Table of contents

A two-layered Ising model is presented which maps to the Ashkin-Teller (AT) model (1943) for certain ratios of the two-spin couplings. Thus the model is able to exhibit the same critical exponents as the AT model, which are in general different from the usual Ising exponents; even continuous dependence of the critical exponents on the energy parameters is to be expected.

The study by differential scanning calorimetry under atmospheric pressure, of the cooling down to the metastability breakdown and then the heating of chloroform, 1-2 dichlorobenzene, o-xylene, cyclohexane and carbon tetrachloride with volumes about a few mu m³ provides evidence of new metastable crystalline phases of these compounds. For each of these compounds, during heating, one could determine the temperature corresponding to its transformation into either a stable liquid or solid phase or into another metastable phase and also evaluate the molar heat of the corresponding transformation.

The thermodynamics of Wigner crystallization is considered. The melting curve in the classical regime is p=AT⁴. In the T=0 limit, the change in potential energy is related to the volume change. A dimensional argument is given to show that in four dimensions, the melting curve in the rho -T plane is given by T=K rho ¹2/, a fully quantal result. Finally, a schematic plot of critical density versus dimensionality is achieved.

The mobility of negative ions in superfluid ³He is calculated by making the assumptions that the differential scattering cross section is constant and that the scattering of quasiparticles is elastic. The mobility is anisotropic in the A phase and depends on the angle between the direction of motion and the l vector of the superfluid.

The effect of a resonant intermediate state on a two-photon transition is experimentally investigated in a three-level paramagnetic spin system. It is shown that, together with transitions which involve all three levels, a distinct Raman-like process is always present, to which the intermediate does not take part.

A new CPA theory for spin waves in the diluted ferromagnet gives excellent results for the simple cubic nearest-neighbour case.

The theory of thermal dielectric relaxation, developed by Gupta and van Overstraeten (see ibid., vol.7, p.3560 (1974)), has been verified experimentally, using the system Al-amorphous As₂Se₃-Al. The observed dependence of the temperature T_m, at which the relaxation current is a maximum, upon applied voltage is quite different from that predicted by theory.

Wavelength-modulated absorption measurements on MgO:Mn show the presence of Mn³⁺ and Mn²⁺. The lowest spin-allowed transition of Mn³⁺ occurs at 520 nm. Weak bands at 301, 356, 389 and 426 nm are attributed to transitions from ⁶A_1g to the ⁴T_1g(P), ⁴T_2g(D), ⁴E_g(G)+⁴T_2g(G) and ⁴T_2g(G) states of Mn²⁺, respectively. The latter band shows four zero-phonon lines with an over-all splitting of 34 cm^-1 revealing a spin-orbit splitting of the ⁴T_2g(G) state reduced by a factor of four by the action of a dynamic Jahn-Teller effect. Stress experiments indicate that the dominating Jahn-Teller interaction is with T₂ symmetry vibrations.

The scattering cross section of slow neutrons for a proton in low-temperature hydrogenous solids is simply related to the frequency of molecular motion divided by the incident neutron energy and the effective mass of the proton. Experiments applied to solid o-xylene and mesitylene give satisfactory results, showing great differences in the dynamics of the methyl groups in these materials.

Because of current interest in charged fluids the problem of the structure of a mixture of charged hard spheres of unequal diameters sigma ₁ and sigma ₂ is studied in the limit sigma ₁/ sigma ₂ to 0. In particular, the mean spherical model (MSM) has been solved in this limit. The thermodynamics of the mixture is discussed and some typical results for the partial radial distributions are presented. The MSM has the defect in the limiting case sigma ₁/ sigma ₂ to 0 that the pair correlation function of the point ions always becomes negative at sufficiently short distances. Therefore, to test the predictions of the model, Monte Carlo calculations are presented for this same system for two molten-like states. One of these is just above the expected melting point and the other at an extremely high temperature. In the light of these results, the model's relevance to real systems is briefly discussed, CuCl BeF₂ and HF each being referred to. An interesting property of the model which we demonstrate is that polymerization can occur.

Pair interaction potentials for NaI are obtained by fitting to solid state data at 0K and to some properties of the diatomic molecule. In order to examine the effects of polarization on properties of molten NaI, molecular dynamics simulations are performed with rigid ion and shell model potentials the shell model potentials being fitted to the same data as are used for the rigid ion potential with the additional parameters being determined from dielectric constant data. Two shell models are considered; one is fitted to diatomic molecule properties and the other is more in line with empirical ionic radii. Simulations with 216 ions have been carried out for these potentials and the following results are presented: radial distribution functions velocity and force autocorrelation functions and mean square displacements.

The elastic stiffness constant tensor components of single crystals of bismuth and its alloys (3 at.%Sb, 5 at.%Sb, 7 at.%Sb and 10 at.%Sb) with antimony have been obtained between 4.2K and room temperature from measurements of ultrasonic wave velocities made by the pulse echo overlap technique. In contradiction with previous work on polycrystalline alloys the ultrasonic velocities are found to increase smoothly with antimony composition. The electronic contribution to the elastic constants is negligibly small. The temperature dependences of the elastic constants, which are remarkably similar for bismuth and the alloys, have been fitted by an anharmonic oscillator model.

Solid state phase transitions are treated as thermodynamic instabilities. Limiting relations between the specific heat c_p, thermal expansion coefficients and elastic compliance elements are obtained for certain phases as the transition is approached. For example, such relations hold for alpha -quartz, but not necessarily for beta -quartz. A criterion is given to show whether the behaviour of the high-temperature phase, in regard to such relations, is different to that of the low-temperature form. For alpha -quartz it is shown, using only elastic constant and thermal expansion data, that c_p diverges, while for beta -quartz it remains finite, consistent with experiment. The relations derived for the low-temperature forms are similar to the Pippard relations, but have a different constant of proportionality.

Both isolated anion vacancies and vacancy pairs are found to contribute to the anion mass transport in AgCl and AgBr, as determined from the anion tracer self-diffusion in pure and in heavily doped specimens. The data were analysed by means of the Lidiard-Debye-Huckel theory, despite some very serious questions as to the validity of this model when the defect concentrations are as large as in the present experiments. In the case of AgCl, the diffusion parameters appear to be normal, and both pairs and single vacancies are found to make comparable contributions to anion diffusion. In AgBr, however, the effective activation energies and entropies appear to be very anomalously large, especially those for the single vacancy, indicating the involvement of some phenomenon not included in the usual simple model of point defects in ionic crystals.

A system is described which has been successfully used to study the propagation of high-frequency phonons in liquid ⁴He at T=0.1K and pressures up to 24 bar. The properties of superconducting tunnel junction detectors are discussed in some detail and the various contributions to the received signal shape are considered. A reliable and accurate method is described of linearly translating specimens in ³He-⁴He refrigerators which does not give an excessive heat load. Examples of received signals are presented which show the difference between the frequency-selective tunnel junction detectors and the broad band graphite bolometers.

Using a quantum mechanical non-equilibrium formalism, the momentum distribution of an electron is evaluated for various times after it has been inserted with a given momentum into a dissipative medium. The medium is assumed to have an excitation threshold, and so might represent plasmons or optical phonons. The initial momentum of the electron is taken to be large, allowing an approximation based on the neglect of recoil correlations to be used. The distributions obtained are compared with those resulting from the Boltzmann equation, and the effects of virtual processes and of recoil correlations illustrated. At short times, considerable differences from the Boltzmann predictions are seen. At longer times, the distributions approach the Boltzmann predictions if the coupling of the electron to the medium is weak.

The steady-state form of the distribution function of electrons in the conduction band of a semiconductor, when the electrons are photoexcited from an impurity level by one or two monochromatic laser beams, is analysed for non-polar acoustic and for both non-polar and polar optical phonon scattering. A single laser line does not alter the Maxwellian distribution, but inverts the population near the band edge. Two laser lines induce non-Maxwellian elements into the distribution function whose character depends upon the laser bandwidths relative to the bandwidth for acoustic phonon scattering. Small bandwidths give rise to spikes in the distribution, but bandwidths comparable to the range of frequencies involved in acoustic phonon scattering may produce, in the absence of strong optical phonon scattering, profound deviations from the Maxwellian form. Numerical solutions of the Boltzmann equation for a few illustrative cases are presented.

The phenomenon of superlinearity in photoconductors is investigated using the generalized theory of photoconductivity developed in a previous paper (see ibid., vol.8, p.3360 (1975)). Superlinearity is shown to occur as a result of the changes in the photoconductive capture cross section with light intensity. The necessary conditions which are required for superlinearity are deduced from the analytical formulation of the problem. Several trapping configurations for which superlinearity may occur are examined. The resultant superlinearity is studied in detail and the variation in the superlinear characteristics with the trap parameters is discussed. Very good correlation is demonstrated between existing experimental data and computed theoretical results.

Measurements are reported of the magnetization of single crystals of ErAl₂ between 4.2K and 16K for magnetic fields up to 150 kOe applied along the (111), (110) and (100) directions. The results are interpreted in terms of the crystal field using a two-dimensional molecular-field approach. Within this microscopic description of the magnetization and the related magnetocrystalline anisotropy the authors use only two temperature-independent crystal field parameters and the Curie temperature. A least-square fitting procedure gives B₄=1.10*10^-4 meV, B₆=-1.34*10^-6 meV and T_c=14K. With these parameters they obtain good agreement between calculated and measured magnetization curves.

A model similar to the Syozi-Rapaport model (1965 and 1972) of a dilute Ising ferromagnet is considered, in which the magnetic field, rather than the interaction, is a random variable taking values H_a+h and H_a-h with probabilities p and 1-p, respectively. For p=¹/₂, it is shown that an analogy can be drawn between the two models; however, in the present model the magnetic field and susceptibility are 'renormalized', as opposed to the interaction and specific heat in the Syozi-Rapaport case. The possible occurrence of a two-phase region below T_c, in which up and down spins are segregated, is discussed.

Measurements are reported of the nuclear magnetic resonance absorption lineshape and spin-lattice relaxation time of solid cycloheptane from 50K to the melting point of 265K. Considerable molecular motion is found in the various solid phases but conclusions about the types of motion involved are difficult to reach due to a lack of knowledge of the crystal structure. Although the results in phase III can be explained by molecular pseudorotation process with an activation energy of 1.7 kcal mol^-1, it is quite possible that the motion of this very flexible molecule is not of a well defined nature but is a complex and irregular mixture of motions which have comparable restricting barriers. In the higher solid phases, it appears that free isotropic molecular rotation commences and that this is followed by a molecular diffusion process approximately 40K below the melting point.

The complex dielectric constant has been measured at five audio frequencies (10²-10⁴ Hz) over the temperature range 4.2-400K for eight concentrations (0.001-3.0 mol%) of erbium in calcium fluoride. Relaxation processes with activation energies of about 0.15, 0.4, 0.5 and 0.7 eV have been observed which correspond to previously reported dipolar complexes in rare-earth doped alkaline-earth fluorides. In addition, a previously unreported relaxation with an activation energy of approximately 0.028 eV has been found at low temperatures and high rare-earth concentrations. It is concluded that this relaxation is cluster-associated.

The oriented gas approximation for the polarizability of a molecular crystal neglects the Coulomb field of induced dipoles throughout the crystal. This would at first appear to be a serious shortcoming since the Coulomb field is of the same order as the applied field. The oriented gas model is extended by including the Coulomb field and draw a comparison to determine its effect. Sulphur is taken as an example for the calculation of Raman scattering tensors derived from the polarizability model. This extension of the oriented gas approximation gives a better justification of its validity with, in cases where the molecules are symmetrically equivalent, no great encumbrance of the end result.

The Green functions for excitations of bound electrons and magnons interacting with phonons are studied, linearizing the equations of motion for the operators that define the system. These two systems are treated simultaneously due to their similarities. The light-scattering cross section is calculated on the basis of the response functions obtained. The effect of the bound electron or magnon-phonon interaction is shown to be important in the vicinity of the point where the dispersion curves of the free excitations cross each other. It is in this region where real mixed modes exist. It is demonstrated that Raman scattering is a very sensible way of detecting these mixed modes and the several variables involved in the interaction process. The temperature, external magnetic field and q-direction dependence of the cross section for crystals like cerium ethylsulphate and YIG is studied.

Far-infrared absorption spectroscopy has revealed the presence of a strong absorption line at 38 cm^-1 in the Jahn-Teller distorted phase of TbVO₄. The fact that this is at a lower energy than any previous observations would indicate, is attributed to a Davydov splitting caused by coupling to odd-parity phonons. The temperature dependence and the splitting of this line in a magnetic field are also reported. The construction of a Hamiltonian incorporating this odd-parity coupling is discussed and solutions are found using Green function techniques.

High resolution M_4,5 N_4,5 N_4,5 Auger spectra have been observed from solid cadmium using X-ray photoelectron spectroscopy. The multiplet structure is similar to that observed from free Cd atoms by Aksela and Aksela (see J. Phys. B, vol.7, p.1262 (1974)), but the solid state spectrum is shifted to higher kinetic energy by 12.1+or-0.7 eV. Detailed comparisons of solid state and free-atom Auger and one-electron binding energies are used to evaluate current methods of calculating Auger energies. The relationships expected between relaxation terms introduced into one- and two-step models of the Auger process are shown to hold. The failure of Hartree-Fock calculations to predict the observed multiplet splittings is shown to arise from overestimates of the F² and F⁴ electrostatic integrals. Empirical values of these quantities are derived which, when combined with the spin-orbit coupling constant xi _4d predict the observed multiplet splittings.