Table of contents

Molecular dynamics calculations of the intermediate scattering function for liquid aluminium have been performed for two pair potentials. The potential consistent with both phonon dispersion curves and the isothermal compressibility shows collective peaks in the dynamical structure factor.

The interpretation of the infrared spectrum from MgAl₂O₄ has been the subject of some controversy. Recent proposals by Striefler and Boldish (1978) contradict an earlier theoretical analysis of the vibrational spectrum according to which there are only nine translatory optic modes (3 longitudinal+3*2 transverse). Re-examination of the data derived from a Kramers-Kronig transformation of the single crystal reflectance spectrum shows that the latter is more consistent with experiment and with the Lyddane-Sachs-Teller relation. It is concluded that there can be, at most, three longitudinal mode-transverse mode splittings at zero wavevector, and that, of these, two are clearly associated with the strong infrared absorption peaks at 670 and 485 cm^-1 respectively.

It is shown how thermal fluctuations in liquids can be studied in molecular dynamics 'experiments' by measuring the response to a weak velocity-dependent perturbation.

The first vertex correction to the self-energy makes only a small contribution, about 65 meV, to the band gap in a nearly-free-electron system having the parameters of silicon. The contribution is expected to be larger in a more tightly bound system.

The electron density of states in a four-dimensional disordered system is studied using the Feynman path integral method. It is shown that the density of states deep in the tail does not disappear as the 'white noise' limit is taken which is in agreement with the conclusion given by Thouless (1976).

The site-diluted Ising ferromagnet is treated by a position space renormalisation group method. The method is briefly outlined and results obtained by considering three different two-dimensional clusters are presented. The results include the dependence of transition temperature T_c on concentration p and the thermal exponents for the percolation and Ising fixed points. Corresponding results are also presented for the bond-diluted Ising ferromagnet.

Using inelastic-neutron scattering techniques, the spin wave energy dispersion relation has been investigated at three temperatures in a two-dimensional Ising-like antiferromagnet, Rb₂CoF₄. The results show there is relatively little dispersion across the Brillouin zone with a very large energy gap at zero wavevector. As the temperature is increased to just below T_N there is relatively little renormalisation of the spin waves over the region of wavevectors examined.

Diffuse elastic magnetic scattering of unpolarised neutrons from weakly ferromagnetic PtCo alloys appear to show that critical scattering, caused by concentration induced critical fluctuations of the order parameter (the spontaneous magnetisation), occurs in the critical concentration region for the onset of ferromagnetism.

A random-bond Ising model which exhibits ferromagnetic, antiferromagnetic and spin-glass transitions is studied using the n-replica method. A mean-field phase diagram is obtained for the model near the percolation threshold and it is found that only a small concentration of antiferromagnetic bonds is necessary to destroy ferromagnetism and lead to the formation of a spin-glass state. The fixed points corresponding to the different transitions are located and critical exponents calculated near six dimensions.

Measurements are reported on the GR 2-3 doublet under uniaxial stresses of up to 3 GPa. The stress parameters are derived, allowing for the stress-induced interactions among the two excited T states and among the near-degenerate E, A ground states of the T_d centre.

The luminescence associated with bound multi-exciton complexes in phosphorus doped silicon has been investigated as a function of excitation density. The variation of the relative intensities of the luminescence lines with excitation density is in agreement with the predictions of the Kirczenow shell model (1977) but in conflict with recent decay time studies. New features in the luminescence spectrum are also reported.

The L_2,3MM Auger electron spectra of clean solid gallium and zinc excited by Al K alpha and Mg K alpha X-rays have been measured over energy ranges of 400 eV. The total inelastically scattered electron background, normalised to the principle Auger lines increases in gallium when the energy of the X-rays is increased to allow L₁ photoemission. This change in background may be quantitatively accounted for by assuming that L_2,3MM Auger electrons are emitted by doubly ionised gallium after the L₁L_2,3M Coster-Kronig emission which follows L₁ photoemission. The zinc Auger electron spectrum shows no such change in scattered electron background as L₁ photoemission is allowed for both X-ray energies used.

Based on a recently developed theory for classical liquids, results are presented of calculations of the dynamical structure factor S(q omega ) and the velocity auto-correlation function for a classical one-component plasma. The calculations show a strong coupling between self- and collective motions and change in the behaviour of the plasma dispersion relation with increasing density, in agreement with computer simulations.

The electronic theory of III-V and II-VI tetrahedrally covalent compounds is presented using a perturbation treatment based on a model potential. In the theory, according to the Jones-zone scheme of Heine and Jones (1969) the higher-order terms with respect to the pseudopotential are considered. Numerical results for the cohesive energy and bulk modulus for these crystals such as AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe and CdTe are in good agreement with the observed data.

For pt.I see ibid., vol.11, p.2669 (1978). The covalent-metallic phase transition to the beta -Sn structure or covalent-ionic transition to the NaCl structure of III-V and II-VI zincblende-type covalent compounds are investigated using our perturbation treatment according to the Jones-zone scheme of Heine and Jones (1969). Numerical results of transition pressure, volume discontinuity, transition heat and lattice parameters in the high-pressure phase for these crystals, such as AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe and CdTe, are discussed together with the observed data.

Cohesive properties of the NaF crystal have been calculated by evaluation of the electrostatic, valence repulsion, induction, and dispersion contributions. All quantities have been computed with an accuracy up to S² terms using high quality Hartree-Fock wavefunctions for the Na⁺ and F^- ions. Two- and three-body forces as well as the nearest- and the next-nearest-neighbour exchange interactions have been considered. The role of further neighbour interactions has been estimated. The results are in satisfactory agreement with the experimental data.

The relaxation about a vacancy in diamond results from modifications in the local chemical bonding. Further relaxation occurs to lower the electronic degeneracy through the Jahn-Teller effect. Both effects are considered by using a semi-empirical molecular-orbital cluster-model of the vacancy to calculate the relaxation of the lattice about it. An ¹E ground state of the neutral vacancy is found with a Jahn-Teller energy of 460 meV coupled to tetragonal modes. The negative vacancy is found to have an ⁴A₂ ground state. Both give rise to substantial, totally symmetric, inwards relaxation.

Pure tellurium single crystals were irradiated with 1 MeV electrons at low temperatures. Two annealing stages appear in the temperature range from 4 to 130K. In contrast to findings for other materials an increase of the carrier mobility is observed in the orientation j perpendicular to c. A simple phenomenological model is developed which explains quantitatively all experimental data between 4 and 130K. It is shown that the vacancies are mobile above the second stage and that the first stage (50K) is caused by a defect rearrangement. The activation energy for vacancy-migration is determined as 170 meV, in accordance with theoretical calculations.

High-resolution inelastic neutron scattering measurements on polycrystalline U(C_0.60N_0.40) have shown that the optical phonon modes are split into two peaks corresponding respectively to local vibrations of carbon and nitrogen. This confirms a simple Einstein oscillator model for these light atoms in rocksalt-structure uranium and thorium compounds.

The critical behaviour of the planar rotator model on a square lattice is investigated using the one-hypercube approximate renormalisation group transformation. An isolated critical fixed point emerges from this approximation. Critical exponents are calculated by standard methods. A lower bound on the free energy is obtained by integration on the flow in the space of the coupling constants.

The 1,0,0 face of a Lennard-Jones crystal has been examined for surface premelting effects along the crystal-vapour coexistence line by the method of molecular dynamics. The outermost crystal layer becomes quasi-fluid within the narrow temperature range 0.48-0.50 epsilon /k, as evidenced by a rapid increase in diffusivity in the surface plane, and by discontinuities in equilibrium properties characteristic of anomalous first-order transition behaviour. Similar melting is observed for the second and third layers at 0.60-0.62 epsilon /k and 0.67-0.69 epsilon /k respectively, the latter being close to the triple-point temperature. Several properties of the system are reported and discussed in the context of both melting models and available techniques, indicating how surface melting might be detected by LEED experiments. It is conjectured that surface melting should occur for all single-component crystal-vapour interfaces by a similar mechanism to that reported here. A simple empirical melting rule is suggested: Each layer melts when the ratio of kinetic to potential energy per atom in that layer becomes equal to the same ratio as for the bulk crystal at its melting point.

A theory of freezeout is presented for semiconductors for which the freezeout occurs in the ultra-quantum regime, taking into account the level broadening due to the overlap effects. The main purpose of the paper is to obtain the regime of the fields and concentrations for which a freezeout occurs at a given temperature. The theory is illustrated by applying it to GaAs. A reasonably good agreement is obtained with the experimental data.

The formalism of Matsubara-Toyozawa for impurity bands in semiconductors is extended by including the correlations between electrons and between impurities, as well as the overlap effect. The electronic correlation is introduced through an alternant molecular orbital method and the correlation between the impurities is approximated by an extended chain of hard-core pair correlation functions. The calculation with various degrees of compensation shows a reduction of the impurity bandwidth, a lowering of the Fermi energy and an increase of the DC conductivity in comparison with those derived by Matsubara-Toyozawa. We found that the electronic correlation plays the dominating role in all the results, while the effect of correlation between impurities shows up only at high impurity concentrations. The calculated DC conductivity agrees reasonably well with experiments.

The magnetisation density associated with the susceptibility of vanadium dioxide in the metallic phase has been measured using the polarised neutron technique. The results have been interpreted as giving the spatial distribution of the conduction electrons. Fourier transformation of the measured magnetic structure factors gives a projection in which the density is well localised on the vanadium sites. The density around the vanadium sites is not spherically symmetrical but shows a small elongation towards the oxygen neighbours in (110) directions. The results have been compared with calculations of the magnetic structure factors corresponding to current models of the band structure of VO₂. The comparisons show that to obtain adequate agreement between theory and experiment it must be assumed that there are electrons in all three sub-bands of the T_2g manifold.

The zero-temperature dynamical properties of the one-dimensional Ising model with exchange constant J in a skew uniform magnetic field (H^x,H^z) are given by analytic expressions neglecting corrections of order (H^x/J)² and (H^z/J)². The lowest multiplet of the excitation spectrum and the transverse frequency and wavenumber dependent susceptibility are expressed in terms of Bessel functions. In a small longitudinal field the excitation spectrum has a multibranch structure which for vanishing longitudinal field merges into a band. The singular character of the transition between the semi-infinite discrete spectrum and the band gives rise to a power-law behaviour. The energy levels depend on H^x to the power ¹/₃ and on H^z to the power ²/₃. An experimental search for systems revealing the above effects is suggested.

Atomic and magnetic ordering are described in a pair model. Some exact results are obtained for short-range correlation parameters in a one-dimensional alloy. Then, for the more realistic three-dimensional case, a generalised quasi-chemical approximation is introduced: long-range and short-range atomic and magnetic parameters are obtained as functions of temperature.

A phenomenological renormalisation transformation is used to calculate critical properties of two-dimensional spin s Ising systems with lattice anisotropy. Systems with s=¹/₂, 1, ³/₂, 2, ⁵/₂ are considered for a large range of ratios, R=K_y/K_x, of exchange constants in the x and y spatial directions. Agreement with the exact solution for s=¹/₂ is good, with the percentage error in T_c becoming very small as R approaches zero. The results for nu are consistent with universality arguments. The estimates of the critical curves suggest an asymptotic form, as R to 0, of K_y approximately 2s exp(-2K_x).

A renormalisation group approach for the self-avoiding walk is developed. The approach enables the calculation of the exponent nu directly, without reference to the n-component spin model. The cluster approximation is used and nu =0.70 for the triangular lattice is obtained.

The information about the critical behaviour of an ideal isotropic two-dimensional Heisenberg magnet which can be obtained from measurements on layered systems is investigated by renormalisation group methods and within the spherical model. It is found that, provided the interplanar coupling is down by a factor of 10^-4 on the intraplanar coupling and any spin anisotropies are small enough, there is a range of temperatures over which the characteristic exponential behaviour of the susceptibility should be observable. The experimental data presently available shows this behaviour.

Recently a CPA-RPA theory has been proposed for treating site and bond randomness in antiferromagnets which experience exchange couplings of arbitrary range. As a simple application of this theory, the behaviour of the Neel temperature, T_c(x), is analysed in the mixed system (Mn)_x(Zn)_1-xF₂. The results are found to be in reasonable agreement with the experimental data of Baker, Lourens and Stevenson (1961).

The enhanced staggered field obtained by subjecting CoF₂ crystals to uniaxial stress in the (110) direction has been used to produce nearly single 180 degrees domain crystals. The effect of the staggered field has been monitored using polarised neutron diffraction by measuring the variation in polarisation ratios of mixed magnetic and nuclear reflections. A quantitative determination of the domain population has been obtained using a simple model to correct for extinction in the crystal. The results show that the domain population is determined very largely by the conditions of stress and magnetic field as the crystal is cooled through the Neel temperature. A stress of 550*10⁶ dyne cm^-2 and an applied field of 48 kOe was sufficient to obtain an imbalance of 94% in the domain populations.

Two new rhombic U⁵⁺ EPR spectra have been observed after gamma -irradiation on heat treatment of fluorite crystals doped with uranium. The main axis Z of the two spectra lies along (110), the X and Y axes being in the (110) plane tilted by an angle delta from the (111) and (112) directions, respectively. The g-values and the tilt angle delta for the two spectra have been determined.

On the basis of the existing experimental data it is assumed that the mechanism responsible for the ferroelectric transition of potassium ferrocyanide trihydrate is a rotational reorientation of the water molecules. Accordingly, the electrostatic energy of the water molecules (approximated by three point charges) is calculated as a function of their orientation. The low temperature configuration is obtained by minimising the electrostatic energy. A possible model is then proposed for the ferroelectric to paraelectric transition, consisting in the switching of the water molecules between two energetically equivalent configurations. The results are in good agreement with the experimental data.

For practical numerical reasons the inversion of the dielectric matrix of the elemental semiconductors has proved to be a difficult problem. Simplifications to the Wannier function based inversion technique are presented based upon physical models of the semiconductor system. Results have been obtained for the diagonal part of the response function with and without local fields. These are compared to previous theories and a practical scheme for the systematic inclusion of local fields in phonon calculations presented.

The Faraday rotation and MCD spectrum about absorption bands in erbium-doped soda glass have been studied. The measurements were made in the saturation region and the g-value of the ⁴I_15/2 ground state determined by use of the method of moments. The dominant nature of C-terms in rare-earth doped glasses are confirmed and the Faraday parameters derived for all optical transitions. Some comments are made on the existence of trigonal and tetragonal sites for the erbium ion in the glass matrix. By selective doping with erbium it is possible to produce a glass that has a zero Verdet constant.