The motion of conduction electrons in a metal in an electric field, scattered by an irregular static potential, is considered; this model is applicable to the resistance due to lattice waves at high temperatures, and to imperfections at any temperature. In §2 the Boltzmann equation is re-derived without the customary perturbation theory, avoiding the usual necessity of averaging over phases of different electron states after repeated small time intervals. The assumption that the scattering centres are distributed at random in the crystal is alone sufficient. The theory is, however, still dependent on assuming that h/τ<<kT, where τ is the collision time, as is the usual perturbation theory. §3 gives a general formula for the conductivity of the model, not subject to any assumption. This helps to justify an argument by Landau according to which the usual theory is valid provided h/τ<<η, where η is the cut-off energy of the Fermi distribution. No direct evaluation of the formula has been achieved.
C T Chudley and R J Elliott 1961 Proc. Phys. Soc. 77 353
The incoherent inelastic scattering cross section of slow neutrons from liquids is calculated using a simple model in which the liquid is assumed to have appreciable short range order in a quasi-crystalline form. Diffusive motion takes place in large discrete jumps, between which the atoms oscillate as in a solid. The model predicts a definite, easily calculable cross section which is not dominated by diffusion effects as when continuous diffusion is assumed, but shows a characteristic variation with angle which could be looked for experimentally. The related pair correlation functions are dominated at small r and t by vibrational effects. Although simple and extreme the model explains several aspects of the observations of Brockhouse and Pope in 1959 and others. A brief discussion of the coherent scattering cross sections for the model is given although explicit formulae are not obtained.
G V Chester and A Thellung 1961 Proc. Phys. Soc. 77 1005
The exact expressions for the transport coefficients of a metal are used to show that the Wiedemann-Franz law is valid provided that (a) the electrons do not interact with each other and form a degenerate Fermi-Dirac assembly, (b) the scattering of the electrons is due to impurities or lattice vibrations and is elastic. The derivation is valid no matter how strong the scattering and it is therefore more general than the usual weak-coupling derivation of the Wiedemann-Franz law.
E H Putley and W H Mitchell 1958 Proc. Phys. Soc. 72 193
The electrical conductivity and Hall effect have been measured over the temperature range 20°K to 500°K on single crystals of silicon with extrinsic carrier concentrations between 2 and 5 × 1012 cm-3. The Hall mobility for electrons and holes can be represented between 100° and 300°K by the expression 1.2 × 108T-2 and 2.9 × 109T-2.7 respectively. Both these results indicate a higher Hall mobility than has been previously reported, and the result for holes is greater than values reported for the drift mobility. From the results between 350° and 500°K the expression ni = 3.10 × 1016T3/2 exp -0.603/kT was obtained for the intrinsic concentration. Attempts were made to estimate the total impurity concentration in these specimens. The variation of extrinsic carrier concentration with temperature and the effect of impurity scattering at 20°K both indicate that the total concentration of impurities is less than 1014 cm-3.
R M Wood 1962 Proc. Phys. Soc. 80 783
Lattice constants have been determined for a specimen of alpha titanium of greater purity than hitherto examined. Values of a0 = 2.95111 Å ± 6 × 10-5 and c0 = 4.684 33 Å ± 10 × 10-5 differ significantly from previous, accepted figures obtained by Clark in 1949. Comparative impurity contents for two grades of pure titanium are given.
E Rabinowicz 1958 Proc. Phys. Soc. 71 668
Stick-slip oscillations are normally analysed in terms of the kinetic friction-velocity and the static friction-time of stick characteristics of the rubbing surfaces. It is shown that, in addition, a critical distance, of the order of 10-3 cm, enters into the calculations, being the minimum resolving power of the friction process. Stick-slip oscillations must normally have an amplitude greater than the critical distance, and thus increased spring stiffness is often effective in eliminating stick-slip. Using the critical distance concept, it is possible to deduce a simple relationship between the static and kinetic coefficients of friction, and this is confirmed by experimental data.
B K Ridley 1963 Proc. Phys. Soc. 82 954
The inherent instability associated with a specific differential negative resistance in a solid is discussed for the two cases voltage-controlled and current-controlled differential negative resistance. In the case of voltage-controlled differential negative resistance, it is shown that domains of high electric field occur. These domains are generally mobile and their movement is discussed. In the case, of current-controlled differential negative resistance, high current filaments form. The sizes of the domains and filaments are governed by the size of the specimen and by the principle of least entropy production. The effect of an external circuit is to inhibit stable filament formation in the case of current-controlled differential negative resistance and impose conditions under which stable domain formation can be observed in the case of voltage-controlled differential negative resistance.
J C Rivière 1962 Proc. Phys. Soc. 80 124
The average work functions of vacuum-deposited thorium films and of thorium foil have been measured by the Kelvin contact potential difference method, under ultra-high vacuum conditions. A reproducible value of 3.455 ± 0.012 ev was found for the work function of the vacuum-deposited films. In the case of the foil, the work function increased continuously with the duration of electron bombardment, eventually reaching a limiting value of 3.728 ± 0.010 ev after ninety-seven hours of bombardment. Reasons are discussed for identifying this value with the average work function of well-aged, polycrystalline thorium.
D J Sandiford 1958 Proc. Phys. Soc. 71 1002
Measurements of carrier lifetime have been made on both n- and p-type silicon crystals over the temperature range 0°C to 200°C. Results are given for both high and low values of injected carrier concentrations. A comparison is made with the Shockley-Read picture of carrier recombination. The results and theory may be reconciled on the assumption that the capture probabilities of the recombination centres are temperature dependent, and that the energy levels of the centres lie 0.45±0.05 eV above the valence band.
N Cusack and P Kendall 1958 Proc. Phys. Soc. 72 898
J W Tucker 1967 Proc. Phys. Soc. 92 1143
An examination is made of the decoupling procedures which have previously been used in a Green function treatment of the spin-phonon interaction in paramagnetic crystals An exact equation connecting the Green function of the phonons with those of the spin system is derived.
T A Green 1967 Proc. Phys. Soc. 92 1144
The wave function used by Rudge as a basis for modifying the Ochkur approximation is generalized The results obtained with the new function cast doubt on the validity of the arguments used by Rudge and Crothers in support of Rudge's modification.
S J Czyzak et al 1967 Proc. Phys. Soc. 92 1146
Using methods described by Saraph, Seaton and Shemming in 1966, collision strengths have been calculated for the isoelectronic sequences 2p3, 2p4, 3p2 and 3p4.
A Joseph 1967 Proc. Phys. Soc. 92 847
A general study of a new system, known as a spin dipole, is made. Its properties are contrasted with those of a point dipole, a system which has recently received some attention. The Schrödinger equation for the eigenvalue problem associated with zero energy is solved. This makes it possible to give conditions for the existence of bound states for the finite (spin) dipole.
P L Altick and E N Moore 1967 Proc. Phys. Soc. 92 853
The structure of some low-lying autoionizing D states in helium has been investigated. Eigenvectors are presented which show that a plus-minus classification is appropriate. The relationship between structure and width is discussed.
M Ryle 1965 Proc. Phys. Soc. 85 201
The exciting contributions made by radio astronomical observations over the last decade would not have been possible without the development of radio telescopes of increasing sensitivity and resolving power. In particular the study of the `radio galaxies' has depended very much on the availability of instruments capable of determining their positions with accuracy, investigating their detailed angular structure and their radio spectrum. These sources have a radio emission very much greater than that of our own Galaxy, and the mechanism by which this intense radiation is produced is of great astrophysical interest; the socalled `quasi-stellar' sources in which the whole radio emission originates in a region only about one hundredth of the dimensions of the galaxy, represent an extreme case involving unknown sources of energy.
By using radio telescopes of great sensitivity and angular resolving power, radio galaxies can be detected at very large distances; owing to the time taken for the radio waves to reach the earth, they are consequently observed as they were some thousands of millions of years ago, and such observations offer the possibility of exploring evolutionary changes in the Universe. In order to extend these types of observation, more powerful instruments became necessary, but the construction of larger steerable paraboloids of sufficient accuracy presents very great engineering difficulties. More economical instruments have been built by using fixed parabolic cr spherical reflectors, which can be supported from the ground at many points, but even with these instruments the cost becomes very great if an angular resolution better than five minutes of arc is sought.
Alternative methods of building large telescopes have been developed, in one of which advantage is taken of the fact that for most observations the sky can be regarded as unchanging over the period of observation; it is then not necessary to have the whole of the telescope present at the same time, and a large effective instrument may be `synthesized' by using two small elementary aerials arranged successively in all the positions present in the large area. The observations may be combined in a computer to produce a map of the sky having a resolution and signal-to-noise very much greater than that associated with the small elementary aerials.
Four large instruments have been built using this principle, two of which have been in use for six years. They have been particularly valuable both in enabling large resolving powers to be attained at long wavelengths in order to establish the radio spectra of the sources, and in extending the observations to the weakest sources yet observed.