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Synopsis An attempt is made to study in a simplified model of a binary substitutional alloy the influence of the differences in atomic radii of the constituent atoms and in the potential energies of the various possible pairs of atoms. The theory is developed for linear, simple cubic, and body centred cubic lattices, and it is found that the order-disorder transition in the three-dimensional lattices can be either first or second order depending on the differences between the various potential energies. The results are applied to the case of -brass. The agreement of theory with experiment is as good as can be expected from a theory involving necessarily a large number of simplifying assumptions. The effect of lattice vibrations on our results is considered briefly.

Summary The difficulty of the redundant zeros in the theory of the characteristic matrix, which has been pointed out by Ma 4) is studied in some detail. Another difficulty inherent to the theory in its present form is pointed out.

Synopsis Kramers' variational method is used to derive the partition functions per spin for the cubic ferromagnetic structures. These partition functions are compared with the partition functions derived by the approximate methods of Bethe, Kirkwood and Zernike. The case of the two dimensional square ferromagnet with both nearest and next nearest neighbour interactions is also briefly discussed.

Synopsis It is shown how simple kinetic arguments can be used to derive approximate expressions for the thermal conductivity, electrical conductivity, thermoelectric power, Hall constant, and magnetoresistance of metals and semi-conductors, including in some cases the contribution from lattice currents.

We develop a theory for the attenuation of sound in liquid helium, valid at temperatures below about 1°K, by considering three-phonon processes. We also consider some higher-order contributions to the attenuation and consider the influence of finite lifetimes on the velocity of sound. We compare our results with experimental data and also discuss theories developed by other authors.

After a brief introduction to the problem and a discussion of the basic assumptions to be made, we derive the Bloch equation—relaxing to zero magnetization and containing one relaxation time only—through a coarse-graining in time. We also derive an integro-differential relaxation equation which is shown to lead to the Bloch equation in the case where there is no driving field.

We present a Green function calculation for the susceptibility of a Heisenberg antiferromagnet. In the random phase approximation the susceptibility at the Neel point has the molecular field value and the perpendicular susceptibility is independent of temperature. These results are modified in the generalised Callen approximation which we also consider. We include a brief mention of spin-flopping and give an expression for the temperature dependence of the critical field.

Synopsis We have applied the results of a previous paper to evaluate the Hall coefficient of bismuth at liquid helium temperatures, using a generalisation of Dingle's expression for the Fermi level as a function of the magnetic field strength and Shoenberg's parameters for the energy surfaces. The oscillatory part of the Hall coefficient is satisfactorily reproduced, but our theory predicts a linear behaviour of the non-oscillatory part, while a quadratic dependence is found experimentally. Including the contribution to the conductivity due to holes changes the field dependence of the steady part of the Hall coefficient from H to H1.3, and does not significantly alter the absolute magnitude or the oscillatory part.

Synopsis It is suggested that the conductivity tensor may give useful information about the shape of the Fermi-surface.

It is pointed out that the density matrices p HF used by quantum chemists and others in the discussion of the Hartree-Fock self-consistent field method differ from the density matrices p SM introduced in statistical physics, and that the idempotency condition for p HF has therefore a physical meaning which is different from the same condition for p SM . A suggestion is made for a consistent nomenclature.

The equations of motion of the Fourier components of the density are used to derive both the hydrodynamic equation of continuity and the hydrodynamic equation of motion. A brief discussion is given of the quantum mechanical case.

Synopsis The variational method developed by Kramers and Wannier is applied to the I s i n g model of a simple cubic ferromagnet and in this way equations are derived from which the approximate values of the partition function and thus of the configurational energy and specific heat can be obtained. These equations are solved both by series expansions and by numerical methods at temperatures above the Curie temperature.

Synopsis A Lennard-Jones and an “exp-6” potential function for neon are investigated for the possible existence of a bound state of a neon molecule, by a method used by de Boer in the case of helium. It is concluded that there exists a bound state with an energy of about 5 × 10-5 atomic units ( 0.002 eV).

From the experiments on the deviation of the cornea's surface from a sphere, information can be obtained about the anisotropy of the tangential tensions acting in the cornea.

A proof is presented of a statement in an earlier paper by the authors 1) that the “ladder diagrams” which are made up entirely of vertices, in which a pair of quasi- particles is annihilated and another pair of different energy is created to take its place, do not lead to a divergence.

This paper discusses the properties of a single 3He impurity in liquid 4He at zero temperature. An exact perturbation expansion is developed. All properties of the boson system are assumed known and the single particle fermion propagator is expressed in terms of these. An approximation is introduced which makes the diagrammatic expansion correspond to the fermion interacting with the elementary excitations of the Bose system. The analytical properties of the boson-fermion vertices are investigated. Various expressions for the effective mass of the fermion are discussed and temperature corrections are shown to be negligible. The main contribution to the change in mass is found to come from the interaction with virtual rotons. Experiments are used to estimate some of the parameters of the theory. It is found that the weight of the quasiparticle pole is only about 1 3 . Finally a comparison with other recent theoretical work is made.

We compare the results obtained by Ginzburg and Fain by a self-consistent field method with those obtained by Tahir-Kheli and ter Haar by a Green function method, and find them comparable in accuracy over most of the temperature range. Their results for the Curie temperature for s.c., b.c.c., and f.c.c. lattices with spin 1 2 , 1, 3 2 , 2, 5 2 , and 3 are also compared with results obtained by Rushbrooke and Wood. Tahir-Kheli, Brown and Luttinger, and Callen.

Synopsis A rigorous series expansion for the partition function per spin for a three-dimensional simple cubic ferromagnet in decreasing powers of the absolute temperature, 1 2 λ = 1 + 3 2 K 2 + 31 8 K 4 + 5 461 240 K 6 + 2 436 211 13 440 K 8 + … , ( K = J / 2 k T ) is found and compared with expansions obtained by various approximation methods.

This paper is a continuation of an earlier one 1 ) †) ) giving the general theory. In the present paper this general theory is applied to experimental results. In the first section we discuss the influence of the finite period of stretching prior to a relaxation or creep experiment. The physical meaning of the relaxation spectrum function N(v) is also discussed. The second section describes an approximate method to obtain a rough impression of the relaxation spectrum from relaxation experiments 2 ). This method is compared with the approximate method proposed by A l f r e y 3 ). In section 3 we determine relaxation spectra from experimental data of various authors, after having first dealt with the influence of the fact that any experiment only extends over a limited, finite time interval. Section 4 deals with and compares various methods of exactly obtaining the relaxation spectrum. Section 5 briefly discusses the question of the yield value and shows how experimental restrictions often will produce an apparent yield point which would not have been found, if the experiment could have been performed more accurately. We also briefly discuss the question of non-linear elements and the phenomenon of the brittlepoint, or rather the glass-transitionregion.

Synopsis The considerations of the statistical aspect of the second law of thermodynamics of a previous paper are extended. The influence of fluctuations in a class of simple models is investigated generally, and expressions found for the mean life and average time of recurrence of non-equilibrium states which agree with previous results. The models include the Lorentz model of conduction electrons in a metal and the Ehrenfest wind-wood model. The results are used to illustrate the time behaviour of an ensemble of such systems.