Table of contents

Cluster size distributions are obtained for the directed percolation problem on a square lattice using Monte Carlo simulation. The critical probability and the critical exponents beta , gamma , tau , phi are determined, and evidence is obtained for a scaling form of the cluster distribution function.

Measurements of the effects of uniaxial stress on the 0.97 eV line in both absorption and luminescence are reported and the symmetry of the centre is established as monoclinic I. The relative intensities of the stress-split components vary with stress as a result of preferential population of the inequivalent populations under stress.

The longitudinal magnetostriction of Bi has been measured in the bisectrix direction up to 5 T, at 4.2K and 2K. It is found that, above the last quantum limit, when the oscillatory magnetostriction vanishes, the negative induced strain displays a monotonic increase against field. This behaviour is ascribed to the change of carrier population in the different Fermi pockets of bismuth, in agreement with the known high-field band model and the deformation potential theory.

A method has been developed to carry out potential energy calculations of molecular and crystal structures in Fourier space. Although this method is equivalent to conventional calculations in physical space, special features of the Fourier formalism make it advantageous in terms of savings in computational time in some cases. This suggests that a prior analysis of the alternative methods should be made before the start of an extended potential energy calculation.

The temperature dependences of the c axis thermal expansion and elastic constant c₄₄ have been measured in single-crystal samples of dysprosium between the Neel temperature T_N and Curie temperature T_C. Anomalous behaviour is observed at several temperatures in the range T_C<T<T_N, and the anomalies are attributed to the occurrence of helical turn angles which are commensurate with the periodicity of the basal plane hexagonal crystal structure. The mechanisms which may be responsible for this behaviour are discussed in the light of the model employed to describe similar effects previously observed in holmium at approximately 24K. It is proposed that the anisotropy leads to instabilities in the magnetic structure whenever the commensurate turn angle condition is met.

The Hamiltonian of a topologically disordered system of impurities in a semiconductor matrix is studied in a random cell representation. It is shown that at any doping level most of the non-interacting cells are treated by a cluster expansion, the convergence of which is controlled by the respective statistical weight. It is shown that at any doping level most of the non-interacting cells are occupied by small clusters, while for large clusters the interaction cannot be neglected. The authors approach allows a systematic investigation of the single-particle excitation spectrum. Approximate inclusion of the non-diagonal part of the Hamiltonian leads to a generalised Anderson-type model on a coarse-grained cell structure.

The temperature-induced high-spin(HS)-low-spin(LS) transition of the 3d⁴-3d⁷ transition-metal ions in crystals (oxides and sulphides) are investigated on a semiquantitative basis by taking into account the elastic interaction between HS (or LS) clusters produced in a LS (or HS) crystal. The critical temperature at which the discontinuous phase transition takes place is evaluated as a function of the ligand-field strength Delta in units of spin-pairing energy Pi . It is shown that the 'crossover range' where this critical temperature exists is restricted to a finite range of Delta / Pi around the crossover point. The crossover ranges are evaluated for the crystals MO, MS₂, M₂O₃, and LaMO₃ where M represents transition-metal ions. The temperature variation of the equilibrium concentrations of HS and LS clusters in LS and HS crystals, respectively, is calculated for several values of Delta / Pi in perovskite LaMO₃ crystals. It is pointed out that two discontinuous transitions from HS to LS and LS to HS with decreasing temperature may be expected in the d⁶ and the d⁷ systems.

A new method of correlation reduction near the critical temperature is introduced for a classical spin system. This method is based on an assumption much less restrictive than the usual mean-field approximation. It permits an important parameter to be determined realistically. The transition temperature of the Ising ferromagnet is expressed very simply in a closed form. The values of the transition temperature evaluated with various approximations in this method are presented for three-dimensional Ising lattices.

In RbCaF₃, CsCaF₃, and RbCdF₃ crystals the ⁸S Gd³⁺ ion is substituted for the sixfold coordinated Ca²⁺ or Cd²⁺ ions. The authors discuss the superhyperfine interaction with the ligands and the hexadecapolar crystal-field term for cubic centres. Tetragonal centres, in which the quadrupolar crystal field terms range from 1.5*10^-4 to 0.3 cm^-1, were obtained through uniaxial stress, a structural phase change below T_c, or charge compensation by vacancies and O^2- impurities. The authors discuss this term by using theoretical results within an ionic model or an empirical superposition model proposed by Newman (1975).

The formation of Z₁ centres in KCl:Sr single crystals as well as microcrystalline powders is studied with the help of optical absorption and TL measurements. Upon F light bleaching of an irradiated crystal, a new glow peak at 405K is introduced in the glow curves. The peak at 405K is attributed to Z₁ centres. A similar peak observed at 385K in microcrystalline powders is attributed to the combined action of deformation and Z₁ centres. Their results led to the conclusion that Z₁ centres are formed along with the F centres during irradiation and even the mechanical bleaching of F centres is sufficient to produce an appreciable number of Z₁ centres without any optical bleaching.

Results of self-consistent band structure calculations on unsupported single-layer films of Fe, Co, Ni and Pd are presented. The calculations are based on one-particle equations where exchange and correlation effects are accounted for by the spin-dependent local-density potential suggested by von Barth and Hedin (1972). The one-particle states and the associated band structure are determined by applying the recently developed linear rigorous cellular method. After minor rearrangements this method readily provides comparative data on the bulk materials as well. The results arrived at clearly demonstrate the fact that spin polarisation in single layers of ferromagnetic materials is generally larger than in the bulk. The associated magnetic moment per atom lies between the value of the respective free atom and that of the bulk.