Table of contents

The present theory of X-ray scattering by simple fluids and binary mixtures is applied to the phenomenon of critical opalescence in binary mixtures. Firstly, the condition for phase separation is expressed in terms of the three radial distribution functions for a binary mixture, and then it is shown that, at phase separation, these functions are all of the same form, although they differ in scale. The form of these functions can then, in principle, be determined from experimental observations of visible opalescence, although the normalization requires further discussion.

The theory is then applied to the work of Furth and Williams, and of Quantie, who suggested analytic representations of two types of radial distribution function. Only one of these is found to be acceptable.

Calculations are given of certain collision-free hydromagnetic disturbances produced by the rapid compression of a plasma containing a magnetic field.

The effects of optical illumination and impurities on colloid formation are studied in additively coloured KCl and in NaBr coloured by ultra-violet light. It is shown that at elevated temperatures additively coloured KCl behaves as an auto-sensitized photographic system. A theory of the colloid band is presented which takes account of ion core polarization and harmonic mean effective mass for arbitrary ellipsoidal particles. The colloid band is identified as a bounded plasma resonance, shifted into the visible region by the boundary conditions. Plasma frequencies computed from the positions of the colloid bands are in good agreement with other estimates. The spectral dependence of photoconductivity associated with the colloid band is related to the band structure of the host medium.

The optical constants of aluminium from the near ultra-violet (2500Å) to the near infra-red (5μ) can be described, at least qualitatively, in terms of the Drude formula by the two parameters N and τ, the density of free electrons and the relaxation time, respectively. The value for N is taken to correspond to 2.4 free electrons per atom and the value for τ is taken to be 1.2×10^-15 second.

A procedure is proposed, involving a coupling parameter, for the determination of the partition function and free energy of a classical condensed system of particles in terms of the structure of the system (that is, short range order) represented by the pair distribution. The present paper forms a sequence with two previous papers by the author, published in 1959 and 1960, concerned with the accurate calculation of the pair distribution. The present paper, when taken together with these previous papers, gives a theory for the determination of the thermodynamic properties of a classical fluid in terms of the partition function, and using the principles of particle dynamics. Errors due to the use of the superposition approximation in the calculation of the structure can be controlled. The theory may be applied equally to spherical or non-spherical constituent particles.

The treatment used in a previous paper dealing with the effect of spherical aberration on optical response functions has been extended to cases of coma, an aberration which is not an even function in the pupil coordinates x and y, and consequently gives rise to lateral shifting in the image.

Different positions of the focal plane, the state of correction for higher order aberration, and different azimuths of the line structure in the object are considered. Detailed results are given first for primary circular coma, when the wave-front aberration coefficient has the values w₃₁ = +0.63, +1.26 and +1.89 wavelengths three focal planes and the azimuths ψ = 0 (radial lines) and ψ = π/2 (tangential lines) are treated. Results are also given for secondary coma for the values w₅₁ = -2.6, -3.9, -5.85 and -7.8 wavelengths, with three different states of correction and again in three focal planes and two azimuths.

It is found with negative values of w₅₁ that the relative phase shifting of frequency components within the image has no appreciable effect on the image quality in the cases considered when this negative secondary coma is compensated with a suitable numerically larger positive primary coma (w₃₁+w₅₁>0), if focal planes situated a long way from the paraxial focal plane are excepted.

An attempt has been made to analyse the data on the last nucleon binding energies of transuranic elements. Some interesting results are obtained regarding the behaviour of the λ term introduced by Ghoshal. Some confirmatory evidence is also obtained regarding the sub-shell at N = 152.

Cone fractures have been produced in fused silica, by indenters ranging from fraction one-sixtyfourths inch to ¼ inch diameter. In some respects these differ from cone cracks in silicate glass. Those in silica have a significantly smaller semi-angle, 65.5 as opposed to 68.5° in glass. Whereas cracks in glass grow indefinitely under a constant load, and remain visibly open when the load is removed, those in quartz cease to grow about ten minutes after each increment of the load, and cannot be seen when the specimen is unloaded.

The weak binding approximation to the electronic energy spectrum is applied to a one-dimensional model of a liquid. The energy is expanded in a perturbation series, every term depending upon the positions of all atoms. The absence of long distance order is taken into account by assigning to the coordinates of the atoms a probability distribution by means of which the statistical expectation of the energy levels is obtained. Hereby the separations between neighbouring atoms are assumed to be statistically independent. At those energies which would be forbidden in a periodic chain the density of states is reduced but would vanish, presumably, only in the limit of a very large number of terms in the series being taken into account.

The optical-frequency response function is used to obtain the intensity distribution in the image of a step function of intensity, and from this the image intensity distributions for strips and Cobb test units are obtained. Detectors having a Gaussian type response function of different equivalent bandwidths s_o are assumed. The treatment is applied to systems having secondary spherical aberration of amounts w₆₀ = - 6λ, - 9λ, - 12λ, with different amounts of primary spherical aberration and several planes of focus in each case, and for a range of values of s_o, the equivalent bandwidth of the detector. From these calculations the edge gradient in the image of a step function of intensity, the limit of detection and the limit of resolution, using a criterion of 0.2 for the necessary image contrast, are found; these different methods for the assessment of optical systems are then intercompared. It is shown for example that if two systems are assessed by two different test methods the order of the figure of merit for the two systems can be significantly different, and furthermore the order of merit in which the two systems are placed depends strongly on the response function of the detector employed. The differences are large enough to be of real significance in practice.

It is generally known from qualitative considerations of optical image formation that when the detector employed has a narrow bandwidth the shape of the frequency response function is of greater importance for low values of the spatial frequency s, the response function for higher spatial frequencies having little influence on the image quality, while for a system employing a detector of wide bandwidth the shape of the frequency response function for the higher frequencies is important, as these frequencies can now contribute to the formation of the image. An attempt has been made to study quantitatively the effect of detector bandwidth on the formation of the images of some standard test objects.

Observations were made of pre-breakdown phenomena in uniform field gaps under ambient atmospheric conditions and measured irradiation intensities, in which current and light pulses were recorded. From measurements of the current pulse duration a value for the mobility of positive ions of 2 6 cm² sec^-1 v^-1 was obtained at field strengths approaching the breakdown value.

The (percentage breakdown, voltage) curves obtained by applying 1/50 μsec impulse voltages to an enclosed unventilated and non-irradiated uniform field gap have been examined and compared with curves obtained under a variety of conditions of ventilation.

In the course of the investigations both straight and stepped spark paths were observed, and preliminary results of an investigation of this phenomenon are described.

Certain features of the thermomagnetic behaviour of a single crystal specimen of silicon-iron when being magnetized in an easy direction of magnetization are explained in terms of the presence of domain nuclei in the specimen, following the work of Bates, Christoffel, Clow and Davis.

Angular distributions have been measured of some proton, deuteron and α-particle groups arising from the bombardment of ¹²C with 5.98, 8.83, 9.37 and 10.14 MeV ³He particles. Excitation functions have also been measured at a laboratory angle of 10° in the energy interval 5.7 to 10.23 MeV. The results indicate that at most energies the (³He, d) and the (³He, α) reactions proceed predominantly by a direct process, but this is not true for the (³He, p) reaction.

Angular distributions and excitation functions have been measured of ten proton and five deuteron groups arising from the bombardment of ⁹Be with 5.7 to 10.2 MeV ³He particles The proton excitation functions, measured at 10, are essentially smooth and most of the angular distributions exhibit strong forward peaks which appear to be consistent with a predominantly direct process All of the deuteron angular distribution and excitation functions are consistent with stripping theory

This paper describes measurements of the formative time lag to breakdown in hydrogen in uniform electric field for a range of E/p from 50 to 250 v cm^-1 (mm Hg)^-1. The preliminary work showed that the time lag was critically dependent upon the state and nature of the cathode surface. The formative time lags were therefore measured with different cathode surfaces, and the state of each surface was specified by measuring its work function. Previous work in this laboratory has shown that measurements of formative time lags can be analysed in terms of Davidson's current growth equation to yield determinations of the individual secondary ionization coefficients. A similar analysis has been carried out of the results of the present experimental data, and it was found that if the cathode work function was decreased by 0.25 ev, the magnitudes of the secondary coffiecients were increased by a factor of two.

The reactions ¹¹B(³He, α)¹⁰B, ¹⁰B(³He, α)⁹B, ¹⁴N(³He, α)¹³N, ¹⁶O(³He, α)¹⁵O and ²⁷Al(³He, α)²⁶Al, have been investigated at an incident energy of 5.2 MeV, using a broad range magnetic spectrograph. Angular distributions and absolute cross sections for alpha particles leading to the ground states and several excited states of the final nuclei have been measured The angular distributions of many of the alpha-particle groups suggest the predominance of a direct interaction mechanism for these reactions, and in several cases features which are indicative of a pick-up process are mentioned.

The magnetostriction and magnetization of an ellipsoid of polycrystalline gadolinium have been measured in the temperature range 78°K to 365°K. The results show that gadolinium has a large volume magnetostriction which is proportional to the square of the paramagnetic magnetization above the Curie point. The saturation magnetostriction shows an anomaly at 150°K, and becomes zero at 233°K. The contribution of the volume magnetostriction to the thermal expansion of gadolinium is shown to be too small to account for the thermal expansion anomaly.

Correction to Proc. Phys. Soc.75 2