/p. Within the limits of experimental error α/p was found to be a function of E/p only.

The present values of α/p were in good agreement with the values calculated by Dunlop in 1949, by Abdelnabi and Massey in 1953 and by Phelps in 1960. This result suggests that the Smit distribution of electron velocities, Maier-Leibnitz's inelastic collision cross section data and Nielsen's electron mobility values are applicable to the data.

The variation of breakdown potential in an electrodeless discharge has been studied in air in a discharge tube of length 9 cm, the pressure varying from a few microns to 300 microns and the magnetic field from 20 gauss to 200 gauss, the discharge being excited by means of a transformer (10 kV). The breakdown voltage is always found to be higher than when no magnetic field is present for all values of pressure, and the pressure at which the breakdown voltage becomes a minimum increases gradually as the magnetic field is increased. It is observed that the expression for equivalent pressure, as deduced by Blevin and Haydon in 1958, can explain the observed results at low pressure and for low values of magnetic field (below 50 gauss), but for higher magnetic fields the variation of Townsend's second coefficient in a magnetic field also has to be taken into consideration. Consequently a new expression for VSH, the breakdown voltage in crossed electric and magnetic fields, has been deduced, taking into consideration the effect of both the equivalent pressure and the variation of Townsend's second coefficient in a magnetic field. This new expression can explain not only the increase of breakdown voltage in a magnetic field for all values of pressure, but can account satisfactorily for the shift of pressure for minimum breakdown voltage as the value of magnetic field is gradually increased.

An analysis is given of the limits of the sensitivity of static susceptibility balances arising from Brownian motion. The analysis is constructed in a general way so that the result may be used for a great number of different balances.

Special consideration is given to the influence of the limit imposed by Brownian motion in the study of free radicals, in nuclear magnetic measurements, and in phenomena which are amenable to study by static susceptibility measurements only.

Measurements of the magnetocrystalline anisotropy constants have been made on a single crystal of gadolinium using a torque magnetometer. The apparatus used is briefly described and the application of corrections for lack of saturation and for a paramagnetic component are explained. Measurements have been made between 37.5 °K and 315 °K and it is found that three constants are required to represent the results. It is shown that at temperatures greater than 240 °K the easy direction is the hexagonal axis. Below this temperature the easy direction lies on a cone whose axis is the c axis, and the variation of cone angle with temperature is calculated from the values of the anisotropy constants.

Further analysis of the band structure domains which occur in cube-textured silicon-iron shows that the bands are normal closure domains, the main domains being magnetized normal to the sheet. Experiments show that this is because the grains in the sheet are subjected to compressive stresses.

A measurement of the decay rate of bound negative muons in several elements ranging from vanadium to lead is reported. The results are given as a fraction of the free decay rate. They contradict the anomalously high values previously obtained in the iron region by other workers, and are also in better agreement with recent theoretical predictions for the heavy elements.

A measurement of the lifetime and capture rate of negative muons in various elements is reported. The timing system was calibrated in terms of the accurately known positive muon lifetime. The values obtained are in reasonable agreement with previous experimental data, and have a comparable accuracy.

It has been found that specular reflection by nearly polished surfaces can be explained, not by a normal distribution of surface heights, but by a different distribution. This distribution, empirically extended to allow for coherence between neighbouring points, also seems to explain the angular dependence of radar scattering by the sea and by the surface of the moon.

The theories of three non-linear optical processes are given: (i) the creation of excitons by simultaneous absorption of two photons of different frequency; the particular case of Cu₂O is treated in detail; (ii) the generation of second-harmonic radiation from a monochromatic primary beam in a crystal without a centre of inversion symmetry; the case of quartz is treated as an example; (3) the generation of third-harmonic radiation from a monochromatic primary beam in a crystal having a centre of inversion.

The paper considers the approach to a stable steady state of a thermodynamic system in which certain of the forces have fixed values. These fixed forces are supposed large, so that the steady state is far from equilibrium. The equations of the system are linearized near the steady state.

It is shown that two matrices occurring in the linearized equations are symmetric and positive definite. A Lyapunov function exists for the system. When the steady state is near to equilibrium the Lyapunov function reduces to the rate of production of entropy, measured from its value at the steady state.

At low lattice temperature (similar 4 °K) a relatively weak electric field is known to increase considerably the electronic energy in germanium (hot electrons). In the present paper it is shown that this in turn may appreciably alter the distribution of those phonons which principally interact with the hot electrons, although the total phonon energy is changed by a small amount only. This effect depends on the phonon-phonon interaction and may have an important influence on the mobility of the electrons. A reasonable assumption on this interaction leads to qualitative agreement with the experimental observations made by Zavaritiskaya in 1961 on the field dependence of the conductivity in germanium at 4 °K.

It is pointed out that, strictly, neither the localized model nor the collective electron model predicts the Curie-Weiss law; consequently, its application to experimental data would lead to results of doubtful significance. It is suggested that it is more advantageous to plot Q(=(χT)^-1) against T^-1. This is illustrated with recently evaluated magnetic susceptibility curves for a face-centred cubic system, taking into account ferromagnetic and antiferromagnetic, first and second neighbour Heisenberg interactions.

Correction to Proc. Phys. Soc.79, 1069