Table of contents

The authors calculate exact upper and lower bounds for the Helmholtz free energy of a 1D tight-binding disordered alloy as a function of temperature. They show that the average of the upper and lower bounds, calculated using very few (of the order of five) exact moments of the density of states, is an excellent approximation to the free energy of the system. They also use three different approximations for the density of states of the disordered alloy and show that they all give quite similar and precise values for the free energy. Thus, if only the free energy of a disordered system is required, the average of upper and lower bounds seems to be the most convenient procedure to use. If other properties are calculated as well, then obviously some approximation to the density of states will be needed, which will certainly be sufficient for the calculation of the free energy.

A new numerical method is presented, which allows for the calculation of the conductivity and the localisation properties of the eigenstates in a one-dimensional disordered system described by the Anderson Hamiltonian. The computer storage requirements of the procedure are independent of the length of the system, the maximum system length treatable being only limited by the computer time available. First results obtained for a system containing up to 10⁸ sites indicate that the DC conductivity obeys the central limit theorem. It vanishes in the limit of zero temperature and fulfils a scaling law.

The previous derivation of a cluster model for the spectrum is extended to finite temperatures. It is shown that the zero temperature spectrum calculated for a cluster model with temperature-dependent parameters matches the finite temperature spectrum of a multimode Jahn-Teller system.

The structure of the high-temperature, plastic form of lithium sulphate has been determined from neutron powder diffraction data collected at 908K. The structure is face-centred cubic, a=7.07 AA with the SO₄^2- ion situated at the origin and the oxygen atoms rotationally disordered about the sulphur atom. The Li⁺ ions occupy the +or-(¹/₄,¹/₄,¹/₄) positions. The large isotropic temperature factors (B(SO₄)=17.5 AA² and B(Li)=33 AA²) suggest that the lithium ions occupy a statistical distribution of sites instantaneously displaced from +or-(¹/₄,¹/₄,¹/₄), in short-range correlation with the instantaneous orientations of the surrounding SO₄^2- ions. This is the first example of a fast ionic conductor where ionic motion is shown to be enhanced by rotational motion of the translationally static counter ions, although closer study of simple alkali salts may reveal several other examples.

The acoustic impedance of superfluid ³He for the transverse mode in the collisionless limit ( omega tau = infinity ) is calculated under conditions h(cross) omega <<2 Delta and h(cross) omega <<kT. The boundary condition is chosen to be consistent with diffuse scattering for quasiparticles. Graphs for the temperature dependence of the impedance in the B phase are given as results of numerical calculations. In the A phase, at low temperatures, leading contributions are either like T³, T⁴ or T⁵ for l//e, l//q or l perpendicular to e, q respectively.

The conductivities of five single crystals of silver chloride have been measured from room temperature to close to their melting point: one crystal was pure and the others doped in the range 50-500 ppm with Cd²⁺. These conductivity data were first analysed using non-linear least squares techniques and the standard model. The resulting defect parameters and the defect concentrations and ionic mobilities with which they reproduce the experimental data are then compared with the same quantities derived in a second analysis which incorporates a recently determined temperature-dependent Frenkel defect formation energy. The value of the enthalpy of association of the cadmium-vacancy complexes is in reasonable agreement with recent estimates as are the values of the parameters governing migration by the vacancy and two interstitialcy mechanisms.

A new effect has been observed by M. Pepper (1979) at low temperatures when the conduction is restricted to two dimensions in an n-type GaAs impurity band: at carrier concentrations less than about 1.5*10¹¹ cm^-2 the conductance is found to oscillate as a function of concentration. The sub-band structure of the Pepper device is studied here by means of a variational calculation. In particular the authors find that the oscillations in the conductance must be restricted to the lowest band since the concentration at which the Fermi level enters the second band closely agrees with Pepper's value above.

Properties at zero temperature are studied for a random-bond Ising model on a linear triangular lattice, i.e. the straight polyiamond lattice, which is such a one-dimensional disposition of equilateral triangles that two successive triangles have a common side. The exchange integrals on the bonds which are the common sides of two triangles take values J(J>0) and -J with probabilities p and 1-p, respectively, and the exchange integrals on the other bonds take the value J. The entropy and the spin glass order parameter at zero temperature are both non-zero, while the spontaneous magnetisation is zero. In addition to the entropy and the spin glass order parameter, the authors give the ground state energy per site as a function of p.

Frequency crossing experiments using thermal phonons carried out on V-doped Al₂O₃ show that the 280 MHz hyperfine splitting of V³⁺ can easily be resolved by this technique at a phonon frequency of 166 GHz. From the values of the linewidths of the hyperfine lines it is clear that the effect of T₂ symmetry strains is very much less than that of E-type strains. This suggests that the effect of T₂ strains is quenched by a dynamic Jahn-Teller effect with gamma <<1. The data also indicate that the magnetoelastic constants mod G_- mod and mod G₁₅ mod are very similar to mod G₄₄ mod and mod G₅₁ mod and not larger as previously found.

The nuclear relaxation times and the linewidths of ²⁷Al resonance in amorphous and crystalline compounds Al₂O₃.MnO.SiO₂ were measured as a function of temperature. There is evidence of a strong relaxation around the freezing point T_f in the amorphous system whereas nearly constant relaxation time is observed above the Neel temperature T_N in the crystalline system. The nuclear relaxation above T_f is governed by the electronic correlation time and the short-range 'order'. Below T_f the inhomogeneous linewidth is related to the hyperfine field H_n while the relaxation rate is due to the rapid fluctuating part of the latter.

Audiofrequency dielectric measurements down to 4 mK on gamma-irradiated natural quartz crystals revealed the existence of anomalous dielectric behaviour. The results show a dielectric relaxation time which decreases with decreasing temperature and suggest a new relaxation mechanism in smoky quartz.

The audio frequency dielectric constant has been determined over the temperature range 5.5-400K for various samples of alkali-doped strontium and barium fluoride. For strontium fluoride, strong relaxations are found for sodium, potassium, and rubidium dopants and the activation energy is largest for the potassium dopant. For barium fluoride, strong relaxations are observed for potassium and rubidium and the activation energy is larger for rubidium. A physical argument based on ion size and activation energy is given supporting the assignment of the principal peaks to substitutional alkali-metal-nearest neighbour-vacancy pairs. The activation energy for the motion of the bound vacancy in rubidium-doped barium fluoride is found to be about the same as that reported for the motion of 'free' vacancies and consequently the current interpretation is consistent with empirical observation that in all materials studied to data the energy for reorientation of a bound interstitial or vacancy around a substitutional ion is less than or equal to the energy for motion of the free species.

The results of photo-EPR and optical absorption measurements are presented for chromium doped ZnS, ZnSe and ZnTe. An analysis of these experiments enables the authors to determine the character of the absorption bands observed beneath the 'band-band' transitions as being due to the Cr²⁺ to Cr⁺ photogeneration processes. The experimental results are interpreted within the framework of the theory for the photoionisation transitions, associated with the lattice relaxation. In particular, it has been possible to establish the E_th and E_opt energies of the Cr²⁺ to or from Cr⁺ processes.

Measurements of the electrostriction of three single crystals of YIG have been made in order to investigate a hypothesis that a combination of electrostriction and inverse magnetostriction might contribute to the magnetoelectric effect in YIG. The electrostriction was found to be large, the values being such that the entire observed magnetoelectric effect in YIG can be accounted for in terms of the proposed electrostriction-inverse-magnetostriction mechanism.

A strongly temperature-dependent anomalous structure observed in the measured voltage derivative of the dynamic conductance of Al/Alox/Pd tunnel diodes has previously been interpreted in terms of a 'resonant tunnelling via localised impurity states'. This is in some sense supported by further experiments, but it appears that the anomalous structure is due to processes which do not take place in the oxide layer of the diode, but in the top electrode Pd film itself. The structure appears at low temperatures T<T_c (T_c approximately=3-4K) and may be related to an abrupt phase transition. The effects of temperature variation and application of magnetic fields have been examined. It follows that the phase transition may be considered as a magnetic ordering, with the occurrence of hysteresis in the ordered phase. An interpretation in terms of a transition to a ferromagnetic phase in a very dilute alloy of Pd and magnetic impurities (Fe, Ni, Co,...) introduced during the sublimation of Pd from a hot W wire is suggested. Measurements made on films of Pd containing controlled magnetic impurities support this suggestion.