Table of contents

An alternative proof is given of a Saxon-Hutner type theorem for the energy levels of random alloys in an arbitrary number of dimensions. A comparison is made with other similar theorems in the literature.

The mass-action equation for the equilibrium between interstitial F^- ion-substitutional Y³⁺ ion nearest-neighbour pairs and unpaired interstitials and impurities in CaF₂ doped with YF₃ is studied by a statistical-mechanical cluster theory. Results are compared with the Teltow-Lidiard approximation that defect pairs have an activity coefficient of unity and that unpaired defects have Debye-Huckel activity coefficients. Numerical results are given, showing the contributions of various terms in the cluster-theory expressions for the activity coefficients, and the degrees of pairing predicted by the two method are compared. Although the activity coefficient expressions appear rather different, the degree of pairing from the Teltow-Lidiard approximation is accurate at 1173K at impurity concentrations up to 0.8%. However, at 673K, the possibility is found of deviations at relatively low concentrations, 0.2% from the effect of interactions between unpaired defects.

The concentration of Schottky defects in a sodium chloride crystal containing unpaired and paired vacancies, but no larger nearest-neighbour clusters, was calculated using the Debye-Huckel activity coefficients for unpaired defects and also using cluster-theory activity coefficients which allow more fully for the Coulombic interactions between defects. In the range of temperature extending to 150K below the melting point, the cluster-theory concentrations were 7-10 per cent larger than the Debye-Huckel ones and the differences varied slowly with temperature. Such differences are likely to be unimportant in the analysis of ionic conductivity data.

A general method is presented of incorporating the effects of clusters of constituent atoms in the calculation of the excitation density of states in a disordered material. An unknown parameter is introduced into the logarithm of the secular determinant of the problem and subsequently determined self-consistently by minimizing approximately the interaction between clusters. The single-site version of this procedure reproduces the density of states of the coherent potential approximation whilst an expansion in terms of important clusters leads to results exhibiting the fine structure attributed to localized modes. The results for the phonon spectra of a one-dimensional random binary alloy are in good agreement with those of previous 'exact' methods.

The matrix elements of the lattice Green function for Pitzer's model (describing the out-of-plane skeletal vibrations of an extended polyethylene chain) have been calculated analytically and discussed as to singularities, asymptotic behaviour, density of states, incoherent neutron scattering cross section and localized modes due to an isotropic mass defect. In addition, analytical formulae are presented for the torsional part of the dynamical matrix for a chain in arbitrary conformation.

The electrical conductivity and thermal EMF of liquid Se_1-x-Te_x(x<or=0.3) were measured up to 1000 degrees C. All investigated liquids showed a negative thermopower below a characteristic temperature T* and a positive one above it. The position of E_F relative to E_C and E_V have been ascertained. It was found that E_F is displaced from the midpoint between E_V and E_C as a result of increasing Te concentration. The conduction band seems to develop a more marked tail than the valence band upon the addition of tellurium. This is explained by the strong pi -orbital bonding complex responsible for the forming of the valence band.

The electrical conductivity has been measured on the pellets of Ag₁₃(Me₄N)₂I₁₅, and Ag₁₃(Et₄N)₂I₁₅ as a function of pelletizing pressure and temperature. The density of the pellets formed at different pressures is also reported. It has been found that the conductivity attains its maximum value of pellets compressed at pressures of 2800 kg cm^-2 or higher, while the density approaches its maximum value (99% of the theoretical density) at pressures of approximately 3300 kg cm^-2 or higher, for both the solid electrolytes. The conductivity is corrected for electrode-electrolyte contact resistance at room temperature. The temperature dependence of the conductivity is described by the equations log₁₀ sigma =4.38-993.2/T-log₁₀T and log₁₀ sigma =5.13-1315.8/T-log_1oT for Me and Et electrolytes, respectively, in the temperature range investigated. The associated transport parameters are calculated and various characteristics of 'silver-based superionic conductors' are compared.

The spontaneous magnetization of the Ising model with pure three-spin interactions on a Union Jack lattice is obtained in terms of the magnetic and the ferroelectric orderings of the eight-vertex model. Magnetizations of the two sublattices are found to possess different critical exponents.

Electron spin resonance has been studied in V_1-xCr_xO₂ compounds in the range fo compositions (0.3%<x<3%). The behaviour of the Cr³⁺ resonance in the three insulating phases M₁, T and M₂ has been examined. Strong modifications of this resonance occur at the M₁-T phase transition, for which an interpretation involving charge redistribution is proposed. An intense resonance due to vanadium d-electrons has been observed in the M₂ and T phase. Its characteristics are discussed in terms of localized-electron picture for these compounds.

The time for the recovery after prolonged saturation of the electron spin resonance signal of free radicals in gamma -irradiated 4-methyl-2,6 ditertiarybutylphenol exhibits a remarkable peak in its magnetic-field dependence. At a temperature of 4.2K it may be more than fifty times greater at a field of 0.34 T than at 0.27 T. At 0.34 T the electron Larmor frequency coincides with the frequency of tunnelling rotation of the 4-methyl groups of neighbouring undamaged molecules with a consequent exchange of energy between the magnetic energy of the electron and the mechanical rotational energy of the methyl groups. The effect is to couple the electron Zeeman energy reservoir to a thermal system whose heat capacity is large and which is itself uncoupled to the lattice. The coupling can be switched on and off simply by changing the magnetic field, providing a simple means of studying the rate constants involved. The effect provides a new way of investigating quantum motions in molecular solids.

Existing experimental data for the ground states of Fe²⁺:Al₂O₃ are accounted for by a multimode dynamic Jahn-Teller model in which an Fe²⁺ ion substitutes for an Al³⁺ ion. The first- and second-order Jahn-Teller reduction factors are found to be gamma =0.19, F_a= 0.0015 (cm^-1)^-1 and F_b=0.0024 (cm^-1)^-1 and satisfactorily account for the quenching of the trigonal field. The relaxation time T₁, of the Fe²⁺ ion is then calculated to be approximately 2 mu s at 1.2K confirming that the Fe²⁺ ion is strongly coupled to the Al₂O₃ lattice. The main contribution to T₁ is from the E_theta , E_epsilon components of the lattice momentum acting through the spin-orbit coupling and trigonal-field perturbations. The contributions to T₁ from displacements due to other lattice modes are found to be smaller. An analysis of the APR or EF-EPR lineshape on the Jahn-Teller model is in agreement with all the experimental data.

Measurements of the spin-lattice relaxations times of Cr³⁺ and Fe³⁺ ions in Al₂O₃ are reported for crystals in which Fe²⁺ ions are also known to be present. Marked cross-relaxation to Fe²⁺ is observed when the Fe²⁺ level splitting equals that of Cr³⁺ or Fe³⁺ and a quadrupole-electric-field interaction Hamiltonian is used to explain the results. Other cross-relaxation mechanisms are discussed. It is also shown that an analysis of the temperature dependence of the measured relaxation time and its minimum gives a value for the zero-field splitting of Fe²⁺, even though the Fe²⁺ concentration is very small.

A careful study of the specific magnetic rotation in the crystal field bands of CrBr₃ has been performed at 4.2K. The structures bounds to the spin-forbidden ²E and ²T₁ transitions have also been clearly observed. The results have been compared with the analogous data on CrCl₃ presented in a previous paper (see abstr. A5179 of 1973). For both crystals a complete crystal field calculation, inclusive of the trigonal field perturbation and spin-orbit interaction, has been performed and discussed in relation to the experiments.

Spectral investigations of Pr³⁺ and Nd³⁺ in an aprotic solvent, SeOCl₂+SnCl₄, have been carried out in the visible region. The results of a least-squares fit of the energy levels and intensities of the bands are reported in terms of interaction parameters and Judd-Ofelt intensity parameters. These parameters have been compared with those of the beta -diketonates.

A sharp emission line at 682.8 nm has been found in luminescent CaO containing F-centres. Zeeman data were similar to those obtained on the well-documented ³P to ¹S emission line at 574.1 nm from the F-centre. The effect of uniaxial stress on the 682.8 nm line was qualitatively similar to that on the 574.1 nm line. The 682.8 nm emission line may derive from H^- ions, although the presence of F-centres appears to be necessary for the existence of the emission line. Further evidence is presented that the adsorption lines at 571 and 1731 nm, previously reported in neutron-irradiated CaO, both derive from an even-electron system with orthorhombic I symmetry. F-centres also appear to be required for this centre to exist in CaO and the centre may be a nearest-neighbour pair of F-centres.

The theoretical L_2,3 MM Auger transition rates for selenium are calculated using the radial integrals computed by McGuire. The calculation procedure assumes LS coupling for the initial hole state and either LS or intermediate coupling, as appropriate, for the final hole state. The theoretical rates are found to be in good agreement with the relative intensities observed in experimental spectra.