Table of contents

In many liquids the absorption of sound waves is very much larger than can be explained classically, in terms of viscosity and heat conduction. It is now fairly well established that different types of liquids behave very differently in this respect, and that the cause of the excess absorption in unassociated, polyatomic liquids like benzene and carbon disulphide lies in the incomplete excitation, by the sound wave, of the vibrational degrees of freedom. It is shown that this effect leads to mean dispersion frequencies in the range 10⁹ to 10¹⁰ c/s. at 300° K. This frequency range shows that, as in the case of gases, the efficiency of collisions in producing excitation or de-excitation of vibrational degrees of freedom is fairly low; a theoretical treatment of this effect is outlined. Detailed considerations of temperature coefficients of absorption lead to the conclusion that all the vibrational levels of a liquid do not relax at the same frequency but that high excited levels relax at relatively low frequencies. In the case of carbon disulphide a numerical estimate of these individual dispersion frequencies is made. It is also shown that the variation of absorption with concentration in binary mixtures can be described quite simply in terms of the analysis developed in this paper.

In this paper some theoretical consequences of the existence of second sound in helium II are discussed. A method is suggested for setting up a quantitative phenomenological description of the thermodynamical behaviour of helium II. It is known that expressions for the velocities of first and second sound may be obtained by using quite general models. The thermodynamical behaviour may be described in terms of the velocities of these two types of sound, so that it becomes possible, in principle, to obtain explicit values of the unknowns by combining the two sets of equations. On the basis of these ideas a discussion is given of the coefficient of thermal expansion of helium, the ordinary thermal conductivity, and the attenuation of second sound.

The paper contains a discussion of the modifications necessary to the Debye theory of specific heats when the sound velocities are temperature-dependent.

It is shown that the surface energies of inert-gas crystals are proportional to their sublimation energies. The constant of proportionality is evaluated for the {111},- {100} and {110} faces for different assumed forms of the interatomic repulsive forces; to within 15% it is independent of the face, and of the form of the repulsive force. The distance of the outermost plane of atoms from the next at a {100} face is 2.54% greaterthan normal; this distortion makes a negative contribution of 1% to the surface energy.

The surface energies of sodium and potassium halide crystals are calculated; the ratio-of the energies of {110} and {100} faces is about 2.5. The contribution of van der Waals-type forces to the surface energy of a {100} face is almost half the total.

Elementary methods are given for the evaluation of lattice sums.

For the purpose of calculating the surface energy and surface double layer for a number of monovalent metals, a simple and yet adequate model is proposed, which does not have the disadvantages of models employed by previous authors. In this the valence electrons are treated according to a simple Sommerfeld model, and the positive charge of the ions is distributed uniformly through the metal. It is shown that by a suitable combination of the methods of Thomas-Fermi and of direct wave mechanics, both the surface energy and the strength of the double layer can be calculated The surface double layers for the metals considered are found to be in the range 0.1-0.5 ev. The contribution to the surface energy from the electrostatic energy in the double layer is found to be very small. In estimating the surface energy, the electrons in a metal can be considered as moving in a box with finite potential walls of suitably determined height ϕ. A temperature-dependent term in the surface free energy due to the change in lattice vibrations caused by the free surface is also considered. The surface energies obtained from ϕ determined in two independent ways agree closely and are found to agree with the experimental values of the surface tension of the liquid metals to within a factor 1.5.

Observations on the spectrum of sodium hydride have been extended to longer wavelengths (from 4600 A. to 6450 Å) and photographed under high dispersion. Analysis of the data thus obtained gives values of the vibrational and rotational constants for several new vibrational levels, among which the lowest levels of the excited state are of especial interest.

The intensity distribution has been calculated from the wave functions appropriate to potential energy curves based on the constants derived from the analysis of the band system. The theoretical estimates are found to be in fair agreement with the experimental results.

The bending frequencies of a linear chain of n mass points have been calculated using a harmonic potential function involving forces between second neighbours. The proper boundary conditions are introduced and a general formula for the bending frequencies is derived.