Table of contents

Random Ising models are conveniently treated by the replica method. The authors study the duality relations for general symmetrically coupled Ising models on a square lattice in two dimensions. General conditions for self-duality are found and a number of new self-dual models are presented. Recently conjectured transition temperatures for the dilute Ising model, by Nishimori (1979), are shown not to obey these general conditions.

The authors report new angle-dependent light scattering spectra and thermal diffusivity data in BaMnF₄ which show that the light scattering central peak recently reported (1979) may be interpreted as phason scattering. The thermal diffusivity measurements demonstrate that the peak is not due to entropy fluctuation scattering. This interpretation provides evidence for a strong anisotropy in the phason dispersion, as suggested by theory.

It is shown for the first time that the Sternheimer correction associated with the overlap contribution to the electric field gradient in ionic crystals can be assigned the constant values of 0.4, -0.8, -5.7 and -16.4 for F^-, Cl^-, Br^- and I^- respectively.

The author has investigated further the previously developed theory of Matsubara and Toyozawa (see Prog. Theor. Phys., vol.26, p.739, 1961) for impurity bands in doped semiconductors by including the effect of correlation via an alternant molecular orbital (AMO) method in order to calculate the impurity resistivity of CdS:In. Good agreement with experimental data is found.

SmO, EuO and YbO have been investigated theoretically with the aid of analytical wavefunctions for the excited 4f^N-15d configurations. The following parameters have been calculated: (i) two-centre overlap integrals of the type ( nu /4f) and ( nu /5d), where nu =2s, 2p sigma and 2p pi ; (ii) b₄ and b₆ from both point charge and covalent contributions within the 4f^N-1 open shell; (iii) b₄ and 10Dq for the 5d electron.

The thermal expansion of beta -AgI single crystals has been measured from 4 to 270K along the c direction, and is found to be negative throughout the range. The results are explained in terms of the negative Gruneisen gamma s which have been reported for both transverse acoustic and optic modes in beta -AgI.

Electrodiffusion of lattice defects in CdS, CdS:Li, CdS:Cu crystals and its effect on the photoelectric and luminescent properties of these crystals is investigated. Evidence is found to show that in the temperature range 250-400K, shallow donors, namely Li_i and Cd_i, drift in an electric field.

Energy-gap (E_g) data for I-VII, II-VI and III-V binary compounds (MX) are examined in an attempt to correlate E_g with the electron-transfer (charge-transfer) spectra of the related complex ions M'X_n^m- and MX'_n^m-. Reasons are advanced for excluding oxides and fluorides in this study. Electron-transfer spectra can be parametrised in terms of optical electronegativity ( chi _opt) values which are assigned to cations and anions. It is found that the chi _opt values can be modified slightly to take account of the discrete energy levels changing to energy bands in transferring from the complexes, M'X_n^m- and MX'_n^m-, to the compounds MX. These modified values then provide a simple means for predicting energy gaps both of N-(8-N) and non-N-(8-N) binary compounds. There are theoretical grounds for anticipating the correlation to be inapplicable to the 'inter-shell type' compounds such as the copper(I) and silver(I) halides, and the experimental data bear this out.

The parameters which describe the mean-squared displacement (R²(t)) of a random walker on a random network have a characteristic singular dependence on epsilon =(p-p_c)/p_c near the percolation threshold. The critical exponents, which characterise the singularities of the diffusion constant, moment of inertia of finite clusters, and time constants for development of the long-time behaviour, are related by a scaling theory. They may also be related to the exponent theories for the percolation and percolation conduction problems. An equivalent resistor network can be described which is equivalent to the time Laplace transform of the diffusion problem. These problems will be given explicit treatment for the Cayley tree.

Ionic thermocurrents (ITC) are measured in the 'pure' Harshaw NaI crystal. Although the atomic absorption technique shows that the concentration of the divalent cation inclusions is lower than 2 ppm, the ITC bands are intense. A comparison of the DC conductivity between the samples used and those doped with Ca²⁺ indicates that the 'pure' NaI contains small amounts of divalent cations; the ionic thermocurrents observed must therefore be attributed to the reorientation process of the dipoles of the form: 'divalent cation-cation bound vacancy'. By analysing the more intense ITC band the migration enthalpy and entropy for the bound-cation vacancy are found to be 0.59 eV and 1.7 k respectively. The enthalpy value of 0.59 eV is comparable to the values 0.58-0.60 eV obtained by the DC conductivity technique for the free-cation vacancy motion. On the other hand the entropy value of 1.7 k is appreciably smaller than the values 3.02-3.23 k which correspond to free-cation motion.

Numerical calculations for the relaxation of magnetisation in a one-dimensional random Glauber model are described for two probability distributions of the exchange constant. One probability distribution allows both the ferromagnetic and antiferromagnetic interactions, while the other only ferromagnetic. The Glauber kinetic equations for chains of 5000 and 9000 spins are solved for the appropriate initial conditions by the method of Laplace transformation followed by a continued-fraction expansion of the required Green function. For the probability distribution with both ferromagnetic and antiferromagnetic interactions, it is found that the magnetisation decay is characterised by two time regimes, a fast exponential-like decay followed by a slow decay, in which the magnetisation decays logarithmically with time. The slow decay regime is interpreted in terms of thermally activated tunnelling through energy barriers. A distribution function for the energy barriers is explicitly obtained.

Rigorous results are presented for the dynamics of the nearest-neighbour Heisenberg chain, for fixed but arbitrary wavevector and frequency, to lowest non-trivial order in the temperature. The authors obtain the two-spin correlation function, in the antiferromagnet for all wavevectors, and in the ferromagnet for wavelengths shorter than a coherence length. The energy correlation function at T=0 is obtained exactly, and is identical in the two systems. They find a violation of dynamical scaling in the form of the spectral function in the antiferromagnet for a range of wavevectors. An extension of the perturbative results for the ferromagnet to treat wavelengths longer than a coherence length shows that the diffusion coefficient vanishes logarithmically, in contrast to the scaling prediction that it is constant. An approximate value for the coefficient of the logarithmic term is obtained which agrees well with the results of simulations.

The temperature dependence of the linear polarisation of the A_T emission of a Ga⁺ centre is studied in NaCl, KCl, KBr and KI. A strong reduction of the polarisation in KCl and KBr between 1.6 and 10K is attributed to relaxation inside the Jahn-Teller wells and to transitions between the orthorhombic wells associated with a main Jahn-Teller tetragonal distortion with an activation energy of 30-40K. The existence of a plateau at higher temperature shows that transitions to trigonal Jahn-Teller wells take place before the transitions between the main tetragonal Jahn-Teller wells become effective.

The luminescence spectrum of AgBr at 1.6K reveals a number of sharp lines which are associated with excitons bound to residual impurities and crystalline defects. Two lines are identified as excitons bound to iodine ( epsilon _b=43 meV) and cadmium ( epsilon _b=8 meV). Several lines are observed in the neighbourhood of the phonon-assisted free-exciton emission, two of them corresponding to excitons bound to unidentified centres with energies of 1 meV and 0.25 meV. Electron-hole exchange coupling is found to be weak for excitons bound to the isoelectronic centres and their Zeeman spectra are described quite adequately by a simple L-S coupling scheme. The Zeeman spectra of the unidentified shallow states are found to be qualitatively similar to those of the isoelectronic traps. The g-values obtained decrease with increasing binding energy from g_e=2.29 and g_h=0.76 for the shallow states to g_e=1.97 and g_h=0.66 for the iodine trap.

A simple semi-experimental method of Gianturco and Coulson (1968) has been employed to estimate the effective charges on B, C, N, O, F, P and S ions in various compounds for which the measured ESCA shifts are available. The present values are compared with those obtained from other theoretical methods.