Table of contents

X-ray crystallographic studies, electrical resistivity and thermal analysis measurements have been performed on (Ti_0.994V_0.006)₄O₇ single crystals. It is shown that the incorporation of V stabilizes the disordered intermediate phase of pure Ti₄O₇.

The random-bond Ising model with continuous (rectangular) distribution of exchange interactions is treated in the Bethe approximation and is shown to have the glass-like phase. The phase diagram similar to that by Sherrington and Kirkpatrick (1975) is obtained. The random-bond Ising model on the infinite Bethe lattice is regarded as an exactly solvable model showing the spin glass.

Series expansion methods have been used to estimate the critical probability, p_c, and to investigate percolation behaviour for the directed-bond problem on most of the usual lattices. High-density series expansions of P(p) and low-density series expansions of S(p) were obtained for the acyclic directed square (SQ), triangular (T), SC, BCC and FCC lattices, and also the cyclic directed triangular lattice. The results suggest that directed models need not fall into the same universality class as the corresponding undirected models. The results for the acyclic and cyclic directed triangular lattices further suggest that different directings of the same lattice may yield models falling into different universality classes.

The directed d-weight method is used to obtain the expansion of the mean-size series, S(p), for the simple acyclic hypercubic lattices, to order p⁹. The following expansion is also derived: p_c(d)=1/d+1/2d³+1/d⁴+3/d⁵+21/2d⁶+479/12d⁷+O(d^-8).

A structure analysis of the clean (001) surface of body-centred cubic iron by low-energy electron diffraction (LEED) is described. The surface was cleaned by a series of argon-ion bombardments followed by annealing treatments. The intensity analysis of 16 non-degenerate beams at three angles of incidence in the energy range from about 30 to 160 eV revealed that the structure of Fe (001) essentially corresponds to simple truncation of the bulk, with a probable contraction of 1.4% in the first interlayer spacing compared to bulk. The uncertainty in this figure, however, is +or-3% of the interlayer spacing.

The authors describe a stationary solution to the non-linear, dispersive field equation, rho u_tt=cu_xx+Cu_xu_xx+hu_xxxx for the field u(x,t), (a) defined in the range -l<or=x<or=l and (b) clamped at the boundaries u(+or-l,t)=0. The solution is characterized by a cyclic exchange of energy between the two lowest-frequency modes. Expressions are derived for the period and amplitudes of the energy exchange in terms of the parameters rho , c, C, h and l.

The model may be viewed both as giving the exact solution to the vibrational properties of a Bethe lattice of coordination number q, and also as giving a variational upper bound on the free energy of a Bravais lattice with coordination q. It does not rely on a perturbation treatment involving a Taylor expansion of the interaction potential. The method is applied to the two-dimensional square net (q=4) with Lennard-Jones 12-6 interactions between nearest-neighbour atoms, and the anharmonic free energy has been calculated by several different numerical methods for a series of values of temperature, T, and lattice parameter, a.

The 423K phase transition of CsCuCl₃ is attributed to a cooperative Jahn-Teller effect. Using results of the group-theoretical analysis of phonon modes, it is shown that helical atomic displacements in the low-temperature phase can be represented by a suitable linear combination of the polarization vectors of the Jahn-Teller active E₁ modes with wavevectors q=+or-(0 0 2 pi /3c) of the high-temperature phase. The transition may be regarded as an order-disorder limit of the pseudospin-phonon coupled-type phase transition. Formation of the helical structure through the first-order transition is explained on the basis of the group-theoretical formulation of the Landau theory of phase transitions.

A simple model of non-local exchange and correlation is proposed for the valence bands of silicon which could be used to include non-locality in a pseudopotential calculation. The model was fitted to a calculation of the exchange and correlation energy which went beyond previous calculations in using a dynamic dielectric function. It was found that the Gamma point is sensitive to whether a dynamic interaction is used or not. It is hoped to extend the model to conduction bands.

The resistivity along the chain axis in polymeric sulphur nitride has been followed under pressure using a variety of hydrostatic and quasi hydrostatic techniques. The large increase in conductivity with pressure at room temperature previously reported up to 9 kbar is confirmed, and is seen to level off above 30 kbar at a conductivity ratio sigma (p)/ sigma (0) approximately 10. The T² dependence of the resistivity seen at atmospheric pressure, associated with electron-electron scattering has been followed with pressure. At moderate pressures this dependence is more complicated; there are two regimes with different T² coefficients which both saturate below room temperature, pointing to a semimetallic band structure with small pockets of electrons and holes present. The high-pressure limit of sigma (p)/ sigma (0) is seen to correspond to the level of electron-phonon scattering that can be expected from the superconductivity data.

The two charge density wave (CDW) transitions in 4H_b TaS₂ have been followed under pressure. The two transition temperatures were lowered when pressure was applied; the 315K atmospheric pressure transition associated with CDW formation in the octahedral layers was suppressed by 35 kbar, the 22K transition associated with CDW formation in the trigonal prismatic layers was suppressed at 8.5 kbar. The fall in the 22K transition correlates with the rise in superconducting transition temperature. The behaviour of the resistivity at the CDW transitions is discussed and charge transfer from the octahedral layers to the trigonal prismatic layers is proposed. The effect of pressure on CDW formation in trigonal prismatic material is related to its superconducting behaviour under pressure through the microscopic CDW theory of Chan and Heine (1973).

A classical Heisenberg ferromagnet with fluctuations in the nearest-neighbour exchange interaction is investigated by the Bethe-Peierls-Weiss method. The fluctuations, assumed to arise from the structural disorder, depress the values of the Curie temperature, the high-temperature magnetic susceptibility and the magnetization relative to the corresponding values for the average crystal. For small values of the fluctuation parameter, explicit expressions for the amount of decrease in the above quantities are obtained. The critical indices are, however, found to be unaffected by fluctuations. The same formalism is employed to study the chemical disorder introduced by substituting magnetic impurities in a non-magnetic structurally disordered host. It is shown that the critical concentration of magnetic atoms for the appearance of long-range magnetic order is not influenced by fluctuations.

Excitations in a two-dimensional diluted ferromagnet with an anisotropic exchange interaction are studied by using the moment expansion method. Spectra at various points in the Brillouin zone and the imaginary part of the Green function at a central site (equivalent to the state density) are presented over the whole range of the concentration of non-magnetic ions, by analysing a moment expansion using both the Pade approximation and the continued-fraction representation. The exponential (Lifschitz) tail and the response from the dangling bonds are observed. Comparison with experiments is also made.

Magnetic properties of samples of FeGa₂O₄ have been measured by Mossbauer spectroscopy, neutron diffraction and magnetization techniques. Superparamagnetic behaviour has been found above about 10K, below which temperature long-range magnetic coupling develops. The neutron diffraction results also indicate that in FeGa₂O₄ spinel, Ga³⁺ ions do not have preference for either A or B sites in the presence of Fe²⁺ ions.

It is found that small terms of the form S³I are needed in the spin Hamiltonian to give a correct account of the ligand ENDOR for Gd³⁺ in CdF₂, CaF₂ and SrF₂. Comparison of the ligand hyperfine parameters for Gd³⁺ in these materials and for BaF₂ suggests that there may be a significant contribution from electrostatic polarization of the ligands.

The temperature dependence of the one-phonon Raman bands in single crystals of CaF₂, BaF₂, SrF₂ and SrCl₂ has been investigated over the temperature range 15-1300K. The frequency shifts and linewidths are calculated according to quasi-harmonic theory. Agreement is satisfactory for T< Theta , the Debye temperature, indicating a two-phonon decay process. A small contribution due to anharmonic effects becomes evident above the Debye temperature for all crystals. The temperature dependence of the Raman-active frequencies is found to increase in the order CaF₂<SrF₂<BaF₂. Gruneisen parameters are determined and the results compared with pressure dependent measurements of the optical phonon frequencies.

A quantitative theory is given for the dominant absorption maximum in the infrared observed in incommensurate one-dimensional conductors. This is achieved by reinvestigation and extension to finite temperatures of Sadovskii's (1974) highly renormalized theory of electrons interacting with the soft phonon of twice the Fermi wavevector. Numerical results for Re sigma ( omega ,T) are evaluated and compared with experimental results of KCP and TTF-TCNQ. Quantitative agreement is found for absolute magnitude and temperature shift of the infrared absorption peak. The asymptotic frequency behaviour of Re sigma ( omega ) is also investigated implying a free-particle relaxation time linearly increasing with frequency, again in accordance with measurements.

Normal-incidence reflectivity spectra in the photon energy range 4.5 to 14 eV have been measured on the basal faces of single crystals of the layered disulphides and diselenides of Ti, Zr and Hf. The spectra are interpreted in terms of chemical trends in the band structures, and based on this interpretation, models for the conduction of these materials are proposed.

In single crystals of KCl irradiated with gamma rays at room temperature, the relationship between the photoluminescence emitted at 440 nm induced by shining F light on the irradiated samples and the thermoluminescence of these samples has been studied. It has been concluded that this photoluminescence is due to the recombination of F centres and trapped interstitials (chlorine atoms). Under the action of light, the F centres migrate through the lattice; when an F centre gets close to a trapped interstitial, they recombine and light is emitted. It has been found that mobile F centres are formed when anion vacancies trap electrons which are thermally or optically released from traps. It is concluded that the F* centre is the mobile entity in these experiments.

Photoelectron emission from pure and benzene-doped solid samples of Ne, Ar and Kr was measured following excitation of the range of exciton states (below the direct threshold, i.e. E<E_TH) and interband transition. For benzene (C₆H₆) doped samples, two mechanisms are exhibited, namely (a) energy transfer from the rare-gas (host) crystal exciton states to benzene (impurity states) resulting in exciton-induced photoionization of C₆H₆; and (b) direct photoemission from the host at energies >or=E_TH( identical to E_G-V_O). The photoemission yield in the exciton range (process (a)) shows an efficient transfer of energy from exciton states to C₆H₆, and provides information about the free exciton kinetics. The drift length of electrons in argon and krypton has been estimated from the thickness dependence of photoemission yield.