Table of contents

It is shown that, in alternant lattices with a half-filled nondegenerate tight-binding band, the static zero temperature dielectric function diverges logarithmically for a wavevector Q=( pi , pi , pi ) in the reciprocal lattice. This implies that such three-dimensional systems may distort in a way which results in a non-conducting ground state.

Results are reported on absorption spectra of Nd³⁺ ions trapped in ice at atmospheric pressure and at temperatures from 225K to 2K in the spectral range 11300-34000 cm^-1. The rare earth energy levels are split by the crystalline field, and the spectra can be interpreted by considering all Nd³⁺ ions occupying identical sites of axial (or lower) symmetry in the ice matrix.

Four sharp features in the ³A_2g to ¹T_2g absorption spectrum of CaO:Ni²⁺ are shown to arise from the electron-vibration splitting of the vibronic levels associated with a T_1u localized mode. This is the first time that a splitting of this type has been observed.

Beryllium-doped GaAs grown by the liquid phase epitaxial technique shows an infrared absorption line due to the localized vibrations of ⁹Be_Ga at 482 cm^-1. This is discussed in relation to vibrations of ⁹Be_Ga in GaP and boron in GaAs and GaP.

Generalized Landau-Ginsburg models for systems with coupled order parameters are introduced. Detailed discussion is given for a particular model with biquadratic coupling between two (second-order) order parameters. This includes the complete, rather interesting, phase diagrams within the Landau-theory approximation and a discussion of fluctuation effects. For these, simple expectations are presented based on the topology of the Landau free-energy surfaces and renormalization group results including an identification of the limitations of the latter. It is argued that these models are very general and relevant to many systems of experimental interest.

A system of crossed Ising chains that can be interpreted as a multiply decorated square Ising lattice is considered and the local spontaneous magnetization which 'hangs through' between the crossing points is discussed. With growing chain distance the coupling constant along the decorated horizontal bonds is allowed to increase such that the critical temperature of the second-order transition remains constant. A narrowing of the critical region with increasing chain distance is observed; in the limit of infinite distance spontaneous magnetization, specific heat and susceptibility exhibit a first-order transition. Thus the model serves as an example for the continuous variation of the character of a phase transition from second to first kind as a function of the 'external parameter' chain distance.

Samples of silicon doped with oxygen alone, or with oxygen and carbon have been irradiated with fast neutrons up to a maximum dose of 10²⁰ cm^-2. It is shown that there is a progressive decrease in the resolution of the fine structure of the 9 mu m band due to oxygen, and a corresponding increase in the width of the band at 12 mu m due to (O-V)⁰ centres. These measurements have also been made on samples containing group III and/or group V impurities; the degree of disorder in these samples is greater showing that there are important impurity effects. These results are compared with the structure of the 9 mu m band found in silicon after implantation with 400 keV oxygen ions.

An investigation has been made of the lattice dynamics of the molecular crystal orthorhombic sulphur. Coherent, inelastic neutron scattering experiments have been performed on a single-crystal specimen and the experimental results are reported and compared with computer model calculations of the dynamics. These calculations assume that the dynamics of sulphur can be formulated in terms of interactions between molecular groups of S₈ rings which behave as rigid bodies. The interactions between non-bonded atom pairs are then described by a '6-exp' potential function. The model is also compared with available Raman data in terms of both frequency and intensity predictions. The agreement between calculation and experiment is particularly good for modes of the Gamma ₁⁺ and Gamma ₄⁺ representations.

Conventional ceramic methods for pure oxide materials were applied to the processing of zinc ferrites; the composition of the starting materials was (1-y)ZnO+y alpha -Fe₂O₃. The ferrite was prepared by quenching into water from some 'soak temperature' T (1300 degrees C, 1400 degrees C), at which temperature it was presumed to be in equilibrium X-ray diffraction examination was used to measure the extent of solid solution formation by detecting the characteristic reflection of the various phases which have not entered into solid solution and by measuring the change in unit cell dimension of the spinel. When the parameter y mentioned above increased, zinc spinel existing at high temperature showed two types of change in its lattice constants. These changes were explained by applying the concept of normality lambda to the ZnO-Fe₂O₃ phase diagram.

The LCAO-MT method recently applied by the authors to polyethylene is used with some improvements, to calculate electronic energy band structures, density of states profiles, and atomic electron populations for polyacetylene and the polyfluoroethylenes. Improved results for polyethylene are also presented. The calculated density of states profiles are shown to be in good overall agreement with available photoelectron spectra.

Extremal positions in experimental recordings of the transverse magnetophonon resonance effect are usually phase-shifted with respect to magnetic field from the simple expression omega _c= omega _opt/n. This phase shift arises from the variation in amplitude of the resonance peaks, and is examined as a feature of both differentiated and undifferentiated recordings of the phenomenon; it is greater in the former case. Tables are presented that quote this shift both for power law and exponential amplitude functions.

Workfunction measurements of atomically clean silicon (111) surfaces produced by cleavage and of evaporated simple-metal films have been carried out in a UHV system at a base pressure of about 5*10^-11 Torr. The barrier heights of the resulting intimate metal-silicon contacts have also been measured without breaking the vacuum. The barrier height values derived from I-V and photoelectric measurements are in excellent agreement. However, they are lower than the barrier height values obtained from differential capacitance measurements by about 0.1 eV depending on the metal. This discrepancy is in qualitative agreement with the Heine and Inkson theories for intimate metal-semiconductor contacts. The dependence of barrier height on metal workfunction cannot be described by a simple effect on the potential barrier of intimate metal-semiconductor contacts, over and above the effect of the metal workfunction.

Mixtures of Ising dipoles A and non-magnetic atoms B on Bethe lattices (Cayley trees) are considered. Random mixtures, with all A B distributions equally probable, and equilibrium mixtures are both treated. Equations of state for equilibrium mixtures are obtained by the Rushbrooke-Scions method (1955) and the zero-field susceptibility derived. The susceptibility is derived for the random mixture by a high-temperature series expansion. The linear lattice is treated as a special case and the relation of susceptibility to mean A-cluster size is discussed for both equilibrium and random mixtures. Curves of critical temperature against x_A are considered for general coordination number, especially in the equilibrium case with w<0. The relation of susceptibility to cluster size at absolute zero is discussed for x_A less than the minimum value for the appearance of spontaneous magnetization. The critical index y_T for variation of susceptibility with temperature at constant x_A and the corresponding index Y_x for variation with x_A at constant temperature are found to be equal to unity except at isolated points. It is shown that an attempt to apply Bethe pair statistics to the random mixture gives instead results corresponding to an equilibrium mixture subject to constraints.

The critical behaviour of a compressible Ising model on a BCC lattice with a harmonic lattice potential and a spin-lattice interaction linear in the strains, and exposed to a pressure p is studied by means of statistical methods. The problem is formulated in terms of three fields: homogeneous strains e, acoustic phonons and spins. After integrating e out exactly it is shown that the partition function of the problem can be expressed as an integral of the partition function of the ideal Ising model and a Guassian integrated over the infinite space of coupling constants. Approximate integration suggests that the system undergoes a phase transition of the first kind.

A theory is formulated to calculate the exchange constants J₁ and J₂ for first and second neighbours in the transition-metal monoxides. The calculation is based on the previous model (see abstr. A20548 of 1974) for the electronic structure of these materials and involves d-s and d-p hybridization to fourth order in perturbation theory. Results for NiO yield an antiferromagnetic J₁, approximately equal to 0.3*10^-4 eV, and a J₂ of the order of 0.4*10^-2 eV. The last value is within a factor of 4 from the best experimental estimates. These calculations confirm the validity of our model for the electronic structure.

For pt. III, see abstr. A79114 of 1974. A single crystal of UN was studied at low temperatures by X-ray diffraction. Below the Neel temperature ( approximately 55K) a very small tetragonal distortion (c/a=0.99935 at 4.2K) of the NaCl-type lattice was observed, which is consistent with the tetragonal (type I) antiferromagnetic structure inferred from neutron diffraction. A small discontinuity in the lattice spacing of UAs was observed at the transition (around 60K) from type I to type IA antiferromagnetic ordering (at low temperatures).

The spectrum of short-closed chains up to N=12 are studied by exact diagonalization to obtain the spin-wave spectrum of the Hamiltonian H=2J Sigma _i=1^Ns_i.s_i+1+2J alpha Sigma _i=1^Ns_i.s_i+2, -1.0<or= alpha <or=1.0 with J<0. The spin-wave spectrum is fairly well described for small alpha by the spin-wave formula obtained by the Anderson approximation (1952). The results of short chains indicate that S=0 bound magnon states lie partly below the spin-wave states with S=1 only for alpha >or=0.3 and alpha <or=-0.5. A few remarks are made concerning the low-lying excitations.

Experimental results show the deviation of the trigonal axis of the paramagnetic Mn²⁺ centre from the c axis of a corundum crystal. The direction is derived from forbidden line intensity and line position measurements.

A highly crystalline polymer is described in which all the polymer chains are parallel and the backbone of the chains is conjugated. It is postulated that the low-lying (<5 eV) electronic excitations are electrons and holes in one-dimensional bands confined to individual chains. The band structure is deduced. The crystal is a semiconductor, E_G approximately=2 eV, for charge transfer along the chain direction and an insulator in perpendicular directions. Singular Van Hove optical transitions characteristic of one dimension are discussed and shown to lead to peaks in the reflectivity. The optical and Raman properties of the model are compared with experimental results.