Table of contents

Two melting mechanisms are necessary to explain the melting of the two-dimensional Wigner solid. The zero-point lattice vibrations dominate the melting in the quantum region of the temperature T and the areal density n, whereas the Kosterlitz-Thouless dislocation mechanism dominates in the classical region. The phase diagram is found in the T-n plane.

The application of the recursion method to a disordered system is considered. It is argued that in this case the recursion coefficients a_n and b_n will continue to fluctuate at infinity and that these fluctuations are due to localised states. They may be related to the inverse participation ratio of such states. Numerical calculations corroborate this interpretation quantitatively.

The behaviour of the 'image-potential' for a point charge in the dielectric near its boundary with a medium having Debye-like screening by free charge carriers, is discussed. Simple approximate expressions are proposed for it.

A simple molecular-field model taking into account the characteristic volume distribution of an assembly of magnetically ordered microcrystals is developed to explain the observed high-temperature behaviour of the magnetisation. It is also shown that the volume distribution implies a distribution of critical temperatures.

Interacting spin wave theory is used to calculate the limit of stability of the antiferromagnetic phase in FeF₂. It is found that, due to the role of the strong anisotropy four-magnon interaction in the frequency renormalisation, the antiferromagnetic spin flop transition field decreases substantially with increasing temperature.

The Beckmann and Clough theory (see ibid., vol.10, p.L231 (1977)) of proton spin-lattice relaxation due to coupling of lattice vibrations with rotational motion of methyl groups is extended to the case of ammonium ions. It is found that the effect may be dependent on magnitudes of tunnelling and Zeeman splittings. For ammonium perchlorate the activation energy obtained from T₁ measurements is demonstrated to be approximately equal to the position of the optical phonon peak in the lattice spectrum in agreement with the theoretical prediction.

Thermal stimulated depolarisation and polarisation measurements of CdF₂, doped with various concentrations of NaF, were carried out and the data concerning the complex peak were evaluated by fitting with a Debye equation. It was found that the data suit this equation in all its aspects only if the temperature difference, which occurs in the transient state between sample and electrode is taken into account. The values of the kinetic parameters (activation energy of reorientation 0.15 eV and frequency factor approximately 10^-8 s) which thus emerge are surprisingly low. As explained in the discussion this is obviously a consequence of the specific arrangement of the fluorite lattice.

The changes which occur in the elastic modulus C₁₁ of p-type Si monocrystalline platelets (specific resistance about 10⁵ ohm cm), caused by illumination with light from the intrinsic absorption range are investigated. The dependences of these changes on the wavelength and intensity of the incident light are given. The proposed phenomenological model gives a good explanation of the experimental results obtained. The excitation of vibrations in crystals on illumination with light outside the intrinsic absorption range was also observed. For their explanation it is supposed that the absorption of light on the surface states leads to a change in the surface tension of the crystals.

The results of a study of the diffusivity of Sr²⁺ ion in AgCl doped with various concentrations of impurities are reported. With the assumption of the saturation limit of the diffusivity as a function of impurity doping the activation enthalpies for solute migration and solute-vacancy association are estimated to be 0.38 eV and 0.12 eV respectively.

In this work the authors extend the KKRZ method of band structure calculation for crystalline solids to the disordered systems of substitutional alloys and amorphous solids. In the case of substitutional alloys the average T-matrix approximation was employed whereby the l-dependent pseudopotential became complex, making the secular determinant complex. For amorphous solids, a positional averaging was taken following Kramer (1970), whereby a complex function phi _n^alpha (k+K_n,E) of a disorder parameter alpha appeared in the diagonal term of the secular determinant, again making the secular determinant complex. In both cases the energy eigenvalues obtained are complex in nature, the imaginary part being interpreted by a lifetime broadening of the energy state. Finally, the authors have applied this method to three binary substitutional alloys MgLi, MgCd and MgIn to obtain the complex energy band of these alloys. From these band structure data, density of states and optical properties have also been calculated and compared with the pure case.

The contributions made by successive atomic shells to the band gap in diamond are examined in detail. It is found that even though the energy levels lie above the maxima in the potential energy, the influence of shells beyond the third is slight.

The density of states in the two-dimensional white noise problem is calculated from the coherent potential approximation at high energy and from fluctuation theory at low energies; both the exponent and the power of E in the prefactor for the density of fluctuation states are evaluated. Comparison is made with the results of a tight binding simulation of the white noise problem, and good agreement between theory and calculation is obtained. Calculation of the conductivity of different sized samples enables the mobility edge to be determined, and it is found that the critical value of g=n(E_c)/n₀ is more than 0.8, in contrast with much lower values suggested earlier. The metallic conductivity is compared with the CPA result, and found to be lower by a factor of 0.4. Some modifications are introduced into the theory when account is taken of orbital degeneracy. Comparison is made with Pollitt's experiments on the inversion layer.

The thermoelectric power in different compositions of WO₃-P₂O₅, V₂O₅-P₂O₅ and MoO₃-P₂O₅ has been measured in the temperature range 150 to 400K for tungsten and vanadium phosphate glasses and 300 to 450K for molybdenum glasses. Heikes' formula for the thermal power and the small polaron model can adequately explain the experimental results in tungsten and vanadium phosphate glasses. However, the contribution of alpha (heat of transport associated with kinetic energy) in Heikes' formula cannot be ignored. Molybdenum phosphate glasses give an extremely low value of thermal power ( approximately 10 mu V K^-1) and the measured values cannot be explained by Heikes' formula.

A detailed theoretical analysis of the Cr²⁺:Al₂O₃ system has been undertaken using experimental data obtained from thermally-detected electric-field-induced EPR experiments, to be published shortly, and previously obtained APR data. It is found that all the data are accounted for if a multimode Jahn-Teller model is used in the analysis. Values for the electronic parameters are deduced by computer. It is also found that the Jahn-Teller reduction factors are such that q=0.306 and r=0.70 while p is probably between 0.2 and 0.3. The model predicts another line in the EF-EPR not used in the original analysis, in agreement with experiment, and gives a satisfactory account of data previously obtained by thermal conductivity and cross-spin-lattice relaxation techniques.

The states of two spin deviations from the completely aligned ferromagnetic state are investigated for a spin-1 system with isotropic Heisenberg and biquadratic-exchange. The conditions for the appearance of bound pairs are found. The region of stability of the ferromagnetic state with respect to formation of these states is found to agree well with the region for which the ferromagnetic state is the ground state for short chains of spin-1 atoms.

A system of spins localised on lattice sites is investigated at low temperatures. The Hamiltonian contains the bilinear (Heisenberg) and biquadratic pair interactions as well as the three-atom exchange of the form (S_fS_g)(S_gS_f'). The spectra of non-interacting spin waves and quadrons are calculated by means of the diagrammatic technique applied to green functions. All calculations are carried out in the zeroth-order approximation in 1/z, where z is the number of spins interacting with any given spin. In the ferromagnetic phase at T=0 the spectra are calculated for arbitrary spin s. The spin-wave spectrum in this case is then rederived by a more elementary method of solving the energy eigenproblem in the one-particle subspace of the system. For s=1 the spectra are determined for T not=0, the magnon spectrum in arbitrary one-sublattice phase and the quadron spectrum in the ferromagnetic phase. The particular case of magnons in the ferromagnetic and quadrupolar phases at T=0 in the nearest-neighbours approximation is illustrated graphically.

The authors find the dispersion relation of the coupled magnetic-electromagnetic modes in a ferromagnetic slab in the Voigt geometry (applied static field H₀ and magnetisation M₀ in the plane of the slab, propagation in the perpendicular direction in the plane). The results differ significantly from those found by Hartstein et al. (1973) for a single interface, and from those found by Damon and Eshbach (1961) using the magnetostatic approximation. The difference from the Damon and Eshbach results increases as H₀ increases.

Electron spin resonance studies have been made on single crystals of Cu²⁺ doped monopyrazine zinc sulphate trihydrate in the temperature range 300-77K. The unimolecular unit cell of the lattice, with one occupation site (Zn²⁺) of the substitutional type, showed ESR spectra characteristic of three sites. Possibilities of interstitial occupation sites have been diligently checked and overruled. This has led to the suggestion of a possible static Jahn-Teller effect of unusual nature. The results can be explained by assuming the potential barrier height to be greater than the thermal energy at 250K (approximately 200 cm^-1).

The thermoluminescence and the thermal stability of the F centres in pure KI, KBr, NaCl and NaF single crystals x and gamma irradiated at room temperature have been studied. It is concluded that the observed thermoluminescence is due to the recombination with F centres of halogen interstitial atoms which are thermally released from traps. The kinetics, activation energy and pre-exponential factors of these thermally activated processes are given. Some measurements of the M centre thermal stability are presented.

The contributions of substrate multiple scatterings to ultraviolet photoemission spectra from overlayer covered systems are analysed. Using simple examples, the authors illustrate that an important effect of substrate reflection is the channelling of electrons from directions of strong emission into directions of weak emission. Plots of total elastically reflected intensities (TERI) from substrates Al(100), Ni(100), W(110), Ni(111) and Pt(111) are presented. The relation between LEED TERI plots of substrates and phi -dependences of angle-resolved photoemission spectra is discussed.

A theory for describing the angular dependence of the photoemission intensity emitted from small molecules adsorbed on single crystal surfaces is presented, in which the influence of the atomic potentials upon the excited electronic states is taken into account. It is assumed that the photoemission process is described by a coherent sum of spherical waves emanating from each of the atomic sites contributing to the initial state. The dependence of the photoemission intensity upon the direction of the electric field can be described in terms of a dipole vector associated with the symmetry of every atomic orbital in the initial state. The theory differs from those based upon a plane wave final state in that (i) the photoionisation process is governed by atomic-like dipole selection rules, and (ii) the phase of the outgoing wave from atom is perturbed by the atomic potential. Examples are discussed that illustrate how the details of the wavefunctions and structure of the molecules can be determined from the angle-resolved photoemission intensity.

The structure of monolayers adsorbed on solids is investigated and the consequences of particular force laws explored. The dipole-dipole interaction is assumed to predominate and a model is developed which explains the experimentally observed commensurate and incommensurate monolayer structures and the behaviour of the Debye-Waller factor.